Finite Group Databasebeta

← C83×#62927 #35290751

Subgroups — C83×#62927 #35290751

Order 21248.

7096 conjugacy classes of subgroups.

The subgroup lattice has 1584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3560C214yesmaximal, complemented
2C83×#3559C214yesmaximal, complemented
3C83×#3551C214yesmaximal, complemented
4C83×#3547C214yesmaximal, complemented
5C83×#3542C214yesmaximal, complemented
6C83×#3541C214yesmaximal, complemented
7C83×#3539C214yesmaximal, complemented
8C83×#3538C214yesmaximal, complemented
9C83×#3534C214yesmaximal, complemented
10C83×#3520C214yesmaximal, complemented
11C83×#3512C212yesmaximal, complemented
12C83×#3505C214yesmaximal, complemented
13C83×#3497C211yesmaximal, characteristic, complemented
14C83×#3494C214yesmaximal, complemented
15C83×#3493C211yesmaximal, characteristic, complemented
16C83×#3492C211yesmaximal, characteristic, complemented
17C83×#3489C212yesmaximal, complemented
18C83×#3489C212yesmaximal, complemented
19C2×#552×C83C211yesmaximal, characteristic, complemented
20D4×#41×C83C212yesmaximal, complemented
21C83×#3461C211yesmaximal, characteristic, complemented
22C83×#3449C211yesmaximal, characteristic, complemented
23C2×#537×C83C211yesmaximal, characteristic, complemented
24C2×2−1+4×C83C2212yescomplemented
25C22×#41×C83C2212yescomplemented
26C22×#41×C83C2212yescomplemented
27#563×C83C2218yescomplemented
28#563×C83C2218yescomplemented
29#562×C83C2218yescomplemented
30#562×C83C2218yescomplemented
31#560×C83C2218yescomplemented
32#560×C83C2218yescomplemented
33#556×C83C2214yescomplemented
34#555×C83C2214yescomplemented
35#555×C83C2218yescomplemented
36#554×C83C2214yescomplemented
37#554×C83C2218yescomplemented
38#553×C83C2218yescomplemented
39#553×C83C2218yescomplemented
40#553×C83C2214yescomplemented
41#553×C83C2218yescomplemented
42#553×C83C2214yescomplemented
43#553×C83C2214yescomplemented
44#553×C83C2218yescomplemented
45#553×C83C2214yescomplemented
46#553×C83C2218yescomplemented
47#552×C83C2214yescomplemented
48#552×C83C2214yescomplemented
49#552×C83C2214yescomplemented
50#552×C83C2214yescomplemented
51#552×C83C2214yescomplemented
52#552×C83C2214yescomplemented
53#552×C83C2214yescomplemented
54#552×C83C2214yescomplemented
55#551×C83C2218yescomplemented
56#551×C83C2218yescomplemented
57#551×C83C2218yescomplemented
58#551×C83C2218yescomplemented
59#550×C83C2212yescomplemented
60#550×C83C2214yescomplemented
61D4×Q8×C83C2212yescomplemented
62D4×Q8×C83C2214yescomplemented
63D4×Q8×C83C2214yescomplemented
64D4×Q8×C83C2214yescomplemented
65#548×C83C2212yes—
66#548×C83C2214yescomplemented
67#548×C83C2214yescomplemented
68#548×C83C2212yescomplemented
69#548×C83C2214yescomplemented
70#548×C83C2214yescomplemented
71#547×C83C2214yescomplemented
72#547×C83C2214yescomplemented
73#547×C83C2212yescomplemented
74#547×C83C2214yescomplemented
75#547×C83C2214yescomplemented
76#547×C83C2218yescomplemented
77#547×C83C2218yescomplemented
78#546×C83C2212yes—
79#546×C83C2218yescomplemented
80#546×C83C2218yescomplemented
81#546×C83C2218yescomplemented
82#546×C83C2214yescomplemented
83#546×C83C2214yescomplemented
84#546×C83C2212yescomplemented
85#546×C83C2214yescomplemented
86#546×C83C2214yescomplemented
87D42×C83C2214yes—
88D42×C83C2212yescomplemented
89#544×C83C2214yescomplemented
90#544×C83C2218yescomplemented
91#544×C83C2211yescharacteristic, complemented
92#542×C83C2214yescomplemented
93#542×C83C2214yescomplemented
94#542×C83C2214yescomplemented
95#542×C83C2218yescomplemented
96#541×C83C2214yescomplemented
97#541×C83C2214yescomplemented
98#540×C83C2218yescomplemented
99#540×C83C2214yescomplemented
100#540×C83C2214yescomplemented
101#540×C83C2218yescomplemented
102#540×C83C2214yescomplemented
103#539×C83C2218yescomplemented
104#539×C83C2214yescomplemented
105#539×C83C2218yescomplemented
106#539×C83C2218yescomplemented
107#539×C83C2218yescomplemented
108#539×C83C2214yescomplemented
109#538×C83C2218yescomplemented
110#538×C83C2214yescomplemented
111#538×C83C2218yescomplemented
112#538×C83C2218yescomplemented
113#537×C83C2211yescharacteristic
114#537×C83C2214yescomplemented
115#537×C83C2214yescomplemented
116#537×C83C2214yescomplemented
117#537×C83C2214yescomplemented
118#537×C83C2214yescomplemented
119#537×C83C2214yescomplemented
120#537×C83C2212yescomplemented
121#537×C83C2211yescharacteristic, complemented
122#537×C83C2212yescomplemented
123#537×C83C2211yescharacteristic, complemented
124#536×C83C2214yescomplemented
125#536×C83C2214yescomplemented
126#536×C83C2214yescomplemented
127#536×C83C2212yescomplemented
128#535×C83C2214yescomplemented
129#535×C83C2214yescomplemented
130#534×C83C2218yescomplemented
131#534×C83C2214yescomplemented
132#533×C83C2214yescomplemented
133#532×C83C2214yescomplemented
134#532×C83C2214yescomplemented
135#532×C83C2214yescomplemented
136#532×C83C2212yescomplemented
137#529×C83C2214yescomplemented
138#529×C83C2214yescomplemented
139#529×C83C2214yescomplemented
140#529×C83C2214yescomplemented
141#529×C83C2214yescomplemented
142C2×#126×C83C2212yescomplemented
143C2×#125×C83C2212yescomplemented
144C2×#125×C83C2211yescharacteristic, complemented
145#525×C83C2214yes—
146#525×C83C2214yescomplemented
147#525×C83C2214yescomplemented
148#525×C83C2214yescomplemented
149#525×C83C2214yescomplemented
150#525×C83C2214yescomplemented
151#525×C83C2214yescomplemented
152#525×C83C2212yescomplemented
153#525×C83C2212yescomplemented
154C2×#123×C83C2212yes—
155C2×C22⋊Q8×C83C2214yescomplemented
156C2×C22⋊Q8×C83C2214yescomplemented
157C2×C22⋊Q8×C83C2214yescomplemented
158C2×C22⋊Q8×C83C2211yescharacteristic, complemented
159C2×C22⋊Q8×C83C2211yescharacteristic, complemented
160C2×#121×C83C2214yescomplemented
161C2×#121×C83C2214yescomplemented
162#520×C83C2212yescomplemented
163#520×C83C2212yescomplemented
164#520×C83C2214yescomplemented
165#518×C83C2214yescomplemented
166C4×#41×C83C2212yescomplemented
167C2×C4×Q8×C83C2211yescharacteristic, complemented
168C2×C4×D4×C83C2211yescharacteristic
169C2×C4×D4×C83C2214yescomplemented
170C2×#117×C83C2211yescharacteristic, complemented
171C2×#117×C83C2212yescomplemented
172C22×C4⋊C4×C83C2211yescharacteristic, complemented
1732−1+4×C83—48no—
174C2×#41×C83—48no—
175C2×#41×C83—48no—
176C2×#41×C83C2312yes—
177C2×#41×C83C2312yes—
178C2×#41×C83C2312yes—
179C2×#41×C83C2314yes—
180C2×#41×C83C2314yes—
181C2×#41×C83C2312yes—
182C2×#41×C83C2312yes—
183C2×#41×C83C2314yes—
184C2×#41×C83C2314yes—
185C2×#41×C83C2314yes—
186C2×#41×C83C2314yes—
187C2×#41×C83C2318yes—
188C2×#41×C83C2314yes—
189C2×#41×C83C2312yes—
190C2×#41×C83C2312yes—
191C22×Q8×C83C2311yescharacteristic
192C22×Q8×C83C2312yes—
193C22×Q8×C83C2314yes—
194C22×Q8×C83C2314yes—
195C22×Q8×C83C2312yes—
196C22×D4×C83C2311yescharacteristic
197C22×D4×C83C2314yes—
198C22×D4×C83C2314yes—
199C22×D4×C83C2314yes—
200C22×D4×C83C2312yes—
201C22×D4×C83C2314yes—
202C22×D4×C83C2312yes—
203C23×C4×C83C2311yescharacteristic
204C23×C4×C83C2311yescharacteristic
205C23×C4×C83C2312yes—
206C23×C4×C83C2314yes—
207C23×C4×C83C2314yes—
208C4⋊Q8×C83C2314yes—
209C4⋊Q8×C83C2312yes—
210C4⋊Q8×C83C2314yes—
211C4⋊Q8×C83C2314yes—
212C4⋊Q8×C83C2314yes—
213C4⋊Q8×C83C2314yes—
214C4⋊Q8×C83C2318yes—
215C4⋊Q8×C83C2318yes—
216#127×C83C2314yes—
217#127×C83C2314yes—
218#127×C83C2314yes—
219#127×C83C2312yes—
220#126×C83C2318yes—
221#126×C83C2318yes—
222#126×C83C2318yes—
223#126×C83C2318yes—
224#126×C83C2318yes—
225#126×C83C2318yes—
226#126×C83C2318yes—
227#126×C83C2318yes—
228#126×C83C2318yes—
229#126×C83C2318yes—
230#126×C83C2318yes—
231#125×C83C2314yes—
232#125×C83C2318yes—
233#125×C83C2314yes—
234#125×C83C2318yes—
235#125×C83C2314yes—
236#125×C83C2314yes—
237#125×C83C2314yes—
238#125×C83C2318yes—
239#125×C83C2318yes—
240#125×C83C2318yes—
241#125×C83C2318yes—
242#124×C83C2312yes—
243#124×C83C2312yes—
244#124×C83C2314yes—
245#124×C83C2314yes—
246#124×C83C2314yes—
247#124×C83C2318yes—
248#124×C83C2318yes—
249#124×C83C2314yes—
250#124×C83C2314yes—
251#124×C83C2318yes—
252#124×C83C2318yes—
253#124×C83C2318yes—
254#123×C83C2318yes—
255#123×C83C2318yes—
256#123×C83C2314yes—
257#123×C83C2314yes—
258#123×C83C2314yes—
259#123×C83C2318yes—
260#123×C83C2318yes—
261#123×C83C2318yes—
262#123×C83C2314yes—
263#123×C83C2314yes—
264#123×C83C2318yes—
265#123×C83C2318yes—
266#123×C83C2314yes—
267#123×C83C2318yes—
268#123×C83C2318yes—
269#123×C83C2318yes—
270#123×C83C2318yes—
271#123×C83C2318yes—
272#123×C83C2318yes—
273#123×C83C2318yes—
274#123×C83C2318yes—
275#123×C83C2318yes—
276#123×C83C2318yes—
277#123×C83C2318yes—
278#123×C83C2318yes—
279C22⋊Q8×C83C2312yes—
280C22⋊Q8×C83C2314yes—
281C22⋊Q8×C83C2312yes—
282C22⋊Q8×C83C2314yes—
283C22⋊Q8×C83C2314yes—
284C22⋊Q8×C83C2314yes—
285C22⋊Q8×C83C2314yes—
286C22⋊Q8×C83C2314yes—
287C22⋊Q8×C83C2314yes—
288C22⋊Q8×C83C2314yes—
289C22⋊Q8×C83C2314yes—
290C22⋊Q8×C83C2318yes—
291C22⋊Q8×C83C2314yes—
292C22⋊Q8×C83C2314yes—
293C22⋊Q8×C83C2318yes—
294C22⋊Q8×C83C2318yes—
295C22⋊Q8×C83C2318yes—
296C22⋊Q8×C83C2318yes—
297C22⋊Q8×C83C2318yes—
298C22⋊Q8×C83C2314yes—
299C22⋊Q8×C83C2314yes—
300C22⋊Q8×C83C2314yes—
301C22⋊Q8×C83C2312yes—
302C22⋊Q8×C83C2312yes—
303C22⋊Q8×C83C2314yes—
304C22⋊Q8×C83C2314yes—
305C22⋊Q8×C83C2314yes—
306C22⋊Q8×C83C2314yes—
307C22⋊Q8×C83C2314yes—
308C22⋊Q8×C83C2318yes—
309C22⋊Q8×C83C2318yes—
310C22⋊Q8×C83C2318yes—
311C22⋊Q8×C83C2318yes—
312C22⋊Q8×C83C2318yes—
313C22⋊Q8×C83C2318yes—
314#121×C83C2314yes—
315#121×C83C2314yes—
316#121×C83C2314yes—
317#121×C83C2314yes—
318#121×C83C2318yes—
319#121×C83C2314yes—
320#121×C83C2314yes—
321#121×C83C2318yes—
322#121×C83C2314yes—
323#121×C83C2314yes—
324#121×C83C2318yes—
325#121×C83C2318yes—
326#121×C83C2314yes—
327#121×C83C2314yes—
328#121×C83C2312yes—
329#121×C83C2312yes—
330#121×C83C2314yes—
331#121×C83C2314yes—
332#121×C83C2314yes—
333#121×C83C2314yes—
334#121×C83C2312yes—
335#121×C83C2312yes—
336#121×C83C2314yes—
337#121×C83C2314yes—
338#121×C83C2314yes—
339#121×C83C2314yes—
340#121×C83C2318yes—
341#121×C83C2314yes—
342#121×C83C2314yes—
343#121×C83C2314yes—
344#121×C83C2314yes—
345#121×C83C2314yes—
346#121×C83C2318yes—
347#121×C83C2318yes—
348#121×C83C2318yes—
349#121×C83C2318yes—
350#121×C83C2318yes—
351#121×C83C2318yes—
352#121×C83C2318yes—
353#121×C83C2318yes—
354#121×C83C2318yes—
355#121×C83C2318yes—
356#121×C83C2318yes—
357#120×C83C2314yes—
358#120×C83C2314yes—
359#120×C83C2314yes—
360#120×C83C2318yes—
361#120×C83C2318yes—
362#120×C83C2318yes—
363#120×C83C2318yes—
364#120×C83C2314yes—
365#120×C83C2314yes—
366#120×C83C2314yes—
367C4×Q8×C83C2314yes—
368C4×Q8×C83C2314yes—
369C4×Q8×C83C2312yes—
370C4×Q8×C83C2312yes—
371C4×Q8×C83C2314yes—
372C4×Q8×C83C2314yes—
373C4×Q8×C83C2314yes—
374C4×Q8×C83C2314yes—
375C4×D4×C83C2312yes—
376C4×D4×C83C2312yes—
377C4×D4×C83C2312yes—
378C4×D4×C83C2312yes—
379C4×D4×C83C2314yes—
380C4×D4×C83C2314yes—
381C4×D4×C83C2314yes—
382C4×D4×C83C2314yes—
383C4×D4×C83C2314yes—
384C4×D4×C83C2314yes—
385C4×D4×C83C2314yes—
386C4×D4×C83C2312yes—
387C4×D4×C83C2314yes—
388C4×D4×C83C2314yes—
389C4×D4×C83C2312yes—
390C4×D4×C83C2314yes—
391C4×D4×C83C2318yes—
392C4×D4×C83C2314yes—
393C4×D4×C83C2318yes—
394C4×D4×C83C2314yes—
395C4×D4×C83C2314yes—
396C4×D4×C83C2314yes—
397C4×D4×C83C2318yes—
398C4×D4×C83C2318yes—
399C4×D4×C83C2318yes—
400C4×D4×C83C2314yes—
401C4×D4×C83C2314yes—
402C4×D4×C83C2314yes—
403C4×D4×C83C2314yes—
404C4×D4×C83C2314yes—
405C4×D4×C83C2314yes—
406C4×D4×C83C2318yes—
407C4×D4×C83C2318yes—
408C4×D4×C83C2318yes—
409C4×D4×C83C2318yes—
410C4×D4×C83C2318yes—
411C4×D4×C83C2318yes—
412#117×C83C2314yes—
413#117×C83C2314yes—
414#117×C83C2314yes—
415#117×C83C2314yes—
416#117×C83C2314yes—
417#117×C83C2314yes—
418#117×C83C2312yes—
419#117×C83C2314yes—
420#117×C83C2314yes—
421#117×C83C2314yes—
422#117×C83C2314yes—
423#117×C83C2318yes—
424#117×C83C2318yes—
425#117×C83C2318yes—
426#117×C83C2318yes—
427C2×C4⋊C4×C83C2311yescharacteristic
428C2×C4⋊C4×C83C2311yescharacteristic
429C2×C4⋊C4×C83C2314yes—
430C2×C4⋊C4×C83C2312yes—
431C2×C4⋊C4×C83C2314yes—
432C2×C4⋊C4×C83C2311yescharacteristic
433C2×C4⋊C4×C83C2312yes—
434C2×C4⋊C4×C83C2312yes—
435C2×C4⋊C4×C83C2311yescharacteristic
436C2×C4⋊C4×C83C2314yes—
437C2×C4⋊C4×C83C2312yes—
438C2×C4⋊C4×C83C2314yes—
439C2×C4⋊C4×C83C2314yes—
440C2×C4⋊C4×C83C2314yes—
441C2×C4⋊C4×C83C2318yes—
442C2×C4⋊C4×C83C2312yes—
443C2×C4⋊C4×C83C2318yes—
444C2×C4⋊C4×C83C2312yes—
445C2×C22⋊C4×C83C2311yescharacteristic
446C2×C22⋊C4×C83C2312yes—
447C2×C22⋊C4×C83C2312yes—
448C2×C22⋊C4×C83C2311yescharacteristic
449C2×C22⋊C4×C83C2314yes—
450C2×C22⋊C4×C83C2314yes—
451C2×C22⋊C4×C83C2318yes—
452C2×C22⋊C4×C83C2318yes—
453C2×C22⋊C4×C83C2312yes—
454C2×C22⋊C4×C83C2318yes—
455C2×C42×C83C2312yes—
456C2×C42×C83C2312yes—
457C2×C42×C83C2311yescharacteristic
458C2×C42×C83C2314yes—
459C24×C83C2411yescharacteristic
460C24×C83C2411yescharacteristic
461C24×C83C2414yes—
462C24×C83C2414yes—
463#41×C83—28no—
464#41×C83—28no—
465#41×C83—28no—
466#41×C83—48no—
467#41×C83—48no—
468#41×C83—48no—
469#41×C83—48no—
470#41×C83—48no—
471#41×C83—416no—
472#41×C83—44no—
473#41×C83—44no—
474#41×C83—44no—
475#41×C83—44no—
476#41×C83—48no—
477#41×C83—48no—
478C2×Q8×C83—24no—
479C2×Q8×C83—44no—
480C2×Q8×C83—44no—
481C2×Q8×C83—48no—
482C2×Q8×C83—48no—
483C2×Q8×C83C2414yes—
484C2×Q8×C83C2412yes—
485C2×Q8×C83C2412yes—
486C2×Q8×C83C2412yes—
487C2×Q8×C83C2414yes—
488C2×Q8×C83C2414yes—
489C2×Q8×C83C2418yes—
490C2×Q8×C83C2414yes—
491C2×D4×C83—44no—
492C2×D4×C83—44no—
493C2×D4×C83—48no—
494C2×D4×C83—42no—
495C2×D4×C83—48no—
496C2×D4×C83—48no—
497C2×D4×C83—48no—
498C2×D4×C83C2414yes—
499C2×D4×C83C2412yes—
500C2×D4×C83C2414yes—
501C2×D4×C83C2414yes—
502C2×D4×C83C2414yes—
503C2×D4×C83C2412yes—
504C2×D4×C83C2412yes—
505C2×D4×C83C2412yes—
506C2×D4×C83C2414yes—
507C2×D4×C83C2418yes—
508C2×D4×C83C2414yes—
509C2×D4×C83C2414yes—
510C2×D4×C83C2414yes—
511C2×D4×C83C2414yes—
512C2×D4×C83C2414yes—
513C2×D4×C83C2412yes—
514C2×D4×C83C2418yes—
515C2×D4×C83C2414yes—
516C2×D4×C83C2414yes—
517C2×D4×C83C2414yes—
518C2×D4×C83C2418yes—
519C2×D4×C83C2414yes—
520C2×D4×C83C2414yes—
521C2×D4×C83C2414yes—
522C2×D4×C83C2414yes—
523C2×D4×C83C2414yes—
524C22×C4×C83—24no—
525C22×C4×C83—24no—
526C22×C4×C83—48no—
527C22×C4×C83—48no—
528C22×C4×C83—44no—
529C22×C4×C83C2411yescharacteristic
530C22×C4×C83C2412yes—
531C22×C4×C83C2414yes—
532C22×C4×C83C2414yes—
533C22×C4×C83C2411yescharacteristic
534C22×C4×C83C2412yes—
535C22×C4×C83C2412yes—
536C22×C4×C83C2414yes—
537C22×C4×C83C2414yes—
538C22×C4×C83C2412yes—
539C22×C4×C83C2412yes—
540C22×C4×C83C2411yescharacteristic
541C22×C4×C83C2412yes—
542C22×C4×C83C2412yes—
543C22×C4×C83C2414yes—
544C22×C4×C83C2411yescharacteristic
545C22×C4×C83C2414yes—
546C22×C4×C83C2414yes—
547C22×C4×C83C2412yes—
548C22×C4×C83C2418yes—
549C22×C4×C83C2418yes—
550C22×C4×C83C2414yes—
551C22×C4×C83C2418yes—
552C22×C4×C83C2418yes—
553C22×C4×C83C2414yes—
554C22×C4×C83C2414yes—
555C22×C4×C83C2414yes—
556C22×C4×C83C2414yes—
557C22×C4×C83C2414yes—
558C22×C4×C83C2411yescharacteristic
559C4⋊C4×C83C2414yes—
560C4⋊C4×C83C2414yes—
561C4⋊C4×C83C2414yes—
562C4⋊C4×C83C2412yes—
563C4⋊C4×C83C2414yes—
564C4⋊C4×C83C2418yes—
565C4⋊C4×C83C2414yes—
566C4⋊C4×C83C2412yes—
567C4⋊C4×C83C2412yes—
568C4⋊C4×C83C2418yes—
569C4⋊C4×C83C2418yes—
570C4⋊C4×C83C2414yes—
571C4⋊C4×C83C2414yes—
572C4⋊C4×C83C2414yes—
573C4⋊C4×C83C2414yes—
574C4⋊C4×C83C2418yes—
575C4⋊C4×C83C2418yes—
576C4⋊C4×C83C2418yes—
577C4⋊C4×C83C2414yes—
578C4⋊C4×C83C2412yes—
579C4⋊C4×C83C2414yes—
580C4⋊C4×C83C2414yes—
581C4⋊C4×C83C2414yes—
582C4⋊C4×C83C2418yes—
583C4⋊C4×C83C2418yes—
584C4⋊C4×C83C2418yes—
585C4⋊C4×C83C2418yes—
586C4⋊C4×C83C2414yes—
587C4⋊C4×C83C2418yes—
588C4⋊C4×C83C2414yes—
589C4⋊C4×C83C2414yes—
590C4⋊C4×C83C2414yes—
591C4⋊C4×C83C2414yes—
592C4⋊C4×C83C2414yes—
593C22⋊C4×C83C2411yescharacteristic
594C22⋊C4×C83C2414yes—
595C22⋊C4×C83C2414yes—
596C22⋊C4×C83C2412yes—
597C22⋊C4×C83C2418yes—
598C22⋊C4×C83C2414yes—
599C22⋊C4×C83C2418yes—
600C22⋊C4×C83C2411yescharacteristic
601C22⋊C4×C83C2411yescharacteristic
602C22⋊C4×C83C2411yescharacteristic
603C22⋊C4×C83C2414yes—
604C22⋊C4×C83C2418yes—
605C22⋊C4×C83C2414yes—
606C22⋊C4×C83C2418yes—
607C22⋊C4×C83C2418yes—
608C22⋊C4×C83C2418yes—
609C22⋊C4×C83C2418yes—
610C22⋊C4×C83C2414yes—
611C22⋊C4×C83C2414yes—
612C22⋊C4×C83C2412yes—
613C22⋊C4×C83C2414yes—
614C22⋊C4×C83C2418yes—
615C22⋊C4×C83C2418yes—
616C22⋊C4×C83C2414yes—
617C22⋊C4×C83C2414yes—
618C22⋊C4×C83C2414yes—
619C22⋊C4×C83C2414yes—
620C22⋊C4×C83C2414yes—
621C22⋊C4×C83C2414yes—
622C22⋊C4×C83C2418yes—
623C22⋊C4×C83C2418yes—
624C22⋊C4×C83C2418yes—
625C22⋊C4×C83C2414yes—
626C22⋊C4×C83C2418yes—
627C22⋊C4×C83C2414yes—
628C22⋊C4×C83C2414yes—
629C42×C83C2412yes—
630C42×C83C2414yes—
631C42×C83C2414yes—
632C42×C83C2414yes—
633C42×C83C2414yes—
634C42×C83C2414yes—
635C42×C83C2412yes—
636C42×C83C2414yes—
637C42×C83C2414yes—
638C42×C83C2418yes—
639C42×C83C2418yes—
640C23×C83—22no—
641C23×C83—22no—
642C23×C83—22no—
643C23×C83—28no—
644C23×C83—41no—
645C23×C83—44no—
646C23×C83—44no—
647C23×C83—41no—
648C23×C83—44no—
649C23×C83—41no—
650C23×C83—44no—
651C23×C83—44no—
652C23×C83C2512yes—
653C23×C83C2514yes—
654C23×C83C2511yescharacteristic
655C23×C83C2514yes—
656C23×C83C2514yes—
657C23×C83C2511yescharacteristic
658C23×C83C2511yescharacteristic
659Q8×C83—28no—
660Q8×C83—24no—
661Q8×C83—24no—
662Q8×C83—24no—
663Q8×C83—48no—
664Q8×C83—44no—
665Q8×C83—44no—
666Q8×C83—44no—
667D4×C83—28no—
668D4×C83—28no—
669D4×C83—28no—
670D4×C83—24no—
671D4×C83—28no—
672D4×C83—24no—
673D4×C83—24no—
674D4×C83—24no—
675D4×C83—48no—
676D4×C83—44no—
677D4×C83—44no—
678D4×C83—42no—
679D4×C83—44no—
680D4×C83—44no—
681D4×C83—44no—
682D4×C83—44no—
683D4×C83—44no—
684D4×C83—44no—
685D4×C83—44no—
686D4×C83—44no—
687D4×C83—44no—
688D4×C83—48no—
689D4×C83—44no—
690D4×C83—44no—
691D4×C83—44no—
692D4×C83—48no—
693C2×C4×C83—22no—
694C2×C4×C83—22no—
695C2×C4×C83—24no—
696C2×C4×C83—28no—
697C2×C4×C83—24no—
698C2×C4×C83—24no—
699C2×C4×C83—24no—
700C2×C4×C83—24no—
701C2×C4×C83—28no—
702C2×C4×C83—28no—
703C2×C4×C83—28no—
704C2×C4×C83—42no—
705C2×C4×C83—44no—
706C2×C4×C83—42no—
707C2×C4×C83—44no—
708C2×C4×C83—44no—
709C2×C4×C83—44no—
710C2×C4×C83—44no—
711C2×C4×C83—44no—
712C2×C4×C83—44no—
713C2×C4×C83—44no—
714C2×C4×C83—41no—
715C2×C4×C83—42no—
716C2×C4×C83—48no—
717C2×C4×C83—41no—
718C2×C4×C83—44no—
719C2×C4×C83—48no—
720C2×C4×C83—48no—
721C2×C4×C83—48no—
722C2×C4×C83H(5,𝔽2)14yes—
723C2×C4×C83C2511yescharacteristic
724C2×C4×C83C2511yescharacteristic
725C2×C4×C83C2514yes—
726C2×C4×C83C2514yes—
727C2×C4×C83C2514yes—
728C2×C4×C83C2514yes—
729C2×C4×C83C2512yes—
730C2×C4×C83C2511yescharacteristic
731C2×C4×C83C2511yescharacteristic
732C2×C4×C83C2514yes—
733C2×C4×C83C2514yes—
734C2×C4×C83C2514yes—
735C2×C4×C83C2514yes—
736C2×C4×C83C2514yes—
737C2×C4×C83C2512yes—
738C2×C4×C83C2512yes—
739C22×C83—21no—
740C22×C83—21no—
741C22×C83—21no—
742C22×C83—21no—
743C22×C83—22no—
744C22×C83—21no—
745C22×C83—24no—
746C22×C83—24no—
747C22×C83—24no—
748C22×C83—21no—
749C22×C83—24no—
750C22×C83—24no—
751C22×C83—22no—
752C22×C83—24no—
753C22×C83—24no—
754C22×C83—24no—
755C22×C83—21no—
756C22×C83—24no—
757C22×C83—22no—
758C22×C83—44no—
759C22×C83—88no—
760C22×C83—82no—
761C22×C83—88no—
762C22×C83C2×H(5,𝔽2)12yes—
763C22×C83#58512yes—
764C22×C83C2611yescharacteristic
765C4×C83—21no—
766C4×C83—22no—
767C4×C83—21no—
768C4×C83—24no—
769C4×C83—24no—
770C4×C83—24no—
771C4×C83—24no—
772C4×C83—24no—
773C4×C83—24no—
774C4×C83—22no—
775C4×C83—24no—
776C4×C83—21no—
777C4×C83—24no—
778C4×C83—24no—
779C4×C83—21no—
780C4×C83C2×H(5,𝔽2)14yes—
781#62927C8311yesmaximal, characteristic, direct product factor, Sylow
782C2×C83—22no—
783C2×C83—22no—
784C2×C83—41no—
785C2×C83—44no—
786C2×C83—44no—
787C2×C83—44no—
788C2×C83—42no—
789C2×C83C22×H(5,𝔽2)11yescharacteristic
790C2×C83C2×#58511yescharacteristic
791C2×C832−1+611yescharacteristic
792#3560C2×C8314yescomplemented
793#3559C2×C8314yescomplemented
794#3551C2×C8314yescomplemented
795#3547C2×C8314yescomplemented
796#3542C2×C8314yescomplemented
797#3541C2×C8314yescomplemented
798#3539C2×C8314yescomplemented
799#3538C2×C8314yescomplemented
800#3534C2×C8314yescomplemented
801#3520C2×C8314yescomplemented
802#3512C2×C8312yescomplemented
803#3505C2×C8314yescomplemented
804#3497C2×C8311yescharacteristic, complemented
805#3494C2×C8314yescomplemented
806#3493C2×C8311yescharacteristic, complemented
807#3492C2×C8311yescharacteristic, complemented
808#3489C2×C8312yescomplemented
809#3489C2×C8312yescomplemented
810C2×#552C2×C8311yescharacteristic, complemented
811D4×#41C2×C8312yescomplemented
812#3461C2×C8311yescharacteristic, complemented
813#3449C2×C8311yescharacteristic, complemented
814C2×#537C2×C8311yescharacteristic, complemented
815C83#6292711yescharacteristic, direct product factor, Sylow
816C2×2−1+4C22×C8312yescomplemented
817C22×#41C22×C8312yescomplemented
818C22×#41C22×C8312yescomplemented
819#563C22×C8318yescomplemented
820#563C22×C8318yescomplemented
821#562C22×C8318yescomplemented
822#562C22×C8318yescomplemented
823#560C22×C8318yescomplemented
824#560C22×C8318yescomplemented
825#556C22×C8314yescomplemented
826#555C22×C8314yescomplemented
827#555C22×C8318yescomplemented
828#554C22×C8314yescomplemented
829#554C22×C8318yescomplemented
830#553C22×C8314yescomplemented
831#553C22×C8314yescomplemented
832#553C22×C8318yescomplemented
833#553C22×C8318yescomplemented
834#553C22×C8314yescomplemented
835#553C22×C8318yescomplemented
836#553C22×C8318yescomplemented
837#553C22×C8318yescomplemented
838#553C22×C8314yescomplemented
839#552C22×C8314yescomplemented
840#552C22×C8314yescomplemented
841#552C22×C8314yescomplemented
842#552C22×C8314yescomplemented
843#552C22×C8314yescomplemented
844#552C22×C8314yescomplemented
845#552C22×C8314yescomplemented
846#552C22×C8314yescomplemented
847#551C22×C8318yescomplemented
848#551C22×C8318yescomplemented
849#551C22×C8318yescomplemented
850#551C22×C8318yescomplemented
851#550C22×C8312yescomplemented
852#550C22×C8314yescomplemented
853D4×Q8C22×C8312yescomplemented
854D4×Q8C22×C8314yescomplemented
855D4×Q8C22×C8314yescomplemented
856D4×Q8C22×C8314yescomplemented
857#548C22×C8312yes—
858#548C22×C8312yescomplemented
859#548C22×C8314yescomplemented
860#548C22×C8314yescomplemented
861#548C22×C8314yescomplemented
862#548C22×C8314yescomplemented
863#547C22×C8312yescomplemented
864#547C22×C8314yescomplemented
865#547C22×C8318yescomplemented
866#547C22×C8314yescomplemented
867#547C22×C8314yescomplemented
868#547C22×C8318yescomplemented
869#547C22×C8314yescomplemented
870#546C22×C8312yes—
871#546C22×C8314yescomplemented
872#546C22×C8312yescomplemented
873#546C22×C8314yescomplemented
874#546C22×C8318yescomplemented
875#546C22×C8314yescomplemented
876#546C22×C8318yescomplemented
877#546C22×C8314yescomplemented
878#546C22×C8318yescomplemented
879D42C22×C8314yes—
880D42C22×C8312yescomplemented
881#544C22×C8311yescharacteristic, complemented
882#544C22×C8314yescomplemented
883#544C22×C8318yescomplemented
884#542C22×C8314yescomplemented
885#542C22×C8314yescomplemented
886#542C22×C8314yescomplemented
887#542C22×C8318yescomplemented
888#541C22×C8314yescomplemented
889#541C22×C8314yescomplemented
890#540C22×C8314yescomplemented
891#540C22×C8314yescomplemented
892#540C22×C8314yescomplemented
893#540C22×C8318yescomplemented
894#540C22×C8318yescomplemented
895#539C22×C8314yescomplemented
896#539C22×C8314yescomplemented
897#539C22×C8318yescomplemented
898#539C22×C8318yescomplemented
899#539C22×C8318yescomplemented
900#539C22×C8318yescomplemented
901#538C22×C8314yescomplemented
902#538C22×C8318yescomplemented
903#538C22×C8318yescomplemented
904#538C22×C8318yescomplemented
905#537C22×C8311yescharacteristic
906#537C22×C8312yescomplemented
907#537C22×C8311yescharacteristic, complemented
908#537C22×C8314yescomplemented
909#537C22×C8314yescomplemented
910#537C22×C8314yescomplemented
911#537C22×C8312yescomplemented
912#537C22×C8311yescharacteristic, complemented
913#537C22×C8314yescomplemented
914#537C22×C8314yescomplemented
915#537C22×C8314yescomplemented
916#536C22×C8314yescomplemented
917#536C22×C8312yescomplemented
918#536C22×C8314yescomplemented
919#536C22×C8314yescomplemented
920#535C22×C8314yescomplemented
921#535C22×C8314yescomplemented
922#534C22×C8314yescomplemented
923#534C22×C8318yescomplemented
924#533C22×C8314yescomplemented
925#532C22×C8314yescomplemented
926#532C22×C8312yescomplemented
927#532C22×C8314yescomplemented
928#532C22×C8314yescomplemented
929#529C22×C8314yescomplemented
930#529C22×C8314yescomplemented
931#529C22×C8314yescomplemented
932#529C22×C8314yescomplemented
933#529C22×C8314yescomplemented
934C2×#126C22×C8312yescomplemented
935C2×#125C22×C8311yescharacteristic, complemented
936C2×#125C22×C8312yescomplemented
937#525C22×C8314yes—
938#525C22×C8314yescomplemented
939#525C22×C8314yescomplemented
940#525C22×C8312yescomplemented
941#525C22×C8312yescomplemented
942#525C22×C8314yescomplemented
943#525C22×C8314yescomplemented
944#525C22×C8314yescomplemented
945#525C22×C8314yescomplemented
946C2×#123C22×C8312yes—
947C2×C22⋊Q8C22×C8314yescomplemented
948C2×C22⋊Q8C22×C8311yescharacteristic, complemented
949C2×C22⋊Q8C22×C8311yescharacteristic, complemented
950C2×C22⋊Q8C22×C8314yescomplemented
951C2×C22⋊Q8C22×C8314yescomplemented
952C2×#121C22×C8314yescomplemented
953C2×#121C22×C8314yescomplemented
954#520C22×C8312yescomplemented
955#520C22×C8312yescomplemented
956#520C22×C8314yescomplemented
957#518C22×C8314yescomplemented
958C4×#41C22×C8312yescomplemented
959C2×C4×Q8C22×C8311yescharacteristic, complemented
960C2×C4×D4C22×C8311yescharacteristic
961C2×C4×D4C22×C8314yescomplemented
962C2×#117C22×C8311yescharacteristic, complemented
963C2×#117C22×C8312yescomplemented
964C22×C4⋊C4C22×C8311yescharacteristic, complemented
9652−1+4—48no—
966C2×#41—48no—
967C2×#41—48no—
968C2×#41C23×C8312yes—
969C2×#41C23×C8312yes—
970C2×#41C23×C8312yes—
971C2×#41C23×C8314yes—
972C2×#41C23×C8314yes—
973C2×#41C23×C8312yes—
974C2×#41C23×C8312yes—
975C2×#41C23×C8314yes—
976C2×#41C23×C8314yes—
977C2×#41C23×C8314yes—
978C2×#41C23×C8314yes—
979C2×#41C23×C8318yes—
980C2×#41C23×C8314yes—
981C2×#41C23×C8312yes—
982C2×#41C23×C8312yes—
983C22×Q8C23×C8311yescharacteristic
984C22×Q8C23×C8312yes—
985C22×Q8C23×C8314yes—
986C22×Q8C23×C8314yes—
987C22×Q8C23×C8312yes—
988C22×D4C23×C8311yescharacteristic
989C22×D4C23×C8314yes—
990C22×D4C23×C8314yes—
991C22×D4C23×C8314yes—
992C22×D4C23×C8312yes—
993C22×D4C23×C8314yes—
994C22×D4C23×C8312yes—
995C23×C4C23×C8311yescharacteristic
996C23×C4C23×C8311yescharacteristic
997C23×C4C23×C8312yes—
998C23×C4C23×C8314yes—
999C23×C4C23×C8314yes—
1000C4⋊Q8C23×C8314yes—
1001C4⋊Q8C23×C8312yes—
1002C4⋊Q8C23×C8314yes—
1003C4⋊Q8C23×C8314yes—
1004C4⋊Q8C23×C8314yes—
1005C4⋊Q8C23×C8314yes—
1006C4⋊Q8C23×C8318yes—
1007C4⋊Q8C23×C8318yes—
1008#127C23×C8314yes—
1009#127C23×C8314yes—
1010#127C23×C8314yes—
1011#127C23×C8312yes—
1012#126C23×C8318yes—
1013#126C23×C8318yes—
1014#126C23×C8318yes—
1015#126C23×C8318yes—
1016#126C23×C8318yes—
1017#126C23×C8318yes—
1018#126C23×C8318yes—
1019#126C23×C8318yes—
1020#126C23×C8318yes—
1021#126C23×C8318yes—
1022#126C23×C8318yes—
1023#125C23×C8314yes—
1024#125C23×C8318yes—
1025#125C23×C8314yes—
1026#125C23×C8318yes—
1027#125C23×C8314yes—
1028#125C23×C8314yes—
1029#125C23×C8314yes—
1030#125C23×C8318yes—
1031#125C23×C8318yes—
1032#125C23×C8318yes—
1033#125C23×C8318yes—
1034#124C23×C8312yes—
1035#124C23×C8312yes—
1036#124C23×C8314yes—
1037#124C23×C8314yes—
1038#124C23×C8314yes—
1039#124C23×C8318yes—
1040#124C23×C8318yes—
1041#124C23×C8314yes—
1042#124C23×C8314yes—
1043#124C23×C8318yes—
1044#124C23×C8318yes—
1045#124C23×C8318yes—
1046#123C23×C8318yes—
1047#123C23×C8318yes—
1048#123C23×C8314yes—
1049#123C23×C8314yes—
1050#123C23×C8314yes—
1051#123C23×C8318yes—
1052#123C23×C8318yes—
1053#123C23×C8318yes—
1054#123C23×C8314yes—
1055#123C23×C8314yes—
1056#123C23×C8318yes—
1057#123C23×C8318yes—
1058#123C23×C8314yes—
1059#123C23×C8318yes—
1060#123C23×C8318yes—
1061#123C23×C8318yes—
1062#123C23×C8318yes—
1063#123C23×C8318yes—
1064#123C23×C8318yes—
1065#123C23×C8318yes—
1066#123C23×C8318yes—
1067#123C23×C8318yes—
1068#123C23×C8318yes—
1069#123C23×C8318yes—
1070#123C23×C8318yes—
1071C22⋊Q8C23×C8312yes—
1072C22⋊Q8C23×C8314yes—
1073C22⋊Q8C23×C8312yes—
1074C22⋊Q8C23×C8314yes—
1075C22⋊Q8C23×C8314yes—
1076C22⋊Q8C23×C8314yes—
1077C22⋊Q8C23×C8314yes—
1078C22⋊Q8C23×C8314yes—
1079C22⋊Q8C23×C8314yes—
1080C22⋊Q8C23×C8314yes—
1081C22⋊Q8C23×C8314yes—
1082C22⋊Q8C23×C8318yes—
1083C22⋊Q8C23×C8314yes—
1084C22⋊Q8C23×C8314yes—
1085C22⋊Q8C23×C8318yes—
1086C22⋊Q8C23×C8318yes—
1087C22⋊Q8C23×C8318yes—
1088C22⋊Q8C23×C8318yes—
1089C22⋊Q8C23×C8318yes—
1090C22⋊Q8C23×C8314yes—
1091C22⋊Q8C23×C8314yes—
1092C22⋊Q8C23×C8314yes—
1093C22⋊Q8C23×C8312yes—
1094C22⋊Q8C23×C8312yes—
1095C22⋊Q8C23×C8314yes—
1096C22⋊Q8C23×C8314yes—
1097C22⋊Q8C23×C8314yes—
1098C22⋊Q8C23×C8314yes—
1099C22⋊Q8C23×C8314yes—
1100C22⋊Q8C23×C8318yes—
1101C22⋊Q8C23×C8318yes—
1102C22⋊Q8C23×C8318yes—
1103C22⋊Q8C23×C8318yes—
1104C22⋊Q8C23×C8318yes—
1105C22⋊Q8C23×C8318yes—
1106#121C23×C8314yes—
1107#121C23×C8314yes—
1108#121C23×C8314yes—
1109#121C23×C8314yes—
1110#121C23×C8318yes—
1111#121C23×C8314yes—
1112#121C23×C8314yes—
1113#121C23×C8318yes—
1114#121C23×C8314yes—
1115#121C23×C8314yes—
1116#121C23×C8318yes—
1117#121C23×C8318yes—
1118#121C23×C8314yes—
1119#121C23×C8314yes—
1120#121C23×C8312yes—
1121#121C23×C8312yes—
1122#121C23×C8314yes—
1123#121C23×C8314yes—
1124#121C23×C8314yes—
1125#121C23×C8314yes—
1126#121C23×C8312yes—
1127#121C23×C8312yes—
1128#121C23×C8314yes—
1129#121C23×C8314yes—
1130#121C23×C8314yes—
1131#121C23×C8314yes—
1132#121C23×C8318yes—
1133#121C23×C8314yes—
1134#121C23×C8314yes—
1135#121C23×C8314yes—
1136#121C23×C8314yes—
1137#121C23×C8314yes—
1138#121C23×C8318yes—
1139#121C23×C8318yes—
1140#121C23×C8318yes—
1141#121C23×C8318yes—
1142#121C23×C8318yes—
1143#121C23×C8318yes—
1144#121C23×C8318yes—
1145#121C23×C8318yes—
1146#121C23×C8318yes—
1147#121C23×C8318yes—
1148#121C23×C8318yes—
1149#120C23×C8314yes—
1150#120C23×C8314yes—
1151#120C23×C8314yes—
1152#120C23×C8318yes—
1153#120C23×C8318yes—
1154#120C23×C8318yes—
1155#120C23×C8318yes—
1156#120C23×C8314yes—
1157#120C23×C8314yes—
1158#120C23×C8314yes—
1159C4×Q8C23×C8314yes—
1160C4×Q8C23×C8314yes—
1161C4×Q8C23×C8312yes—
1162C4×Q8C23×C8312yes—
1163C4×Q8C23×C8314yes—
1164C4×Q8C23×C8314yes—
1165C4×Q8C23×C8314yes—
1166C4×Q8C23×C8314yes—
1167C4×D4C23×C8312yes—
1168C4×D4C23×C8312yes—
1169C4×D4C23×C8312yes—
1170C4×D4C23×C8312yes—
1171C4×D4C23×C8314yes—
1172C4×D4C23×C8314yes—
1173C4×D4C23×C8314yes—
1174C4×D4C23×C8314yes—
1175C4×D4C23×C8314yes—
1176C4×D4C23×C8314yes—
1177C4×D4C23×C8314yes—
1178C4×D4C23×C8312yes—
1179C4×D4C23×C8314yes—
1180C4×D4C23×C8314yes—
1181C4×D4C23×C8312yes—
1182C4×D4C23×C8314yes—
1183C4×D4C23×C8318yes—
1184C4×D4C23×C8314yes—
1185C4×D4C23×C8318yes—
1186C4×D4C23×C8314yes—
1187C4×D4C23×C8314yes—
1188C4×D4C23×C8314yes—
1189C4×D4C23×C8318yes—
1190C4×D4C23×C8318yes—
1191C4×D4C23×C8318yes—
1192C4×D4C23×C8314yes—
1193C4×D4C23×C8314yes—
1194C4×D4C23×C8314yes—
1195C4×D4C23×C8314yes—
1196C4×D4C23×C8314yes—
1197C4×D4C23×C8314yes—
1198C4×D4C23×C8318yes—
1199C4×D4C23×C8318yes—
1200C4×D4C23×C8318yes—
1201C4×D4C23×C8318yes—
1202C4×D4C23×C8318yes—
1203C4×D4C23×C8318yes—
1204#117C23×C8314yes—
1205#117C23×C8314yes—
1206#117C23×C8314yes—
1207#117C23×C8314yes—
1208#117C23×C8314yes—
1209#117C23×C8314yes—
1210#117C23×C8312yes—
1211#117C23×C8314yes—
1212#117C23×C8314yes—
1213#117C23×C8314yes—
1214#117C23×C8314yes—
1215#117C23×C8318yes—
1216#117C23×C8318yes—
1217#117C23×C8318yes—
1218#117C23×C8318yes—
1219C2×C4⋊C4C23×C8311yescharacteristic
1220C2×C4⋊C4C23×C8311yescharacteristic
1221C2×C4⋊C4C23×C8314yes—
1222C2×C4⋊C4C23×C8312yes—
1223C2×C4⋊C4C23×C8314yes—
1224C2×C4⋊C4C23×C8311yescharacteristic
1225C2×C4⋊C4C23×C8312yes—
1226C2×C4⋊C4C23×C8312yes—
1227C2×C4⋊C4C23×C8311yescharacteristic
1228C2×C4⋊C4C23×C8314yes—
1229C2×C4⋊C4C23×C8312yes—
1230C2×C4⋊C4C23×C8314yes—
1231C2×C4⋊C4C23×C8314yes—
1232C2×C4⋊C4C23×C8314yes—
1233C2×C4⋊C4C23×C8318yes—
1234C2×C4⋊C4C23×C8312yes—
1235C2×C4⋊C4C23×C8318yes—
1236C2×C4⋊C4C23×C8312yes—
1237C2×C22⋊C4C23×C8311yescharacteristic
1238C2×C22⋊C4C23×C8312yes—
1239C2×C22⋊C4C23×C8312yes—
1240C2×C22⋊C4C23×C8311yescharacteristic
1241C2×C22⋊C4C23×C8314yes—
1242C2×C22⋊C4C23×C8314yes—
1243C2×C22⋊C4C23×C8318yes—
1244C2×C22⋊C4C23×C8318yes—
1245C2×C22⋊C4C23×C8312yes—
1246C2×C22⋊C4C23×C8318yes—
1247C2×C42C23×C8312yes—
1248C2×C42C23×C8312yes—
1249C2×C42C23×C8311yescharacteristic
1250C2×C42C23×C8314yes—
1251C24C24×C8311yescharacteristic
1252C24C24×C8311yescharacteristic
1253C24C24×C8314yes—
1254C24C24×C8314yes—
1255#41—28no—
1256#41—28no—
1257#41—28no—
1258#41—48no—
1259#41—48no—
1260#41—48no—
1261#41—48no—
1262#41—416no—
1263#41—48no—
1264#41—44no—
1265#41—44no—
1266#41—44no—
1267#41—44no—
1268#41—48no—
1269#41—48no—
1270C2×Q8—24no—
1271C2×Q8—44no—
1272C2×Q8—44no—
1273C2×Q8—48no—
1274C2×Q8—48no—
1275C2×Q8C24×C8314yes—
1276C2×Q8C24×C8312yes—
1277C2×Q8C24×C8312yes—
1278C2×Q8C24×C8312yes—
1279C2×Q8C24×C8314yes—
1280C2×Q8C24×C8314yes—
1281C2×Q8C24×C8318yes—
1282C2×Q8C24×C8314yes—
1283C2×D4—44no—
1284C2×D4—44no—
1285C2×D4—48no—
1286C2×D4—48no—
1287C2×D4—48no—
1288C2×D4—42no—
1289C2×D4—48no—
1290C2×D4C24×C8314yes—
1291C2×D4C24×C8312yes—
1292C2×D4C24×C8314yes—
1293C2×D4C24×C8314yes—
1294C2×D4C24×C8314yes—
1295C2×D4C24×C8312yes—
1296C2×D4C24×C8312yes—
1297C2×D4C24×C8312yes—
1298C2×D4C24×C8314yes—
1299C2×D4C24×C8318yes—
1300C2×D4C24×C8314yes—
1301C2×D4C24×C8314yes—
1302C2×D4C24×C8314yes—
1303C2×D4C24×C8314yes—
1304C2×D4C24×C8314yes—
1305C2×D4C24×C8312yes—
1306C2×D4C24×C8318yes—
1307C2×D4C24×C8314yes—
1308C2×D4C24×C8314yes—
1309C2×D4C24×C8314yes—
1310C2×D4C24×C8318yes—
1311C2×D4C24×C8314yes—
1312C2×D4C24×C8314yes—
1313C2×D4C24×C8314yes—
1314C2×D4C24×C8314yes—
1315C2×D4C24×C8314yes—
1316C22×C4—24no—
1317C22×C4—24no—
1318C22×C4—48no—
1319C22×C4—48no—
1320C22×C4—44no—
1321C22×C4C24×C8311yescharacteristic
1322C22×C4C24×C8312yes—
1323C22×C4C24×C8314yes—
1324C22×C4C24×C8314yes—
1325C22×C4C24×C8311yescharacteristic
1326C22×C4C24×C8312yes—
1327C22×C4C24×C8312yes—
1328C22×C4C24×C8314yes—
1329C22×C4C24×C8314yes—
1330C22×C4C24×C8312yes—
1331C22×C4C24×C8312yes—
1332C22×C4C24×C8311yescharacteristic
1333C22×C4C24×C8312yes—
1334C22×C4C24×C8312yes—
1335C22×C4C24×C8314yes—
1336C22×C4C24×C8311yescharacteristic
1337C22×C4C24×C8314yes—
1338C22×C4C24×C8314yes—
1339C22×C4C24×C8312yes—
1340C22×C4C24×C8318yes—
1341C22×C4C24×C8318yes—
1342C22×C4C24×C8314yes—
1343C22×C4C24×C8318yes—
1344C22×C4C24×C8318yes—
1345C22×C4C24×C8314yes—
1346C22×C4C24×C8314yes—
1347C22×C4C24×C8314yes—
1348C22×C4C24×C8314yes—
1349C22×C4C24×C8314yes—
1350C22×C4C24×C8311yescharacteristic
1351C4⋊C4C24×C8314yes—
1352C4⋊C4C24×C8314yes—
1353C4⋊C4C24×C8314yes—
1354C4⋊C4C24×C8312yes—
1355C4⋊C4C24×C8314yes—
1356C4⋊C4C24×C8318yes—
1357C4⋊C4C24×C8314yes—
1358C4⋊C4C24×C8312yes—
1359C4⋊C4C24×C8312yes—
1360C4⋊C4C24×C8318yes—
1361C4⋊C4C24×C8318yes—
1362C4⋊C4C24×C8314yes—
1363C4⋊C4C24×C8314yes—
1364C4⋊C4C24×C8314yes—
1365C4⋊C4C24×C8314yes—
1366C4⋊C4C24×C8318yes—
1367C4⋊C4C24×C8318yes—
1368C4⋊C4C24×C8318yes—
1369C4⋊C4C24×C8314yes—
1370C4⋊C4C24×C8312yes—
1371C4⋊C4C24×C8314yes—
1372C4⋊C4C24×C8314yes—
1373C4⋊C4C24×C8314yes—
1374C4⋊C4C24×C8318yes—
1375C4⋊C4C24×C8318yes—
1376C4⋊C4C24×C8318yes—
1377C4⋊C4C24×C8318yes—
1378C4⋊C4C24×C8314yes—
1379C4⋊C4C24×C8318yes—
1380C4⋊C4C24×C8314yes—
1381C4⋊C4C24×C8314yes—
1382C4⋊C4C24×C8314yes—
1383C4⋊C4C24×C8314yes—
1384C4⋊C4C24×C8314yes—
1385C22⋊C4C24×C8311yescharacteristic
1386C22⋊C4C24×C8314yes—
1387C22⋊C4C24×C8314yes—
1388C22⋊C4C24×C8312yes—
1389C22⋊C4C24×C8318yes—
1390C22⋊C4C24×C8314yes—
1391C22⋊C4C24×C8318yes—
1392C22⋊C4C24×C8311yescharacteristic
1393C22⋊C4C24×C8311yescharacteristic
1394C22⋊C4C24×C8311yescharacteristic
1395C22⋊C4C24×C8314yes—
1396C22⋊C4C24×C8318yes—
1397C22⋊C4C24×C8314yes—
1398C22⋊C4C24×C8318yes—
1399C22⋊C4C24×C8318yes—
1400C22⋊C4C24×C8318yes—
1401C22⋊C4C24×C8318yes—
1402C22⋊C4C24×C8314yes—
1403C22⋊C4C24×C8314yes—
1404C22⋊C4C24×C8312yes—
1405C22⋊C4C24×C8314yes—
1406C22⋊C4C24×C8318yes—
1407C22⋊C4C24×C8318yes—
1408C22⋊C4C24×C8314yes—
1409C22⋊C4C24×C8314yes—
1410C22⋊C4C24×C8314yes—
1411C22⋊C4C24×C8314yes—
1412C22⋊C4C24×C8314yes—
1413C22⋊C4C24×C8314yes—
1414C22⋊C4C24×C8318yes—
1415C22⋊C4C24×C8318yes—
1416C22⋊C4C24×C8318yes—
1417C22⋊C4C24×C8314yes—
1418C22⋊C4C24×C8318yes—
1419C22⋊C4C24×C8314yes—
1420C22⋊C4C24×C8314yes—
1421C42C24×C8312yes—
1422C42C24×C8314yes—
1423C42C24×C8314yes—
1424C42C24×C8314yes—
1425C42C24×C8314yes—
1426C42C24×C8314yes—
1427C42C24×C8312yes—
1428C42C24×C8314yes—
1429C42C24×C8314yes—
1430C42C24×C8318yes—
1431C42C24×C8318yes—
1432C23—22no—
1433C23—22no—
1434C23—22no—
1435C23—28no—
1436C23—41no—
1437C23—44no—
1438C23—44no—
1439C23—41no—
1440C23—44no—
1441C23—41no—
1442C23—44no—
1443C23—44no—
1444C23C25×C8312yes—
1445C23C25×C8314yes—
1446C23C25×C8311yescharacteristic
1447C23C25×C8314yes—
1448C23C25×C8314yes—
1449C23C25×C8311yescharacteristic
1450C23C25×C8311yescharacteristic
1451Q8—28no—
1452Q8—24no—
1453Q8—24no—
1454Q8—24no—
1455Q8—48no—
1456Q8—44no—
1457Q8—44no—
1458Q8—44no—
1459D4—28no—
1460D4—28no—
1461D4—28no—
1462D4—24no—
1463D4—28no—
1464D4—24no—
1465D4—24no—
1466D4—24no—
1467D4—44no—
1468D4—44no—
1469D4—44no—
1470D4—44no—
1471D4—44no—
1472D4—44no—
1473D4—48no—
1474D4—44no—
1475D4—44no—
1476D4—42no—
1477D4—44no—
1478D4—44no—
1479D4—48no—
1480D4—44no—
1481D4—44no—
1482D4—48no—
1483D4—44no—
1484D4—44no—
1485C2×C4—22no—
1486C2×C4—22no—
1487C2×C4—24no—
1488C2×C4—28no—
1489C2×C4—24no—
1490C2×C4—24no—
1491C2×C4—24no—
1492C2×C4—24no—
1493C2×C4—28no—
1494C2×C4—28no—
1495C2×C4—28no—
1496C2×C4—44no—
1497C2×C4—44no—
1498C2×C4—44no—
1499C2×C4—44no—
1500C2×C4—44no—
1501C2×C4—44no—
1502C2×C4—42no—
1503C2×C4—44no—
1504C2×C4—42no—
1505C2×C4—41no—
1506C2×C4—44no—
1507C2×C4—48no—
1508C2×C4—48no—
1509C2×C4—48no—
1510C2×C4—44no—
1511C2×C4—41no—
1512C2×C4—42no—
1513C2×C4—48no—
1514C2×C4H(5,𝔽2)×C8314yes—
1515C2×C4C25×C8311yescharacteristic
1516C2×C4C25×C8311yescharacteristic
1517C2×C4C25×C8314yes—
1518C2×C4C25×C8314yes—
1519C2×C4C25×C8314yes—
1520C2×C4C25×C8314yes—
1521C2×C4C25×C8312yes—
1522C2×C4C25×C8311yescharacteristic
1523C2×C4C25×C8311yescharacteristic
1524C2×C4C25×C8314yes—
1525C2×C4C25×C8314yes—
1526C2×C4C25×C8314yes—
1527C2×C4C25×C8314yes—
1528C2×C4C25×C8314yes—
1529C2×C4C25×C8312yes—
1530C2×C4C25×C8312yes—
1531C22—21no—
1532C22—21no—
1533C22—21no—
1534C22—21no—
1535C22—22no—
1536C22—21no—
1537C22—24no—
1538C22—24no—
1539C22—24no—
1540C22—21no—
1541C22—24no—
1542C22—24no—
1543C22—22no—
1544C22—24no—
1545C22—24no—
1546C22—24no—
1547C22—21no—
1548C22—24no—
1549C22—22no—
1550C22—44no—
1551C22—88no—
1552C22—82no—
1553C22—88no—
1554C22C2×H(5,𝔽2)×C8312yes—
1555C22#585×C8312yes—
1556C22C26×C8311yescharacteristic
1557C4—21no—
1558C4—22no—
1559C4—21no—
1560C4—24no—
1561C4—24no—
1562C4—24no—
1563C4—24no—
1564C4—24no—
1565C4—24no—
1566C4—22no—
1567C4—24no—
1568C4—21no—
1569C4—24no—
1570C4—24no—
1571C4—21no—
1572C4C2×H(5,𝔽2)×C8314yes—
1573C2—22no—
1574C2—22no—
1575C2—41no—
1576C2—42no—
1577C2—44no—
1578C2—44no—
1579C2—44no—
1580C2C22×H(5,𝔽2)×C8311yescharacteristic
1581C2C2×#585×C8311yescharacteristic
1582C2C83×2−1+611yescharacteristic
subgroupG/H
center, socleC22×C83C26
commutator, Frattini, cosocleC22C26×C83
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C83×#3560C2semidirect
2. C83×#3559C2semidirect
3. C83×#3551C2semidirect
4. C83×#3547C2semidirect
5. C83×#3542C2semidirect
6. C83×#3541C2semidirect
7. C83×#3539C2semidirect
8. C83×#3538C2semidirect
9. C83×#3534C2semidirect
10. C83×#3520C2semidirect
11. C83×#3512C2semidirect
12. C83×#3505C2semidirect
13. C83×#3497C2semidirect
14. C83×#3494C2semidirect
15. C83×#3493C2semidirect
16. C83×#3492C2semidirect
17. C83×#3489C2semidirect
18. C83×#3489C2semidirect
19. C2×#552×C83C2semidirect
20. D4×#41×C83C2semidirect
21. C83×#3461C2semidirect
22. C83×#3449C2semidirect
23. C2×#537×C83C2semidirect
24. C2×2−1+4×C83C22semidirect
25. C22×#41×C83C22semidirect
26. C22×#41×C83C22semidirect
27. #563×C83C22semidirect
28. #563×C83C22semidirect
29. #562×C83C22semidirect
30. #562×C83C22semidirect
31. #560×C83C22semidirect
32. #560×C83C22semidirect
33. #556×C83C22semidirect
34. #555×C83C22semidirect
35. #555×C83C22semidirect
36. #554×C83C22semidirect
37. #554×C83C22semidirect
38. #553×C83C22semidirect
39. #553×C83C22semidirect
40. #553×C83C22semidirect
41. #553×C83C22semidirect
42. #553×C83C22semidirect
43. #553×C83C22semidirect
44. #553×C83C22semidirect
45. #553×C83C22semidirect
46. #553×C83C22semidirect
47. #552×C83C22semidirect
48. #552×C83C22semidirect
49. #552×C83C22semidirect
50. #552×C83C22semidirect
51. #552×C83C22semidirect
52. #552×C83C22semidirect
53. #552×C83C22semidirect
54. #552×C83C22semidirect
55. #551×C83C22semidirect
56. #551×C83C22semidirect
57. #551×C83C22semidirect
58. #551×C83C22semidirect
59. #550×C83C22semidirect
60. #550×C83C22semidirect
61. D4×Q8×C83C22semidirect
62. D4×Q8×C83C22semidirect
63. D4×Q8×C83C22semidirect
64. D4×Q8×C83C22semidirect
66. #548×C83C22semidirect
67. #548×C83C22semidirect
68. #548×C83C22semidirect
69. #548×C83C22semidirect
70. #548×C83C22semidirect
71. #547×C83C22semidirect
72. #547×C83C22semidirect
73. #547×C83C22semidirect
74. #547×C83C22semidirect
75. #547×C83C22semidirect
76. #547×C83C22semidirect
77. #547×C83C22semidirect
79. #546×C83C22semidirect
80. #546×C83C22semidirect
81. #546×C83C22semidirect
82. #546×C83C22semidirect
83. #546×C83C22semidirect
84. #546×C83C22semidirect
85. #546×C83C22semidirect
86. #546×C83C22semidirect
88. D42×C83C22semidirect
89. #544×C83C22semidirect
90. #544×C83C22semidirect
91. #544×C83C22semidirect
92. #542×C83C22semidirect
93. #542×C83C22semidirect
94. #542×C83C22semidirect
95. #542×C83C22semidirect
96. #541×C83C22semidirect
97. #541×C83C22semidirect
98. #540×C83C22semidirect
99. #540×C83C22semidirect
100. #540×C83C22semidirect
101. #540×C83C22semidirect
102. #540×C83C22semidirect
103. #539×C83C22semidirect
104. #539×C83C22semidirect
105. #539×C83C22semidirect
106. #539×C83C22semidirect
107. #539×C83C22semidirect
108. #539×C83C22semidirect
109. #538×C83C22semidirect
110. #538×C83C22semidirect
111. #538×C83C22semidirect
112. #538×C83C22semidirect
114. #537×C83C22semidirect
115. #537×C83C22semidirect
116. #537×C83C22semidirect
117. #537×C83C22semidirect
118. #537×C83C22semidirect
119. #537×C83C22semidirect
120. #537×C83C22semidirect
121. #537×C83C22semidirect
122. #537×C83C22semidirect
123. #537×C83C22semidirect
124. #536×C83C22semidirect
125. #536×C83C22semidirect
126. #536×C83C22semidirect
127. #536×C83C22semidirect
128. #535×C83C22semidirect
129. #535×C83C22semidirect
130. #534×C83C22semidirect
131. #534×C83C22semidirect
132. #533×C83C22semidirect
133. #532×C83C22semidirect
134. #532×C83C22semidirect
135. #532×C83C22semidirect
136. #532×C83C22semidirect
137. #529×C83C22semidirect
138. #529×C83C22semidirect
139. #529×C83C22semidirect
140. #529×C83C22semidirect
141. #529×C83C22semidirect
142. C2×#126×C83C22semidirect
143. C2×#125×C83C22semidirect
144. C2×#125×C83C22semidirect
146. #525×C83C22semidirect
147. #525×C83C22semidirect
148. #525×C83C22semidirect
149. #525×C83C22semidirect
150. #525×C83C22semidirect
151. #525×C83C22semidirect
152. #525×C83C22semidirect
153. #525×C83C22semidirect
155. C2×C22⋊Q8×C83C22semidirect
156. C2×C22⋊Q8×C83C22semidirect
157. C2×C22⋊Q8×C83C22semidirect
158. C2×C22⋊Q8×C83C22semidirect
159. C2×C22⋊Q8×C83C22semidirect
160. C2×#121×C83C22semidirect
161. C2×#121×C83C22semidirect
162. #520×C83C22semidirect
163. #520×C83C22semidirect
164. #520×C83C22semidirect
165. #518×C83C22semidirect
166. C4×#41×C83C22semidirect
167. C2×C4×Q8×C83C22semidirect
169. C2×C4×D4×C83C22semidirect
170. C2×#117×C83C22semidirect
171. C2×#117×C83C22semidirect
172. C22×C4⋊C4×C83C22semidirect
781. #62927C83direct (N × H)
792. #3560C2×C83semidirect
793. #3559C2×C83semidirect
794. #3551C2×C83semidirect
795. #3547C2×C83semidirect
796. #3542C2×C83semidirect
797. #3541C2×C83semidirect
798. #3539C2×C83semidirect
799. #3538C2×C83semidirect
800. #3534C2×C83semidirect
801. #3520C2×C83semidirect
802. #3512C2×C83semidirect
803. #3505C2×C83semidirect
804. #3497C2×C83semidirect
805. #3494C2×C83semidirect
806. #3493C2×C83semidirect
807. #3492C2×C83semidirect
808. #3489C2×C83semidirect
809. #3489C2×C83semidirect
810. C2×#552C2×C83semidirect
811. D4×#41C2×C83semidirect
812. #3461C2×C83semidirect
813. #3449C2×C83semidirect
814. C2×#537C2×C83semidirect
815. C83#62927direct (N × H)
816. C2×2−1+4C22×C83semidirect
817. C22×#41C22×C83semidirect
818. C22×#41C22×C83semidirect
819. #563C22×C83semidirect
820. #563C22×C83semidirect
821. #562C22×C83semidirect
822. #562C22×C83semidirect
823. #560C22×C83semidirect
824. #560C22×C83semidirect
825. #556C22×C83semidirect
826. #555C22×C83semidirect
827. #555C22×C83semidirect
828. #554C22×C83semidirect
829. #554C22×C83semidirect
830. #553C22×C83semidirect
831. #553C22×C83semidirect
832. #553C22×C83semidirect
833. #553C22×C83semidirect
834. #553C22×C83semidirect
835. #553C22×C83semidirect
836. #553C22×C83semidirect
837. #553C22×C83semidirect
838. #553C22×C83semidirect
839. #552C22×C83semidirect
840. #552C22×C83semidirect
841. #552C22×C83semidirect
842. #552C22×C83semidirect
843. #552C22×C83semidirect
844. #552C22×C83semidirect
845. #552C22×C83semidirect
846. #552C22×C83semidirect
847. #551C22×C83semidirect
848. #551C22×C83semidirect
849. #551C22×C83semidirect
850. #551C22×C83semidirect
851. #550C22×C83semidirect
852. #550C22×C83semidirect
853. D4×Q8C22×C83semidirect
854. D4×Q8C22×C83semidirect
855. D4×Q8C22×C83semidirect
856. D4×Q8C22×C83semidirect
858. #548C22×C83semidirect
859. #548C22×C83semidirect
860. #548C22×C83semidirect
861. #548C22×C83semidirect
862. #548C22×C83semidirect
863. #547C22×C83semidirect
864. #547C22×C83semidirect
865. #547C22×C83semidirect
866. #547C22×C83semidirect
867. #547C22×C83semidirect
868. #547C22×C83semidirect
869. #547C22×C83semidirect
871. #546C22×C83semidirect
872. #546C22×C83semidirect
873. #546C22×C83semidirect
874. #546C22×C83semidirect
875. #546C22×C83semidirect
876. #546C22×C83semidirect
877. #546C22×C83semidirect
878. #546C22×C83semidirect
880. D42C22×C83semidirect
881. #544C22×C83semidirect
882. #544C22×C83semidirect
883. #544C22×C83semidirect
884. #542C22×C83semidirect
885. #542C22×C83semidirect
886. #542C22×C83semidirect
887. #542C22×C83semidirect
888. #541C22×C83semidirect
889. #541C22×C83semidirect
890. #540C22×C83semidirect
891. #540C22×C83semidirect
892. #540C22×C83semidirect
893. #540C22×C83semidirect
894. #540C22×C83semidirect
895. #539C22×C83semidirect
896. #539C22×C83semidirect
897. #539C22×C83semidirect
898. #539C22×C83semidirect
899. #539C22×C83semidirect
900. #539C22×C83semidirect
901. #538C22×C83semidirect
902. #538C22×C83semidirect
903. #538C22×C83semidirect
904. #538C22×C83semidirect
906. #537C22×C83semidirect
907. #537C22×C83semidirect
908. #537C22×C83semidirect
909. #537C22×C83semidirect
910. #537C22×C83semidirect
911. #537C22×C83semidirect
912. #537C22×C83semidirect
913. #537C22×C83semidirect
914. #537C22×C83semidirect
915. #537C22×C83semidirect
916. #536C22×C83semidirect
917. #536C22×C83semidirect
918. #536C22×C83semidirect
919. #536C22×C83semidirect
920. #535C22×C83semidirect
921. #535C22×C83semidirect
922. #534C22×C83semidirect
923. #534C22×C83semidirect
924. #533C22×C83semidirect
925. #532C22×C83semidirect
926. #532C22×C83semidirect
927. #532C22×C83semidirect
928. #532C22×C83semidirect
929. #529C22×C83semidirect
930. #529C22×C83semidirect
931. #529C22×C83semidirect
932. #529C22×C83semidirect
933. #529C22×C83semidirect
934. C2×#126C22×C83semidirect
935. C2×#125C22×C83semidirect
936. C2×#125C22×C83semidirect
938. #525C22×C83semidirect
939. #525C22×C83semidirect
940. #525C22×C83semidirect
941. #525C22×C83semidirect
942. #525C22×C83semidirect
943. #525C22×C83semidirect
944. #525C22×C83semidirect
945. #525C22×C83semidirect
947. C2×C22⋊Q8C22×C83semidirect
948. C2×C22⋊Q8C22×C83semidirect
949. C2×C22⋊Q8C22×C83semidirect
950. C2×C22⋊Q8C22×C83semidirect
951. C2×C22⋊Q8C22×C83semidirect
952. C2×#121C22×C83semidirect
953. C2×#121C22×C83semidirect
954. #520C22×C83semidirect
955. #520C22×C83semidirect
956. #520C22×C83semidirect
957. #518C22×C83semidirect
958. C4×#41C22×C83semidirect
959. C2×C4×Q8C22×C83semidirect
961. C2×C4×D4C22×C83semidirect
962. C2×#117C22×C83semidirect
963. C2×#117C22×C83semidirect
964. C22×C4⋊C4C22×C83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C83×#35602
C83×#35592
C83×#35512
C83×#35472
C83×#35422
C83×#35412
C83×#35392
C83×#35382
C83×#35342
C83×#35202
C83×#35122
C83×#35052
C83×#34972
C83×#34942
C83×#34932
C83×#34922
C83×#34892
C2×#552×C832
D4×#41×C832
C83×#34612
C83×#34492
C2×#537×C832
#6292783