Finite Group Databasebeta

← C83×#62928 #35290752

Subgroups — C83×#62928 #35290752

Order 21248.

6360 conjugacy classes of subgroups.

The subgroup lattice has 1460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3565C214yesmaximal, complemented
2C83×#3565C214yesmaximal, complemented
3C83×#3564C214yesmaximal, complemented
4C83×#3563C214yesmaximal, complemented
5C83×#3563C214yesmaximal, complemented
6C83×#3563C214yesmaximal, complemented
7C83×#3555C214yesmaximal, complemented
8C83×#3544C214yesmaximal, complemented
9C83×#3535C214yesmaximal, complemented
10C83×#3515C214yesmaximal, complemented
11C83×#3509C214yesmaximal, complemented
12C83×#3504C212yesmaximal, complemented
13C83×#3502C211yesmaximal, characteristic, complemented
14C83×#3495C212yesmaximal, complemented
15C83×#3495C212yesmaximal, complemented
16C83×#3495C214yesmaximal, complemented
17C83×#3493C211yesmaximal, characteristic, complemented
18C83×#3492C211yesmaximal, characteristic, complemented
19C83×#3475C212yesmaximal, complemented
20C2×#552×C83C211yesmaximal, characteristic, complemented
21C83×#3461C211yesmaximal, characteristic, complemented
22C83×#3458C211yesmaximal, characteristic, complemented
23C2×#544×C83C211yesmaximal, characteristic, complemented
24#564×C83C2218yescomplemented
25#563×C83C2218yes—
26#563×C83C2218yescomplemented
27#563×C83C2218yescomplemented
28#563×C83C2218yescomplemented
29#562×C83C2218yes—
30Q82×C83C2214yescomplemented
31#557×C83C2214yescomplemented
32#557×C83C2218yescomplemented
33#557×C83C2214yescomplemented
34#557×C83C2214yescomplemented
35#557×C83C2214yescomplemented
36#557×C83C2214yescomplemented
37#556×C83C2212yes—
38#556×C83C2218yescomplemented
39#556×C83C2214yescomplemented
40#556×C83C2214yescomplemented
41#556×C83C2218yescomplemented
42#556×C83C2214yescomplemented
43#555×C83C2212yes—
44#555×C83C2214yescomplemented
45#554×C83C2218yes—
46#554×C83C2212yes—
47#554×C83C2218yes—
48#554×C83C2214yescomplemented
49#554×C83C2214yescomplemented
50#554×C83C2214yescomplemented
51#554×C83C2214yescomplemented
52#554×C83C2214yescomplemented
53#553×C83C2212yes—
54#553×C83C2212yes—
55#553×C83C2214yescomplemented
56#553×C83C2214yescomplemented
57#552×C83C2218yes—
58#552×C83C2214yes—
59#552×C83C2214yes—
60#552×C83C2212yes—
61#552×C83C2214yes—
62#552×C83C2218yes—
63#552×C83C2214yes—
64#552×C83C2218yes—
65#552×C83C2214yes—
66#552×C83C2212yes—
67#552×C83C2218yescomplemented
68#552×C83C2214yescomplemented
69#552×C83C2214yescomplemented
70#552×C83C2214yescomplemented
71#552×C83C2218yescomplemented
72#552×C83C2214yescomplemented
73#552×C83C2214yescomplemented
74#552×C83C2218yescomplemented
75#552×C83C2218yescomplemented
76#552×C83C2214yescomplemented
77#552×C83C2218yescomplemented
78#551×C83C2218yes—
79#551×C83C2218yes—
80#551×C83C2214yes—
81#551×C83C2214yes—
82#547×C83C2218yes—
83#547×C83C2212yes—
84#547×C83C2214yescomplemented
85#546×C83C2214yes—
86#544×C83C2214yes—
87#544×C83C2214yes—
88#544×C83C2211yescharacteristic
89#544×C83C2211yescharacteristic
90#544×C83C2212yes—
91#544×C83C2211yescharacteristic
92#544×C83C2212yes—
93#544×C83C2214yescomplemented
94#544×C83C2218yescomplemented
95#544×C83C2214yescomplemented
96#544×C83C2214yescomplemented
97#544×C83C2214yescomplemented
98#544×C83C2214yescomplemented
99#544×C83C2214yescomplemented
100#544×C83C2214yescomplemented
101#543×C83C2214yes—
102#542×C83C2218yes—
103#542×C83C2218yescomplemented
104#542×C83C2214yescomplemented
105#542×C83C2214yescomplemented
106#542×C83C2214yescomplemented
107#542×C83C2214yescomplemented
108#542×C83C2214yescomplemented
109#541×C83C2214yescomplemented
110#541×C83C2218yescomplemented
111#541×C83C2214yescomplemented
112#541×C83C2214yescomplemented
113#541×C83C2218yescomplemented
114#541×C83C2218yescomplemented
115#541×C83C2214yescomplemented
116#541×C83C2214yescomplemented
117#541×C83C2218yescomplemented
118#541×C83C2218yescomplemented
119#539×C83C2218yes—
120#539×C83C2214yes—
121#539×C83C2218yes—
122#539×C83C2214yes—
123#539×C83C2218yescomplemented
124#538×C83C2214yes—
125#537×C83C2211yescharacteristic
126#536×C83C2218yes—
127#536×C83C2212yes—
128#536×C83C2214yescomplemented
129#533×C83C2214yes—
130#533×C83C2214yes—
131#533×C83C2212yes—
132#533×C83C2214yescomplemented
133#533×C83C2214yescomplemented
134#533×C83C2214yescomplemented
135#533×C83C2214yescomplemented
136#533×C83C2214yescomplemented
137#533×C83C2214yescomplemented
138C2×C4⋊Q8×C83C2214yescomplemented
139#529×C83C2214yes—
140#529×C83C2214yes—
141#529×C83C2214yes—
142#529×C83C2214yes—
143#529×C83C2214yes—
144#529×C83C2214yescomplemented
145#529×C83C2214yescomplemented
146#529×C83C2214yescomplemented
147C2×#126×C83C2212yes—
148C2×#125×C83C2212yes—
149C2×#125×C83C2211yescharacteristic
150C2×#125×C83C2214yescomplemented
151C2×#125×C83C2214yescomplemented
152#525×C83C2214yes—
153#525×C83C2212yes—
154#525×C83C2212yes—
155C2×#123×C83C2212yes—
156C2×C22⋊Q8×C83C2214yes—
157C2×C22⋊Q8×C83C2211yescharacteristic
158C2×C22⋊Q8×C83C2211yescharacteristic
159#520×C83C2212yes—
160#520×C83C2212yes—
161#520×C83C2214yescomplemented
162#519×C83C2212yes—
163#519×C83C2214yescomplemented
164C4×#41×C83C2212yes—
165C4×#41×C83C2214yes—
166C2×C4×Q8×C83C2211yescharacteristic
167C2×C4×D4×C83C2211yescharacteristic
168C2×#117×C83C2212yes—
169C2×#117×C83C2211yescharacteristic
170C2×#117×C83C2212yes—
171C2×#117×C83C2212yes—
172C22×C4⋊C4×C83C2211yescharacteristic
173C2×#41×C83C2312yes—
174C2×#41×C83C2314yes—
175C2×#41×C83C2314yes—
176C22×Q8×C83C2311yescharacteristic
177C22×Q8×C83C2314yes—
178C22×D4×C83C2311yescharacteristic
179C23×C4×C83C2311yescharacteristic
180C23×C4×C83C2311yescharacteristic
181C23×C4×C83C2312yes—
182C4⋊Q8×C83C2314yes—
183C4⋊Q8×C83C2314yes—
184C4⋊Q8×C83C2318yes—
185C4⋊Q8×C83C2314yes—
186C4⋊Q8×C83C2314yes—
187C4⋊Q8×C83C2318yes—
188C4⋊Q8×C83C2314yes—
189C4⋊Q8×C83C2314yes—
190C4⋊Q8×C83C2314yes—
191C4⋊Q8×C83C2314yes—
192C4⋊Q8×C83C2312yes—
193C4⋊Q8×C83C2312yes—
194C4⋊Q8×C83C2314yes—
195C4⋊Q8×C83C2314yes—
196C4⋊Q8×C83C2314yes—
197C4⋊Q8×C83C2314yes—
198C4⋊Q8×C83C2318yes—
199C4⋊Q8×C83C2318yes—
200C4⋊Q8×C83C2318yes—
201C4⋊Q8×C83C2318yes—
202#126×C83C2318yes—
203#126×C83C2318yes—
204#126×C83C2314yes—
205#126×C83C2314yes—
206#126×C83C2314yes—
207#126×C83C2314yes—
208#126×C83C2314yes—
209#126×C83C2314yes—
210#126×C83C2318yes—
211#126×C83C2318yes—
212#126×C83C2318yes—
213#126×C83C2318yes—
214#126×C83C2318yes—
215#126×C83C2318yes—
216#126×C83C2318yes—
217#126×C83C2318yes—
218#126×C83C2318yes—
219#126×C83C2318yes—
220#126×C83C2318yes—
221#126×C83C2318yes—
222#126×C83C2318yes—
223#125×C83C2314yes—
224#125×C83C2318yes—
225#125×C83C2318yes—
226#125×C83C2314yes—
227#125×C83C2314yes—
228#125×C83C2312yes—
229#125×C83C2314yes—
230#125×C83C2314yes—
231#125×C83C2318yes—
232#125×C83C2318yes—
233#125×C83C2318yes—
234#125×C83C2314yes—
235#125×C83C2318yes—
236#125×C83C2314yes—
237#125×C83C2314yes—
238#125×C83C2314yes—
239#125×C83C2314yes—
240#125×C83C2314yes—
241#125×C83C2314yes—
242#125×C83C2312yes—
243#125×C83C2318yes—
244#125×C83C2318yes—
245#125×C83C2318yes—
246#125×C83C2318yes—
247#125×C83C2318yes—
248#125×C83C2314yes—
249#125×C83C2314yes—
250#125×C83C2318yes—
251#125×C83C2318yes—
252#125×C83C2318yes—
253#125×C83C2318yes—
254#125×C83C2318yes—
255#125×C83C2318yes—
256#125×C83C2318yes—
257#125×C83C2318yes—
258#125×C83C2318yes—
259#124×C83C2314yes—
260#124×C83C2314yes—
261#124×C83C2314yes—
262#124×C83C2314yes—
263#124×C83C2314yes—
264#124×C83C2314yes—
265#124×C83C2318yes—
266#124×C83C2318yes—
267#124×C83C2318yes—
268#123×C83C2318yes—
269#123×C83C2318yes—
270#123×C83C2314yes—
271#123×C83C2318yes—
272#123×C83C2314yes—
273#123×C83C2314yes—
274#123×C83C2318yes—
275#123×C83C2314yes—
276#123×C83C2314yes—
277#123×C83C2314yes—
278#123×C83C2314yes—
279#123×C83C2314yes—
280#123×C83C2318yes—
281#123×C83C2318yes—
282#123×C83C2318yes—
283#123×C83C2318yes—
284#123×C83C2318yes—
285#123×C83C2318yes—
286#123×C83C2318yes—
287C22⋊Q8×C83C2314yes—
288C22⋊Q8×C83C2314yes—
289C22⋊Q8×C83C2314yes—
290C22⋊Q8×C83C2314yes—
291C22⋊Q8×C83C2314yes—
292C22⋊Q8×C83C2314yes—
293C22⋊Q8×C83C2314yes—
294C22⋊Q8×C83C2314yes—
295C22⋊Q8×C83C2318yes—
296C22⋊Q8×C83C2318yes—
297C22⋊Q8×C83C2314yes—
298C22⋊Q8×C83C2312yes—
299C22⋊Q8×C83C2312yes—
300C22⋊Q8×C83C2312yes—
301C22⋊Q8×C83C2312yes—
302C22⋊Q8×C83C2314yes—
303C22⋊Q8×C83C2314yes—
304C22⋊Q8×C83C2314yes—
305C22⋊Q8×C83C2314yes—
306C22⋊Q8×C83C2314yes—
307C22⋊Q8×C83C2314yes—
308C22⋊Q8×C83C2318yes—
309C22⋊Q8×C83C2314yes—
310C22⋊Q8×C83C2318yes—
311C22⋊Q8×C83C2318yes—
312C22⋊Q8×C83C2318yes—
313C22⋊Q8×C83C2318yes—
314C22⋊Q8×C83C2314yes—
315C22⋊Q8×C83C2314yes—
316C22⋊Q8×C83C2318yes—
317C22⋊Q8×C83C2318yes—
318C22⋊Q8×C83C2318yes—
319C22⋊Q8×C83C2318yes—
320C22⋊Q8×C83C2318yes—
321C22⋊Q8×C83C2318yes—
322C22⋊Q8×C83C2318yes—
323C22⋊Q8×C83C2318yes—
324C22⋊Q8×C83C2318yes—
325C22⋊Q8×C83C2318yes—
326C22⋊Q8×C83C2318yes—
327C22⋊Q8×C83C2318yes—
328#121×C83C2314yes—
329#121×C83C2312yes—
330#121×C83C2312yes—
331#121×C83C2312yes—
332#121×C83C2312yes—
333#121×C83C2314yes—
334#121×C83C2314yes—
335#121×C83C2314yes—
336#121×C83C2314yes—
337#121×C83C2314yes—
338#121×C83C2318yes—
339#120×C83C2314yes—
340#120×C83C2314yes—
341C4×Q8×C83C2314yes—
342C4×Q8×C83C2314yes—
343C4×Q8×C83C2314yes—
344C4×Q8×C83C2312yes—
345C4×Q8×C83C2314yes—
346C4×Q8×C83C2312yes—
347C4×Q8×C83C2314yes—
348C4×Q8×C83C2314yes—
349C4×Q8×C83C2314yes—
350C4×Q8×C83C2314yes—
351C4×Q8×C83C2314yes—
352C4×Q8×C83C2314yes—
353C4×Q8×C83C2314yes—
354C4×Q8×C83C2314yes—
355C4×Q8×C83C2318yes—
356C4×Q8×C83C2318yes—
357C4×Q8×C83C2314yes—
358C4×Q8×C83C2314yes—
359C4×Q8×C83C2314yes—
360C4×Q8×C83C2314yes—
361C4×Q8×C83C2314yes—
362C4×Q8×C83C2318yes—
363C4×Q8×C83C2318yes—
364C4×Q8×C83C2318yes—
365C4×Q8×C83C2318yes—
366C4×D4×C83C2312yes—
367C4×D4×C83C2312yes—
368C4×D4×C83C2312yes—
369C4×D4×C83C2312yes—
370C4×D4×C83C2314yes—
371C4×D4×C83C2314yes—
372C4×D4×C83C2314yes—
373C4×D4×C83C2314yes—
374C4×D4×C83C2312yes—
375C4×D4×C83C2314yes—
376C4×D4×C83C2314yes—
377C4×D4×C83C2314yes—
378C4×D4×C83C2312yes—
379C4×D4×C83C2318yes—
380C4×D4×C83C2318yes—
381C4×D4×C83C2314yes—
382C4×D4×C83C2314yes—
383C4×D4×C83C2314yes—
384C4×D4×C83C2314yes—
385C4×D4×C83C2318yes—
386C4×D4×C83C2314yes—
387C4×D4×C83C2314yes—
388C4×D4×C83C2318yes—
389C4×D4×C83C2318yes—
390#117×C83C2312yes—
391#117×C83C2312yes—
392#117×C83C2312yes—
393#117×C83C2314yes—
394#117×C83C2314yes—
395#117×C83C2314yes—
396#117×C83C2314yes—
397#117×C83C2314yes—
398#117×C83C2312yes—
399#117×C83C2312yes—
400#117×C83C2314yes—
401#117×C83C2314yes—
402#117×C83C2314yes—
403#117×C83C2314yes—
404#117×C83C2314yes—
405#117×C83C2312yes—
406#117×C83C2312yes—
407#117×C83C2314yes—
408#117×C83C2314yes—
409#117×C83C2314yes—
410#117×C83C2314yes—
411#117×C83C2318yes—
412#117×C83C2314yes—
413#117×C83C2318yes—
414#117×C83C2314yes—
415#117×C83C2314yes—
416#117×C83C2318yes—
417#117×C83C2318yes—
418#117×C83C2318yes—
419#117×C83C2318yes—
420#117×C83C2318yes—
421C2×C4⋊C4×C83C2311yescharacteristic
422C2×C4⋊C4×C83C2311yescharacteristic
423C2×C4⋊C4×C83C2312yes—
424C2×C4⋊C4×C83C2314yes—
425C2×C4⋊C4×C83C2314yes—
426C2×C4⋊C4×C83C2311yescharacteristic
427C2×C4⋊C4×C83C2312yes—
428C2×C4⋊C4×C83C2312yes—
429C2×C4⋊C4×C83C2312yes—
430C2×C4⋊C4×C83C2312yes—
431C2×C4⋊C4×C83C2312yes—
432C2×C4⋊C4×C83C2312yes—
433C2×C4⋊C4×C83C2311yescharacteristic
434C2×C4⋊C4×C83C2312yes—
435C2×C4⋊C4×C83C2314yes—
436C2×C4⋊C4×C83C2314yes—
437C2×C4⋊C4×C83C2314yes—
438C2×C4⋊C4×C83C2318yes—
439C2×C4⋊C4×C83C2312yes—
440C2×C4⋊C4×C83C2318yes—
441C2×C4⋊C4×C83C2312yes—
442C2×C4⋊C4×C83C2318yes—
443C2×C22⋊C4×C83C2311yescharacteristic
444C2×C22⋊C4×C83C2314yes—
445C2×C22⋊C4×C83C2312yes—
446C2×C22⋊C4×C83C2312yes—
447C2×C22⋊C4×C83C2314yes—
448C2×C22⋊C4×C83C2311yescharacteristic
449C2×C22⋊C4×C83C2312yes—
450C2×C42×C83C2312yes—
451C2×C42×C83C2312yes—
452C2×C42×C83C2314yes—
453C2×C42×C83C2314yes—
454C2×C42×C83C2311yescharacteristic
455C2×C42×C83C2314yes—
456C24×C83C2411yescharacteristic
457C24×C83C2411yescharacteristic
458#41×C83—28no—
459#41×C83—48no—
460#41×C83—48no—
461C2×Q8×C83—24no—
462C2×Q8×C83—48no—
463C2×Q8×C83C2414yes—
464C2×Q8×C83C2412yes—
465C2×Q8×C83C2418yes—
466C2×Q8×C83C2414yes—
467C2×Q8×C83C2418yes—
468C2×Q8×C83C2414yes—
469C2×Q8×C83C2414yes—
470C2×Q8×C83C2414yes—
471C2×Q8×C83C2414yes—
472C2×D4×C83—42no—
473C2×D4×C83C2414yes—
474C2×D4×C83C2412yes—
475C2×D4×C83C2414yes—
476C2×D4×C83C2412yes—
477C2×D4×C83C2414yes—
478C2×D4×C83C2414yes—
479C2×D4×C83C2414yes—
480C2×D4×C83C2414yes—
481C2×D4×C83C2412yes—
482C22×C4×C83—24no—
483C22×C4×C83—24no—
484C22×C4×C83—44no—
485C22×C4×C83C2411yescharacteristic
486C22×C4×C83C2412yes—
487C22×C4×C83C2412yes—
488C22×C4×C83C2412yes—
489C22×C4×C83C2414yes—
490C22×C4×C83C2414yes—
491C22×C4×C83C2411yescharacteristic
492C22×C4×C83C2414yes—
493C22×C4×C83C2412yes—
494C22×C4×C83C2412yes—
495C22×C4×C83C2411yescharacteristic
496C22×C4×C83C2412yes—
497C22×C4×C83C2412yes—
498C22×C4×C83C2414yes—
499C22×C4×C83C2414yes—
500C22×C4×C83C2414yes—
501C22×C4×C83C2411yescharacteristic
502C22×C4×C83C2414yes—
503C22×C4×C83C2414yes—
504C22×C4×C83C2412yes—
505C22×C4×C83C2418yes—
506C22×C4×C83C2418yes—
507C22×C4×C83C2414yes—
508C22×C4×C83C2411yescharacteristic
509C4⋊C4×C83C2414yes—
510C4⋊C4×C83C2412yes—
511C4⋊C4×C83C2414yes—
512C4⋊C4×C83C2412yes—
513C4⋊C4×C83C2414yes—
514C4⋊C4×C83C2418yes—
515C4⋊C4×C83C2414yes—
516C4⋊C4×C83C2412yes—
517C4⋊C4×C83C2412yes—
518C4⋊C4×C83C2414yes—
519C4⋊C4×C83C2418yes—
520C4⋊C4×C83C2418yes—
521C4⋊C4×C83C2414yes—
522C4⋊C4×C83C2418yes—
523C4⋊C4×C83C2412yes—
524C4⋊C4×C83C2412yes—
525C4⋊C4×C83C2414yes—
526C4⋊C4×C83C2412yes—
527C4⋊C4×C83C2414yes—
528C4⋊C4×C83C2414yes—
529C4⋊C4×C83C2414yes—
530C4⋊C4×C83C2414yes—
531C4⋊C4×C83C2414yes—
532C4⋊C4×C83C2414yes—
533C4⋊C4×C83C2418yes—
534C4⋊C4×C83C2418yes—
535C4⋊C4×C83C2418yes—
536C4⋊C4×C83C2418yes—
537C4⋊C4×C83C2418yes—
538C4⋊C4×C83C2412yes—
539C4⋊C4×C83C2414yes—
540C4⋊C4×C83C2418yes—
541C4⋊C4×C83C2418yes—
542C4⋊C4×C83C2414yes—
543C4⋊C4×C83C2418yes—
544C4⋊C4×C83C2418yes—
545C4⋊C4×C83C2414yes—
546C4⋊C4×C83C2418yes—
547C4⋊C4×C83C2414yes—
548C4⋊C4×C83C2414yes—
549C4⋊C4×C83C2414yes—
550C4⋊C4×C83C2414yes—
551C4⋊C4×C83C2414yes—
552C4⋊C4×C83C2414yes—
553C4⋊C4×C83C2414yes—
554C4⋊C4×C83C2414yes—
555C4⋊C4×C83C2418yes—
556C4⋊C4×C83C2418yes—
557C4⋊C4×C83C2418yes—
558C4⋊C4×C83C2418yes—
559C4⋊C4×C83C2418yes—
560C4⋊C4×C83C2414yes—
561C4⋊C4×C83C2414yes—
562C4⋊C4×C83C2414yes—
563C22⋊C4×C83C2414yes—
564C22⋊C4×C83C2411yescharacteristic
565C22⋊C4×C83C2414yes—
566C22⋊C4×C83C2414yes—
567C22⋊C4×C83C2414yes—
568C22⋊C4×C83C2411yescharacteristic
569C22⋊C4×C83C2411yescharacteristic
570C22⋊C4×C83C2411yescharacteristic
571C22⋊C4×C83C2412yes—
572C22⋊C4×C83C2418yes—
573C22⋊C4×C83C2414yes—
574C22⋊C4×C83C2414yes—
575C22⋊C4×C83C2414yes—
576C22⋊C4×C83C2414yes—
577C22⋊C4×C83C2414yes—
578C22⋊C4×C83C2418yes—
579C22⋊C4×C83C2412yes—
580C22⋊C4×C83C2414yes—
581C22⋊C4×C83C2414yes—
582C22⋊C4×C83C2414yes—
583C22⋊C4×C83C2418yes—
584C22⋊C4×C83C2414yes—
585C22⋊C4×C83C2414yes—
586C22⋊C4×C83C2418yes—
587C22⋊C4×C83C2414yes—
588C22⋊C4×C83C2414yes—
589C22⋊C4×C83C2418yes—
590C22⋊C4×C83C2418yes—
591C22⋊C4×C83C2414yes—
592C22⋊C4×C83C2414yes—
593C22⋊C4×C83C2418yes—
594C22⋊C4×C83C2414yes—
595C42×C83C2414yes—
596C42×C83C2412yes—
597C42×C83C2414yes—
598C42×C83C2414yes—
599C42×C83C2414yes—
600C42×C83C2414yes—
601C42×C83C2414yes—
602C42×C83C2414yes—
603C42×C83C2414yes—
604C42×C83C2412yes—
605C42×C83C2414yes—
606C42×C83C2414yes—
607C42×C83C2414yes—
608C42×C83C2414yes—
609C42×C83C2414yes—
610C42×C83C2418yes—
611C42×C83C2418yes—
612C42×C83C2418yes—
613C42×C83C2418yes—
614C23×C83—22no—
615C23×C83—22no—
616C23×C83—22no—
617C23×C83—41no—
618C23×C83—41no—
619C23×C83—41no—
620C23×C83C2511yescharacteristic
621C23×C83C2512yes—
622C23×C83C2514yes—
623C23×C83C2511yescharacteristic
624C23×C83C2511yescharacteristic
625Q8×C83—28no—
626Q8×C83—24no—
627Q8×C83—48no—
628Q8×C83—44no—
629Q8×C83—44no—
630Q8×C83—44no—
631Q8×C83—48no—
632Q8×C83—44no—
633Q8×C83—44no—
634D4×C83—28no—
635D4×C83—24no—
636D4×C83—28no—
637D4×C83—24no—
638D4×C83—42no—
639D4×C83—44no—
640D4×C83—44no—
641D4×C83—44no—
642D4×C83—44no—
643C2×C4×C83—22no—
644C2×C4×C83—22no—
645C2×C4×C83—24no—
646C2×C4×C83—28no—
647C2×C4×C83—28no—
648C2×C4×C83—24no—
649C2×C4×C83—24no—
650C2×C4×C83—24no—
651C2×C4×C83—24no—
652C2×C4×C83—28no—
653C2×C4×C83—42no—
654C2×C4×C83—44no—
655C2×C4×C83—42no—
656C2×C4×C83—44no—
657C2×C4×C83—41no—
658C2×C4×C83—44no—
659C2×C4×C83—48no—
660C2×C4×C83—42no—
661C2×C4×C83—44no—
662C2×C4×C83—41no—
663C2×C4×C83—48no—
664C2×C4×C83—44no—
665C2×C4×C83—44no—
666C2×C4×C832−1+414yes—
667C2×C4×C83C2511yescharacteristic
668C2×C4×C83C2511yescharacteristic
669C2×C4×C83C2514yes—
670C2×C4×C83C2511yescharacteristic
671C2×C4×C83C2514yes—
672C2×C4×C83C2514yes—
673C2×C4×C83C2514yes—
674C2×C4×C83C2511yescharacteristic
675C2×C4×C83C2512yes—
676C2×C4×C83C2514yes—
677C2×C4×C83C2514yes—
678C2×C4×C83C2514yes—
679C2×C4×C83C2514yes—
680C2×C4×C83C2514yes—
681C2×C4×C83C2514yes—
682C2×C4×C83C2512yes—
683C2×C4×C83C2514yes—
684C2×C4×C83C2512yes—
685C22×C83—21no—
686C22×C83—21no—
687C22×C83—21no—
688C22×C83—21no—
689C22×C83—21no—
690C22×C83—22no—
691C22×C83—24no—
692C22×C83—21no—
693C22×C83—24no—
694C22×C83—22no—
695C22×C83—24no—
696C22×C83—22no—
697C22×C83—21no—
698C22×C83—44no—
699C22×C83—82no—
700C22×C83C2×2−1+412yes—
701C22×C83#58512yes—
702C22×C83C2611yescharacteristic
703C4×C83—21no—
704C4×C83—21no—
705C4×C83—22no—
706C4×C83—24no—
707C4×C83—24no—
708C4×C83—24no—
709C4×C83—24no—
710C4×C83—24no—
711C4×C83—24no—
712C4×C83—22no—
713C4×C83—24no—
714C4×C83—21no—
715C4×C83—24no—
716C4×C83—24no—
717C4×C83—24no—
718C4×C83—24no—
719C4×C83—21no—
720C4×C83C2×2−1+414yes—
721#62928C8311yesmaximal, characteristic, direct product factor, Sylow
722C2×C83—22no—
723C2×C83—22no—
724C2×C83—44no—
725C2×C83—41no—
726C2×C83—42no—
727C2×C83C22×2−1+411yescharacteristic
728C2×C83C2×#58511yescharacteristic
729C2×C832−1+611yescharacteristic
730#3565C2×C8314yescomplemented
731#3565C2×C8314yescomplemented
732#3564C2×C8314yescomplemented
733#3563C2×C8314yescomplemented
734#3563C2×C8314yescomplemented
735#3563C2×C8314yescomplemented
736#3555C2×C8314yescomplemented
737#3544C2×C8314yescomplemented
738#3535C2×C8314yescomplemented
739#3515C2×C8314yescomplemented
740#3509C2×C8314yescomplemented
741#3504C2×C8312yescomplemented
742#3502C2×C8311yescharacteristic, complemented
743#3495C2×C8312yescomplemented
744#3495C2×C8312yescomplemented
745#3495C2×C8314yescomplemented
746#3493C2×C8311yescharacteristic, complemented
747#3492C2×C8311yescharacteristic, complemented
748#3475C2×C8312yescomplemented
749C2×#552C2×C8311yescharacteristic, complemented
750#3461C2×C8311yescharacteristic, complemented
751#3458C2×C8311yescharacteristic, complemented
752C2×#544C2×C8311yescharacteristic, complemented
753C83#6292811yescharacteristic, direct product factor, Sylow
754#564C22×C8318yescomplemented
755#563C22×C8318yes—
756#563C22×C8318yescomplemented
757#563C22×C8318yescomplemented
758#563C22×C8318yescomplemented
759#562C22×C8318yes—
760Q82C22×C8314yescomplemented
761#557C22×C8314yescomplemented
762#557C22×C8314yescomplemented
763#557C22×C8314yescomplemented
764#557C22×C8314yescomplemented
765#557C22×C8314yescomplemented
766#557C22×C8318yescomplemented
767#556C22×C8312yes—
768#556C22×C8314yescomplemented
769#556C22×C8314yescomplemented
770#556C22×C8318yescomplemented
771#556C22×C8314yescomplemented
772#556C22×C8318yescomplemented
773#555C22×C8312yes—
774#555C22×C8314yescomplemented
775#554C22×C8312yes—
776#554C22×C8318yes—
777#554C22×C8318yes—
778#554C22×C8314yescomplemented
779#554C22×C8314yescomplemented
780#554C22×C8314yescomplemented
781#554C22×C8314yescomplemented
782#554C22×C8314yescomplemented
783#553C22×C8312yes—
784#553C22×C8312yes—
785#553C22×C8314yescomplemented
786#553C22×C8314yescomplemented
787#552C22×C8314yes—
788#552C22×C8314yes—
789#552C22×C8314yes—
790#552C22×C8314yes—
791#552C22×C8312yes—
792#552C22×C8312yes—
793#552C22×C8314yes—
794#552C22×C8318yes—
795#552C22×C8318yes—
796#552C22×C8318yes—
797#552C22×C8314yescomplemented
798#552C22×C8314yescomplemented
799#552C22×C8318yescomplemented
800#552C22×C8314yescomplemented
801#552C22×C8314yescomplemented
802#552C22×C8318yescomplemented
803#552C22×C8314yescomplemented
804#552C22×C8314yescomplemented
805#552C22×C8318yescomplemented
806#552C22×C8318yescomplemented
807#552C22×C8318yescomplemented
808#551C22×C8314yes—
809#551C22×C8314yes—
810#551C22×C8318yes—
811#551C22×C8318yes—
812#547C22×C8312yes—
813#547C22×C8318yes—
814#547C22×C8314yescomplemented
815#546C22×C8314yes—
816#544C22×C8311yescharacteristic
817#544C22×C8311yescharacteristic
818#544C22×C8312yes—
819#544C22×C8314yes—
820#544C22×C8311yescharacteristic
821#544C22×C8312yes—
822#544C22×C8314yes—
823#544C22×C8314yescomplemented
824#544C22×C8314yescomplemented
825#544C22×C8314yescomplemented
826#544C22×C8314yescomplemented
827#544C22×C8314yescomplemented
828#544C22×C8314yescomplemented
829#544C22×C8314yescomplemented
830#544C22×C8318yescomplemented
831#543C22×C8314yes—
832#542C22×C8318yes—
833#542C22×C8314yescomplemented
834#542C22×C8314yescomplemented
835#542C22×C8314yescomplemented
836#542C22×C8314yescomplemented
837#542C22×C8314yescomplemented
838#542C22×C8318yescomplemented
839#541C22×C8314yescomplemented
840#541C22×C8314yescomplemented
841#541C22×C8314yescomplemented
842#541C22×C8314yescomplemented
843#541C22×C8314yescomplemented
844#541C22×C8318yescomplemented
845#541C22×C8318yescomplemented
846#541C22×C8318yescomplemented
847#541C22×C8318yescomplemented
848#541C22×C8318yescomplemented
849#539C22×C8314yes—
850#539C22×C8314yes—
851#539C22×C8318yes—
852#539C22×C8318yes—
853#539C22×C8318yescomplemented
854#538C22×C8314yes—
855#537C22×C8311yescharacteristic
856#536C22×C8312yes—
857#536C22×C8318yes—
858#536C22×C8314yescomplemented
859#533C22×C8314yes—
860#533C22×C8312yes—
861#533C22×C8314yes—
862#533C22×C8314yescomplemented
863#533C22×C8314yescomplemented
864#533C22×C8314yescomplemented
865#533C22×C8314yescomplemented
866#533C22×C8314yescomplemented
867#533C22×C8314yescomplemented
868C2×C4⋊Q8C22×C8314yescomplemented
869#529C22×C8314yes—
870#529C22×C8314yes—
871#529C22×C8314yes—
872#529C22×C8314yes—
873#529C22×C8314yes—
874#529C22×C8314yescomplemented
875#529C22×C8314yescomplemented
876#529C22×C8314yescomplemented
877C2×#126C22×C8312yes—
878C2×#125C22×C8311yescharacteristic
879C2×#125C22×C8312yes—
880C2×#125C22×C8314yescomplemented
881C2×#125C22×C8314yescomplemented
882#525C22×C8312yes—
883#525C22×C8312yes—
884#525C22×C8314yes—
885C2×#123C22×C8312yes—
886C2×C22⋊Q8C22×C8314yes—
887C2×C22⋊Q8C22×C8311yescharacteristic
888C2×C22⋊Q8C22×C8311yescharacteristic
889#520C22×C8312yes—
890#520C22×C8312yes—
891#520C22×C8314yescomplemented
892#519C22×C8312yes—
893#519C22×C8314yescomplemented
894C4×#41C22×C8312yes—
895C4×#41C22×C8314yes—
896C2×C4×Q8C22×C8311yescharacteristic
897C2×C4×D4C22×C8311yescharacteristic
898C2×#117C22×C8312yes—
899C2×#117C22×C8311yescharacteristic
900C2×#117C22×C8312yes—
901C2×#117C22×C8312yes—
902C22×C4⋊C4C22×C8311yescharacteristic
903C2×#41C23×C8312yes—
904C2×#41C23×C8314yes—
905C2×#41C23×C8314yes—
906C22×Q8C23×C8311yescharacteristic
907C22×Q8C23×C8314yes—
908C22×D4C23×C8311yescharacteristic
909C23×C4C23×C8311yescharacteristic
910C23×C4C23×C8311yescharacteristic
911C23×C4C23×C8312yes—
912C4⋊Q8C23×C8314yes—
913C4⋊Q8C23×C8314yes—
914C4⋊Q8C23×C8318yes—
915C4⋊Q8C23×C8314yes—
916C4⋊Q8C23×C8314yes—
917C4⋊Q8C23×C8318yes—
918C4⋊Q8C23×C8314yes—
919C4⋊Q8C23×C8314yes—
920C4⋊Q8C23×C8314yes—
921C4⋊Q8C23×C8314yes—
922C4⋊Q8C23×C8312yes—
923C4⋊Q8C23×C8312yes—
924C4⋊Q8C23×C8314yes—
925C4⋊Q8C23×C8314yes—
926C4⋊Q8C23×C8314yes—
927C4⋊Q8C23×C8314yes—
928C4⋊Q8C23×C8318yes—
929C4⋊Q8C23×C8318yes—
930C4⋊Q8C23×C8318yes—
931C4⋊Q8C23×C8318yes—
932#126C23×C8318yes—
933#126C23×C8318yes—
934#126C23×C8314yes—
935#126C23×C8314yes—
936#126C23×C8314yes—
937#126C23×C8314yes—
938#126C23×C8314yes—
939#126C23×C8314yes—
940#126C23×C8318yes—
941#126C23×C8318yes—
942#126C23×C8318yes—
943#126C23×C8318yes—
944#126C23×C8318yes—
945#126C23×C8318yes—
946#126C23×C8318yes—
947#126C23×C8318yes—
948#126C23×C8318yes—
949#126C23×C8318yes—
950#126C23×C8318yes—
951#126C23×C8318yes—
952#126C23×C8318yes—
953#125C23×C8314yes—
954#125C23×C8318yes—
955#125C23×C8318yes—
956#125C23×C8314yes—
957#125C23×C8314yes—
958#125C23×C8312yes—
959#125C23×C8314yes—
960#125C23×C8314yes—
961#125C23×C8318yes—
962#125C23×C8318yes—
963#125C23×C8318yes—
964#125C23×C8314yes—
965#125C23×C8318yes—
966#125C23×C8314yes—
967#125C23×C8314yes—
968#125C23×C8314yes—
969#125C23×C8314yes—
970#125C23×C8314yes—
971#125C23×C8314yes—
972#125C23×C8312yes—
973#125C23×C8318yes—
974#125C23×C8318yes—
975#125C23×C8318yes—
976#125C23×C8318yes—
977#125C23×C8318yes—
978#125C23×C8314yes—
979#125C23×C8314yes—
980#125C23×C8318yes—
981#125C23×C8318yes—
982#125C23×C8318yes—
983#125C23×C8318yes—
984#125C23×C8318yes—
985#125C23×C8318yes—
986#125C23×C8318yes—
987#125C23×C8318yes—
988#125C23×C8318yes—
989#124C23×C8314yes—
990#124C23×C8314yes—
991#124C23×C8314yes—
992#124C23×C8314yes—
993#124C23×C8314yes—
994#124C23×C8314yes—
995#124C23×C8318yes—
996#124C23×C8318yes—
997#124C23×C8318yes—
998#123C23×C8318yes—
999#123C23×C8318yes—
1000#123C23×C8314yes—
1001#123C23×C8318yes—
1002#123C23×C8314yes—
1003#123C23×C8314yes—
1004#123C23×C8318yes—
1005#123C23×C8314yes—
1006#123C23×C8314yes—
1007#123C23×C8314yes—
1008#123C23×C8314yes—
1009#123C23×C8314yes—
1010#123C23×C8318yes—
1011#123C23×C8318yes—
1012#123C23×C8318yes—
1013#123C23×C8318yes—
1014#123C23×C8318yes—
1015#123C23×C8318yes—
1016#123C23×C8318yes—
1017C22⋊Q8C23×C8314yes—
1018C22⋊Q8C23×C8314yes—
1019C22⋊Q8C23×C8314yes—
1020C22⋊Q8C23×C8314yes—
1021C22⋊Q8C23×C8314yes—
1022C22⋊Q8C23×C8314yes—
1023C22⋊Q8C23×C8314yes—
1024C22⋊Q8C23×C8314yes—
1025C22⋊Q8C23×C8318yes—
1026C22⋊Q8C23×C8318yes—
1027C22⋊Q8C23×C8314yes—
1028C22⋊Q8C23×C8312yes—
1029C22⋊Q8C23×C8312yes—
1030C22⋊Q8C23×C8312yes—
1031C22⋊Q8C23×C8312yes—
1032C22⋊Q8C23×C8314yes—
1033C22⋊Q8C23×C8314yes—
1034C22⋊Q8C23×C8314yes—
1035C22⋊Q8C23×C8314yes—
1036C22⋊Q8C23×C8314yes—
1037C22⋊Q8C23×C8314yes—
1038C22⋊Q8C23×C8318yes—
1039C22⋊Q8C23×C8314yes—
1040C22⋊Q8C23×C8318yes—
1041C22⋊Q8C23×C8318yes—
1042C22⋊Q8C23×C8318yes—
1043C22⋊Q8C23×C8318yes—
1044C22⋊Q8C23×C8314yes—
1045C22⋊Q8C23×C8314yes—
1046C22⋊Q8C23×C8318yes—
1047C22⋊Q8C23×C8318yes—
1048C22⋊Q8C23×C8318yes—
1049C22⋊Q8C23×C8318yes—
1050C22⋊Q8C23×C8318yes—
1051C22⋊Q8C23×C8318yes—
1052C22⋊Q8C23×C8318yes—
1053C22⋊Q8C23×C8318yes—
1054C22⋊Q8C23×C8318yes—
1055C22⋊Q8C23×C8318yes—
1056C22⋊Q8C23×C8318yes—
1057C22⋊Q8C23×C8318yes—
1058#121C23×C8314yes—
1059#121C23×C8312yes—
1060#121C23×C8312yes—
1061#121C23×C8312yes—
1062#121C23×C8312yes—
1063#121C23×C8314yes—
1064#121C23×C8314yes—
1065#121C23×C8314yes—
1066#121C23×C8314yes—
1067#121C23×C8314yes—
1068#121C23×C8318yes—
1069#120C23×C8314yes—
1070#120C23×C8314yes—
1071C4×Q8C23×C8314yes—
1072C4×Q8C23×C8314yes—
1073C4×Q8C23×C8314yes—
1074C4×Q8C23×C8312yes—
1075C4×Q8C23×C8314yes—
1076C4×Q8C23×C8312yes—
1077C4×Q8C23×C8314yes—
1078C4×Q8C23×C8314yes—
1079C4×Q8C23×C8314yes—
1080C4×Q8C23×C8314yes—
1081C4×Q8C23×C8314yes—
1082C4×Q8C23×C8314yes—
1083C4×Q8C23×C8314yes—
1084C4×Q8C23×C8314yes—
1085C4×Q8C23×C8318yes—
1086C4×Q8C23×C8318yes—
1087C4×Q8C23×C8314yes—
1088C4×Q8C23×C8314yes—
1089C4×Q8C23×C8314yes—
1090C4×Q8C23×C8314yes—
1091C4×Q8C23×C8314yes—
1092C4×Q8C23×C8318yes—
1093C4×Q8C23×C8318yes—
1094C4×Q8C23×C8318yes—
1095C4×Q8C23×C8318yes—
1096C4×D4C23×C8312yes—
1097C4×D4C23×C8312yes—
1098C4×D4C23×C8312yes—
1099C4×D4C23×C8312yes—
1100C4×D4C23×C8314yes—
1101C4×D4C23×C8314yes—
1102C4×D4C23×C8314yes—
1103C4×D4C23×C8314yes—
1104C4×D4C23×C8312yes—
1105C4×D4C23×C8314yes—
1106C4×D4C23×C8314yes—
1107C4×D4C23×C8314yes—
1108C4×D4C23×C8312yes—
1109C4×D4C23×C8318yes—
1110C4×D4C23×C8318yes—
1111C4×D4C23×C8314yes—
1112C4×D4C23×C8314yes—
1113C4×D4C23×C8314yes—
1114C4×D4C23×C8314yes—
1115C4×D4C23×C8318yes—
1116C4×D4C23×C8314yes—
1117C4×D4C23×C8314yes—
1118C4×D4C23×C8318yes—
1119C4×D4C23×C8318yes—
1120#117C23×C8312yes—
1121#117C23×C8312yes—
1122#117C23×C8312yes—
1123#117C23×C8314yes—
1124#117C23×C8314yes—
1125#117C23×C8314yes—
1126#117C23×C8314yes—
1127#117C23×C8314yes—
1128#117C23×C8312yes—
1129#117C23×C8312yes—
1130#117C23×C8314yes—
1131#117C23×C8314yes—
1132#117C23×C8314yes—
1133#117C23×C8314yes—
1134#117C23×C8314yes—
1135#117C23×C8312yes—
1136#117C23×C8312yes—
1137#117C23×C8314yes—
1138#117C23×C8314yes—
1139#117C23×C8314yes—
1140#117C23×C8314yes—
1141#117C23×C8318yes—
1142#117C23×C8314yes—
1143#117C23×C8318yes—
1144#117C23×C8314yes—
1145#117C23×C8314yes—
1146#117C23×C8318yes—
1147#117C23×C8318yes—
1148#117C23×C8318yes—
1149#117C23×C8318yes—
1150#117C23×C8318yes—
1151C2×C4⋊C4C23×C8311yescharacteristic
1152C2×C4⋊C4C23×C8311yescharacteristic
1153C2×C4⋊C4C23×C8312yes—
1154C2×C4⋊C4C23×C8314yes—
1155C2×C4⋊C4C23×C8314yes—
1156C2×C4⋊C4C23×C8311yescharacteristic
1157C2×C4⋊C4C23×C8312yes—
1158C2×C4⋊C4C23×C8312yes—
1159C2×C4⋊C4C23×C8312yes—
1160C2×C4⋊C4C23×C8312yes—
1161C2×C4⋊C4C23×C8312yes—
1162C2×C4⋊C4C23×C8312yes—
1163C2×C4⋊C4C23×C8311yescharacteristic
1164C2×C4⋊C4C23×C8312yes—
1165C2×C4⋊C4C23×C8314yes—
1166C2×C4⋊C4C23×C8314yes—
1167C2×C4⋊C4C23×C8314yes—
1168C2×C4⋊C4C23×C8318yes—
1169C2×C4⋊C4C23×C8312yes—
1170C2×C4⋊C4C23×C8318yes—
1171C2×C4⋊C4C23×C8312yes—
1172C2×C4⋊C4C23×C8318yes—
1173C2×C22⋊C4C23×C8311yescharacteristic
1174C2×C22⋊C4C23×C8314yes—
1175C2×C22⋊C4C23×C8312yes—
1176C2×C22⋊C4C23×C8312yes—
1177C2×C22⋊C4C23×C8314yes—
1178C2×C22⋊C4C23×C8311yescharacteristic
1179C2×C22⋊C4C23×C8312yes—
1180C2×C42C23×C8312yes—
1181C2×C42C23×C8312yes—
1182C2×C42C23×C8314yes—
1183C2×C42C23×C8314yes—
1184C2×C42C23×C8311yescharacteristic
1185C2×C42C23×C8314yes—
1186C24C24×C8311yescharacteristic
1187C24C24×C8311yescharacteristic
1188#41—28no—
1189#41—48no—
1190#41—48no—
1191C2×Q8—24no—
1192C2×Q8—48no—
1193C2×Q8C24×C8314yes—
1194C2×Q8C24×C8312yes—
1195C2×Q8C24×C8318yes—
1196C2×Q8C24×C8314yes—
1197C2×Q8C24×C8318yes—
1198C2×Q8C24×C8314yes—
1199C2×Q8C24×C8314yes—
1200C2×Q8C24×C8314yes—
1201C2×Q8C24×C8314yes—
1202C2×D4—42no—
1203C2×D4C24×C8314yes—
1204C2×D4C24×C8312yes—
1205C2×D4C24×C8314yes—
1206C2×D4C24×C8312yes—
1207C2×D4C24×C8314yes—
1208C2×D4C24×C8314yes—
1209C2×D4C24×C8314yes—
1210C2×D4C24×C8314yes—
1211C2×D4C24×C8312yes—
1212C22×C4—24no—
1213C22×C4—24no—
1214C22×C4—44no—
1215C22×C4C24×C8311yescharacteristic
1216C22×C4C24×C8312yes—
1217C22×C4C24×C8312yes—
1218C22×C4C24×C8312yes—
1219C22×C4C24×C8314yes—
1220C22×C4C24×C8314yes—
1221C22×C4C24×C8311yescharacteristic
1222C22×C4C24×C8314yes—
1223C22×C4C24×C8312yes—
1224C22×C4C24×C8312yes—
1225C22×C4C24×C8311yescharacteristic
1226C22×C4C24×C8312yes—
1227C22×C4C24×C8312yes—
1228C22×C4C24×C8314yes—
1229C22×C4C24×C8314yes—
1230C22×C4C24×C8314yes—
1231C22×C4C24×C8311yescharacteristic
1232C22×C4C24×C8314yes—
1233C22×C4C24×C8314yes—
1234C22×C4C24×C8312yes—
1235C22×C4C24×C8318yes—
1236C22×C4C24×C8318yes—
1237C22×C4C24×C8314yes—
1238C22×C4C24×C8311yescharacteristic
1239C4⋊C4C24×C8314yes—
1240C4⋊C4C24×C8312yes—
1241C4⋊C4C24×C8314yes—
1242C4⋊C4C24×C8312yes—
1243C4⋊C4C24×C8314yes—
1244C4⋊C4C24×C8318yes—
1245C4⋊C4C24×C8314yes—
1246C4⋊C4C24×C8312yes—
1247C4⋊C4C24×C8312yes—
1248C4⋊C4C24×C8314yes—
1249C4⋊C4C24×C8318yes—
1250C4⋊C4C24×C8318yes—
1251C4⋊C4C24×C8314yes—
1252C4⋊C4C24×C8318yes—
1253C4⋊C4C24×C8312yes—
1254C4⋊C4C24×C8312yes—
1255C4⋊C4C24×C8314yes—
1256C4⋊C4C24×C8312yes—
1257C4⋊C4C24×C8314yes—
1258C4⋊C4C24×C8314yes—
1259C4⋊C4C24×C8314yes—
1260C4⋊C4C24×C8314yes—
1261C4⋊C4C24×C8314yes—
1262C4⋊C4C24×C8314yes—
1263C4⋊C4C24×C8318yes—
1264C4⋊C4C24×C8318yes—
1265C4⋊C4C24×C8318yes—
1266C4⋊C4C24×C8318yes—
1267C4⋊C4C24×C8318yes—
1268C4⋊C4C24×C8312yes—
1269C4⋊C4C24×C8314yes—
1270C4⋊C4C24×C8318yes—
1271C4⋊C4C24×C8318yes—
1272C4⋊C4C24×C8314yes—
1273C4⋊C4C24×C8318yes—
1274C4⋊C4C24×C8318yes—
1275C4⋊C4C24×C8314yes—
1276C4⋊C4C24×C8318yes—
1277C4⋊C4C24×C8314yes—
1278C4⋊C4C24×C8314yes—
1279C4⋊C4C24×C8314yes—
1280C4⋊C4C24×C8314yes—
1281C4⋊C4C24×C8314yes—
1282C4⋊C4C24×C8314yes—
1283C4⋊C4C24×C8314yes—
1284C4⋊C4C24×C8314yes—
1285C4⋊C4C24×C8318yes—
1286C4⋊C4C24×C8318yes—
1287C4⋊C4C24×C8318yes—
1288C4⋊C4C24×C8318yes—
1289C4⋊C4C24×C8318yes—
1290C4⋊C4C24×C8314yes—
1291C4⋊C4C24×C8314yes—
1292C4⋊C4C24×C8314yes—
1293C22⋊C4C24×C8314yes—
1294C22⋊C4C24×C8311yescharacteristic
1295C22⋊C4C24×C8314yes—
1296C22⋊C4C24×C8314yes—
1297C22⋊C4C24×C8314yes—
1298C22⋊C4C24×C8311yescharacteristic
1299C22⋊C4C24×C8311yescharacteristic
1300C22⋊C4C24×C8311yescharacteristic
1301C22⋊C4C24×C8312yes—
1302C22⋊C4C24×C8318yes—
1303C22⋊C4C24×C8314yes—
1304C22⋊C4C24×C8314yes—
1305C22⋊C4C24×C8314yes—
1306C22⋊C4C24×C8314yes—
1307C22⋊C4C24×C8314yes—
1308C22⋊C4C24×C8318yes—
1309C22⋊C4C24×C8312yes—
1310C22⋊C4C24×C8314yes—
1311C22⋊C4C24×C8314yes—
1312C22⋊C4C24×C8314yes—
1313C22⋊C4C24×C8318yes—
1314C22⋊C4C24×C8314yes—
1315C22⋊C4C24×C8314yes—
1316C22⋊C4C24×C8318yes—
1317C22⋊C4C24×C8314yes—
1318C22⋊C4C24×C8314yes—
1319C22⋊C4C24×C8318yes—
1320C22⋊C4C24×C8318yes—
1321C22⋊C4C24×C8314yes—
1322C22⋊C4C24×C8314yes—
1323C22⋊C4C24×C8318yes—
1324C22⋊C4C24×C8314yes—
1325C42C24×C8314yes—
1326C42C24×C8312yes—
1327C42C24×C8314yes—
1328C42C24×C8314yes—
1329C42C24×C8314yes—
1330C42C24×C8314yes—
1331C42C24×C8314yes—
1332C42C24×C8314yes—
1333C42C24×C8314yes—
1334C42C24×C8312yes—
1335C42C24×C8314yes—
1336C42C24×C8314yes—
1337C42C24×C8314yes—
1338C42C24×C8314yes—
1339C42C24×C8314yes—
1340C42C24×C8318yes—
1341C42C24×C8318yes—
1342C42C24×C8318yes—
1343C42C24×C8318yes—
1344C23—22no—
1345C23—22no—
1346C23—22no—
1347C23—41no—
1348C23—41no—
1349C23—41no—
1350C23C25×C8311yescharacteristic
1351C23C25×C8312yes—
1352C23C25×C8314yes—
1353C23C25×C8311yescharacteristic
1354C23C25×C8311yescharacteristic
1355Q8—28no—
1356Q8—24no—
1357Q8—48no—
1358Q8—44no—
1359Q8—44no—
1360Q8—44no—
1361Q8—44no—
1362Q8—44no—
1363Q8—48no—
1364D4—28no—
1365D4—24no—
1366D4—28no—
1367D4—24no—
1368D4—42no—
1369D4—44no—
1370D4—44no—
1371D4—44no—
1372D4—44no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—28no—
1377C2×C4—28no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—28no—
1383C2×C4—42no—
1384C2×C4—44no—
1385C2×C4—42no—
1386C2×C4—41no—
1387C2×C4—48no—
1388C2×C4—44no—
1389C2×C4—44no—
1390C2×C4—44no—
1391C2×C4—41no—
1392C2×C4—44no—
1393C2×C4—48no—
1394C2×C4—42no—
1395C2×C4—44no—
1396C2×C42−1+4×C8314yes—
1397C2×C4C25×C8311yescharacteristic
1398C2×C4C25×C8311yescharacteristic
1399C2×C4C25×C8314yes—
1400C2×C4C25×C8311yescharacteristic
1401C2×C4C25×C8314yes—
1402C2×C4C25×C8314yes—
1403C2×C4C25×C8314yes—
1404C2×C4C25×C8311yescharacteristic
1405C2×C4C25×C8312yes—
1406C2×C4C25×C8314yes—
1407C2×C4C25×C8314yes—
1408C2×C4C25×C8314yes—
1409C2×C4C25×C8314yes—
1410C2×C4C25×C8314yes—
1411C2×C4C25×C8314yes—
1412C2×C4C25×C8312yes—
1413C2×C4C25×C8314yes—
1414C2×C4C25×C8312yes—
1415C22—21no—
1416C22—21no—
1417C22—21no—
1418C22—21no—
1419C22—21no—
1420C22—22no—
1421C22—24no—
1422C22—21no—
1423C22—24no—
1424C22—22no—
1425C22—24no—
1426C22—22no—
1427C22—21no—
1428C22—44no—
1429C22—82no—
1430C22C2×2−1+4×C8312yes—
1431C22#585×C8312yes—
1432C22C26×C8311yescharacteristic
1433C4—21no—
1434C4—21no—
1435C4—22no—
1436C4—24no—
1437C4—24no—
1438C4—24no—
1439C4—24no—
1440C4—24no—
1441C4—24no—
1442C4—22no—
1443C4—24no—
1444C4—21no—
1445C4—24no—
1446C4—24no—
1447C4—24no—
1448C4—24no—
1449C4—21no—
1450C4C2×2−1+4×C8314yes—
1451C2—22no—
1452C2—22no—
1453C2—41no—
1454C2—42no—
1455C2—44no—
1456C2C22×2−1+4×C8311yescharacteristic
1457C2C2×#585×C8311yescharacteristic
1458C2C83×2−1+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×#3565C2semidirect
2. C83×#3565C2semidirect
3. C83×#3564C2semidirect
4. C83×#3563C2semidirect
5. C83×#3563C2semidirect
6. C83×#3563C2semidirect
7. C83×#3555C2semidirect
8. C83×#3544C2semidirect
9. C83×#3535C2semidirect
10. C83×#3515C2semidirect
11. C83×#3509C2semidirect
12. C83×#3504C2semidirect
13. C83×#3502C2semidirect
14. C83×#3495C2semidirect
15. C83×#3495C2semidirect
16. C83×#3495C2semidirect
17. C83×#3493C2semidirect
18. C83×#3492C2semidirect
19. C83×#3475C2semidirect
20. C2×#552×C83C2semidirect
21. C83×#3461C2semidirect
22. C83×#3458C2semidirect
23. C2×#544×C83C2semidirect
24. #564×C83C22semidirect
26. #563×C83C22semidirect
27. #563×C83C22semidirect
28. #563×C83C22semidirect
30. Q82×C83C22semidirect
31. #557×C83C22semidirect
32. #557×C83C22semidirect
33. #557×C83C22semidirect
34. #557×C83C22semidirect
35. #557×C83C22semidirect
36. #557×C83C22semidirect
38. #556×C83C22semidirect
39. #556×C83C22semidirect
40. #556×C83C22semidirect
41. #556×C83C22semidirect
42. #556×C83C22semidirect
44. #555×C83C22semidirect
48. #554×C83C22semidirect
49. #554×C83C22semidirect
50. #554×C83C22semidirect
51. #554×C83C22semidirect
52. #554×C83C22semidirect
55. #553×C83C22semidirect
56. #553×C83C22semidirect
67. #552×C83C22semidirect
68. #552×C83C22semidirect
69. #552×C83C22semidirect
70. #552×C83C22semidirect
71. #552×C83C22semidirect
72. #552×C83C22semidirect
73. #552×C83C22semidirect
74. #552×C83C22semidirect
75. #552×C83C22semidirect
76. #552×C83C22semidirect
77. #552×C83C22semidirect
84. #547×C83C22semidirect
93. #544×C83C22semidirect
94. #544×C83C22semidirect
95. #544×C83C22semidirect
96. #544×C83C22semidirect
97. #544×C83C22semidirect
98. #544×C83C22semidirect
99. #544×C83C22semidirect
100. #544×C83C22semidirect
103. #542×C83C22semidirect
104. #542×C83C22semidirect
105. #542×C83C22semidirect
106. #542×C83C22semidirect
107. #542×C83C22semidirect
108. #542×C83C22semidirect
109. #541×C83C22semidirect
110. #541×C83C22semidirect
111. #541×C83C22semidirect
112. #541×C83C22semidirect
113. #541×C83C22semidirect
114. #541×C83C22semidirect
115. #541×C83C22semidirect
116. #541×C83C22semidirect
117. #541×C83C22semidirect
118. #541×C83C22semidirect
123. #539×C83C22semidirect
128. #536×C83C22semidirect
132. #533×C83C22semidirect
133. #533×C83C22semidirect
134. #533×C83C22semidirect
135. #533×C83C22semidirect
136. #533×C83C22semidirect
137. #533×C83C22semidirect
138. C2×C4⋊Q8×C83C22semidirect
144. #529×C83C22semidirect
145. #529×C83C22semidirect
146. #529×C83C22semidirect
150. C2×#125×C83C22semidirect
151. C2×#125×C83C22semidirect
161. #520×C83C22semidirect
163. #519×C83C22semidirect
721. #62928C83direct (N × H)
730. #3565C2×C83semidirect
731. #3565C2×C83semidirect
732. #3564C2×C83semidirect
733. #3563C2×C83semidirect
734. #3563C2×C83semidirect
735. #3563C2×C83semidirect
736. #3555C2×C83semidirect
737. #3544C2×C83semidirect
738. #3535C2×C83semidirect
739. #3515C2×C83semidirect
740. #3509C2×C83semidirect
741. #3504C2×C83semidirect
742. #3502C2×C83semidirect
743. #3495C2×C83semidirect
744. #3495C2×C83semidirect
745. #3495C2×C83semidirect
746. #3493C2×C83semidirect
747. #3492C2×C83semidirect
748. #3475C2×C83semidirect
749. C2×#552C2×C83semidirect
750. #3461C2×C83semidirect
751. #3458C2×C83semidirect
752. C2×#544C2×C83semidirect
753. C83#62928direct (N × H)
754. #564C22×C83semidirect
756. #563C22×C83semidirect
757. #563C22×C83semidirect
758. #563C22×C83semidirect
760. Q82C22×C83semidirect
761. #557C22×C83semidirect
762. #557C22×C83semidirect
763. #557C22×C83semidirect
764. #557C22×C83semidirect
765. #557C22×C83semidirect
766. #557C22×C83semidirect
768. #556C22×C83semidirect
769. #556C22×C83semidirect
770. #556C22×C83semidirect
771. #556C22×C83semidirect
772. #556C22×C83semidirect
774. #555C22×C83semidirect
778. #554C22×C83semidirect
779. #554C22×C83semidirect
780. #554C22×C83semidirect
781. #554C22×C83semidirect
782. #554C22×C83semidirect
785. #553C22×C83semidirect
786. #553C22×C83semidirect
797. #552C22×C83semidirect
798. #552C22×C83semidirect
799. #552C22×C83semidirect
800. #552C22×C83semidirect
801. #552C22×C83semidirect
802. #552C22×C83semidirect
803. #552C22×C83semidirect
804. #552C22×C83semidirect
805. #552C22×C83semidirect
806. #552C22×C83semidirect
807. #552C22×C83semidirect
814. #547C22×C83semidirect
823. #544C22×C83semidirect
824. #544C22×C83semidirect
825. #544C22×C83semidirect
826. #544C22×C83semidirect
827. #544C22×C83semidirect
828. #544C22×C83semidirect
829. #544C22×C83semidirect
830. #544C22×C83semidirect
833. #542C22×C83semidirect
834. #542C22×C83semidirect
835. #542C22×C83semidirect
836. #542C22×C83semidirect
837. #542C22×C83semidirect
838. #542C22×C83semidirect
839. #541C22×C83semidirect
840. #541C22×C83semidirect
841. #541C22×C83semidirect
842. #541C22×C83semidirect
843. #541C22×C83semidirect
844. #541C22×C83semidirect
845. #541C22×C83semidirect
846. #541C22×C83semidirect
847. #541C22×C83semidirect
848. #541C22×C83semidirect
853. #539C22×C83semidirect
858. #536C22×C83semidirect
862. #533C22×C83semidirect
863. #533C22×C83semidirect
864. #533C22×C83semidirect
865. #533C22×C83semidirect
866. #533C22×C83semidirect
867. #533C22×C83semidirect
868. C2×C4⋊Q8C22×C83semidirect
874. #529C22×C83semidirect
875. #529C22×C83semidirect
876. #529C22×C83semidirect
880. C2×#125C22×C83semidirect
881. C2×#125C22×C83semidirect
891. #520C22×C83semidirect
893. #519C22×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35652
C83×#35642
C83×#35632
C83×#35552
C83×#35442
C83×#35352
C83×#35152
C83×#35092
C83×#35042
C83×#35022
C83×#34952
C83×#34932
C83×#34922
C83×#34752
C2×#552×C832
C83×#34612
C83×#34582
C2×#544×C832
#6292883