Finite Group Databasebeta

← C83×#62886 #35290710

Subgroups — C83×#62886 #35290710

Order 21248.

6918 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3551C214yesmaximal, complemented
2C83×#3550C214yesmaximal, complemented
3C83×#3547C218yesmaximal, complemented
4C83×#3545C214yesmaximal, complemented
5C83×#3544C214yesmaximal, complemented
6C83×#3541C218yesmaximal, complemented
7C83×#3540C214yesmaximal, complemented
8C83×#3538C214yesmaximal, complemented
9C83×#3533C218yesmaximal, complemented
10C83×#3495C214yesmaximal, complemented
11C83×#3493C212yesmaximal, complemented
12C83×#3489C214yesmaximal, complemented
13C83×#3486C212yesmaximal, complemented
14C83×#3449C212yesmaximal, complemented
15C2×#536×C83C211yesmaximal, characteristic, complemented
16C2×2−1+4×C83C2212yes—
17C22×#41×C83C2211yescharacteristic
18C22×#41×C83C2212yescomplemented
19C23×Q8×C83C2211yescharacteristic, complemented
20#563×C83C2218yescomplemented
21#563×C83C2214yescomplemented
22#563×C83C2218yescomplemented
23#563×C83C2218yescomplemented
24#562×C83C22116yescomplemented
25#562×C83C2218yescomplemented
26H(3,𝔽4)×C83C2214yescomplemented
27#560×C83C2218yescomplemented
28#559×C83C2218yescomplemented
29Q82×C83C2214yescomplemented
30#556×C83C2218yescomplemented
31#556×C83C2218yescomplemented
32#555×C83C2218yescomplemented
33#555×C83C2214yescomplemented
34#555×C83C2218yescomplemented
35#554×C83C2218yescomplemented
36#554×C83C2218yescomplemented
37#553×C83C22116yescomplemented
38#553×C83C2218yescomplemented
39#552×C83C22116yescomplemented
40#552×C83C2218yescomplemented
41#552×C83C2218yescomplemented
42#552×C83C2218yescomplemented
43#551×C83C2218yescomplemented
44#551×C83C22116yescomplemented
45#551×C83C2218yescomplemented
46D4×Q8×C83C2218yescomplemented
47D4×Q8×C83C2218yescomplemented
48D4×Q8×C83C2218yescomplemented
49#548×C83C2218yescomplemented
50#548×C83C2218yescomplemented
51#548×C83C2218yescomplemented
52#547×C83C22116yescomplemented
53#547×C83C2218yescomplemented
54#546×C83C22116yescomplemented
55#546×C83C2218yescomplemented
56#544×C83C22116yescomplemented
57#544×C83C2212yescomplemented
58#542×C83C22116yescomplemented
59#542×C83C2218yescomplemented
60#542×C83C22116yescomplemented
61#542×C83C22116yescomplemented
62#541×C83C2218yescomplemented
63#540×C83C22116yescomplemented
64#539×C83C22116yescomplemented
65#538×C83C2218yescomplemented
66#538×C83C22116yescomplemented
67#538×C83C22116yescomplemented
68#537×C83C2214yes—
69#537×C83C2212yes—
70#537×C83C2214yescomplemented
71#537×C83C2218yescomplemented
72#536×C83C2212yes—
73#536×C83C2214yes—
74#536×C83C2214yescomplemented
75#536×C83C2214yescomplemented
76#536×C83C2218yescomplemented
77#536×C83C2214yescomplemented
78#536×C83C2218yescomplemented
79#536×C83C2212yescomplemented
80#536×C83C2214yescomplemented
81#536×C83C2214yescomplemented
82#535×C83C2214yes—
83#535×C83C2212yes—
84#535×C83C2212yescomplemented
85#534×C83C2214yes—
86#534×C83C2214yescomplemented
87#533×C83C2218yescomplemented
88#532×C83C2214yes—
89#532×C83C2214yescomplemented
90C2×C4⋊Q8×C83C2212yescomplemented
91#529×C83C2218yescomplemented
92#529×C83C2218yescomplemented
93C2×#124×C83C2212yes—
94#525×C83C2214yes—
95#525×C83C2214yes—
96#525×C83C2218yescomplemented
97#525×C83C2218yescomplemented
98#525×C83C2214yescomplemented
99#525×C83C2214yescomplemented
100C2×#123×C83C2214yescomplemented
101C2×C22⋊Q8×C83C2218yescomplemented
102C2×C22⋊Q8×C83C2214yescomplemented
103#520×C83C2214yescomplemented
104#519×C83C2212yescomplemented
105C2×#117×C83C2211yescharacteristic, complemented
106C2×#117×C83C2212yescomplemented
1072−1+4×C83—48no—
108C2×#41×C83—44no—
109C2×#41×C83—48no—
110C2×#41×C83C2314yes—
111C2×#41×C83C2312yes—
112C2×#41×C83C2312yes—
113C2×#41×C83C2318yes—
114C2×#41×C83C2318yes—
115C2×#41×C83C2312yes—
116C2×#41×C83C2314yes—
117C2×#41×C83C2312yes—
118C2×#41×C83C2314yes—
119C2×#41×C83C2314yes—
120C22×Q8×C83—44no—
121C22×Q8×C83C2312yes—
122C22×Q8×C83C2318yes—
123C22×Q8×C83C2312yes—
124C22×Q8×C83C2311yescharacteristic
125C22×Q8×C83C2314yes—
126C22×Q8×C83C2312yes—
127C22×Q8×C83C2314yes—
128C22×D4×C83C2312yes—
129C22×D4×C83C2311yescharacteristic
130C22×D4×C83C2314yes—
131C22×D4×C83C2312yes—
132C23×C4×C83C2312yes—
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2314yes—
135C23×C4×C83C2312yes—
136C4⋊Q8×C83C2318yes—
137C4⋊Q8×C83C2314yes—
138C4⋊Q8×C83C2314yes—
139C4⋊Q8×C83C2314yes—
140C4⋊Q8×C83C2314yes—
141C4⋊Q8×C83C2318yes—
142C4⋊Q8×C83C2318yes—
143C4⋊Q8×C83C2318yes—
144C4⋊Q8×C83C23116yes—
145C4⋊Q8×C83C2318yes—
146#127×C83C2314yes—
147#127×C83C2314yes—
148#126×C83C23116yes—
149#126×C83C23116yes—
150#126×C83C23116yes—
151#126×C83C23116yes—
152#126×C83C23116yes—
153#126×C83C23116yes—
154#125×C83C2318yes—
155#125×C83C2318yes—
156#125×C83C23116yes—
157#125×C83C23116yes—
158#125×C83C23116yes—
159#124×C83C2314yes—
160#124×C83C2318yes—
161#124×C83C2314yes—
162#124×C83C2318yes—
163#124×C83C2318yes—
164#124×C83C2314yes—
165#124×C83C2314yes—
166#124×C83C2314yes—
167#124×C83C2314yes—
168#124×C83C2318yes—
169#124×C83C23116yes—
170#124×C83C2318yes—
171#124×C83C23116yes—
172#124×C83C23116yes—
173#123×C83C2318yes—
174#123×C83C2318yes—
175#123×C83C2318yes—
176#123×C83C2318yes—
177#123×C83C2314yes—
178#123×C83C2318yes—
179#123×C83C2314yes—
180#123×C83C2318yes—
181#123×C83C2314yes—
182#123×C83C2314yes—
183#123×C83C23116yes—
184#123×C83C23116yes—
185#123×C83C23116yes—
186#123×C83C23116yes—
187#123×C83C23116yes—
188#123×C83C23116yes—
189#123×C83C23116yes—
190C22⋊Q8×C83C2314yes—
191C22⋊Q8×C83C2318yes—
192C22⋊Q8×C83C2318yes—
193C22⋊Q8×C83C2318yes—
194C22⋊Q8×C83C2318yes—
195C22⋊Q8×C83C2318yes—
196C22⋊Q8×C83C2318yes—
197C22⋊Q8×C83C23116yes—
198C22⋊Q8×C83C23116yes—
199C22⋊Q8×C83C2314yes—
200C22⋊Q8×C83C2318yes—
201C22⋊Q8×C83C2314yes—
202C22⋊Q8×C83C2318yes—
203C22⋊Q8×C83C2314yes—
204C22⋊Q8×C83C2318yes—
205C22⋊Q8×C83C23116yes—
206C22⋊Q8×C83C2318yes—
207C22⋊Q8×C83C23116yes—
208C22⋊Q8×C83C23116yes—
209C22⋊Q8×C83C23116yes—
210C22⋊Q8×C83C23116yes—
211C22⋊Q8×C83C23116yes—
212#121×C83C2314yes—
213#121×C83C2314yes—
214#121×C83C2318yes—
215#121×C83C2314yes—
216#121×C83C2318yes—
217#121×C83C2314yes—
218#121×C83C2318yes—
219#121×C83C23116yes—
220#121×C83C2318yes—
221#121×C83C2318yes—
222#121×C83C2318yes—
223#121×C83C2318yes—
224#121×C83C2318yes—
225#121×C83C23116yes—
226#121×C83C23116yes—
227#121×C83C23116yes—
228#121×C83C23116yes—
229#120×C83C2318yes—
230#120×C83C2314yes—
231#120×C83C2314yes—
232#120×C83C2318yes—
233#120×C83C2314yes—
234#120×C83C2314yes—
235#120×C83C23116yes—
236C4×Q8×C83C2318yes—
237C4×Q8×C83C2318yes—
238C4×Q8×C83C2318yes—
239C4×Q8×C83C2318yes—
240C4×Q8×C83C23116yes—
241C4×D4×C83C23116yes—
242C4×D4×C83C2318yes—
243C4×D4×C83C2318yes—
244C4×D4×C83C2318yes—
245C4×D4×C83C2318yes—
246C4×D4×C83C2318yes—
247C4×D4×C83C23116yes—
248C4×D4×C83C23116yes—
249C4×D4×C83C23116yes—
250C4×D4×C83C23116yes—
251C4×D4×C83C2318yes—
252C4×D4×C83C23116yes—
253#117×C83C2314yes—
254#117×C83C2314yes—
255#117×C83C2314yes—
256#117×C83C2312yes—
257#117×C83C2312yes—
258#117×C83C2314yes—
259#117×C83C2314yes—
260#117×C83C2318yes—
261#117×C83C2318yes—
262#117×C83C23116yes—
263#117×C83C23116yes—
264#117×C83C23116yes—
265C2×C4⋊C4×C83C2312yes—
266C2×C4⋊C4×C83C2314yes—
267C2×C4⋊C4×C83C2318yes—
268C2×C4⋊C4×C83C2318yes—
269C2×C4⋊C4×C83C23116yes—
270C2×C22⋊C4×C83C2312yes—
271C2×C22⋊C4×C83C2314yes—
272C2×C22⋊C4×C83C2318yes—
273C2×C22⋊C4×C83C23116yes—
274C2×C42×C83C2312yes—
275C2×C42×C83C2314yes—
276C24×C83C2412yes—
277C24×C83C2411yescharacteristic
278C24×C83C2414yes—
279#41×C83—216no—
280#41×C83—44no—
281#41×C83—44no—
282#41×C83—44no—
283#41×C83—44no—
284#41×C83—48no—
285#41×C83—48no—
286#41×C83—416no—
287#41×C83—48no—
288#41×C83—416no—
289C2×Q8×C83—28no—
290C2×Q8×C83—44no—
291C2×Q8×C83—42no—
292C2×Q8×C83—48no—
293C2×Q8×C83—48no—
294C2×Q8×C83—44no—
295C2×Q8×C83—416no—
296C2×Q8×C83C2418yes—
297C2×Q8×C83C2414yes—
298C2×Q8×C83C2418yes—
299C2×Q8×C83C2411yescharacteristic
300C2×Q8×C83C2418yes—
301C2×Q8×C83C2414yes—
302C2×Q8×C83C2414yes—
303C2×Q8×C83C2412yes—
304C2×Q8×C83C2414yes—
305C2×Q8×C83C2411yescharacteristic
306C2×D4×C83—44no—
307C2×D4×C83—42no—
308C2×D4×C83—44no—
309C2×D4×C83—48no—
310C2×D4×C83C2418yes—
311C2×D4×C83C2414yes—
312C2×D4×C83C2418yes—
313C2×D4×C83C2418yes—
314C2×D4×C83C2418yes—
315C2×D4×C83C2418yes—
316C2×D4×C83C2418yes—
317C2×D4×C83C2411yescharacteristic
318C2×D4×C83C2418yes—
319C2×D4×C83C2412yes—
320C2×D4×C83C2412yes—
321C2×D4×C83C2412yes—
322C2×D4×C83C2412yes—
323C2×D4×C83C2418yes—
324C2×D4×C83C2411yescharacteristic
325C2×D4×C83C2412yes—
326C2×D4×C83C2414yes—
327C22×C4×C83—24no—
328C22×C4×C83—28no—
329C22×C4×C83—48no—
330C22×C4×C83—44no—
331C22×C4×C83C2412yes—
332C22×C4×C83C2411yescharacteristic
333C22×C4×C83C2414yes—
334C22×C4×C83C2412yes—
335C22×C4×C83C2412yes—
336C22×C4×C83C2418yes—
337C22×C4×C83C2412yes—
338C22×C4×C83C2412yes—
339C22×C4×C83C2412yes—
340C22×C4×C83C2412yes—
341C22×C4×C83C2414yes—
342C22×C4×C83C2418yes—
343C22×C4×C83C24116yes—
344C22×C4×C83C24116yes—
345C22×C4×C83C2418yes—
346C22×C4×C83C2418yes—
347C22×C4×C83C2414yes—
348C22×C4×C83C2411yescharacteristic
349C4⋊C4×C83C2414yes—
350C4⋊C4×C83C2418yes—
351C4⋊C4×C83C2418yes—
352C4⋊C4×C83C24116yes—
353C4⋊C4×C83C2418yes—
354C4⋊C4×C83C2414yes—
355C4⋊C4×C83C2418yes—
356C4⋊C4×C83C24116yes—
357C4⋊C4×C83C24116yes—
358C4⋊C4×C83C24116yes—
359C4⋊C4×C83C2418yes—
360C4⋊C4×C83C24116yes—
361C4⋊C4×C83C2418yes—
362C4⋊C4×C83C24116yes—
363C4⋊C4×C83C24116yes—
364C4⋊C4×C83C2418yes—
365C4⋊C4×C83C2418yes—
366C22⋊C4×C83C2418yes—
367C22⋊C4×C83C24116yes—
368C22⋊C4×C83C2418yes—
369C22⋊C4×C83C2414yes—
370C22⋊C4×C83C2414yes—
371C22⋊C4×C83C2418yes—
372C22⋊C4×C83C24116yes—
373C22⋊C4×C83C24116yes—
374C22⋊C4×C83C24116yes—
375C22⋊C4×C83C2418yes—
376C22⋊C4×C83C2418yes—
377C22⋊C4×C83C2418yes—
378C22⋊C4×C83C24116yes—
379C22⋊C4×C83C2418yes—
380C22⋊C4×C83C2418yes—
381C22⋊C4×C83C2418yes—
382C22⋊C4×C83C2418yes—
383C22⋊C4×C83C24116yes—
384C42×C83C2414yes—
385C42×C83C2414yes—
386C42×C83C2418yes—
387C42×C83C2414yes—
388C42×C83C2414yes—
389C42×C83C2418yes—
390C42×C83C24116yes—
391C42×C83C2418yes—
392C23×C83—22no—
393C23×C83—24no—
394C23×C83—42no—
395C23×C83—44no—
396C23×C83—44no—
397C23×C83—48no—
398C23×C83C2512yes—
399C23×C83C2512yes—
400C23×C83C2512yes—
401C23×C83C2518yes—
402C23×C83C2511yescharacteristic
403Q8×C83—216no—
404Q8×C83—28no—
405Q8×C83—44no—
406Q8×C83—44no—
407Q8×C83—48no—
408Q8×C83—41no—
409Q8×C83—42no—
410Q8×C83—41no—
411Q8×C83—44no—
412Q8×C83—48no—
413D4×C83—216no—
414D4×C83—28no—
415D4×C83—42no—
416D4×C83—42no—
417D4×C83—42no—
418D4×C83—42no—
419D4×C83—44no—
420D4×C83—41no—
421D4×C83—42no—
422D4×C83—41no—
423D4×C83—48no—
424D4×C83—48no—
425D4×C83—48no—
426D4×C83—48no—
427D4×C83—48no—
428D4×C83—48no—
429D4×C83—48no—
430C2×C4×C83—22no—
431C2×C4×C83—24no—
432C2×C4×C83—28no—
433C2×C4×C83—24no—
434C2×C4×C83—24no—
435C2×C4×C83—24no—
436C2×C4×C83—24no—
437C2×C4×C83—24no—
438C2×C4×C83—24no—
439C2×C4×C83—216no—
440C2×C4×C83—44no—
441C2×C4×C83—48no—
442C2×C4×C83—48no—
443C2×C4×C83—416no—
444C2×C4×C83—48no—
445C2×C4×C83—44no—
446C2×C4×C83—416no—
447C2×C4×C83H(5,𝔽2)14yes—
448C2×C4×C83C2518yes—
449C2×C4×C83C2518yes—
450C2×C4×C83C2518yes—
451C2×C4×C83C2511yescharacteristic
452C2×C4×C83C2511yescharacteristic
453C2×C4×C83C2512yes—
454C2×C4×C83C2518yes—
455C2×C4×C83C2518yes—
456C2×C4×C83C2512yes—
457C2×C4×C83C2512yes—
458C22×C83—22no—
459C22×C83—22no—
460C22×C83—22no—
461C22×C83—22no—
462C22×C83—28no—
463C22×C83—24no—
464C22×C83—28no—
465C22×C83—24no—
466C22×C83—28no—
467C22×C83—24no—
468C22×C83—44no—
469C22×C83—84no—
470C22×C83—88no—
471C22×C83C2×H(5,𝔽2)12yes—
472C22×C83C2611yescharacteristic
473C4×C83—22no—
474C4×C83—22no—
475C4×C83—21no—
476C4×C83—21no—
477C4×C83—28no—
478C4×C83—28no—
479C4×C83—28no—
480C4×C83—28no—
481C4×C83—28no—
482C4×C83C2×H(5,𝔽2)14yes—
483#62886C8311yesmaximal, characteristic, direct product factor, Sylow
484C2×C83—22no—
485C2×C83—42no—
486C2×C83—42no—
487C2×C83—48no—
488C2×C83—42no—
489C2×C83C22×H(5,𝔽2)11yescharacteristic
490C2×C832−1+612yes—
491#3551C2×C8314yescomplemented
492#3550C2×C8314yescomplemented
493#3547C2×C8318yescomplemented
494#3545C2×C8314yescomplemented
495#3544C2×C8314yescomplemented
496#3541C2×C8318yescomplemented
497#3540C2×C8314yescomplemented
498#3538C2×C8314yescomplemented
499#3533C2×C8318yescomplemented
500#3495C2×C8314yescomplemented
501#3493C2×C8312yescomplemented
502#3489C2×C8314yescomplemented
503#3486C2×C8312yescomplemented
504#3449C2×C8312yescomplemented
505C2×#536C2×C8311yescharacteristic, complemented
506C83#6288611yescharacteristic, direct product factor, Sylow
507C2×2−1+4C22×C8312yes—
508C22×#41C22×C8311yescharacteristic
509C22×#41C22×C8312yescomplemented
510C23×Q8C22×C8311yescharacteristic, complemented
511#563C22×C8318yescomplemented
512#563C22×C8314yescomplemented
513#563C22×C8318yescomplemented
514#563C22×C8318yescomplemented
515#562C22×C83116yescomplemented
516#562C22×C8318yescomplemented
517H(3,𝔽4)C22×C8314yescomplemented
518#560C22×C8318yescomplemented
519#559C22×C8318yescomplemented
520Q82C22×C8314yescomplemented
521#556C22×C8318yescomplemented
522#556C22×C8318yescomplemented
523#555C22×C8318yescomplemented
524#555C22×C8314yescomplemented
525#555C22×C8318yescomplemented
526#554C22×C8318yescomplemented
527#554C22×C8318yescomplemented
528#553C22×C8318yescomplemented
529#553C22×C83116yescomplemented
530#552C22×C8318yescomplemented
531#552C22×C83116yescomplemented
532#552C22×C8318yescomplemented
533#552C22×C8318yescomplemented
534#551C22×C83116yescomplemented
535#551C22×C8318yescomplemented
536#551C22×C8318yescomplemented
537D4×Q8C22×C8318yescomplemented
538D4×Q8C22×C8318yescomplemented
539D4×Q8C22×C8318yescomplemented
540#548C22×C8318yescomplemented
541#548C22×C8318yescomplemented
542#548C22×C8318yescomplemented
543#547C22×C83116yescomplemented
544#547C22×C8318yescomplemented
545#546C22×C83116yescomplemented
546#546C22×C8318yescomplemented
547#544C22×C8312yescomplemented
548#544C22×C83116yescomplemented
549#542C22×C8318yescomplemented
550#542C22×C83116yescomplemented
551#542C22×C83116yescomplemented
552#542C22×C83116yescomplemented
553#541C22×C8318yescomplemented
554#540C22×C83116yescomplemented
555#539C22×C83116yescomplemented
556#538C22×C8318yescomplemented
557#538C22×C83116yescomplemented
558#538C22×C83116yescomplemented
559#537C22×C8314yes—
560#537C22×C8312yes—
561#537C22×C8314yescomplemented
562#537C22×C8318yescomplemented
563#536C22×C8314yes—
564#536C22×C8312yes—
565#536C22×C8314yescomplemented
566#536C22×C8314yescomplemented
567#536C22×C8314yescomplemented
568#536C22×C8314yescomplemented
569#536C22×C8312yescomplemented
570#536C22×C8314yescomplemented
571#536C22×C8318yescomplemented
572#536C22×C8318yescomplemented
573#535C22×C8314yes—
574#535C22×C8312yes—
575#535C22×C8312yescomplemented
576#534C22×C8314yes—
577#534C22×C8314yescomplemented
578#533C22×C8318yescomplemented
579#532C22×C8314yes—
580#532C22×C8314yescomplemented
581C2×C4⋊Q8C22×C8312yescomplemented
582#529C22×C8318yescomplemented
583#529C22×C8318yescomplemented
584C2×#124C22×C8312yes—
585#525C22×C8314yes—
586#525C22×C8314yes—
587#525C22×C8314yescomplemented
588#525C22×C8314yescomplemented
589#525C22×C8318yescomplemented
590#525C22×C8318yescomplemented
591C2×#123C22×C8314yescomplemented
592C2×C22⋊Q8C22×C8314yescomplemented
593C2×C22⋊Q8C22×C8318yescomplemented
594#520C22×C8314yescomplemented
595#519C22×C8312yescomplemented
596C2×#117C22×C8311yescharacteristic, complemented
597C2×#117C22×C8312yescomplemented
5982−1+4—48no—
599C2×#41—44no—
600C2×#41—48no—
601C2×#41C23×C8314yes—
602C2×#41C23×C8312yes—
603C2×#41C23×C8312yes—
604C2×#41C23×C8318yes—
605C2×#41C23×C8318yes—
606C2×#41C23×C8312yes—
607C2×#41C23×C8314yes—
608C2×#41C23×C8312yes—
609C2×#41C23×C8314yes—
610C2×#41C23×C8314yes—
611C22×Q8—44no—
612C22×Q8C23×C8312yes—
613C22×Q8C23×C8318yes—
614C22×Q8C23×C8312yes—
615C22×Q8C23×C8311yescharacteristic
616C22×Q8C23×C8314yes—
617C22×Q8C23×C8312yes—
618C22×Q8C23×C8314yes—
619C22×D4C23×C8312yes—
620C22×D4C23×C8311yescharacteristic
621C22×D4C23×C8314yes—
622C22×D4C23×C8312yes—
623C23×C4C23×C8312yes—
624C23×C4C23×C8311yescharacteristic
625C23×C4C23×C8314yes—
626C23×C4C23×C8312yes—
627C4⋊Q8C23×C8318yes—
628C4⋊Q8C23×C8314yes—
629C4⋊Q8C23×C8314yes—
630C4⋊Q8C23×C8314yes—
631C4⋊Q8C23×C8314yes—
632C4⋊Q8C23×C8318yes—
633C4⋊Q8C23×C8318yes—
634C4⋊Q8C23×C8318yes—
635C4⋊Q8C23×C83116yes—
636C4⋊Q8C23×C8318yes—
637#127C23×C8314yes—
638#127C23×C8314yes—
639#126C23×C83116yes—
640#126C23×C83116yes—
641#126C23×C83116yes—
642#126C23×C83116yes—
643#126C23×C83116yes—
644#126C23×C83116yes—
645#125C23×C8318yes—
646#125C23×C8318yes—
647#125C23×C83116yes—
648#125C23×C83116yes—
649#125C23×C83116yes—
650#124C23×C8314yes—
651#124C23×C8318yes—
652#124C23×C8314yes—
653#124C23×C8318yes—
654#124C23×C8318yes—
655#124C23×C8314yes—
656#124C23×C8314yes—
657#124C23×C8314yes—
658#124C23×C8314yes—
659#124C23×C8318yes—
660#124C23×C83116yes—
661#124C23×C8318yes—
662#124C23×C83116yes—
663#124C23×C83116yes—
664#123C23×C8318yes—
665#123C23×C8318yes—
666#123C23×C8318yes—
667#123C23×C8318yes—
668#123C23×C8314yes—
669#123C23×C8318yes—
670#123C23×C8314yes—
671#123C23×C8318yes—
672#123C23×C8314yes—
673#123C23×C8314yes—
674#123C23×C83116yes—
675#123C23×C83116yes—
676#123C23×C83116yes—
677#123C23×C83116yes—
678#123C23×C83116yes—
679#123C23×C83116yes—
680#123C23×C83116yes—
681C22⋊Q8C23×C8314yes—
682C22⋊Q8C23×C8318yes—
683C22⋊Q8C23×C8318yes—
684C22⋊Q8C23×C8318yes—
685C22⋊Q8C23×C8318yes—
686C22⋊Q8C23×C8318yes—
687C22⋊Q8C23×C8318yes—
688C22⋊Q8C23×C83116yes—
689C22⋊Q8C23×C83116yes—
690C22⋊Q8C23×C8314yes—
691C22⋊Q8C23×C8318yes—
692C22⋊Q8C23×C8314yes—
693C22⋊Q8C23×C8318yes—
694C22⋊Q8C23×C8314yes—
695C22⋊Q8C23×C8318yes—
696C22⋊Q8C23×C83116yes—
697C22⋊Q8C23×C8318yes—
698C22⋊Q8C23×C83116yes—
699C22⋊Q8C23×C83116yes—
700C22⋊Q8C23×C83116yes—
701C22⋊Q8C23×C83116yes—
702C22⋊Q8C23×C83116yes—
703#121C23×C8314yes—
704#121C23×C8314yes—
705#121C23×C8318yes—
706#121C23×C8314yes—
707#121C23×C8318yes—
708#121C23×C8314yes—
709#121C23×C8318yes—
710#121C23×C83116yes—
711#121C23×C8318yes—
712#121C23×C8318yes—
713#121C23×C8318yes—
714#121C23×C8318yes—
715#121C23×C8318yes—
716#121C23×C83116yes—
717#121C23×C83116yes—
718#121C23×C83116yes—
719#121C23×C83116yes—
720#120C23×C8318yes—
721#120C23×C8314yes—
722#120C23×C8314yes—
723#120C23×C8318yes—
724#120C23×C8314yes—
725#120C23×C8314yes—
726#120C23×C83116yes—
727C4×Q8C23×C8318yes—
728C4×Q8C23×C8318yes—
729C4×Q8C23×C8318yes—
730C4×Q8C23×C8318yes—
731C4×Q8C23×C83116yes—
732C4×D4C23×C83116yes—
733C4×D4C23×C8318yes—
734C4×D4C23×C8318yes—
735C4×D4C23×C8318yes—
736C4×D4C23×C8318yes—
737C4×D4C23×C8318yes—
738C4×D4C23×C83116yes—
739C4×D4C23×C83116yes—
740C4×D4C23×C83116yes—
741C4×D4C23×C83116yes—
742C4×D4C23×C8318yes—
743C4×D4C23×C83116yes—
744#117C23×C8314yes—
745#117C23×C8314yes—
746#117C23×C8314yes—
747#117C23×C8312yes—
748#117C23×C8312yes—
749#117C23×C8314yes—
750#117C23×C8314yes—
751#117C23×C8318yes—
752#117C23×C8318yes—
753#117C23×C83116yes—
754#117C23×C83116yes—
755#117C23×C83116yes—
756C2×C4⋊C4C23×C8312yes—
757C2×C4⋊C4C23×C8314yes—
758C2×C4⋊C4C23×C8318yes—
759C2×C4⋊C4C23×C8318yes—
760C2×C4⋊C4C23×C83116yes—
761C2×C22⋊C4C23×C8312yes—
762C2×C22⋊C4C23×C8314yes—
763C2×C22⋊C4C23×C8318yes—
764C2×C22⋊C4C23×C83116yes—
765C2×C42C23×C8312yes—
766C2×C42C23×C8314yes—
767C24C24×C8312yes—
768C24C24×C8311yescharacteristic
769C24C24×C8314yes—
770#41—216no—
771#41—44no—
772#41—44no—
773#41—44no—
774#41—44no—
775#41—48no—
776#41—48no—
777#41—416no—
778#41—48no—
779#41—416no—
780C2×Q8—28no—
781C2×Q8—44no—
782C2×Q8—42no—
783C2×Q8—48no—
784C2×Q8—48no—
785C2×Q8—44no—
786C2×Q8—416no—
787C2×Q8C24×C8318yes—
788C2×Q8C24×C8314yes—
789C2×Q8C24×C8318yes—
790C2×Q8C24×C8311yescharacteristic
791C2×Q8C24×C8318yes—
792C2×Q8C24×C8314yes—
793C2×Q8C24×C8314yes—
794C2×Q8C24×C8312yes—
795C2×Q8C24×C8314yes—
796C2×Q8C24×C8311yescharacteristic
797C2×D4—44no—
798C2×D4—42no—
799C2×D4—44no—
800C2×D4—48no—
801C2×D4C24×C8318yes—
802C2×D4C24×C8314yes—
803C2×D4C24×C8318yes—
804C2×D4C24×C8318yes—
805C2×D4C24×C8318yes—
806C2×D4C24×C8318yes—
807C2×D4C24×C8318yes—
808C2×D4C24×C8311yescharacteristic
809C2×D4C24×C8318yes—
810C2×D4C24×C8312yes—
811C2×D4C24×C8312yes—
812C2×D4C24×C8312yes—
813C2×D4C24×C8312yes—
814C2×D4C24×C8318yes—
815C2×D4C24×C8311yescharacteristic
816C2×D4C24×C8312yes—
817C2×D4C24×C8314yes—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—48no—
821C22×C4—44no—
822C22×C4C24×C8312yes—
823C22×C4C24×C8311yescharacteristic
824C22×C4C24×C8314yes—
825C22×C4C24×C8312yes—
826C22×C4C24×C8312yes—
827C22×C4C24×C8318yes—
828C22×C4C24×C8312yes—
829C22×C4C24×C8312yes—
830C22×C4C24×C8312yes—
831C22×C4C24×C8312yes—
832C22×C4C24×C8314yes—
833C22×C4C24×C8318yes—
834C22×C4C24×C83116yes—
835C22×C4C24×C83116yes—
836C22×C4C24×C8318yes—
837C22×C4C24×C8318yes—
838C22×C4C24×C8314yes—
839C22×C4C24×C8311yescharacteristic
840C4⋊C4C24×C8314yes—
841C4⋊C4C24×C8318yes—
842C4⋊C4C24×C8318yes—
843C4⋊C4C24×C83116yes—
844C4⋊C4C24×C8318yes—
845C4⋊C4C24×C8314yes—
846C4⋊C4C24×C8318yes—
847C4⋊C4C24×C83116yes—
848C4⋊C4C24×C83116yes—
849C4⋊C4C24×C83116yes—
850C4⋊C4C24×C8318yes—
851C4⋊C4C24×C83116yes—
852C4⋊C4C24×C8318yes—
853C4⋊C4C24×C83116yes—
854C4⋊C4C24×C83116yes—
855C4⋊C4C24×C8318yes—
856C4⋊C4C24×C8318yes—
857C22⋊C4C24×C8318yes—
858C22⋊C4C24×C83116yes—
859C22⋊C4C24×C8318yes—
860C22⋊C4C24×C8314yes—
861C22⋊C4C24×C8314yes—
862C22⋊C4C24×C8318yes—
863C22⋊C4C24×C83116yes—
864C22⋊C4C24×C83116yes—
865C22⋊C4C24×C83116yes—
866C22⋊C4C24×C8318yes—
867C22⋊C4C24×C8318yes—
868C22⋊C4C24×C8318yes—
869C22⋊C4C24×C83116yes—
870C22⋊C4C24×C8318yes—
871C22⋊C4C24×C8318yes—
872C22⋊C4C24×C8318yes—
873C22⋊C4C24×C8318yes—
874C22⋊C4C24×C83116yes—
875C42C24×C8314yes—
876C42C24×C8314yes—
877C42C24×C8318yes—
878C42C24×C8314yes—
879C42C24×C8314yes—
880C42C24×C8318yes—
881C42C24×C83116yes—
882C42C24×C8318yes—
883C23—22no—
884C23—24no—
885C23—42no—
886C23—44no—
887C23—44no—
888C23—48no—
889C23C25×C8312yes—
890C23C25×C8312yes—
891C23C25×C8312yes—
892C23C25×C8318yes—
893C23C25×C8311yescharacteristic
894Q8—216no—
895Q8—28no—
896Q8—44no—
897Q8—44no—
898Q8—48no—
899Q8—41no—
900Q8—42no—
901Q8—41no—
902Q8—44no—
903Q8—48no—
904D4—216no—
905D4—28no—
906D4—42no—
907D4—42no—
908D4—42no—
909D4—42no—
910D4—44no—
911D4—41no—
912D4—42no—
913D4—41no—
914D4—48no—
915D4—48no—
916D4—48no—
917D4—48no—
918D4—48no—
919D4—48no—
920D4—48no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—28no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—216no—
931C2×C4—44no—
932C2×C4—48no—
933C2×C4—48no—
934C2×C4—416no—
935C2×C4—416no—
936C2×C4—48no—
937C2×C4—44no—
938C2×C4H(5,𝔽2)×C8314yes—
939C2×C4C25×C8318yes—
940C2×C4C25×C8318yes—
941C2×C4C25×C8318yes—
942C2×C4C25×C8311yescharacteristic
943C2×C4C25×C8311yescharacteristic
944C2×C4C25×C8312yes—
945C2×C4C25×C8318yes—
946C2×C4C25×C8318yes—
947C2×C4C25×C8312yes—
948C2×C4C25×C8312yes—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—22no—
953C22—28no—
954C22—24no—
955C22—28no—
956C22—24no—
957C22—28no—
958C22—24no—
959C22—44no—
960C22—84no—
961C22—88no—
962C22C2×H(5,𝔽2)×C8312yes—
963C22C26×C8311yescharacteristic
964C4—22no—
965C4—22no—
966C4—21no—
967C4—21no—
968C4—28no—
969C4—28no—
970C4—28no—
971C4—28no—
972C4—28no—
973C4C2×H(5,𝔽2)×C8314yes—
974C2—22no—
975C2—42no—
976C2—42no—
977C2—42no—
978C2—48no—
979C2C22×H(5,𝔽2)×C8311yescharacteristic
980C2C83×2−1+612yes—
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×#3551C2semidirect
2. C83×#3550C2semidirect
3. C83×#3547C2semidirect
4. C83×#3545C2semidirect
5. C83×#3544C2semidirect
6. C83×#3541C2semidirect
7. C83×#3540C2semidirect
8. C83×#3538C2semidirect
9. C83×#3533C2semidirect
10. C83×#3495C2semidirect
11. C83×#3493C2semidirect
12. C83×#3489C2semidirect
13. C83×#3486C2semidirect
14. C83×#3449C2semidirect
15. C2×#536×C83C2semidirect
18. C22×#41×C83C22semidirect
19. C23×Q8×C83C22semidirect
20. #563×C83C22semidirect
21. #563×C83C22semidirect
22. #563×C83C22semidirect
23. #563×C83C22semidirect
24. #562×C83C22semidirect
25. #562×C83C22semidirect
26. H(3,𝔽4)×C83C22semidirect
27. #560×C83C22semidirect
28. #559×C83C22semidirect
29. Q82×C83C22semidirect
30. #556×C83C22semidirect
31. #556×C83C22semidirect
32. #555×C83C22semidirect
33. #555×C83C22semidirect
34. #555×C83C22semidirect
35. #554×C83C22semidirect
36. #554×C83C22semidirect
37. #553×C83C22semidirect
38. #553×C83C22semidirect
39. #552×C83C22semidirect
40. #552×C83C22semidirect
41. #552×C83C22semidirect
42. #552×C83C22semidirect
43. #551×C83C22semidirect
44. #551×C83C22semidirect
45. #551×C83C22semidirect
46. D4×Q8×C83C22semidirect
47. D4×Q8×C83C22semidirect
48. D4×Q8×C83C22semidirect
49. #548×C83C22semidirect
50. #548×C83C22semidirect
51. #548×C83C22semidirect
52. #547×C83C22semidirect
53. #547×C83C22semidirect
54. #546×C83C22semidirect
55. #546×C83C22semidirect
56. #544×C83C22semidirect
57. #544×C83C22semidirect
58. #542×C83C22semidirect
59. #542×C83C22semidirect
60. #542×C83C22semidirect
61. #542×C83C22semidirect
62. #541×C83C22semidirect
63. #540×C83C22semidirect
64. #539×C83C22semidirect
65. #538×C83C22semidirect
66. #538×C83C22semidirect
67. #538×C83C22semidirect
70. #537×C83C22semidirect
71. #537×C83C22semidirect
74. #536×C83C22semidirect
75. #536×C83C22semidirect
76. #536×C83C22semidirect
77. #536×C83C22semidirect
78. #536×C83C22semidirect
79. #536×C83C22semidirect
80. #536×C83C22semidirect
81. #536×C83C22semidirect
84. #535×C83C22semidirect
86. #534×C83C22semidirect
87. #533×C83C22semidirect
89. #532×C83C22semidirect
90. C2×C4⋊Q8×C83C22semidirect
91. #529×C83C22semidirect
92. #529×C83C22semidirect
96. #525×C83C22semidirect
97. #525×C83C22semidirect
98. #525×C83C22semidirect
99. #525×C83C22semidirect
100. C2×#123×C83C22semidirect
101. C2×C22⋊Q8×C83C22semidirect
102. C2×C22⋊Q8×C83C22semidirect
103. #520×C83C22semidirect
104. #519×C83C22semidirect
105. C2×#117×C83C22semidirect
106. C2×#117×C83C22semidirect
483. #62886C83direct (N × H)
491. #3551C2×C83semidirect
492. #3550C2×C83semidirect
493. #3547C2×C83semidirect
494. #3545C2×C83semidirect
495. #3544C2×C83semidirect
496. #3541C2×C83semidirect
497. #3540C2×C83semidirect
498. #3538C2×C83semidirect
499. #3533C2×C83semidirect
500. #3495C2×C83semidirect
501. #3493C2×C83semidirect
502. #3489C2×C83semidirect
503. #3486C2×C83semidirect
504. #3449C2×C83semidirect
505. C2×#536C2×C83semidirect
506. C83#62886direct (N × H)
509. C22×#41C22×C83semidirect
510. C23×Q8C22×C83semidirect
511. #563C22×C83semidirect
512. #563C22×C83semidirect
513. #563C22×C83semidirect
514. #563C22×C83semidirect
515. #562C22×C83semidirect
516. #562C22×C83semidirect
517. H(3,𝔽4)C22×C83semidirect
518. #560C22×C83semidirect
519. #559C22×C83semidirect
520. Q82C22×C83semidirect
521. #556C22×C83semidirect
522. #556C22×C83semidirect
523. #555C22×C83semidirect
524. #555C22×C83semidirect
525. #555C22×C83semidirect
526. #554C22×C83semidirect
527. #554C22×C83semidirect
528. #553C22×C83semidirect
529. #553C22×C83semidirect
530. #552C22×C83semidirect
531. #552C22×C83semidirect
532. #552C22×C83semidirect
533. #552C22×C83semidirect
534. #551C22×C83semidirect
535. #551C22×C83semidirect
536. #551C22×C83semidirect
537. D4×Q8C22×C83semidirect
538. D4×Q8C22×C83semidirect
539. D4×Q8C22×C83semidirect
540. #548C22×C83semidirect
541. #548C22×C83semidirect
542. #548C22×C83semidirect
543. #547C22×C83semidirect
544. #547C22×C83semidirect
545. #546C22×C83semidirect
546. #546C22×C83semidirect
547. #544C22×C83semidirect
548. #544C22×C83semidirect
549. #542C22×C83semidirect
550. #542C22×C83semidirect
551. #542C22×C83semidirect
552. #542C22×C83semidirect
553. #541C22×C83semidirect
554. #540C22×C83semidirect
555. #539C22×C83semidirect
556. #538C22×C83semidirect
557. #538C22×C83semidirect
558. #538C22×C83semidirect
561. #537C22×C83semidirect
562. #537C22×C83semidirect
565. #536C22×C83semidirect
566. #536C22×C83semidirect
567. #536C22×C83semidirect
568. #536C22×C83semidirect
569. #536C22×C83semidirect
570. #536C22×C83semidirect
571. #536C22×C83semidirect
572. #536C22×C83semidirect
575. #535C22×C83semidirect
577. #534C22×C83semidirect
578. #533C22×C83semidirect
580. #532C22×C83semidirect
581. C2×C4⋊Q8C22×C83semidirect
582. #529C22×C83semidirect
583. #529C22×C83semidirect
587. #525C22×C83semidirect
588. #525C22×C83semidirect
589. #525C22×C83semidirect
590. #525C22×C83semidirect
591. C2×#123C22×C83semidirect
592. C2×C22⋊Q8C22×C83semidirect
593. C2×C22⋊Q8C22×C83semidirect
594. #520C22×C83semidirect
595. #519C22×C83semidirect
596. C2×#117C22×C83semidirect
597. C2×#117C22×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35512
C83×#35502
C83×#35472
C83×#35452
C83×#35442
C83×#35412
C83×#35402
C83×#35382
C83×#35332
C83×#34952
C83×#34932
C83×#34892
C83×#34862
C83×#34492
C2×#536×C832
#6288683