Finite Group Databasebeta

← #24921779

Subgroups — #24921779

Order 10624.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128447C212yesmaximal, complemented
2#19128439C212yesmaximal, complemented
3#19128416C211yesmaximal, characteristic, complemented
4#19128397C211yesmaximal, characteristic, complemented
5#19128391C211yesmaximal, characteristic, complemented
6#19128378C212yesmaximal, complemented
7#19128372C211yesmaximal, characteristic, complemented
8#19128355C211yesmaximal, characteristic, complemented
9#19128347C211yesmaximal, characteristic, complemented
10#19128347C211yesmaximal, characteristic, complemented
11#19128340C212yesmaximal, complemented
12D4×D332C211yesmaximal, characteristic, complemented
13#19128322C211yesmaximal, characteristic, complemented
14#19128306C211yesmaximal, characteristic, complemented
15#19128303C212yesmaximal, complemented
16#19128287C212yesmaximal, complemented
17#19128279C211yesmaximal, characteristic, complemented
18#19128266C212yesmaximal, complemented
19#19128265C211yesmaximal, characteristic, complemented
20#19128261C212yesmaximal, complemented
21#19128212C211yesmaximal, characteristic, complemented
22C2×#14581766C211yesmaximal, characteristic, complemented
23#525×C83C211yesmaximal, characteristic, complemented
24C2×#13050590C2211yescharacteristic, complemented
25C2×#13050590C2211yescharacteristic, complemented
26C2×#13050589C2212yescomplemented
27C22×D332C2211yescharacteristic
28C22×D332C2211yescharacteristic, complemented
29C22×C22⋊D83C2212yescomplemented
30C2×D4×D83C2212yes—
31#14581792C2211yescharacteristic, complemented
32#14581789C2211yescharacteristic, complemented
33#14581788C2212yescomplemented
34#14581788C2212yescomplemented
35#14581787C2212yescomplemented
36#14581787C2212yescomplemented
37#14581785C2212yescomplemented
38#14581784C2211yescharacteristic, complemented
39#14581782C2212yescomplemented
40#14581781C2212yescomplemented
41#14581780C2211yescharacteristic, complemented
42#14581778C2212yescomplemented
43#14581778C2212yescomplemented
44#14581778C2212yescomplemented
45#14581777C2212yescomplemented
46#14581777C2212yescomplemented
47#14581777C2212yescomplemented
48#14581777C2212yescomplemented
49#14581776C2212yescomplemented
50#14581776C2212yescomplemented
51#14581775C2212yescomplemented
52#14581774C2212yescomplemented
53#14581774C2212yescomplemented
54#14581773C2212yes—
55#14581772C2212yescomplemented
56#14581771C2211yescharacteristic, complemented
57#14581771C2211yescharacteristic, complemented
58#14581771C2211yescharacteristic, complemented
59#14581770C2212yescomplemented
60#14581768C2212yescomplemented
61#14581767C2212yescomplemented
62#14581766C2211yescharacteristic
63#14581766C2211yescharacteristic
64#14581766C2211yescharacteristic
65#14581766C2211yescharacteristic, complemented
66#14581766C2211yescharacteristic, complemented
67#14581766C2211yescharacteristic, complemented
68#14581766C2211yescharacteristic, complemented
69#14581766C2212yescomplemented
70#14581766C2211yescharacteristic, complemented
71#14581766C2212yescomplemented
72#14581766C2211yescharacteristic, complemented
73#14581765C2212yescomplemented
74#14581765C2212yescomplemented
75#14581765C2212yescomplemented
76#14581765C2212yescomplemented
77#14581765C2212yescomplemented
78#14581765C2212yescomplemented
79#14581764C2212yescomplemented
80#14581764C2212yescomplemented
81#14581764C2212yescomplemented
82#14581763C2212yescomplemented
83#14581763C2212yescomplemented
84#14581762C2212yes—
85#14581762C2212yescomplemented
86#14581761C2212yescomplemented
87#14581760C2212yescomplemented
88#14581760C2212yescomplemented
89#14581760C2212yescomplemented
90#14581760C2212yescomplemented
91C4×Dic166C2211yescharacteristic, complemented
92C4×D332C2211yescharacteristic, complemented
93C4×D332C2211yescharacteristic, complemented
94C4×D332C2211yescharacteristic, complemented
95#14581754C2212yescomplemented
96C4×C22⋊D83C2212yescomplemented
97C4×C22⋊D83C2212yescomplemented
98(C22⋊D83)⋊C4C2212yescomplemented
99#14581751C2211yescharacteristic, complemented
100#14581751C2211yescharacteristic, complemented
101#14581750C2212yescomplemented
102#14581748C2212yescomplemented
103C2×C4⋊Dic83C2211yescharacteristic, complemented
104C2×C4⋊Dic83C2211yescharacteristic, complemented
105C2×(C2×D83)⋊C4C2212yescomplemented
106C22⋊C4×D83C2212yescomplemented
107C22⋊C4×D83C2212yescomplemented
108C2×#41×C83C2211yescharacteristic, complemented
109C23×C4×C83C2211yescharacteristic, complemented
110#123×C83C2211yescharacteristic, complemented
111#123×C83C2211yescharacteristic, complemented
112C22⋊Q8×C83C2211yescharacteristic, complemented
113C22⋊Q8×C83C2211yescharacteristic, complemented
114#121×C83C2211yescharacteristic
115#121×C83C2211yescharacteristic, complemented
116#120×C83C2211yescharacteristic
117#120×C83C2211yescharacteristic, complemented
118C4×D4×C83C2211yescharacteristic
119C4×D4×C83C2211yescharacteristic, complemented
120C4×D4×C83C2211yescharacteristic, complemented
121C4×D4×C83C2211yescharacteristic, complemented
122#117×C83C2211yescharacteristic, complemented
123C23×D83C2312yes—
124C23×D83C2312yes—
125#13050590—42no—
126#13050590—42no—
127#13050589—44no—
128C2×Dic166C2311yescharacteristic
129C2×Dic166C2312yes—
130C2×D332—42no—
131C2×D332—42no—
132C2×D332C2311yescharacteristic
133C2×D332C2311yescharacteristic
134C2×D332C2311yescharacteristic
135C2×D332C2312yes—
136C2×D332C2312yes—
137C2×D332C2312yes—
138C2×D332C2312yes—
139C2×C22⋊D83—44no—
140C2×C22⋊D83C2312yes—
141C2×C22⋊D83C2312yes—
142C2×C22⋊D83C2312yes—
143C2×C22⋊D83C2312yes—
144C2×C22⋊D83C2312yes—
145C2×C22⋊D83C2312yes—
146C2×C22⋊D83C2312yes—
147C2×C22⋊D83C2312yes—
148C2×C22⋊D83C2312yes—
149C2×C22⋊D83C2312yes—
150C2×C22⋊D83C2312yes—
151D4×D83—44no—
152C22×Dic83C2312yes—
153C22×Dic83C2312yes—
154C2×C4×D83C2312yes—
155C2×C4×D83C2312yes—
156C2×C4×D83C2312yes—
157C2×C4×D83C2312yes—
158C2×C4×D83C2312yes—
159C4⋊Dic83C2312yes—
160C4⋊Dic83C2312yes—
161C4⋊Dic83C2311yescharacteristic
162C4⋊Dic83C2311yescharacteristic
163C4⋊Dic83C2311yescharacteristic
164C4⋊Dic83C2311yescharacteristic
165C4⋊Dic83C2312yes—
166Dic83⋊C4C2312yes—
167Dic83⋊C4C2312yes—
168Dic83⋊C4C2312yes—
169Dic83⋊C4C2312yes—
170Dic83⋊C4C2312yes—
171Dic83⋊C4C2312yes—
172C22⋊Dic83C2312yes—
173C22⋊Dic83C2312yes—
174C22⋊Dic83C2312yes—
175C22⋊Dic83C2312yes—
176C22⋊Dic83C2312yes—
177(C2×D83)⋊C4C2312yes—
178(C2×D83)⋊C4C2312yes—
179(C2×D83)⋊C4C2312yes—
180(C2×D83)⋊C4C2312yes—
181(C2×D83)⋊C4C2312yes—
182(C2×D83)⋊C4C2312yes—
183(C2×D83)⋊C4C2312yes—
184(C2×D83)⋊C4C2312yes—
185(C2×D83)⋊C4C2312yes—
186(C2×D83)⋊C4C2312yes—
187(C2×D83)⋊C4C2312yes—
188(C2×D83)⋊C4C2312yes—
189(C2×D83)⋊C4C2312yes—
190(C2×D83)⋊C4C2312yes—
191C4×Dic83C2312yes—
192C4×Dic83C2312yes—
193C4×Dic83C2312yes—
194C24×C83C2311yescharacteristic
195#41×C83—42no—
196C2×Q8×C83C2311yescharacteristic
197C2×D4×C83C2311yescharacteristic
198C2×D4×C83C2311yescharacteristic
199C2×D4×C83C2311yescharacteristic
200C2×D4×C83C2311yescharacteristic
201C2×D4×C83C2311yescharacteristic
202C2×D4×C83C2311yescharacteristic
203C2×D4×C83C2311yescharacteristic
204C22×C4×C83—42no—
205C22×C4×C83C2311yescharacteristic
206C22×C4×C83C2311yescharacteristic
207C22×C4×C83C2311yescharacteristic
208C22×C4×C83C2311yescharacteristic
209C22×C4×C83C2311yescharacteristic
210C22×C4×C83C2311yescharacteristic
211C22×C4×C83C2311yescharacteristic
212C22×C4×C83C2311yescharacteristic
213C4⋊C4×C83C2311yescharacteristic
214C4⋊C4×C83C2311yescharacteristic
215C4⋊C4×C83C2311yescharacteristic
216C4⋊C4×C83C2311yescharacteristic
217C4⋊C4×C83C2311yescharacteristic
218C4⋊C4×C83C2311yescharacteristic
219C22⋊C4×C83C2311yescharacteristic
220C22⋊C4×C83C2311yescharacteristic
221C22⋊C4×C83C2311yescharacteristic
222C22⋊C4×C83C2311yescharacteristic
223C22⋊C4×C83C2311yescharacteristic
224C22⋊C4×C83C2311yescharacteristic
225C22⋊C4×C83C2311yescharacteristic
226C22⋊C4×C83C2311yescharacteristic
227C22⋊C4×C83C2311yescharacteristic
228C22⋊C4×C83C2311yescharacteristic
229C42×C83C2311yescharacteristic
230C42×C83C2311yescharacteristic
231C23×C83—22no—
232C23×C83—41no—
233C23×C83—41no—
234C23×C83C2411yescharacteristic
235C23×C83C2411yescharacteristic
236C23×C83C2411yescharacteristic
237C23×C83C2411yescharacteristic
238C23×C83C2411yescharacteristic
239C22×D83—24no—
240C22×D83—42no—
241C22×D83—42no—
242C22×D83—42no—
243C22×D83—42no—
244C22×D83—42no—
245C22×D83C2412yes—
246C22×D83C2412yes—
247C22×D83C2412yes—
248Q8×C83—41no—
249D4×C83—22no—
250D4×C83—22no—
251D4×C83—41no—
252D4×C83—41no—
253D4×C83—41no—
254D4×C83—41no—
255D4×C83—41no—
256C2×C4×C83—22no—
257C2×C4×C83—22no—
258C2×C4×C83—22no—
259C2×C4×C83—22no—
260C2×C4×C83—22no—
261C2×C4×C83—41no—
262C2×C4×C83—41no—
263C2×C4×C83—41no—
264C2×C4×C83C2411yescharacteristic
265C2×C4×C83C2411yescharacteristic
266C2×C4×C83C2411yescharacteristic
267C2×C4×C83C2411yescharacteristic
268C2×C4×C83C2411yescharacteristic
269C2×C4×C83C2411yescharacteristic
270C2×C4×C83C2411yescharacteristic
271C2×C4×C83C2411yescharacteristic
272C2×C4×C83C2411yescharacteristic
273C2×C4×C83C2411yescharacteristic
274C22⋊D83—24no—
275C22⋊D83—42no—
276C22⋊D83—42no—
277C22⋊D83—42no—
278C22⋊D83—42no—
279C22⋊D83—42no—
280C22⋊D83—42no—
281C22⋊D83—42no—
282C22⋊D83—42no—
283C22⋊D83—42no—
284C22⋊D83—42no—
285C2×Dic83—24no—
286C2×Dic83—42no—
287C2×Dic83C2412yes—
288C2×Dic83C2412yes—
289C2×Dic83C2412yes—
290C2×Dic83C2412yes—
291C2×Dic83C2412yes—
292D332—22no—
293D332—22no—
294D332—22no—
295D332—42no—
296D332—42no—
297D332—42no—
298D332—42no—
299C4×D83—42no—
300C4×D83—42no—
301C4×D83—42no—
302C4×D83—42no—
303C4×D83—42no—
304Dic166—22no—
305Dic166—42no—
306C22×C83—21no—
307C22×C83—21no—
308C22×C83—21no—
309C22×C83—21no—
310C22×C83—21no—
311C22×C83—21no—
312C22×C83—21no—
313C22×C83—21no—
314C22×C83—21no—
315C22×C83—21no—
316C22×C83—21no—
317C22×C83—21no—
318C22×C83—21no—
319C22×C83—21no—
320C22×C83—44no—
321C22×C83H(5,𝔽2)12yes—
322C22×C83C2511yescharacteristic
323C2×D83—22no—
324C2×D83—22no—
325C2×D83—22no—
326C2×D83—22no—
327C2×D83—22no—
328C2×D83—22no—
329C2×D83—22no—
330C2×D83—22no—
331C2×D83—22no—
332C2×D83—84no—
333C2×D83—84no—
334C4×C83—21no—
335C4×C83—21no—
336C4×C83—21no—
337C4×C83—21no—
338C4×C83—21no—
339C4×C83—21no—
340C4×C83—21no—
341C4×C83—21no—
342C4×C83—21no—
343C4×C83H(5,𝔽2)12yes—
344Dic83—22no—
345Dic83—22no—
346Dic83—22no—
347Dic83—22no—
348Dic83—22no—
349C2×C83—22no—
350C2×C83—41no—
351C2×C83—41no—
352C2×C83—41no—
353C2×C83—41no—
354C2×C83C2×H(5,𝔽2)11yescharacteristic
355C2×C83C2×H(5,𝔽2)11yescharacteristic
356C2×C83#58511yescharacteristic
357D83—42no—
358D83—42no—
359D83—42no—
360#3542—831nomaximal, Sylow
361C83#354211yescharacteristic, complemented, Sylow
362#562—832no—
363#560—832no—
364#555—831no—
365#553—831no—
366#552—831no—
367#551—832no—
368#550—831no—
369#547—831no—
370#546—832no—
371#546—831no—
372#546—831no—
373D42—831no—
374#542—831no—
375#540—832no—
376#540—831no—
377#538—832no—
378#537—831no—
379#535—831no—
380#535—832no—
381#534—832no—
382#525—831no—
383#525D8311yescharacteristic, complemented
384C2×#121—831no—
385C2×#41—832no—
386C2×#41—831no—
387C2×#41—831no—
388C2×#41C2×D8311yescharacteristic, complemented
389C22×D4—832no—
390C22×D4—832no—
391C22×D4—831no—
392C22×D4—831no—
393C23×C4C2×D8311yescharacteristic, complemented
394C4⋊Q8—831no—
395#127—832no—
396#127—832no—
397#127—831no—
398#126—832no—
399#126—832no—
400#126—832no—
401#125—832no—
402#125—831no—
403#124—832no—
404#124—832no—
405#124—832no—
406#124—832no—
407#124—831no—
408#123—832no—
409#123—832no—
410#123—832no—
411#123—832no—
412#123—832no—
413#123—832no—
414#123—832no—
415#123—832no—
416#123—832no—
417#123—832no—
418#123C2×D8311yescharacteristic, complemented
419#123C2×D8311yescharacteristic, complemented
420C22⋊Q8—832no—
421C22⋊Q8—831no—
422C22⋊Q8—831no—
423C22⋊Q8—831no—
424C22⋊Q8—832no—
425C22⋊Q8—832no—
426C22⋊Q8C2×D8311yescharacteristic, complemented
427C22⋊Q8C2×D8311yescharacteristic, complemented
428#121—832no—
429#121—832no—
430#121—832no—
431#121—832no—
432#121—832no—
433#121—831no—
434#121—831no—
435#121—831no—
436#121—831no—
437#121—832no—
438#121—831no—
439#121—832no—
440#121—831no—
441#121—831no—
442#121—831no—
443#121—831no—
444#121—832no—
445#121—832no—
446#121—832no—
447#121—832no—
448#121—832no—
449#121—832no—
450#121—832no—
451#121C2×D8311yescharacteristic
452#121C2×D8311yescharacteristic, complemented
453#120—832no—
454#120—832no—
455#120—832no—
456#120—832no—
457#120—832no—
458#120—832no—
459#120—832no—
460#120C2×D8311yescharacteristic
461#120C2×D8311yescharacteristic, complemented
462C4×Q8—831no—
463C4×D4—832no—
464C4×D4—832no—
465C4×D4—832no—
466C4×D4—832no—
467C4×D4—831no—
468C4×D4—831no—
469C4×D4—831no—
470C4×D4C2×D8311yescharacteristic
471C4×D4C2×D8311yescharacteristic, complemented
472C4×D4C2×D8311yescharacteristic, complemented
473C4×D4C2×D8311yescharacteristic, complemented
474#117—831no—
475#117—831no—
476#117—832no—
477#117—832no—
478#117C2×D8311yescharacteristic, complemented
479C2×C4⋊C4—831no—
480C2×C4⋊C4—831no—
481C2×C22⋊C4—832no—
482C2×C22⋊C4—832no—
483C2×C22⋊C4—832no—
484C24—832no—
485C24—832no—
486C24C22×D8311yescharacteristic
487#41—42no—
488#41—3322no—
489#41—3322no—
490#41—3324no—
491C2×Q8—832no—
492C2×Q8—831no—
493C2×Q8C22×D8311yescharacteristic
494C2×D4—3322no—
495C2×D4—3322no—
496C2×D4—3324no—
497C2×D4—3324no—
498C2×D4—832no—
499C2×D4—832no—
500C2×D4—832no—
501C2×D4—832no—
502C2×D4—832no—
503C2×D4—832no—
504C2×D4—832no—
505C2×D4—832no—
506C2×D4—832no—
507C2×D4—832no—
508C2×D4—832no—
509C2×D4—832no—
510C2×D4—832no—
511C2×D4—832no—
512C2×D4—832no—
513C2×D4—831no—
514C2×D4—831no—
515C2×D4—831no—
516C2×D4C22×D8311yescharacteristic
517C2×D4C22×D8311yescharacteristic
518C2×D4C22×D8311yescharacteristic
519C2×D4C22×D8311yescharacteristic
520C2×D4C22×D8311yescharacteristic
521C2×D4C22×D8311yescharacteristic
522C2×D4C22×D8311yescharacteristic
523C22×C4—42no—
524C22×C4—832no—
525C22×C4—832no—
526C22×C4—832no—
527C22×C4—832no—
528C22×C4—832no—
529C22×C4—832no—
530C22×C4—832no—
531C22×C4C22×D8311yescharacteristic
532C22×C4C22×D8311yescharacteristic
533C22×C4C22×D8311yescharacteristic
534C22×C4C22×D8311yescharacteristic
535C22×C4C22×D8311yescharacteristic
536C22×C4C22×D8311yescharacteristic
537C22×C4C22×D8311yescharacteristic
538C22×C4C22×D8311yescharacteristic
539C4⋊C4—831no—
540C4⋊C4—831no—
541C4⋊C4—831no—
542C4⋊C4—832no—
543C4⋊C4—832no—
544C4⋊C4—831no—
545C4⋊C4—832no—
546C4⋊C4—832no—
547C4⋊C4—832no—
548C4⋊C4—832no—
549C4⋊C4—832no—
550C4⋊C4—832no—
551C4⋊C4—832no—
552C4⋊C4C22×D8311yescharacteristic
553C4⋊C4C22×D8311yescharacteristic
554C4⋊C4C22×D8311yescharacteristic
555C4⋊C4C22×D8311yescharacteristic
556C4⋊C4C22×D8311yescharacteristic
557C4⋊C4C22×D8311yescharacteristic
558C22⋊C4—832no—
559C22⋊C4—832no—
560C22⋊C4—832no—
561C22⋊C4—832no—
562C22⋊C4—832no—
563C22⋊C4—832no—
564C22⋊C4—832no—
565C22⋊C4—832no—
566C22⋊C4—832no—
567C22⋊C4—832no—
568C22⋊C4—832no—
569C22⋊C4—832no—
570C22⋊C4—832no—
571C22⋊C4—832no—
572C22⋊C4—832no—
573C22⋊C4—832no—
574C22⋊C4—832no—
575C22⋊C4—832no—
576C22⋊C4—832no—
577C22⋊C4C22×D8311yescharacteristic
578C22⋊C4C22×D8311yescharacteristic
579C22⋊C4C22×D8311yescharacteristic
580C22⋊C4C22×D8311yescharacteristic
581C22⋊C4C22×D8311yescharacteristic
582C22⋊C4C22×D8311yescharacteristic
583C22⋊C4C22×D8311yescharacteristic
584C22⋊C4C22×D8311yescharacteristic
585C22⋊C4C22×D8311yescharacteristic
586C22⋊C4C22×D8311yescharacteristic
587C42—832no—
588C42—832no—
589C42—832no—
590C42C22×D8311yescharacteristic
591C42C22×D8311yescharacteristic
592C23—22no—
593C23—41no—
594C23—41no—
595C23—3322no—
596C23—3322no—
597C23—3322no—
598C23—3322no—
599C23—3322no—
600C23—832no—
601C23—832no—
602C23—832no—
603C23—1664no—
604C23C23×D8311yescharacteristic
605C23C23×D8311yescharacteristic
606C23C23×D8311yescharacteristic
607C23C23×D8311yescharacteristic
608C23C23×D8311yescharacteristic
609Q8—41no—
610Q8—3322no—
611Q8—1662no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—3322no—
620D4—3322no—
621D4—3322no—
622D4—3322no—
623D4—3322no—
624D4—3322no—
625D4—3322no—
626D4—3322no—
627D4—3322no—
628D4—3322no—
629D4—3322no—
630D4—3322no—
631D4—3322no—
632D4—3322no—
633D4—1664no—
634D4—1662no—
635D4—1662no—
636D4—1662no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—3322no—
646C2×C4—3322no—
647C2×C4—3322no—
648C2×C4—3322no—
649C2×C4—3322no—
650C2×C4—3322no—
651C2×C4—832no—
652C2×C4—832no—
653C2×C4—832no—
654C2×C4—832no—
655C2×C4—832no—
656C2×C4—1664no—
657C2×C4C23×D8311yescharacteristic
658C2×C4C23×D8311yescharacteristic
659C2×C4C23×D8311yescharacteristic
660C2×C4C23×D8311yescharacteristic
661C2×C4C23×D8311yescharacteristic
662C2×C4C23×D8311yescharacteristic
663C2×C4C23×D8311yescharacteristic
664C2×C4C23×D8311yescharacteristic
665C2×C4C23×D8311yescharacteristic
666C2×C4C23×D8311yescharacteristic
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—44no—
682C22—6644no—
683C22—6644no—
684C22—1662no—
685C22—1662no—
686C22—1662no—
687C22—1662no—
688C22—1662no—
689C22—1662no—
690C22—1662no—
691C22—1662no—
692C22—1662no—
693C22#1458183812yes—
694C22C24×D8311yescharacteristic
695C4—21no—
696C4—21no—
697C4—21no—
698C4—21no—
699C4—21no—
700C4—21no—
701C4—21no—
702C4—21no—
703C4—21no—
704C4—1662no—
705C4—1662no—
706C4—1662no—
707C4—1662no—
708C4—1662no—
709C4#1458183712yes—
710C2—22no—
711C2—41no—
712C2—41no—
713C2—41no—
714C2—41no—
715C2—3322no—
716C2—3322no—
717C2—3322no—
718C2C2×#1458183711yescharacteristic
719C2C2×#1458183811yescharacteristic
720C2#1912853711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D83
commutator, socle, cosocleC22×C83C25
Fitting#525×C83C2
hypercenter#525D83
hypocenterC83#3542
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #19128447C2semidirect
2. #19128439C2semidirect
3. #19128416C2semidirect
4. #19128397C2semidirect
5. #19128391C2semidirect
6. #19128378C2semidirect
7. #19128372C2semidirect
8. #19128355C2semidirect
9. #19128347C2semidirect
10. #19128347C2semidirect
11. #19128340C2semidirect
12. D4×D332C2semidirect
13. #19128322C2semidirect
14. #19128306C2semidirect
15. #19128303C2semidirect
16. #19128287C2semidirect
17. #19128279C2semidirect
18. #19128266C2semidirect
19. #19128265C2semidirect
20. #19128261C2semidirect
21. #19128212C2semidirect
22. C2×#14581766C2semidirect
23. #525×C83C2semidirect
24. C2×#13050590C22semidirect
25. C2×#13050590C22semidirect
26. C2×#13050589C22semidirect
28. C22×D332C22semidirect
29. C22×C22⋊D83C22semidirect
31. #14581792C22semidirect
32. #14581789C22semidirect
33. #14581788C22semidirect
34. #14581788C22semidirect
35. #14581787C22semidirect
36. #14581787C22semidirect
37. #14581785C22semidirect
38. #14581784C22semidirect
39. #14581782C22semidirect
40. #14581781C22semidirect
41. #14581780C22semidirect
42. #14581778C22semidirect
43. #14581778C22semidirect
44. #14581778C22semidirect
45. #14581777C22semidirect
46. #14581777C22semidirect
47. #14581777C22semidirect
48. #14581777C22semidirect
49. #14581776C22semidirect
50. #14581776C22semidirect
51. #14581775C22semidirect
52. #14581774C22semidirect
53. #14581774C22semidirect
55. #14581772C22semidirect
56. #14581771C22semidirect
57. #14581771C22semidirect
58. #14581771C22semidirect
59. #14581770C22semidirect
60. #14581768C22semidirect
61. #14581767C22semidirect
65. #14581766C22semidirect
66. #14581766C22semidirect
67. #14581766C22semidirect
68. #14581766C22semidirect
69. #14581766C22semidirect
70. #14581766C22semidirect
71. #14581766C22semidirect
72. #14581766C22semidirect
73. #14581765C22semidirect
74. #14581765C22semidirect
75. #14581765C22semidirect
76. #14581765C22semidirect
77. #14581765C22semidirect
78. #14581765C22semidirect
79. #14581764C22semidirect
80. #14581764C22semidirect
81. #14581764C22semidirect
82. #14581763C22semidirect
83. #14581763C22semidirect
85. #14581762C22semidirect
86. #14581761C22semidirect
87. #14581760C22semidirect
88. #14581760C22semidirect
89. #14581760C22semidirect
90. #14581760C22semidirect
91. C4×Dic166C22semidirect
92. C4×D332C22semidirect
93. C4×D332C22semidirect
94. C4×D332C22semidirect
95. #14581754C22semidirect
96. C4×C22⋊D83C22semidirect
97. C4×C22⋊D83C22semidirect
98. (C22⋊D83)⋊C4C22semidirect
99. #14581751C22semidirect
100. #14581751C22semidirect
101. #14581750C22semidirect
102. #14581748C22semidirect
103. C2×C4⋊Dic83C22semidirect
104. C2×C4⋊Dic83C22semidirect
105. C2×(C2×D83)⋊C4C22semidirect
106. C22⋊C4×D83C22semidirect
107. C22⋊C4×D83C22semidirect
108. C2×#41×C83C22semidirect
109. C23×C4×C83C22semidirect
110. #123×C83C22semidirect
111. #123×C83C22semidirect
112. C22⋊Q8×C83C22semidirect
113. C22⋊Q8×C83C22semidirect
115. #121×C83C22semidirect
117. #120×C83C22semidirect
119. C4×D4×C83C22semidirect
120. C4×D4×C83C22semidirect
121. C4×D4×C83C22semidirect
122. #117×C83C22semidirect
361. C83#3542semidirect
383. #525D83semidirect
388. C2×#41C2×D83semidirect
393. C23×C4C2×D83semidirect
418. #123C2×D83semidirect
419. #123C2×D83semidirect
426. C22⋊Q8C2×D83semidirect
427. C22⋊Q8C2×D83semidirect
452. #121C2×D83semidirect
461. #120C2×D83semidirect
471. C4×D4C2×D83semidirect
472. C4×D4C2×D83semidirect
473. C4×D4C2×D83semidirect
478. #117C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191284472
#191284392
#191284162
#191283972
#191283912
#191283782
#191283722
#191283552
#191283472
#191283402
D4×D3322
#191283222
#191283062
#191283032
#191282872
#191282792
#191282662
#191282652
#191282612
#191282122
C2×#145817662
#525×C832
#354283