Finite Group Databasebeta

← #36268933

Subgroups — #36268933

Order 21248.

1878 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24920848C211yesmaximal, characteristic
2#24916448C214yesmaximal, complemented
3#24916444C214yesmaximal, complemented
4#24916438C214yesmaximal, complemented
5#24916434C214yesmaximal, complemented
6#24916401C211yesmaximal, characteristic, complemented
7#24916395C211yesmaximal, characteristic, complemented
8#24916179C211yesmaximal, characteristic, complemented
9#24916173C211yesmaximal, characteristic, complemented
10#24916168C211yesmaximal, characteristic, complemented
11#24916164C211yesmaximal, characteristic, complemented
12#24916159C211yesmaximal, characteristic, complemented
13#24916155C211yesmaximal, characteristic, complemented
14#24916115C211yesmaximal, characteristic, complemented
15#24916114C211yesmaximal, characteristic, complemented
16#24916099C211yesmaximal, characteristic, complemented
17C4×#14581798C211yesmaximal, characteristic, complemented
18C2×#19127655C211yesmaximal, characteristic, complemented
19C4×#131×C83C211yesmaximal, characteristic, complemented
20C2×#14581798C2211yescharacteristic
21C2×#14581798C2211yescharacteristic
22C22×#13050573C2211yescharacteristic
23C22×C8×D83C2211yescharacteristic
24#19128323C412yes—
25#19128316C412yes—
26#19128309C412yes—
27#19128302C412yes—
28#19128293C414yes—
29#19128284C414yes—
30#19128254C2211yescharacteristic
31#19128247C2211yescharacteristic
32#19128235C2214yes—
33#19128229C2214yes—
34#19128213C2211yescharacteristic
35#19128208C2211yescharacteristic
36C4×#13050590C2211yescharacteristic
37C2×#14581749C2211yescharacteristic
38#19127831C2214yescomplemented
39#19127829C2214yescomplemented
40#19127829C2214yescomplemented
41C8×Dic166C2214yescomplemented
42#19127780C2214yes—
43#19127777C2214yes—
44#19127777C2214yescomplemented
45#19127774C2214yes—
46#19127774C2214yes—
47#19127772C2214yes—
48#19127772C2214yescomplemented
49#19127770C2214yes—
50#19127770C2214yescomplemented
51C8×D332C2214yes—
52C8×C22⋊D83C2214yes—
53C8×C22⋊D83C2214yescomplemented
54#19127763C2214yes—
55#19127762C2214yescomplemented
56#19127760C2214yes—
57#19127760C2214yescomplemented
58#19127758C2214yescomplemented
59#19127756C2214yescomplemented
60#19127729C2211yescharacteristic
61#19127729C2211yescharacteristic
62#19127728C2211yescharacteristic
63#19127728C2211yescharacteristic
64#19127724C2211yescharacteristic
65#19127724C2211yescharacteristic
66#19127669C2211yescharacteristic
67#19127669C2211yescharacteristic
68#19127668C2211yescharacteristic
69#19127668C2211yescharacteristic
70#19127664C2211yescharacteristic
71#19127664C2211yescharacteristic
72#19127656C2211yescharacteristic
73#19127656C2211yescharacteristic
74#19127655C2212yes—
75#19127655C2212yes—
76#19127655C2212yes—
77#19127655C2212yes—
78#19127655C2212yescomplemented
79#19127655C2212yescomplemented
80C4×#13050574C2211yescharacteristic
81C4×#13050573C2212yescomplemented
82C2×#14581703C2211yescharacteristic
83C2×#14581702C2211yescharacteristic
84C2×C8×Dic83C2211yescharacteristic
85C4×C8×D83C2212yescomplemented
86C2×#131×C83C2211yescharacteristic
87C2×#131×C83C2211yescharacteristic
88C4×#41×C83C2211yescharacteristic
89#405×C83C2211yescharacteristic
90#405×C83C2211yescharacteristic
91#405×C83C2212yescomplemented
92#405×C83C2212yescomplemented
93C4×M16×C83C2211yescharacteristic
94C4×M16×C83C2212yescomplemented
95C2×C4×C8×C83C2211yescharacteristic
96C2×C4×C8×C83C2212yescomplemented
97C2×#13050590C2311yescharacteristic
98C22×C4×D83C2311yescharacteristic
99#14581798—24no—
100#14581798—24no—
101C2×#13050574C2311yescharacteristic
102C2×#13050574C2311yescharacteristic
103C2×#13050573—24no—
104C2×#13050573C2312yes—
105C2×#13050573C2312yes—
106C2×#13050573C2312yes—
107C2×#13050573C2312yes—
108C22×C83⋊C8C2311yescharacteristic
109C22×C83⋊C8C2311yescharacteristic
110C2×C8×D83—24no—
111C2×C8×D83C2312yes—
112C2×C8×D83C2312yes—
113C2×C8×D83C2312yes—
114C2×C8×D83C2312yes—
115#14581791C2×C412yes—
116#14581790C2×C411yescharacteristic
117#14581788C2×C411yescharacteristic
118#14581787C2×C414yes—
119#14581786C2×C414yes—
120#14581786C2×C414yes—
121#14581785C2×C414yes—
122#14581784C2×C414yes—
123#14581783C2×C412yes—
124#14581782C2×C414yes—
125#14581781C2×C411yescharacteristic
126#14581780C2×C414yes—
127#14581779C2×C411yescharacteristic
128#14581778C2×C414yes—
129#14581777C2×C414yes—
130#14581776C2×C412yes—
131#14581775C2×C414yes—
132#14581775C2×C414yes—
133#14581774C2×C414yes—
134#14581773C2×C412yes—
135#14581772C2×C412yes—
136#14581771C2×C414yes—
137#14581770C2×C414yes—
138#14581769C2×C414yes—
139#14581768C2×C412yes—
140#14581767C2×C412yes—
141#14581766C2×C414yes—
142#14581765C2×C414yes—
143#14581764C2×C414yes—
144#14581763C2×C412yes—
145#14581762C2×C412yes—
146#14581760C2×C412yes—
147C4×Dic166C2×C412yes—
148C4×Dic166C2314yes—
149C4×D332C2×C412yes—
150C4×D332C2314yes—
151C4×C22⋊D83C2×C414yes—
152C4×C22⋊D83C2314yes—
153C4×C22⋊D83C2314yes—
154#14581751C2311yescharacteristic
155#14581749C2×C412yes—
156#14581749C2×C412yes—
157#14581749C2312yes—
158#14581749C2312yes—
159#14581749C2312yes—
160C2×Dic83⋊C4C2×C412yes—
161C2×(C2×D83)⋊C4C2×C412yes—
162C2×C4×Dic83C2311yescharacteristic
163C42×D83C2312yes—
164C4⋊(C83⋊C8)C2314yes—
165C4⋊(C83⋊C8)C2314yes—
166Dic83⋊C8C2314yes—
167Dic83⋊C8C2314yes—
168Dic83⋊C8C2314yes—
169Dic83⋊C8C2314yes—
170C22⋊(C83⋊C8)C2314yes—
171C22⋊(C83⋊C8)C2314yes—
172(C2×D83)⋊C8C2314yes—
173(C2×D83)⋊C8C2314yes—
174(C2×D83)⋊C8C2314yes—
175(C2×D83)⋊C8C2314yes—
176#14581703C2312yes—
177#14581703C2312yes—
178#14581703C2312yes—
179#14581702C2312yes—
180#14581702C2312yes—
181#14581702C2312yes—
182#14581702C2312yes—
183C4×C83⋊C8C2312yes—
184C8×Dic83C2312yes—
185C8×Dic83C2312yes—
186C8×Dic83C2312yes—
187C8×Dic83C2312yes—
188C2×#41×C83C2311yescharacteristic
189#131×C83—24no—
190#131×C83—24no—
191C2×M16×C83C2311yescharacteristic
192C2×M16×C83C2311yescharacteristic
193C2×M16×C83C2312yes—
194C2×M16×C83C2312yes—
195C22×C8×C83C2312yes—
196C22×C8×C83C2312yes—
197C22×C8×C83C2311yescharacteristic
198C22×C8×C83C2311yescharacteristic
199C4×Q8×C83C2×C412yes—
200C4×D4×C83C2×C414yes—
201C4×D4×C83C2×C412yes—
202#117×C83C2311yescharacteristic
203#117×C83C2312yes—
204C2×C42×C83C2311yescharacteristic
205C2×C42×C83C2312yes—
206#97×C83C2312yes—
207#97×C83C2312yes—
208#97×C83C2312yes—
209C4×C8×C83C2312yes—
210C4×C8×C83C2312yes—
211C4×C8×C83C2311yescharacteristic
212C4×C8×C83C2311yescharacteristic
213C4×C8×C83C2311yescharacteristic
214C4×C8×C83C2311yescharacteristic
215C4×C8×C83C2312yes—
216C23×D83C22×C411yescharacteristic
217#13050590—22no—
218#13050590—22no—
219C2×Dic166C22×C411yescharacteristic
220C2×Dic166C22×C414yes—
221C2×D332C22×C411yescharacteristic
222C2×D332C22×C414yes—
223C2×C22⋊D83C22×C412yes—
224C2×C22⋊D83C22×C414yes—
225C2×C22⋊D83C22×C414yes—
226C22×Dic83C22×C411yescharacteristic
227C22×Dic83C22×C412yes—
228C2×C4×D83—22no—
229C2×C4×D83—22no—
230C2×C4×D83C22×C412yes—
231C2×C4×D83C22×C414yes—
232C2×C4×D83C2412yes—
233C2×C4×D83C2412yes—
234#13050574—22no—
235#13050574—22no—
236#13050573—24no—
237#13050573—24no—
238#13050573—24no—
239#13050573—24no—
240C2×C83⋊C8—22no—
241C2×C83⋊C8—22no—
242C2×C83⋊C8C2412yes—
243C2×C83⋊C8C2412yes—
244C2×C83⋊C8C2412yes—
245C2×C83⋊C8C2412yes—
246C8×D83—24no—
247C8×D83—24no—
248C8×D83—24no—
249C8×D83—24no—
250C4⋊Dic83C22×C412yes—
251C4⋊Dic83C22×C414yes—
252C4⋊Dic83C22×C414yes—
253Dic83⋊C4C22×C414yes—
254Dic83⋊C4C22×C414yes—
255Dic83⋊C4C22×C414yes—
256Dic83⋊C4C22×C414yes—
257Dic83⋊C4C22×C412yes—
258Dic83⋊C4C22×C412yes—
259Dic83⋊C4C22×C414yes—
260Dic83⋊C4C22×C412yes—
261Dic83⋊C4C22×C412yes—
262C22⋊Dic83C22×C412yes—
263C22⋊Dic83C22×C414yes—
264C22⋊Dic83C22×C414yes—
265(C2×D83)⋊C4C22×C414yes—
266(C2×D83)⋊C4C22×C414yes—
267(C2×D83)⋊C4C22×C414yes—
268(C2×D83)⋊C4C22×C412yes—
269(C2×D83)⋊C4C22×C412yes—
270(C2×D83)⋊C4C22×C414yes—
271(C2×D83)⋊C4C22×C414yes—
272(C2×D83)⋊C4C22×C412yes—
273(C2×D83)⋊C4C22×C412yes—
274C4×Dic83C22×C414yes—
275C4×Dic83C22×C411yescharacteristic
276C4×Dic83C22×C411yescharacteristic
277C4×Dic83C2412yes—
278C4×Dic83C2412yes—
279#41×C83—22no—
280#41×C83—22no—
281C2×Q8×C83C22×C411yescharacteristic
282C2×D4×C83C22×C412yes—
283C2×D4×C83C22×C411yescharacteristic
284C22×C4×C83C22×C414yes—
285C22×C4×C83C22×C412yes—
286C22×C4×C83C2412yes—
287C22×C4×C83C2411yescharacteristic
288M16×C83—22no—
289M16×C83—22no—
290M16×C83—24no—
291M16×C83—24no—
292C2×C8×C83—24no—
293C2×C8×C83—24no—
294C2×C8×C83#4114yes—
295C2×C8×C83#4114yes—
296C2×C8×C83C2412yes—
297C2×C8×C83C2412yes—
298C2×C8×C83C2411yescharacteristic
299C2×C8×C83C2411yescharacteristic
300C2×C8×C83C2411yescharacteristic
301C2×C8×C83C2411yescharacteristic
302C4⋊C4×C83C22×C412yes—
303C4⋊C4×C83C22×C414yes—
304C22⋊C4×C83C22×C412yes—
305C22⋊C4×C83C22×C414yes—
306C42×C83C22×C414yes—
307C42×C83C22×C412yes—
308C42×C83C2411yescharacteristic
309C42×C83C2411yescharacteristic
310C42×C83C2412yes—
311C23×C83C23×C412yes—
312C23×C83C23×C411yescharacteristic
313C22×D83—22no—
314C22×D83—42no—
315C22×D83C23×C412yes—
316C22×D83C23×C412yes—
317Q8×C83—22no—
318D4×C83—24no—
319D4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—44no—
323C2×C4×C83—42no—
324C2×C4×C83C23×C412yes—
325C2×C4×C83C23×C412yes—
326C2×C4×C83C23×C412yes—
327C2×C4×C83C23×C414yes—
328C2×C4×C83C23×C411yescharacteristic
329C2×C4×C83C2×#4112yes—
330C2×C4×C83C2×#4112yes—
331C2×C4×C83C2511yescharacteristic
332C22⋊D83—24no—
333C22⋊D83—44no—
334C22⋊D83—44no—
335C2×Dic83—22no—
336C2×Dic83—42no—
337C2×Dic83C23×C412yes—
338C2×Dic83C23×C412yes—
339C2×Dic83C23×C414yes—
340C2×Dic83C23×C412yes—
341C2×Dic83C23×C412yes—
342D332—22no—
343D332—44no—
344C4×D83—24no—
345C4×D83—22no—
346C4×D83—22no—
347C4×D83—22no—
348C4×D83—22no—
349C4×D83—44no—
350Dic166—22no—
351Dic166—44no—
352C8×C83—22no—
353C8×C83—22no—
354C8×C83C2×#4112yes—
355C8×C83C2×#4112yes—
356C8×C83C2×#4112yes—
357C8×C83C2×#4112yes—
358C83⋊C8—22no—
359C83⋊C8—22no—
360C83⋊C8—22no—
361C83⋊C8—22no—
362C22×C83—22no—
363C22×C83—22no—
364C22×C83—24no—
365C22×C83C4×#4112yes—
366C22×C83C24×C411yescharacteristic
367C2×D83—22no—
368C2×D83—22no—
369C2×D83—24no—
370C2×D83—22no—
371C2×D83—22no—
372C2×D83—44no—
373C4×C83—22no—
374C4×C83—24no—
375C4×C83—22no—
376C4×C83—22no—
377C4×C83C4×#4112yes—
378C4×C83C22×#4111yescharacteristic
379C4×C83C22×#4111yescharacteristic
380Dic83—22no—
381Dic83—22no—
382Dic83—22no—
383Dic83—24no—
384Dic83—22no—
385#60206—831nomaximal, Sylow
386C2×C83—22no—
387C2×C83—42no—
388C2×C83C2×C4×#4111yescharacteristic
389C2×C83#357312yes—
390D83—42no—
391D83—42no—
392#3455—831no—
393#2967—834no—
394#2967—834no—
395#2966—834no—
396#2966—834no—
397#2961—831no—
398#2960—831no—
399#2932—831no—
400#2931—831no—
401#2930—831no—
402#2930—831no—
403#2929—831no—
404#2929—831no—
405#2923—831no—
406#2923—831no—
407#2921—831no—
408C4×#131—831no—
409C4×#131D8311yescharacteristic, complemented
410C2×#405—831no—
411C83#6020611yescharacteristic, complemented, Sylow
412C2×#131—831no—
413C2×#131—831no—
414C2×#131C2×D8311yescharacteristic
415C2×#131C2×D8311yescharacteristic
416C22×M16—831no—
417C23×C8—831no—
418#542—832no—
419#542—832no—
420#541—832no—
421#540—832no—
422#539—834no—
423#538—834no—
424#533—831no—
425#532—831no—
426#529—834no—
427#529—834no—
428#525—831no—
429#525—831no—
430C4×#41—831no—
431C4×#41C2×D8311yescharacteristic
432C2×#117—831no—
433#446—834no—
434#446—834no—
435#446—834no—
436C8×Q8—834no—
437#436—834no—
438#436—834no—
439#436—834no—
440#435—834no—
441#435—834no—
442#435—834no—
443#435—834no—
444#435—834no—
445#435—834no—
446C8×D4—834no—
447C8×D4—834no—
448C8×D4—834no—
449#433—834no—
450#433—834no—
451#433—834no—
452#433—834no—
453#432—834no—
454#432—834no—
455#424—831no—
456#424—831no—
457#424—831no—
458#424—831no—
459#423—831no—
460#423—831no—
461#408—831no—
462#408—831no—
463#408—831no—
464#408—831no—
465#407—831no—
466#407—831no—
467#405—831no—
468#405—831no—
469#405—832no—
470#405—832no—
471#405—832no—
472#405—832no—
473#405—832no—
474#405—832no—
475#405C2×D8311yescharacteristic
476#405C2×D8311yescharacteristic
477#405C2×D8312yescomplemented
478#405C2×D8312yescomplemented
479C4×M16—831no—
480C4×M16—832no—
481C4×M16C2×D8311yescharacteristic
482C4×M16C2×D8312yescomplemented
483C2×#97—831no—
484C2×#97—831no—
485C2×C4×C8—831no—
486C2×C4×C8—832no—
487C2×C4×C8C2×D8311yescharacteristic
488C2×C4×C8C2×D8312yescomplemented
489C2×#41—831no—
490C2×#41C22×D8311yescharacteristic
491C23×C4—831no—
492#131—24no—
493#131—24no—
494#131—1664no—
495#131—1664no—
496C2×M16—831no—
497C2×M16—831no—
498C2×M16—832no—
499C2×M16—832no—
500C2×M16—832no—
501C2×M16—832no—
502C2×M16—1664no—
503C2×M16C22×D8311yescharacteristic
504C2×M16C22×D8311yescharacteristic
505C2×M16C22×D8312yes—
506C2×M16C22×D8312yes—
507C22×C8—831no—
508C22×C8—831no—
509C22×C8—832no—
510C22×C8—832no—
511C22×C8—832no—
512C22×C8—832no—
513C22×C8—1664no—
514C22×C8C22×D8312yes—
515C22×C8C22×D8312yes—
516C22×C8C22×D8311yescharacteristic
517C22×C8C22×D8311yescharacteristic
518C4⋊Q8—831no—
519C4⋊Q8—832no—
520#127—831no—
521#126—834no—
522#126—834no—
523#126—834no—
524#126—834no—
525#125—834no—
526#125—832no—
527#125—834no—
528#124—831no—
529#124—831no—
530#124—834no—
531#124—834no—
532#123—832no—
533#123—834no—
534#123—834no—
535#123—834no—
536#123—832no—
537#123—834no—
538C22⋊Q8—832no—
539C22⋊Q8—834no—
540C22⋊Q8—834no—
541C22⋊Q8—832no—
542C22⋊Q8—834no—
543#121—832no—
544#121—834no—
545#121—834no—
546#121—832no—
547#121—834no—
548#120—832no—
549#120—832no—
550C4×Q8—832no—
551C4×Q8—834no—
552C4×Q8C4×D8312yes—
553C4×D4—834no—
554C4×D4—834no—
555C4×D4—834no—
556C4×D4—832no—
557C4×D4—834no—
558C4×D4C4×D8314yes—
559C4×D4C4×D8312yes—
560#117—831no—
561#117—832no—
562#117—832no—
563#117—832no—
564#117—832no—
565#117—832no—
566#117C22×D8311yescharacteristic
567#117C22×D8312yes—
568C2×C4⋊C4—832no—
569C2×C22⋊C4—832no—
570C2×C42—831no—
571C2×C42—832no—
572C2×C42C22×D8311yescharacteristic
573C2×C42C22×D8312yes—
574C4⋊C8—834no—
575C4⋊C8—834no—
576C4⋊C8—834no—
577C4⋊C8—834no—
578C4⋊C8—834no—
579C4⋊C8—834no—
580C22⋊C8—834no—
581C22⋊C8—834no—
582C22⋊C8—834no—
583C22⋊C8—834no—
584C22⋊C8—834no—
585C22⋊C8—834no—
586#97—832no—
587#97—832no—
588#97—832no—
589#97—832no—
590#97—832no—
591#97—832no—
592#97—832no—
593#97C22×D8312yes—
594#97C22×D8312yes—
595#97C22×D8312yes—
596C4×C8—832no—
597C4×C8—832no—
598C4×C8—832no—
599C4×C8—832no—
600C4×C8—832no—
601C4×C8C22×D8311yescharacteristic
602C4×C8C22×D8311yescharacteristic
603C4×C8C22×D8312yes—
604C4×C8C22×D8312yes—
605C4×C8C22×D8311yescharacteristic
606C4×C8C22×D8311yescharacteristic
607C4×C8C22×D8312yes—
608C24—831no—
609#41—22no—
610#41—22no—
611#41—1662no—
612#41—1662no—
613C2×Q8—834no—
614C2×Q8—831no—
615C2×Q8C2×C4×D8311yescharacteristic
616C2×D4—834no—
617C2×D4—834no—
618C2×D4—832no—
619C2×D4—834no—
620C2×D4—831no—
621C2×D4C2×C4×D8312yes—
622C2×D4C2×C4×D8311yescharacteristic
623C22×C4—832no—
624C22×C4—834no—
625C22×C4—831no—
626C22×C4—832no—
627C22×C4—832no—
628C22×C4—832no—
629C22×C4—1662no—
630C22×C4—1662no—
631C22×C4C2×C4×D8312yes—
632C22×C4C2×C4×D8314yes—
633C22×C4C23×D8312yes—
634C22×C4C23×D8311yescharacteristic
635M16—22no—
636M16—22no—
637M16—24no—
638M16—24no—
639M16—1662no—
640M16—1662no—
641M16—1664no—
642M16—1664no—
643M16—1664no—
644M16—1664no—
645C2×C8—24no—
646C2×C8—24no—
647C2×C8—832no—
648C2×C8—832no—
649C2×C8—832no—
650C2×C8—832no—
651C2×C8—1662no—
652C2×C8—1662no—
653C2×C8—1664no—
654C2×C8—1664no—
655C2×C8—1664no—
656C2×C8—1664no—
657C2×C8#1305059014yes—
658C2×C8#1305059014yes—
659C2×C8C23×D8312yes—
660C2×C8C23×D8312yes—
661C2×C8C23×D8311yescharacteristic
662C2×C8C23×D8311yescharacteristic
663C2×C8C23×D8311yescharacteristic
664C2×C8C23×D8311yescharacteristic
665C4⋊C4—832no—
666C4⋊C4—832no—
667C4⋊C4—832no—
668C4⋊C4—832no—
669C4⋊C4—832no—
670C4⋊C4—834no—
671C4⋊C4—834no—
672C4⋊C4—834no—
673C4⋊C4—834no—
674C4⋊C4—834no—
675C4⋊C4—834no—
676C4⋊C4—834no—
677C4⋊C4C2×C4×D8312yes—
678C4⋊C4C2×C4×D8314yes—
679C22⋊C4—832no—
680C22⋊C4—834no—
681C22⋊C4—834no—
682C22⋊C4—832no—
683C22⋊C4—832no—
684C22⋊C4—832no—
685C22⋊C4—832no—
686C22⋊C4—834no—
687C22⋊C4—834no—
688C22⋊C4—834no—
689C22⋊C4—834no—
690C22⋊C4—834no—
691C22⋊C4C2×C4×D8312yes—
692C22⋊C4C2×C4×D8314yes—
693C42—831no—
694C42—831no—
695C42—834no—
696C42—832no—
697C42—832no—
698C42C2×C4×D8312yes—
699C42C2×C4×D8314yes—
700C42C23×D8311yescharacteristic
701C42C23×D8311yescharacteristic
702C42C23×D8312yes—
703C23—3322no—
704C23—832no—
705C23—832no—
706C23—1662no—
707C23C22×C4×D8312yes—
708C23C22×C4×D8311yescharacteristic
709Q8—22no—
710Q8—3324no—
711Q8—1662no—
712D4—24no—
713D4—22no—
714D4—3324no—
715D4—3324no—
716D4—3324no—
717D4—1664no—
718D4—1662no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—3324no—
724C2×C4—3322no—
725C2×C4—832no—
726C2×C4—834no—
727C2×C4—832no—
728C2×C4—832no—
729C2×C4—832no—
730C2×C4—1662no—
731C2×C4—1664no—
732C2×C4—1662no—
733C2×C4—1662no—
734C2×C4—1662no—
735C2×C4—1662no—
736C2×C4C22×C4×D8312yes—
737C2×C4C22×C4×D8312yes—
738C2×C4C22×C4×D8312yes—
739C2×C4C22×C4×D8314yes—
740C2×C4C22×C4×D8311yescharacteristic
741C2×C4C2×#1305059012yes—
742C2×C4C2×#1305059012yes—
743C2×C4C24×D8311yescharacteristic
744C8—22no—
745C8—22no—
746C8—1662no—
747C8—1662no—
748C8—1662no—
749C8—1662no—
750C8C2×#1305059012yes—
751C8C2×#1305059012yes—
752C8C2×#1305059012yes—
753C8C2×#1305059012yes—
754C22—22no—
755C22—24no—
756C22—22no—
757C22—3324no—
758C22—1664no—
759C22—1662no—
760C22—1662no—
761C22—1662no—
762C22—1662no—
763C22C4×#1305059012yes—
764C22C23×C4×D8311yescharacteristic
765C4—22no—
766C4—22no—
767C4—24no—
768C4—22no—
769C4—1662no—
770C4—1664no—
771C4—1662no—
772C4—1662no—
773C4—1662no—
774C4C4×#1305059012yes—
775C4C22×#1305059011yescharacteristic
776C4C22×#1305059011yescharacteristic
777C2—22no—
778C2—42no—
779C2—3322no—
780C2—3322no—
781C2C2×C4×#1305059011yescharacteristic
782C2#2492217412yes—
subgroupG/H
centerC2×C8C23×D83
commutator, socleC22×C83C24×C4
FrattiniC2×C4C24×D83
FittingC4×#131×C83C2
prime radical#24920848C2
cosocleC2×C4×C83C25
hypercenterC4×#131D83
hypocenterC83#60206
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C8 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. #24916448C2semidirect
3. #24916444C2semidirect
4. #24916438C2semidirect
5. #24916434C2semidirect
6. #24916401C2semidirect
7. #24916395C2semidirect
8. #24916179C2semidirect
9. #24916173C2semidirect
10. #24916168C2semidirect
11. #24916164C2semidirect
12. #24916159C2semidirect
13. #24916155C2semidirect
14. #24916115C2semidirect
15. #24916114C2semidirect
16. #24916099C2semidirect
17. C4×#14581798C2semidirect
18. C2×#19127655C2semidirect
19. C4×#131×C83C2semidirect
38. #19127831C22semidirect
39. #19127829C22semidirect
40. #19127829C22semidirect
41. C8×Dic166C22semidirect
44. #19127777C22semidirect
48. #19127772C22semidirect
50. #19127770C22semidirect
53. C8×C22⋊D83C22semidirect
55. #19127762C22semidirect
57. #19127760C22semidirect
58. #19127758C22semidirect
59. #19127756C22semidirect
78. #19127655C22semidirect
79. #19127655C22semidirect
81. C4×#13050573C22semidirect
85. C4×C8×D83C22semidirect
91. #405×C83C22semidirect
92. #405×C83C22semidirect
94. C4×M16×C83C22semidirect
96. C2×C4×C8×C83C22semidirect
409. C4×#131D83semidirect
411. C83#60206semidirect
477. #405C2×D83semidirect
478. #405C2×D83semidirect
482. C4×M16C2×D83semidirect
488. C2×C4×C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249208482
#249164482
#249164442
#249164382
#249164342
#249164012
#249163952
#249161792
#249161732
#249161682
#249161642
#249161592
#249161552
#249161152
#249161142
#249160992
C4×#145817982
C2×#191276552
C4×#131×C832
#6020683