Finite Group Databasebeta

← #25968948

Subgroups — #25968948

Order 11008.

1686 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583526C211yesmaximal, characteristic, complemented
2#19147987C211yesmaximal, characteristic
3#19145896C214yesmaximal, complemented
4#19145881C214yesmaximal, complemented
5#19145864C214yesmaximal, complemented
6#19145849C214yesmaximal, complemented
7#19145148C211yesmaximal, characteristic, complemented
8#19144996C211yesmaximal, characteristic, complemented
9#19144991C211yesmaximal, characteristic, complemented
10#19144529C212yesmaximal, complemented
11#19144521C212yesmaximal, complemented
12#19144416C212yesmaximal, complemented
13#19144408C212yesmaximal, complemented
14#19143231C211yesmaximal, characteristic, complemented
15C43×#3165C211yesmaximal, characteristic, complemented
16#14583526—22no—
17#14583526—22no—
18#14583526C2214yes—
19#14583526C2214yes—
20#14583523C2212yes—
21#14583523C2212yes—
22#14583512C2212yes—
23#14583505C2212yes—
24#14583498—21no—
25#14583498—21no—
26#14583489—21no—
27#14583489—21no—
28#14583449C2211yescharacteristic
29C2×#13063324C2211yescharacteristic
30C2×#13063323—21no—
31#14583436—22no—
32#14583436—22no—
33C2×#13063317C2211yescharacteristic
34C2×#13063316C2211yescharacteristic
35C2×#13063315—21no—
36#14583411C2212yes—
37C2×#13063303—21no—
38C2×#13063301—21no—
39#14583367C2212yes—
40C2×#13063283C2211yescharacteristic
41C2×#13063282C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583305C2212yescomplemented
44#14583305C2212yescomplemented
45#14583298C2214yescomplemented
46#14583268C2212yescomplemented
47#14583264C2212yescomplemented
48#14583261C2214yescomplemented
49#14583254C2214yescomplemented
50#14583251C2212yescomplemented
51#14583247C2212yescomplemented
52#14583243C2214yes—
53#14583242C2214yes—
54#14583236C2214yes—
55#14583231C2214yes—
56#14583226C2214yes—
57#14583225C2214yes—
58#14583219C2214yes—
59#14583214C2214yes—
60#14583209C2214yescomplemented
61#14583205C2214yescomplemented
62#14583202C2214yescomplemented
63#14583198C2214yescomplemented
64#14583193C2214yescomplemented
65#14583188C2214yescomplemented
66#14583183C2214yescomplemented
67#14583178C2214yescomplemented
68#14582961C2214yes—
69#14582958C2214yes—
70#14582942C2212yes—
71#14582942C2212yes—
72#14582922C2212yes—
73#14582901C2212yes—
74#14582901C2212yes—
75#14582898C2212yes—
76#14582898C2212yes—
77#14582862C2212yes—
78C4×#10621877C2211yescharacteristic
79C43×#533C2211yescharacteristic
80C2×C4⋊Q8×C43C2211yescharacteristic
81C43×#501C2214yescomplemented
82C43×#500C2212yescomplemented
83C43×#498C2212yescomplemented
84C43×#428C2212yes—
85C43×#428C2212yes—
86C4×M16×C43C2211yescharacteristic
87C2×#10621898C2312yes—
88C22×Dic86—21no—
89C22×C4×D43—21no—
90C22×C4×D43C2311yescharacteristic
91C2×#10621877C2312yes—
92#13063325C2311yescharacteristic
93#13063324—22no—
94#13063324C2314yes—
95#13063323—24no—
96#13063323—24no—
97#13063322C2311yescharacteristic
98#13063320—22no—
99#13063320—22no—
100#13063320—22no—
101#13063320—22no—
102#13063317—21no—
103#13063317—21no—
104#13063317C2312yes—
105#13063317C2312yes—
106#13063316—22no—
107#13063316—22no—
108#13063316—22no—
109#13063316C2314yes—
110#13063315—24no—
111#13063315—24no—
112#13063314—22no—
113#13063314—22no—
114#13063313C2312yes—
115#13063310—22no—
116#13063310—22no—
117#13063310—22no—
118#13063310—22no—
119#13063309—22no—
120#13063305C2312yes—
121#13063305C2312yes—
122#13063303—24no—
123#13063303—24no—
124#13063301—24no—
125#13063301—24no—
126#13063301—22no—
127#13063301—22no—
128#13063300—22no—
129#13063300—22no—
130#13063300C2312yes—
131#13063300C2312yes—
132#13063299—21no—
133#13063299—21no—
134#13063295—22no—
135#13063290C2312yes—
136#13063290C2312yes—
137C4×D172—22no—
138C4×D172—22no—
139C4×D172—21no—
140C4×D172—21no—
141#13063287C2312yes—
142#13063287C2312yes—
143(C22⋊D43)⋊C4—22no—
144(C22⋊D43)⋊C4—22no—
145#13063283—22no—
146#13063283C2314yes—
147#13063282—22no—
148#13063282D412yes—
149#13063282D412yes—
150#13063282C2312yes—
151#13063282C2312yes—
152C2×C4⋊Dic43—21no—
153C2×C4⋊Dic43C2311yescharacteristic
154C2×C4⋊Dic43C2311yescharacteristic
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4D411yescharacteristic
161C2×Dic43⋊C4D411yescharacteristic
162C4⋊C4×D43—22no—
163C4⋊C4×D43C2314yes—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4D411yescharacteristic
166C2×(C2×D43)⋊C4D411yescharacteristic
167C2×C4×Dic43—21no—
168C2×C4×Dic43C2311yescharacteristic
169C42×D43—22no—
170#13063258C2314yes—
171#13063258C2314yes—
172#13063256C2314yes—
173#13063256C2314yes—
174Dic43⋊C8C2314yes—
175Dic43⋊C8C2314yes—
176#13063250C2314yes—
177#13063250C2314yes—
178#13063248C2314yes—
179#13063248C2314yes—
180#13063247C2314yes—
181#13063247C2314yes—
182#13063245C2314yes—
183#13063245C2314yes—
184(C2×D43)⋊C8C2314yes—
185(C2×D43)⋊C8C2314yes—
186#13063236C2312yes—
187C4×C43⋊C8C2312yes—
188C22×Q8×C43—21no—
189C2×M16×C43C2312yes—
190C4⋊Q8×C43—21no—
191C4⋊Q8×C43—21no—
192C4⋊Q8×C43C2311yescharacteristic
193C4⋊Q8×C43C2312yes—
194C4⋊Q8×C43C2311yescharacteristic
195C4⋊Q8×C43C2312yes—
196#125×C43C2312yes—
197C22⋊Q8×C43—21no—
198C22⋊Q8×C43—21no—
199C4×Q8×C43—21no—
200C4×Q8×C43—21no—
201#117×C43C2312yes—
202C2×C4⋊C4×C43—21no—
203C2×C4⋊C4×C43C2311yescharacteristic
204C2×C4⋊C4×C43C2311yescharacteristic
205C2×C42×C43C2311yescharacteristic
206#107×C43C2314yes—
207#107×C43C2314yes—
208#106×C43C2314yes—
209#106×C43C2314yes—
210#97×C43C2312yes—
211C4×C8×C43C2312yes—
212C23×D43C2×D411yescharacteristic
213C2×Q8×C43—21no—
214C2×Q8×C43—21no—
215C2×Q8×C43—22no—
216C2×Q8×C43—22no—
217C2×Q8×C43—82no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2411yescharacteristic
223C2×C22⋊D43—22no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229#10621898—28no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172C2412yes—
235C2×C4×D43—24no—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—22no—
239C2×C4×D43—24no—
240C2×C4×D43—82no—
241C2×C4×D43C2×D412yes—
242C2×C4×D43C2412yes—
243C2×Dic86—24no—
244C2×Dic86—82no—
245C2×Dic86C2412yes—
246M16×C43—24no—
247C2×C8×C43C2414yes—
248C4⋊C4×C43—22no—
249C4⋊C4×C43—22no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—22no—
253C4⋊C4×C43—22no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C2412yes—
257C4⋊C4×C43C2412yes—
258C4⋊C4×C43C2412yes—
259C4⋊C4×C43C2412yes—
260C22⋊C4×C43—22no—
261C42×C43—22no—
262C42×C43C2×D411yescharacteristic
263C42×C43C2×D411yescharacteristic
264C42×C43C2411yescharacteristic
265C42×C43C2411yescharacteristic
266(C2×D43)⋊C4—22no—
267(C2×D43)⋊C4—22no—
268(C2×D43)⋊C4—22no—
269(C2×D43)⋊C4—22no—
270(C2×D43)⋊C4—22no—
271(C2×D43)⋊C4—22no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—22no—
274(C2×D43)⋊C4—22no—
275(C2×D43)⋊C4C2×D412yes—
276(C2×D43)⋊C4C2×D412yes—
277(C2×D43)⋊C4C2×D412yes—
278(C2×D43)⋊C4C2×D412yes—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—24no—
284C4⋊Dic43—22no—
285C4⋊Dic43—22no—
286C4⋊Dic43C2412yes—
287C4⋊Dic43C2412yes—
288Dic43⋊C4—22no—
289Dic43⋊C4—22no—
290Dic43⋊C4—22no—
291Dic43⋊C4—22no—
292Dic43⋊C4—24no—
293Dic43⋊C4—24no—
294Dic43⋊C4—24no—
295Dic43⋊C4—22no—
296Dic43⋊C4—22no—
297Dic43⋊C4C2×D412yes—
298Dic43⋊C4C2×D412yes—
299Dic43⋊C4C2×D412yes—
300Dic43⋊C4C2×D412yes—
301C4×Dic43—22no—
302C4×Dic43—22no—
303C4×Dic43—24no—
304C4×Dic43C2×D412yes—
305C4×Dic43C2412yes—
306#10621877—24no—
307C2×C43⋊C8C2414yes—
308C23×C43C22×D411yescharacteristic
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43C22×D412yes—
314Q8×C43—81no—
315Q8×C43—81no—
316Q8×C43—82no—
317Q8×C43—82no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C432−1+414yes—
332C2×C4×C43C2511yescharacteristic
333C22⋊D43—44no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43C22×D412yes—
343C2×Dic43C22×D412yes—
344C2×Dic43C22×D412yes—
345D172—24no—
346D172—81no—
347D172—81no—
348D172—82no—
349D172—82no—
350C4×D43—24no—
351C4×D43—24no—
352C4×D43—44no—
353C4×D43—82no—
354C4×D43—82no—
355C4×D43—84no—
356Dic86—24no—
357Dic86—84no—
358C8×C43—24no—
359C43⋊C8—24no—
360#60867—431nomaximal, Sylow
361C22×C43—21no—
362C22×C43—21no—
363C22×C43#53612yes—
364C22×C43C23×D411yescharacteristic
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—44no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C4×C43—21no—
373C4×C43—21no—
374C4×C43—21no—
375C4×C43—21no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43—42no—
379C4×C43—42no—
380C4×C43#53612yes—
381C4×C43C2×2−1+412yes—
382Dic43—22no—
383Dic43—22no—
384Dic43—22no—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388C2×#544—431no—
389#3455—431no—
390#3244—434no—
391#3243—434no—
392#3242—434no—
393#3241—434no—
394#3166—431no—
395#3165D4311yescharacteristic, complemented
396#3142—431no—
397#3141—431no—
398#3093—432no—
399#3092—432no—
400#3080—432no—
401#3079—432no—
402#2921—431no—
403C2×C43—22no—
404C2×C43C2×#53611yescharacteristic
405C2×C43#358511yescharacteristic
406C2×C43#358611yescharacteristic
407D43—42no—
408D43—82no—
409#544—434no—
410#544—434no—
411#544—862no—
412#544—862no—
413#542—432no—
414#542—432no—
415#541—432no—
416#540—432no—
417#539—861no—
418#539—861no—
419#538—861no—
420#538—861no—
421#533C2×D4311yescharacteristic
422#532—431no—
423C2×C4⋊Q8—431no—
424C2×C4⋊Q8—861no—
425C2×C4⋊Q8C2×D4311yescharacteristic
426#529—862no—
427#529—862no—
428C2×#125—431no—
429C2×#125—431no—
430C2×#125—861no—
431#525—432no—
432C2×C22⋊Q8—861no—
433C2×C22⋊Q8—861no—
434C4×#41—432no—
435C2×#117—431no—
436C2×#117—431no—
437C22×C4⋊C4—431no—
438#501—432no—
439#501—432no—
440#501C2×D4314yescomplemented
441#500C2×D4312yescomplemented
442#499—434no—
443#498C2×D4312yescomplemented
444#491—432no—
445#490—432no—
446#489—434no—
447#488—434no—
448#487—432no—
449#486—432no—
450#485—434no—
451#485—434no—
452#484—434no—
453#483—434no—
454#482—434no—
455#482—434no—
456#481—434no—
457#480—434no—
458#479—434no—
459#479—434no—
460#478—434no—
461#478—434no—
462#477—434no—
463#476—434no—
464#475—434no—
465#474—434no—
466#433—434no—
467#433—434no—
468#428—432no—
469#428—432no—
470#428C2×D4312yes—
471#428C2×D4312yes—
472#423—432no—
473#417—432no—
474#417—432no—
475#417—432no—
476#417—432no—
477#407—432no—
478C4×M16—431no—
479C4×M16C2×D4311yescharacteristic
480C43#6086711yescharacteristic, complemented, Sylow
481C2×#41—432no—
482C22×Q8—21no—
483C22×Q8—861no—
484C23×C4—431no—
485C23×C4—861no—
486C2×M16—432no—
487C2×M16C22×D4312yes—
488C4⋊Q8—21no—
489C4⋊Q8—21no—
490C4⋊Q8—434no—
491C4⋊Q8—431no—
492C4⋊Q8—862no—
493C4⋊Q8—864no—
494C4⋊Q8—864no—
495C4⋊Q8C22×D4312yes—
496C4⋊Q8C22×D4312yes—
497C4⋊Q8C22×D4311yescharacteristic
498C4⋊Q8C22×D4311yescharacteristic
499#127—431no—
500#126—862no—
501#126—862no—
502#126—862no—
503#126—862no—
504#125—434no—
505#125—432no—
506#125—432no—
507#125—862no—
508#125—864no—
509#125—864no—
510#125—862no—
511#125—862no—
512#125—861no—
513#125—861no—
514#125C22×D4312yes—
515#124—432no—
516#124—862no—
517#124—862no—
518#123—862no—
519#123—862no—
520#123—862no—
521#123—862no—
522#123—862no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—432no—
526C22⋊Q8—432no—
527C22⋊Q8—864no—
528C22⋊Q8—864no—
529C22⋊Q8—864no—
530C22⋊Q8—864no—
531C22⋊Q8—862no—
532C22⋊Q8—862no—
533#121—432no—
534#121—432no—
535#121—862no—
536#121—862no—
537#121—861no—
538#121—861no—
539#120—862no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—432no—
543C4×Q8—432no—
544C4×D4—432no—
545C4×D4—432no—
546C4×D4—862no—
547C4×D4—862no—
548C4×D4—862no—
549C4×D4—862no—
550C4×D4—861no—
551C4×D4—861no—
552#117—432no—
553#117—432no—
554#117—432no—
555#117—432no—
556#117—434no—
557#117—862no—
558#117—862no—
559#117C22×D4312yes—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—434no—
566C2×C4⋊C4—862no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4C22×D4311yescharacteristic
574C2×C4⋊C4C22×D4311yescharacteristic
575C2×C22⋊C4—431no—
576C2×C22⋊C4—431no—
577C2×C22⋊C4—861no—
578C2×C42—431no—
579C2×C42—862no—
580C2×C42—861no—
581C2×C42C22×D4311yescharacteristic
582#107—434no—
583#107—434no—
584#107C22×D4314yes—
585#107C22×D4314yes—
586#106—434no—
587#106—434no—
588#106C22×D4314yes—
589#106C22×D4314yes—
590C4⋊C8—434no—
591C4⋊C8—434no—
592#103—434no—
593#103—434no—
594#103—434no—
595#103—434no—
596#102—434no—
597#102—434no—
598#102—434no—
599#102—434no—
600C22⋊C8—434no—
601C22⋊C8—434no—
602#97—432no—
603#97C22×D4312yes—
604C4×C8—432no—
605C4×C8C22×D4312yes—
606C24—431no—
607#41—868no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—82no—
613C2×Q8—432no—
614C2×Q8—864no—
615C2×Q8—3442no—
616C2×D4—432no—
617C2×D4—862no—
618C2×D4—862no—
619C2×D4—862no—
620C2×D4—861no—
621C2×D4—861no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—432no—
628C22×C4—432no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—864no—
632C22×C4—864no—
633C22×C4—861no—
634C22×C4—861no—
635C22×C4—862no—
636C22×C4—3442no—
637C22×C4D4×D4311yescharacteristic
638C22×C4D4×D4311yescharacteristic
639C22×C4C23×D4311yescharacteristic
640M16—24no—
641M16—864no—
642C2×C8—434no—
643C2×C8C23×D4314yes—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—432no—
653C4⋊C4—432no—
654C4⋊C4—432no—
655C4⋊C4—432no—
656C4⋊C4—432no—
657C4⋊C4—432no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—864no—
662C4⋊C4—862no—
663C4⋊C4—862no—
664C4⋊C4—862no—
665C4⋊C4—862no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—862no—
669C4⋊C4—862no—
670C4⋊C4—862no—
671C4⋊C4—862no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4C23×D4312yes—
675C4⋊C4C23×D4312yes—
676C4⋊C4C23×D4312yes—
677C4⋊C4C23×D4312yes—
678C22⋊C4—22no—
679C22⋊C4—432no—
680C22⋊C4—432no—
681C22⋊C4—432no—
682C22⋊C4—432no—
683C22⋊C4—862no—
684C22⋊C4—862no—
685C22⋊C4—862no—
686C22⋊C4—862no—
687C22⋊C4—864no—
688C22⋊C4—862no—
689C22⋊C4—862no—
690C22⋊C4—862no—
691C22⋊C4—862no—
692C42—22no—
693C42—432no—
694C42—432no—
695C42—864no—
696C42—862no—
697C42—862no—
698C42D4×D4311yescharacteristic
699C42D4×D4311yescharacteristic
700C42C23×D4311yescharacteristic
701C42C23×D4311yescharacteristic
702C23—432no—
703C23—862no—
704C23—862no—
705C23—1721no—
706C23—1721no—
707C23C2×D4×D4311yescharacteristic
708Q8—82no—
709Q8—82no—
710Q8—81no—
711Q8—81no—
712Q8—864no—
713Q8—3444no—
714D4—864no—
715D4—3441no—
716D4—3441no—
717D4—3442no—
718D4—3442no—
719D4—1724no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—432no—
729C2×C4—432no—
730C2×C4—432no—
731C2×C4—862no—
732C2×C4—864no—
733C2×C4—864no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—3442no—
738C2×C4—3442no—
739C2×C4—3444no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1722no—
743C2×C4—1722no—
744C2×C4—1724no—
745C2×C4C2×D4×D4311yescharacteristic
746C2×C4C2×D4×D4311yescharacteristic
747C2×C4C2×D4×D4311yescharacteristic
748C2×C4C2×D4×D4311yescharacteristic
749C2×C4C2×D4×D4311yescharacteristic
750C2×C4#1306337314yes—
751C2×C4C24×D4311yescharacteristic
752C8—24no—
753C8—864no—
754C22—21no—
755C22—21no—
756C22—862no—
757C22—862no—
758C22—862no—
759C22—1724no—
760C22—1722no—
761C22—1722no—
762C22—1722no—
763C22#1458347412yes—
764C22C22×D4×D4311yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—862no—
774C4—862no—
775C4—862no—
776C4—1722no—
777C4—1722no—
778C4—1722no—
779C4#1458347412yes—
780C4C2×#1306337312yes—
781C2—22no—
782C2—3442no—
783C2—1722no—
784C2C2×#1458347411yescharacteristic
785C2#1914937111yescharacteristic
786C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3165C2
socleC22×C43C23×D4
prime radical#19147987C2
hypercenter#3165D43
hypocenterC43#60867
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
1. C2×#14583526C2semidirect
3. #19145896C2semidirect
4. #19145881C2semidirect
5. #19145864C2semidirect
6. #19145849C2semidirect
7. #19145148C2semidirect
8. #19144996C2semidirect
9. #19144991C2semidirect
10. #19144529C2semidirect
11. #19144521C2semidirect
12. #19144416C2semidirect
13. #19144408C2semidirect
14. #19143231C2semidirect
15. C43×#3165C2semidirect
43. #14583305C22semidirect
44. #14583305C22semidirect
45. #14583298C22semidirect
46. #14583268C22semidirect
47. #14583264C22semidirect
48. #14583261C22semidirect
49. #14583254C22semidirect
50. #14583251C22semidirect
51. #14583247C22semidirect
60. #14583209C22semidirect
61. #14583205C22semidirect
62. #14583202C22semidirect
63. #14583198C22semidirect
64. #14583193C22semidirect
65. #14583188C22semidirect
66. #14583183C22semidirect
67. #14583178C22semidirect
81. C43×#501C22semidirect
82. C43×#500C22semidirect
83. C43×#498C22semidirect
395. #3165D43semidirect
440. #501C2×D43semidirect
441. #500C2×D43semidirect
443. #498C2×D43semidirect
480. C43#60867semidirect

Maximal subgroups

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

subgroupindex
C2×#145835262
#191479872
#191458962
#191458812
#191458642
#191458492
#191451482
#191449962
#191449912
#191445292
#191445212
#191444162
#191444082
#191432312
C43×#31652
#6086743