Finite Group Databasebeta

← #25968938

Subgroups — #25968938

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×#14583527C211yesmaximal, characteristic, complemented
2#19145887C214yesmaximal, complemented
3#19145872C214yesmaximal, complemented
4#19145857C214yesmaximal, complemented
5#19145842C214yesmaximal, complemented
6#19145148C211yesmaximal, characteristic, complemented
7#19145142C211yesmaximal, characteristic, complemented
8#19144995C211yesmaximal, characteristic, complemented
9#19144988C211yesmaximal, characteristic, complemented
10#19144524C212yesmaximal, complemented
11#19144515C212yesmaximal, complemented
12#19144417C212yesmaximal, complemented
13#19144410C212yesmaximal, complemented
14#19143233C211yesmaximal, characteristic, complemented
15C43×#3455C211yesmaximal, characteristic
16#14583527—22no—
17#14583527—22no—
18#14583527C2214yes—
19#14583527C2214yes—
20C2×#13063325C2211yescharacteristic
21C2×#13063325C2211yescharacteristic
22C2×#13063324—21no—
23C2×#13063317C2211yescharacteristic
24C2×#13063317C2211yescharacteristic
25C2×#13063316—21no—
26C2×#13063302—21no—
27C2×#13063302—21no—
28C2×#13063284C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30#14583309C2214yescomplemented
31#14583305C2212yescomplemented
32#14583305C2212yescomplemented
33#14583302C2212yescomplemented
34#14583298C2214yescomplemented
35#14583295C2212yescomplemented
36#14583267C2212yescomplemented
37#14583263C2212yescomplemented
38#14583258C2214yescomplemented
39#14583253C2214yescomplemented
40#14583249C2212yescomplemented
41#14583245C2212yescomplemented
42#14583237C2214yes—
43#14583237C2214yes—
44#14583232C2214yes—
45#14583227C2214yes—
46#14583220C2214yes—
47#14583220C2214yes—
48#14583215C2214yes—
49#14583210C2214yes—
50#14583206C2214yescomplemented
51#14583206C2214yescomplemented
52#14583199C2214yescomplemented
53#14583199C2214yescomplemented
54#14583194C2214yescomplemented
55#14583189C2214yescomplemented
56#14583184C2214yescomplemented
57#14583179C2214yescomplemented
58#14582960C2214yes—
59#14582960C2214yes—
60#14582942C2212yes—
61#14582942C2212yes—
62#14582942C2212yes—
63#14582942C2212yes—
64#14582923C2212yes—
65#14582900C2212yes—
66#14582900C2212yes—
67#14582900C2212yes—
68#14582900C2212yes—
69#14582863C2212yes—
70C4×#10621877C2211yescharacteristic
71C4×#10621877C2211yescharacteristic
72C43×#542C2212yes—
73C43×#542C2212yes—
74C43×#541C2212yes—
75C43×#540C2212yes—
76C43×#539—21no—
77C43×#539—21no—
78C43×#538—21no—
79C43×#538—21no—
80C43×#533C2211yescharacteristic
81C43×#532C2211yescharacteristic
82C43×#529—22no—
83C43×#529—22no—
84C43×#525C2212yes—
85C4×#41×C43C2212yes—
86C2×#117×C43C2211yescharacteristic
87C22×Dic86—21no—
88C22×Dic86—21no—
89C23×Dic43—21no—
90C2×#10621877C2312yes—
91C2×#10621877C2312yes—
92#13063325—22no—
93#13063325—21no—
94#13063325—21no—
95#13063325C2312yes—
96#13063325C2312yes—
97#13063325C2314yes—
98#13063324—24no—
99#13063324—24no—
100#13063317—22no—
101#13063317—21no—
102#13063317—21no—
103#13063317C2312yes—
104#13063317C2312yes—
105#13063317C2314yes—
106#13063316—24no—
107#13063316—24no—
108#13063302—24no—
109#13063302—24no—
110#13063302—24no—
111#13063302—24no—
112#13063284—22no—
113#13063284C2314yes—
114C2×C4⋊Dic43—21no—
115C2×C4⋊Dic43—22no—
116C2×C4⋊Dic43—21no—
117C2×C4⋊Dic43—21no—
118C2×C4⋊Dic43C2311yescharacteristic
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2314yes—
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×C22⋊Dic43—21no—
128C2×C4×Dic43—21no—
129#13063258C2314yes—
130#13063258C2314yes—
131#13063258C2314yes—
132#13063258C2314yes—
133#13063256C2314yes—
134#13063256C2314yes—
135#13063256C2314yes—
136#13063256C2314yes—
137C4⋊(C43⋊C8)C2314yes—
138C4⋊(C43⋊C8)C2314yes—
139#13063249C2314yes—
140#13063249C2314yes—
141#13063249C2314yes—
142#13063249C2314yes—
143#13063246C2314yes—
144#13063246C2314yes—
145#13063246C2314yes—
146#13063246C2314yes—
147C22⋊(C43⋊C8)C2314yes—
148C22⋊(C43⋊C8)C2314yes—
149#13063236C2312yes—
150#13063236C2312yes—
151C4×C43⋊C8C2312yes—
152C4×C43⋊C8C2312yes—
153C2×#41×C43C2312yes—
154C23×C4×C43C2311yescharacteristic
155C4⋊Q8×C43C2311yescharacteristic
156C4⋊Q8×C43C2311yescharacteristic
157C4⋊Q8×C43C2311yescharacteristic
158#127×C43C2311yescharacteristic
159#126×C43—22no—
160#126×C43—22no—
161#126×C43—22no—
162#126×C43—22no—
163#125×C43—22no—
164#125×C43—22no—
165#125×C43C2312yes—
166#124×C43—22no—
167#124×C43—22no—
168#124×C43C2312yes—
169#123×C43—22no—
170#123×C43—22no—
171#123×C43—22no—
172#123×C43—22no—
173#123×C43—22no—
174C22⋊Q8×C43—21no—
175C22⋊Q8×C43—21no—
176C22⋊Q8×C43—22no—
177C22⋊Q8×C43—22no—
178C22⋊Q8×C43C2312yes—
179C22⋊Q8×C43C2312yes—
180#121×C43—21no—
181#121×C43—21no—
182#121×C43—22no—
183#121×C43—22no—
184#121×C43C2312yes—
185#121×C43C2312yes—
186#120×C43—22no—
187C4×Q8×C43—21no—
188C4×Q8×C43—21no—
189C4×Q8×C43C2312yes—
190C4×Q8×C43C2312yes—
191C4×D4×C43—22no—
192C4×D4×C43—22no—
193C4×D4×C43—22no—
194C4×D4×C43—22no—
195C4×D4×C43—21no—
196C4×D4×C43—21no—
197C4×D4×C43C2312yes—
198C4×D4×C43C2312yes—
199#117×C43—22no—
200#117×C43D412yes—
201#117×C43D412yes—
202#117×C43C2312yes—
203#117×C43C2312yes—
204#117×C43C2312yes—
205C2×C4⋊C4×C43D411yescharacteristic
206C2×C4⋊C4×C43D411yescharacteristic
207C2×C22⋊C4×C43D411yescharacteristic
208C2×C22⋊C4×C43D411yescharacteristic
209C2×C42×C43—22no—
210C2×C42×C43C2311yescharacteristic
211C2×C42×C43C2311yescharacteristic
212C24×C43C2×D411yescharacteristic
213#41×C43—28no—
214C2×Q8×C43—21no—
215C2×Q8×C43—21no—
216C2×Q8×C43C2412yes—
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—22no—
220C2×D4×C43—22no—
221C2×D4×C43—22no—
222C2×D4×C43C2412yes—
223C22×C4×C43—24no—
224C22×C4×C43—22no—
225C22×C4×C43—22no—
226C22×C4×C43—22no—
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2412yes—
234C22×C4×C43C2411yescharacteristic
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—24no—
240C22×Dic43—82no—
241C2×Dic86—24no—
242C2×Dic86—22no—
243C2×Dic86—22no—
244C2×Dic86—82no—
245C2×Dic86—82no—
246C4⋊C4×C43—22no—
247C4⋊C4×C43—22no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—22no—
251C4⋊C4×C43—22no—
252C4⋊C4×C43—22no—
253C4⋊C4×C43—22no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C2×D412yes—
257C4⋊C4×C43C2×D412yes—
258C4⋊C4×C43C2×D412yes—
259C4⋊C4×C43C2×D412yes—
260C4⋊C4×C43C2412yes—
261C4⋊C4×C43C2412yes—
262C22⋊C4×C43—22no—
263C22⋊C4×C43—22no—
264C22⋊C4×C43—22no—
265C22⋊C4×C43—22no—
266C22⋊C4×C43—22no—
267C22⋊C4×C43—22no—
268C22⋊C4×C43—22no—
269C22⋊C4×C43—22no—
270C22⋊C4×C43—22no—
271C22⋊C4×C43C2×D412yes—
272C22⋊C4×C43C2×D412yes—
273C22⋊C4×C43C2×D412yes—
274C22⋊C4×C43C2×D412yes—
275C42×C43—22no—
276C42×C43—22no—
277C42×C43—22no—
278C42×C43C2×D412yes—
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2412yes—
282C42×C43C2411yescharacteristic
283C42×C43C2411yescharacteristic
284C22⋊Dic43—24no—
285C4⋊Dic43—24no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—24no—
289C4⋊Dic43—22no—
290C4⋊Dic43—22no—
291C4⋊Dic43—21no—
292C4⋊Dic43—21no—
293C4⋊Dic43C2412yes—
294C4⋊Dic43C2412yes—
295C4⋊Dic43C2412yes—
296C4⋊Dic43C2412yes—
297Dic43⋊C4—24no—
298Dic43⋊C4—22no—
299Dic43⋊C4—22no—
300Dic43⋊C4—24no—
301Dic43⋊C4—22no—
302Dic43⋊C4—22no—
303C4×Dic43—24no—
304#10621877—24no—
305#10621877—24no—
306C2×C43⋊C8C2414yes—
307C2×C43⋊C8C2414yes—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43C22×D412yes—
313C23×C43C22×D411yescharacteristic
314Q8×C43—24no—
315Q8×C43—81no—
316Q8×C43—81no—
317D4×C43—24no—
318D4×C43—44no—
319D4×C43—81no—
320D4×C43—81no—
321D4×C43—82no—
322D4×C43—82no—
323C2×C4×C43—22no—
324C2×C4×C43—24no—
325C2×C4×C43—24no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—44no—
334C2×C4×C43—82no—
335C2×C4×C43—82no—
336C2×C4×C43C22×D412yes—
337C2×C4×C43C22×D412yes—
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D412yes—
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C432−1+414yes—
345C2×C4×C43C2511yescharacteristic
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—42no—
351C2×Dic43—42no—
352C2×Dic43—42no—
353C2×Dic43—42no—
354C2×Dic43—84no—
355Dic86—84no—
356Dic86—82no—
357Dic86—82no—
358C43⋊C8—24no—
359C43⋊C8—24no—
360#60867—431nomaximal, Sylow
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—44no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43#53612yes—
371C22×C43C23×D411yescharacteristic
372C4×C43—22no—
373C4×C43—21no—
374C4×C43—21no—
375C4×C43—22no—
376C4×C43—21no—
377C4×C43—21no—
378C4×C43—22no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43#53612yes—
383C4×C43C2×2−1+412yes—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388C2×#544—431no—
389#3455D4311yescharacteristic
390#3244—434no—
391#3243—434no—
392#3242—434no—
393#3241—434no—
394#3166—431no—
395#3165—431no—
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×C43—42no—
405C2×C43—82no—
406C2×C43C2×#53611yescharacteristic
407C2×C43#358511yescharacteristic
408C2×C43#358611yescharacteristic
409#544—434no—
410#544—434no—
411#544—862no—
412#544—862no—
413#542C2×D4312yes—
414#542C2×D4312yes—
415#541C2×D4312yes—
416#540C2×D4312yes—
417#539—21no—
418#539—21no—
419#538—21no—
420#538—21no—
421#533C2×D4311yescharacteristic
422#532C2×D4311yescharacteristic
423C2×C4⋊Q8—431no—
424C2×C4⋊Q8—431no—
425C2×C4⋊Q8—861no—
426#529—22no—
427#529—22no—
428C2×#125—431no—
429C2×#125—431no—
430C2×#125—861no—
431#525C2×D4312yes—
432C2×C22⋊Q8—861no—
433C2×C22⋊Q8—861no—
434C4×#41C2×D4312yes—
435C2×#117—431no—
436C2×#117C2×D4311yescharacteristic
437C22×C4⋊C4—431no—
438#501—432no—
439#501—432no—
440#501—434no—
441#500—432no—
442#499—434no—
443#498—432no—
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#428—432no—
471#428—432no—
472#423—432no—
473#417—432no—
474#417—432no—
475#417—432no—
476#417—432no—
477#407—432no—
478C4×M16—431no—
479C4×M16—431no—
480C43#6086711yescharacteristic, complemented, Sylow
481C2×#41C22×D4312yes—
482C22×Q8—861no—
483C22×Q8—861no—
484C23×C4—861no—
485C23×C4C22×D4311yescharacteristic
486C2×M16—432no—
487C2×M16—432no—
488C4⋊Q8—434no—
489C4⋊Q8—432no—
490C4⋊Q8—432no—
491C4⋊Q8—864no—
492C4⋊Q8—864no—
493C4⋊Q8—862no—
494C4⋊Q8—861no—
495C4⋊Q8—861no—
496C4⋊Q8C22×D4311yescharacteristic
497C4⋊Q8C22×D4311yescharacteristic
498C4⋊Q8C22×D4311yescharacteristic
499#127C22×D4311yescharacteristic
500#126—22no—
501#126—22no—
502#126—22no—
503#126—22no—
504#125—22no—
505#125—22no—
506#125—434no—
507#125—432no—
508#125—432no—
509#125—864no—
510#125—864no—
511#125—862no—
512#125—861no—
513#125—861no—
514#125C22×D4312yes—
515#124—22no—
516#124—22no—
517#124C22×D4312yes—
518#123—22no—
519#123—22no—
520#123—22no—
521#123—22no—
522#123—22no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—22no—
526C22⋊Q8—22no—
527C22⋊Q8—864no—
528C22⋊Q8—864no—
529C22⋊Q8—864no—
530C22⋊Q8—864no—
531C22⋊Q8C22×D4312yes—
532C22⋊Q8C22×D4312yes—
533#121—21no—
534#121—21no—
535#121—22no—
536#121—22no—
537#121C22×D4312yes—
538#121C22×D4312yes—
539#120—22no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8C22×D4312yes—
543C4×Q8C22×D4312yes—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—21no—
549C4×D4—21no—
550C4×D4C22×D4312yes—
551C4×D4C22×D4312yes—
552#117—22no—
553#117—434no—
554#117—862no—
555#117C22⋊D4312yes—
556#117C22⋊D4312yes—
557#117C22×D4312yes—
558#117C22×D4312yes—
559#117C22×D4312yes—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—434no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—861no—
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—861no—
576C2×C22⋊C4C22⋊D4311yescharacteristic
577C2×C22⋊C4C22⋊D4311yescharacteristic
578C2×C42—22no—
579C2×C42—861no—
580C2×C42C22×D4311yescharacteristic
581C2×C42C22×D4311yescharacteristic
582#107—434no—
583#107—434no—
584#107—434no—
585#107—434no—
586#106—434no—
587#106—434no—
588#106—434no—
589#106—434no—
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#97—432no—
604C4×C8—432no—
605C4×C8—432no—
606C24C2×C22⋊D4311yescharacteristic
607#41—28no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—864no—
611C2×Q8—862no—
612C2×Q8—862no—
613C2×Q8—3442no—
614C2×Q8—3442no—
615C2×Q8C23×D4312yes—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4C23×D4312yes—
622C22×C4—24no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—864no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—3442no—
632C22×C4C2×C22⋊D4311yescharacteristic
633C22×C4C2×C22⋊D4312yes—
634C22×C4C2×C22⋊D4311yescharacteristic
635C22×C4C2×C22⋊D4311yescharacteristic
636C22×C4C2×C22⋊D4311yescharacteristic
637C22×C4C2×C22⋊D4311yescharacteristic
638C22×C4C23×D4312yes—
639C22×C4C23×D4311yescharacteristic
640M16—864no—
641M16—864no—
642C2×C8—434no—
643C2×C8—434no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—432no—
655C4⋊C4—432no—
656C4⋊C4—432no—
657C4⋊C4—432no—
658C4⋊C4—864no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—864no—
664C4⋊C4—862no—
665C4⋊C4—862no—
666C4⋊C4—864no—
667C4⋊C4—862no—
668C4⋊C4—862no—
669C4⋊C4—864no—
670C4⋊C4—862no—
671C4⋊C4—862no—
672C4⋊C4C2×C22⋊D4312yes—
673C4⋊C4C2×C22⋊D4312yes—
674C4⋊C4C2×C22⋊D4312yes—
675C4⋊C4C2×C22⋊D4312yes—
676C4⋊C4C23×D4312yes—
677C4⋊C4C23×D4312yes—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—864no—
688C22⋊C4C2×C22⋊D4312yes—
689C22⋊C4C2×C22⋊D4312yes—
690C22⋊C4C2×C22⋊D4312yes—
691C22⋊C4C2×C22⋊D4312yes—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—864no—
696C42C2×C22⋊D4312yes—
697C42C2×C22⋊D4311yescharacteristic
698C42C2×C22⋊D4311yescharacteristic
699C42C23×D4311yescharacteristic
700C42C23×D4311yescharacteristic
701C42C23×D4312yes—
702C23—22no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23C22×C22⋊D4312yes—
707C23C22×C22⋊D4311yescharacteristic
708Q8—24no—
709Q8—81no—
710Q8—81no—
711Q8—3444no—
712Q8—3442no—
713Q8—3442no—
714D4—24no—
715D4—44no—
716D4—81no—
717D4—81no—
718D4—82no—
719D4—82no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—44no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—3444no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4C22×C22⋊D4312yes—
743C2×C4C22×C22⋊D4312yes—
744C2×C4C22×C22⋊D4312yes—
745C2×C4C22×C22⋊D4311yescharacteristic
746C2×C4C22×C22⋊D4311yescharacteristic
747C2×C4C22×C22⋊D4311yescharacteristic
748C2×C4C22×C22⋊D4311yescharacteristic
749C2×C4C22×C22⋊D4311yescharacteristic
750C2×C4#1306337214yes—
751C2×C4C24×D4311yescharacteristic
752C8—864no—
753C8—864no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22#1458347012yes—
764C22C23×C22⋊D4311yescharacteristic
765C4—22no—
766C4—21no—
767C4—21no—
768C4—22no—
769C4—21no—
770C4—21no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—1722no—
776C4—1722no—
777C4—1722no—
778C4—1722no—
779C4#1458347012yes—
780C4C2×#1306337212yes—
781C2—22no—
782C2—42no—
783C2—82no—
784C2C2×#1458347011yescharacteristic
785C2#1914937411yescharacteristic
786C2#1914938111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
Fitting, prime radicalC43×#3455C2
socleC22×C43C23×D4
hypercenter#3455D43
hypocenterC43#60867
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. C2×#14583527C2semidirect
2. #19145887C2semidirect
3. #19145872C2semidirect
4. #19145857C2semidirect
5. #19145842C2semidirect
6. #19145148C2semidirect
7. #19145142C2semidirect
8. #19144995C2semidirect
9. #19144988C2semidirect
10. #19144524C2semidirect
11. #19144515C2semidirect
12. #19144417C2semidirect
13. #19144410C2semidirect
14. #19143233C2semidirect
30. #14583309C22semidirect
31. #14583305C22semidirect
32. #14583305C22semidirect
33. #14583302C22semidirect
34. #14583298C22semidirect
35. #14583295C22semidirect
36. #14583267C22semidirect
37. #14583263C22semidirect
38. #14583258C22semidirect
39. #14583253C22semidirect
40. #14583249C22semidirect
41. #14583245C22semidirect
50. #14583206C22semidirect
51. #14583206C22semidirect
52. #14583199C22semidirect
53. #14583199C22semidirect
54. #14583194C22semidirect
55. #14583189C22semidirect
56. #14583184C22semidirect
57. #14583179C22semidirect
480. C43#60867semidirect

Maximal subgroups

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

subgroupindex
C2×#145835272
#191458872
#191458722
#191458572
#191458422
#191451482
#191451422
#191449952
#191449882
#191445242
#191445152
#191444172
#191444102
#191432332
C43×#34552
#6086743