Finite Group Databasebeta

← #25966262

Subgroups — #25966262

Order 11008.

1798 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147998C211yesmaximal, characteristic
2C2×#14583526C211yesmaximal, characteristic
3#19145148C211yesmaximal, characteristic, complemented
4#19145147C211yesmaximal, characteristic, complemented
5#19145145C212yesmaximal, complemented
6#19145139C212yesmaximal, complemented
7#19145137C211yesmaximal, characteristic, complemented
8#19145130C214yesmaximal, complemented
9#19145128C214yesmaximal, complemented
10#19145122C214yesmaximal, complemented
11#19145120C214yesmaximal, complemented
12#19143182C212yesmaximal
13#428×D43C212yesmaximal
14#19143012C211yesmaximal, characteristic
15C43×#3165C211yesmaximal, characteristic, complemented
16C2×M16×D43C2212yes—
17#14583529C2212yes—
18#14583529C2212yes—
19#14583528—21no—
20#14583528—21no—
21#14583526—22no—
22#14583526—22no—
23#14583526C2212yes—
24#14583526C2214yes—
25#14583526C2214yes—
26#14583526C2212yes—
27#14583524—21no—
28#14583524—21no—
29#14583456C2211yescharacteristic
30#14583453—22no—
31#14583453—22no—
32#14583452C2212yes—
33C2×#13063324C2211yescharacteristic
34C2×#13063323—21no—
35C2×#13063317C2211yescharacteristic
36C2×#13063316C2211yescharacteristic
37C2×#13063315—21no—
38C2×#13063303—21no—
39C2×#13063301—21no—
40C2×#13063283C2211yescharacteristic
41C2×#13063282C2211yescharacteristic
42#117×D43C2212yes—
43C2×C4⋊C4×D43C2211yescharacteristic
44#14583308C2212yescomplemented
45#14583308C2212yescomplemented
46#14583307C2214yescomplemented
47#14583307C2214yescomplemented
48#14583306C2214yescomplemented
49#14583306C2214yescomplemented
50#14583305C2212yescomplemented
51#14583305C2214yescomplemented
52#14583305C2212yescomplemented
53#14583303C2214yescomplemented
54#14583302C2212yescomplemented
55#14583301C2214yescomplemented
56#14583300C2214yescomplemented
57#14583299C2214yescomplemented
58#14583298C2214yescomplemented
59#14583296C2214yescomplemented
60#14583295C2212yescomplemented
61#14582942C2212yes—
62#14582942C2212yes—
63#14582941C2212yes—
64#14582941C2212yes—
65#14582940C2214yes—
66#14582940C2214yes—
67#14582939C2212yes—
68#14582939C2212yes—
69#14582938C2214yes—
70#14582938C2214yes—
71#14582936C2214yes—
72#14582934C2214yes—
73#107×D43C2214yes—
74#106×D43C2214yes—
75#14582856C2214yes—
76#14582853C2214yes—
77C4×#10621877C2211yescharacteristic
78M16×Dic43C2212yes—
79C43×#533C2211yescharacteristic
80C2×C4⋊Q8×C43C2211yescharacteristic
81C43×#501C2214yescomplemented
82C43×#500C2212yescomplemented
83C43×#498C2212yescomplemented
84C43×#428C2212yes—
85C43×#428C2212yes—
86C4×M16×C43C2211yescharacteristic
87C22×Dic86—21no—
88C22×C4×D43—21no—
89C22×C4×D43C2311yescharacteristic
90C2×#10621877C2312yes—
91C2×#10621872C2314yes—
92M16×D43Q8116yescomplemented
93C2×C8×D43C2314yes—
94#13063325C2311yescharacteristic
95#13063325C2311yescharacteristic
96#13063324—22no—
97#13063324—22no—
98#13063324—22no—
99#13063324C2312yes—
100#13063324C2314yes—
101#13063324C2312yes—
102#13063323—24no—
103#13063323—24no—
104#13063323—22no—
105#13063323—22no—
106#13063317—21no—
107#13063317—21no—
108#13063317C2312yes—
109#13063317C2312yes—
110#13063317C2312yes—
111#13063316—22no—
112#13063316C2312yes—
113#13063316C2314yes—
114#13063316C2312yes—
115#13063315—24no—
116#13063315—24no—
117#13063315—22no—
118#13063315—22no—
119#13063315—22no—
120#13063315—22no—
121#13063305—22no—
122#13063305—22no—
123#13063304—21no—
124#13063304—21no—
125#13063303—24no—
126#13063303—24no—
127#13063303—22no—
128#13063303—22no—
129#13063303—22no—
130#13063303—22no—
131#13063302—22no—
132#13063302—22no—
133#13063301—24no—
134#13063301—24no—
135#13063301—22no—
136#13063301—22no—
137C4×Dic86—21no—
138C4×Dic86—21no—
139C4×Dic86—22no—
140C4×Dic86—22no—
141#13063284C2312yes—
142#13063283—22no—
143#13063283C2312yes—
144#13063283C2312yes—
145#13063283C2314yes—
146#13063282—22no—
147#13063282D412yes—
148#13063282D412yes—
149#13063282C2312yes—
150#13063282C2312yes—
151#13063281—22no—
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—
164C4⋊C4×D43C2312yes—
165C4⋊C4×D43C2312yes—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C2×(C2×D43)⋊C4D411yescharacteristic
169C22⋊C4×D43—22no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43C2311yescharacteristic
172C42×D43—22no—
173#13063259C2314yes—
174#13063259C2314yes—
175#13063258C2314yes—
176#13063258C2314yes—
177#13063258C2314yes—
178#13063258C2314yes—
179#13063257C2314yes—
180#13063257C2314yes—
181#13063256C2314yes—
182#13063256C2314yes—
183#13063256C2314yes—
184#13063256C2314yes—
185#13063236C2312yes—
186#13063235C2314yes—
187C4×C43⋊C8C2312yes—
188C8×Dic43C2314yes—
189C22×Q8×C43—21no—
190C2×M16×C43C2312yes—
191C4⋊Q8×C43—21no—
192C4⋊Q8×C43—21no—
193C4⋊Q8×C43C2311yescharacteristic
194C4⋊Q8×C43C2312yes—
195C4⋊Q8×C43C2311yescharacteristic
196C4⋊Q8×C43C2312yes—
197#125×C43C2312yes—
198C22⋊Q8×C43—21no—
199C22⋊Q8×C43—21no—
200C4×Q8×C43—21no—
201C4×Q8×C43—21no—
202#117×C43C2312yes—
203C2×C4⋊C4×C43—21no—
204C2×C4⋊C4×C43C2311yescharacteristic
205C2×C4⋊C4×C43C2311yescharacteristic
206C2×C42×C43C2311yescharacteristic
207#107×C43C2314yes—
208#107×C43C2314yes—
209#106×C43C2314yes—
210#106×C43C2314yes—
211#97×C43C2312yes—
212C4×C8×C43C2312yes—
213C23×D43C2×D411yescharacteristic
214C2×Q8×C43—21no—
215C2×Q8×C43—21no—
216C2×Q8×C43—22no—
217C2×Q8×C43—22no—
218C2×Q8×C43—82no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2411yescharacteristic
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43—24no—
232C2×C4×D43—82no—
233C2×C4×D43C2×D412yes—
234C2×C4×D43C2×Q818yes—
235C2×C4×D43C2412yes—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—22no—
239C2×Dic86—22no—
240C2×Dic86—24no—
241C2×Dic86—82no—
242M16×C43C2×Q818yes—
243C2×C8×C43C2414yes—
244C4⋊C4×C43—22no—
245C4⋊C4×C43—22no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—22no—
249C4⋊C4×C43—22no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43C2412yes—
253C4⋊C4×C43C2412yes—
254C4⋊C4×C43C2412yes—
255C4⋊C4×C43C2412yes—
256C22⋊C4×C43—22no—
257C42×C43—22no—
258C42×C43C2×D411yescharacteristic
259C42×C43C2×D411yescharacteristic
260C42×C43C2411yescharacteristic
261C42×C43C2411yescharacteristic
262C22⋊Dic43—22no—
263(C2×D43)⋊C4—22no—
264(C2×D43)⋊C4—22no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4C2×D412yes—
267(C2×D43)⋊C4C2×D412yes—
268(C2×D43)⋊C4C2×D412yes—
269(C2×D43)⋊C4C2×D412yes—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—24no—
275C4⋊Dic43—22no—
276C4⋊Dic43—22no—
277C4⋊Dic43C2412yes—
278C4⋊Dic43C2412yes—
279C4⋊Dic43C2412yes—
280C4⋊Dic43C2412yes—
281Dic43⋊C4—22no—
282Dic43⋊C4—22no—
283Dic43⋊C4—22no—
284Dic43⋊C4—22no—
285Dic43⋊C4—22no—
286Dic43⋊C4—22no—
287Dic43⋊C4—24no—
288Dic43⋊C4—22no—
289Dic43⋊C4—22no—
290Dic43⋊C4—24no—
291Dic43⋊C4—24no—
292Dic43⋊C4—22no—
293Dic43⋊C4—22no—
294Dic43⋊C4—22no—
295Dic43⋊C4—22no—
296Dic43⋊C4C2×D412yes—
297Dic43⋊C4C2×D412yes—
298Dic43⋊C4C2×D412yes—
299Dic43⋊C4C2×D412yes—
300C4×Dic43—22no—
301C4×Dic43—22no—
302C4×Dic43—22no—
303C4×Dic43—24no—
304C4×Dic43C2×D412yes—
305C4×Dic43C2412yes—
306#10621877C2×Q818yes—
307C2×C43⋊C8C2414yes—
308#10621872C2×Q8116yescomplemented
309C8×D43C2×Q8116yescomplemented
310C23×C43C22×D411yescharacteristic
311C22×D43—41no—
312C22×D43—41no—
313C22×D43C4⋊Q814yes—
314C22×D43C22×D412yes—
315Q8×C43—81no—
316Q8×C43—81no—
317Q8×C43—82no—
318Q8×C43—82no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C22×Q814yes—
333C2×C4×C43C2511yescharacteristic
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×Dic43C4⋊Q814yes—
343C2×Dic43C22×D412yes—
344C2×Dic43C22×D412yes—
345C2×Dic43C22×D412yes—
346C4×D43—82no—
347C4×D43—82no—
348C4×D43—84no—
349C4×D43C4⋊Q818yes—
350C4×D43C22×Q814yes—
351C4×D43C22×Q814yes—
352Dic86—82no—
353Dic86—82no—
354Dic86—84no—
355Dic86—81no—
356Dic86—81no—
357C8×C43C22×Q818yes—
358C43⋊C8C22×Q818yes—
359#60664—431nomaximal, Sylow
360C22×C43—21no—
361C22×C43—21no—
362C22×C43C2×C4⋊Q812yes—
363C22×C43C23×D411yescharacteristic
364C2×D43—22no—
365C2×D43—22no—
366C2×D43—44no—
367C2×D43C2×C4⋊Q814yes—
368C4×C43—21no—
369C4×C43—21no—
370C4×C43—21no—
371C4×C43—21no—
372C4×C43—42no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43C2×C4⋊Q812yes—
377C4×C43C23×Q812yes—
378Dic43—22no—
379Dic43—22no—
380Dic43—42no—
381Dic43—42no—
382Dic43—42no—
383Dic43—42no—
384Dic43C2×C4⋊Q814yes—
385#3458—431no—
386C2×#544—431no—
387#3166—432no—
388#3166—431no—
389#3166—431no—
390#3165—432no—
391#3165—431no—
392#3165D4311yescharacteristic, complemented
393#3164—434no—
394#3164—434no—
395#3163—434no—
396#3163—434no—
397#2911—432no—
398C2×#428—432no—
399#2873—431no—
400C2×C43—22no—
401C2×C43C22×C4⋊Q811yescharacteristic
402C2×C43#358511yescharacteristic
403C2×C43#358611yescharacteristic
404D43—24no—
405C22×M16—432no—
406#544—432no—
407#544—434no—
408#544—434no—
409#544—432no—
410#544—432no—
411#544—432no—
412#544—861no—
413#544—861no—
414#544—862no—
415#544—862no—
416#543—861no—
417#543—861no—
418#533—432no—
419#533—431no—
420#533—862no—
421#533—862no—
422#533C2×D4311yescharacteristic
423C2×C4⋊Q8—431no—
424C2×C4⋊Q8—861no—
425C2×C4⋊Q8C2×D4311yescharacteristic
426C2×#125—431no—
427C2×#125—431no—
428C2×#125—861no—
429C2×C22⋊Q8—861no—
430C2×C22⋊Q8—861no—
431C2×#117—431no—
432C2×#117—432no—
433C2×#117—431no—
434C22×C4⋊C4—431no—
435#501—432no—
436#501—434no—
437#501—432no—
438#501—434no—
439#501—434no—
440#501—434no—
441#501—434no—
442#501—432no—
443#501—432no—
444#501C2×D4314yescomplemented
445#500—432no—
446#500—434no—
447#500C2×D4312yescomplemented
448#499—434no—
449#499—434no—
450#499—434no—
451#499—434no—
452#498—432no—
453#498—434no—
454#498C2×D4312yescomplemented
455#428—432no—
456#428—432no—
457#428—432no—
458#428—432no—
459#428—432no—
460#428—432no—
461#428—434no—
462#428—434no—
463#428—434no—
464#428—434no—
465#428C2×D4312yes—
466#428C2×D4312yes—
467#427—434no—
468#427—434no—
469C2×#107—434no—
470C2×#106—434no—
471#405—434no—
472#405—434no—
473C4×M16—432no—
474C4×M16—431no—
475C4×M16C2×D4311yescharacteristic
476C43#6066411yescharacteristic, complemented, Sylow
477C22×Q8—21no—
478C22×Q8—861no—
479C23×C4—431no—
480C23×C4—861no—
481C2×M16—432no—
482C2×M16—4316no—
483C2×M16—434no—
484C2×M16C22×D4312yes—
485C22×C8—434no—
486C4⋊Q8—21no—
487C4⋊Q8—21no—
488C4⋊Q8—434no—
489C4⋊Q8—432no—
490C4⋊Q8—432no—
491C4⋊Q8—431no—
492C4⋊Q8—431no—
493C4⋊Q8—862no—
494C4⋊Q8—862no—
495C4⋊Q8—862no—
496C4⋊Q8—864no—
497C4⋊Q8—864no—
498C4⋊Q8—862no—
499C4⋊Q8—862no—
500C4⋊Q8C22×D4312yes—
501C4⋊Q8C22×D4312yes—
502C4⋊Q8C22×D4311yescharacteristic
503C4⋊Q8C22×D4311yescharacteristic
504#125—434no—
505#125—432no—
506#125—432no—
507#125—432no—
508#125—432no—
509#125—432no—
510#125—862no—
511#125—864no—
512#125—864no—
513#125—862no—
514#125—862no—
515#125—862no—
516#125—862no—
517#125—861no—
518#125—861no—
519#125C22×D4312yes—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—862no—
523C22⋊Q8—862no—
524C22⋊Q8—864no—
525C22⋊Q8—864no—
526C22⋊Q8—862no—
527C22⋊Q8—862no—
528C22⋊Q8—862no—
529C22⋊Q8—862no—
530C22⋊Q8—862no—
531C22⋊Q8—862no—
532C22⋊Q8—864no—
533C22⋊Q8—864no—
534C22⋊Q8—862no—
535C22⋊Q8—862no—
536C22⋊Q8—861no—
537C22⋊Q8—861no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—862no—
541C4×Q8—862no—
542C4×Q8—861no—
543C4×Q8—861no—
544#117—432no—
545#117—432no—
546#117—432no—
547#117—432no—
548#117—432no—
549#117—432no—
550#117—434no—
551#117—432no—
552#117—862no—
553#117—862no—
554#117—862no—
555#117C22×D4312yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—434no—
562C2×C4⋊C4—432no—
563C2×C4⋊C4—432no—
564C2×C4⋊C4—862no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4C22×D4311yescharacteristic
572C2×C4⋊C4C22×D4311yescharacteristic
573C2×C22⋊C4—431no—
574C2×C22⋊C4—431no—
575C2×C22⋊C4—862no—
576C2×C22⋊C4—861no—
577C2×C42—431no—
578C2×C42—862no—
579C2×C42—861no—
580C2×C42C22×D4311yescharacteristic
581#107—434no—
582#107—434no—
583#107—434no—
584#107—434no—
585#107—434no—
586#107—434no—
587#107C22×D4314yes—
588#107C22×D4314yes—
589#106—434no—
590#106—434no—
591#106—434no—
592#106—434no—
593#106—434no—
594#106—434no—
595#106C22×D4314yes—
596#106C22×D4314yes—
597#97—434no—
598#97—432no—
599#97C22×D4312yes—
600C4×C8—434no—
601C4×C8—432no—
602C4×C8C22×D4312yes—
603C24—431no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—82no—
609C2×Q8—862no—
610C2×Q8—862no—
611C2×Q8—864no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×Q8—3442no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—431no—
618C22×C4—432no—
619C22×C4—438no—
620C22×C4—432no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—864no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—3442no—
629C22×C4D4×D4311yescharacteristic
630C22×C4D4×D4311yescharacteristic
631C22×C4C23×D4311yescharacteristic
632M16—438no—
633M16—4316no—
634M16Q8×D4318yes—
635C2×C8—434no—
636C2×C8—4316no—
637C2×C8C23×D4314yes—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—432no—
647C4⋊C4—432no—
648C4⋊C4—432no—
649C4⋊C4—432no—
650C4⋊C4—432no—
651C4⋊C4—432no—
652C4⋊C4—432no—
653C4⋊C4—432no—
654C4⋊C4—864no—
655C4⋊C4—862no—
656C4⋊C4—862no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—862no—
661C4⋊C4—862no—
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—862no—
673C4⋊C4—862no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4C23×D4312yes—
677C4⋊C4C23×D4312yes—
678C4⋊C4C23×D4312yes—
679C4⋊C4C23×D4312yes—
680C22⋊C4—22no—
681C22⋊C4—432no—
682C22⋊C4—432no—
683C22⋊C4—432no—
684C22⋊C4—432no—
685C22⋊C4—862no—
686C22⋊C4—862no—
687C22⋊C4—864no—
688C22⋊C4—862no—
689C42—22no—
690C42—432no—
691C42—432no—
692C42—862no—
693C42—862no—
694C42—864no—
695C42—862no—
696C42D4×D4311yescharacteristic
697C42D4×D4311yescharacteristic
698C42C23×D4311yescharacteristic
699C42C23×D4311yescharacteristic
700C23—432no—
701C23—434no—
702C23—1721no—
703C23—1721no—
704C23C2×D4×D4311yescharacteristic
705Q8—82no—
706Q8—82no—
707Q8—81no—
708Q8—81no—
709Q8—3441no—
710Q8—3441no—
711Q8—3444no—
712Q8—3442no—
713Q8—3442no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—434no—
723C2×C4—432no—
724C2×C4—438no—
725C2×C4—434no—
726C2×C4—434no—
727C2×C4—432no—
728C2×C4—432no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—3444no—
734C2×C4—3442no—
735C2×C4—3442no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4C2×D4×D4311yescharacteristic
742C2×C4C2×D4×D4311yescharacteristic
743C2×C4C2×D4×D4311yescharacteristic
744C2×C4C2×D4×D4311yescharacteristic
745C2×C4C2×Q8×D4314yes—
746C2×C4C24×D4311yescharacteristic
747C8—438no—
748C8C2×Q8×D4318yes—
749C22—21no—
750C22—21no—
751C22—434no—
752C22—862no—
753C22—862no—
754C22—1724no—
755C22C4⋊Q8×D4312yes—
756C22C22×D4×D4311yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—434no—
766C4—862no—
767C4—862no—
768C4—1722no—
769C4—1722no—
770C4—1722no—
771C4—1722no—
772C4C4⋊Q8×D4312yes—
773C4C22×Q8×D4312yes—
774C2—22no—
775C2—864no—
776C2C2×C4⋊Q8×D4311yescharacteristic
777C2#1914937111yescharacteristic
778C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3165C2
socleC22×C43C23×D4
prime radicalC23×D43C2×D4
hypercenter#3165D43
hypocenterC43#60664
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
3. #19145148C2semidirect
4. #19145147C2semidirect
5. #19145145C2semidirect
6. #19145139C2semidirect
7. #19145137C2semidirect
8. #19145130C2semidirect
9. #19145128C2semidirect
10. #19145122C2semidirect
11. #19145120C2semidirect
15. C43×#3165C2semidirect
44. #14583308C22semidirect
45. #14583308C22semidirect
46. #14583307C22semidirect
47. #14583307C22semidirect
48. #14583306C22semidirect
49. #14583306C22semidirect
50. #14583305C22semidirect
51. #14583305C22semidirect
52. #14583305C22semidirect
53. #14583303C22semidirect
54. #14583302C22semidirect
55. #14583301C22semidirect
56. #14583300C22semidirect
57. #14583299C22semidirect
58. #14583298C22semidirect
59. #14583296C22semidirect
60. #14583295C22semidirect
81. C43×#501C22semidirect
82. C43×#500C22semidirect
83. C43×#498C22semidirect
92. M16×D43Q8semidirect
308. #10621872C2×Q8semidirect
309. C8×D43C2×Q8semidirect
392. #3165D43semidirect
444. #501C2×D43semidirect
447. #500C2×D43semidirect
454. #498C2×D43semidirect
476. C43#60664semidirect

Maximal subgroups

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

subgroupindex
#191479982
C2×#145835262
#191451482
#191451472
#191451452
#191451392
#191451372
#191451302
#191451282
#191451222
#191451202
#191431822
#428×D432
#191430122
C43×#31652
#6066443