Finite Group Databasebeta

← #25968974

Subgroups — #25968974

Order 11008.

1690 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147998C211yesmaximal, characteristic, complemented
2C2×#14583523C211yesmaximal, characteristic
3#19145896C214yesmaximal, complemented
4#19145894C214yesmaximal, complemented
5#19145881C214yesmaximal, complemented
6#19145879C214yesmaximal, complemented
7#19145137C211yesmaximal, characteristic, complemented
8#19144984C211yesmaximal, characteristic, complemented
9#19144982C211yesmaximal, characteristic, complemented
10#19144545C212yesmaximal, complemented
11#19144537C212yesmaximal
12#19144399C212yesmaximal, complemented
13#19144391C212yesmaximal, complemented
14#19143231C211yesmaximal, characteristic, complemented
15C43×#3165C211yesmaximal, characteristic, complemented
16#14583529C2212yescomplemented
17#14583529C2212yescomplemented
18#14583528—21no—
19#14583528—21no—
20#14583526C2212yescomplemented
21#14583526C2212yescomplemented
22#14583524—21no—
23#14583524—21no—
24#14583523—22no—
25#14583523—22no—
26#14583523C2214yes—
27#14583523C2214yes—
28#14583456C2211yescharacteristic
29#14583453—22no—
30#14583453—22no—
31#14583452C2212yes—
32C2×#13063320—21no—
33C2×#13063314—21no—
34C2×#13063313C2211yescharacteristic
35C2×#13063310—21no—
36C2×#13063305C2211yescharacteristic
37C2×#13063301—21no—
38C2×#13063300C2211yescharacteristic
39C2×#13063290C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×#13063282C2211yescharacteristic
42#117×D43C2212yes—
43#14583305C2214yescomplemented
44#14583302C2212yescomplemented
45#14583295C2212yescomplemented
46#14583261C2212yescomplemented
47#14583261C2212yescomplemented
48#14583259C2212yescomplemented
49#14583259C2212yescomplemented
50#14583256C2214yescomplemented
51#14583254C2214yescomplemented
52#14583243C2214yescomplemented
53#14583242C2214yescomplemented
54#14583236C2214yescomplemented
55#14583231C2214yescomplemented
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#14582961C2214yescomplemented
69#14582958C2214yescomplemented
70#14582939C2212yes—
71#14582939C2212yes—
72#14582922C2212yes—
73#14582909C2212yes—
74#14582907C2212yes—
75#14582905C2212yes—
76#14582903C2212yes—
77#14582862C2212yes—
78C4×#10621877C2211yescharacteristic
79C43×#533C2211yescharacteristic
80C2×C4⋊Q8×C43C2211yescharacteristic
81C43×#501C2214yescomplemented
82C43×#500C2212yescomplemented
83C43×#498C2212yescomplemented
84C43×#428C2212yes—
85C43×#428C2212yes—
86C4×M16×C43C2211yescharacteristic
87C22×Dic86C2311yescharacteristic
88C22×D172—21no—
89C22×D172C2311yescharacteristic
90C22×C4×D43—21no—
91C22×C4×D43C2311yescharacteristic
92C2×#10621877C2312yes—
93#13063325C2311yescharacteristic
94#13063325C2311yescharacteristic
95#13063324—22no—
96#13063324—22no—
97#13063324C2312yes—
98#13063324C2312yes—
99#13063323—22no—
100#13063323—22no—
101#13063320—24no—
102#13063320—24no—
103#13063317C2312yes—
104#13063316C2312yes—
105#13063316C2312yes—
106#13063315—22no—
107#13063315—22no—
108#13063315—22no—
109#13063315—22no—
110#13063314—24no—
111#13063314—24no—
112#13063313—21no—
113#13063313—21no—
114#13063313C2312yes—
115#13063313C2312yes—
116#13063310—24no—
117#13063310—24no—
118#13063305—22no—
119#13063305—22no—
120#13063305—22no—
121#13063305C2314yes—
122#13063304—21no—
123#13063304—21no—
124#13063303—22no—
125#13063303—22no—
126#13063303—22no—
127#13063303—22no—
128#13063302—22no—
129#13063302—22no—
130#13063301—22no—
131#13063301—22no—
132#13063301—24no—
133#13063301—24no—
134#13063300—22no—
135#13063300C2314yes—
136C4×Dic86—21no—
137C4×Dic86—21no—
138C4×Dic86—22no—
139C4×Dic86—22no—
140#13063290—22no—
141#13063290C2314yes—
142#13063287—22no—
143#13063287C2314yes—
144#13063284C2312yes—
145#13063283C2312yes—
146#13063283C2312yes—
147#13063282—22no—
148#13063282D412yes—
149#13063282D412yes—
150#13063282C2312yes—
151#13063282C2312yes—
152#13063281—22no—
153C2×C4⋊Dic43—21no—
154C2×Dic43⋊C4—21no—
155C2×Dic43⋊C4D411yescharacteristic
156C2×Dic43⋊C4D411yescharacteristic
157C4⋊C4×D43C2312yes—
158C4⋊C4×D43C2312yes—
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4D411yescharacteristic
165C2×(C2×D43)⋊C4D411yescharacteristic
166C22⋊C4×D43—22no—
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×D43—21no—
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×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C2×D172—21no—
229C2×D172—24no—
230C2×D172—24no—
231C2×D172—82no—
232C2×D172C2412yes—
233C2×C4×D43—24no—
234C2×C4×D43—24no—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—82no—
238C2×C4×D43C2×D412yes—
239C2×C4×D43C2412yes—
240C2×Dic86—24no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—22no—
245C2×Dic86—22no—
246C2×Dic86C2412yes—
247M16×C43—24no—
248C2×C8×C43C2414yes—
249C4⋊C4×C43—22no—
250C4⋊C4×C43—22no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—22no—
254C4⋊C4×C43—22no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C2412yes—
258C4⋊C4×C43C2412yes—
259C4⋊C4×C43C2412yes—
260C4⋊C4×C43C2412yes—
261C22⋊C4×C43—22no—
262C42×C43—22no—
263C42×C43C2×D411yescharacteristic
264C42×C43C2×D411yescharacteristic
265C42×C43C2411yescharacteristic
266C42×C43C2411yescharacteristic
267C22⋊Dic43—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—24no—
274(C2×D43)⋊C4—22no—
275(C2×D43)⋊C4—22no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4C2×D412yes—
278(C2×D43)⋊C4C2×D412yes—
279(C2×D43)⋊C4C2×D412yes—
280(C2×D43)⋊C4C2×D412yes—
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—22no—
294Dic43⋊C4—22no—
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—22no—
304C4×Dic43—24no—
305C4×Dic43C2×D412yes—
306C4×Dic43C2412yes—
307#10621877—24no—
308C2×C43⋊C8C2414yes—
309C23×C43C22×D411yescharacteristic
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—42no—
315C22×D43—42no—
316C22×D43—42no—
317C22×D43C22×D412yes—
318Q8×C43—81no—
319Q8×C43—81no—
320Q8×C43—82no—
321Q8×C43—82no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C432−1+414yes—
336C2×C4×C43C2511yescharacteristic
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—42no—
344C2×Dic43C22×D412yes—
345C2×Dic43C22×D412yes—
346C2×Dic43C22×D412yes—
347D172—24no—
348D172—42no—
349D172—84no—
350C4×D43—24no—
351C4×D43—24no—
352C4×D43—84no—
353C4×D43—82no—
354C4×D43—82no—
355Dic86—24no—
356Dic86—42no—
357Dic86—82no—
358Dic86—82no—
359Dic86—81no—
360Dic86—81no—
361C8×C43—24no—
362C43⋊C8—24no—
363#60870—431nomaximal, Sylow
364C22×C43—21no—
365C22×C43—21no—
366C22×C43#53612yes—
367C22×C43C23×D411yescharacteristic
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—82no—
375C2×D43—84no—
376C4×C43—21no—
377C4×C43—21no—
378C4×C43—21no—
379C4×C43—21no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43#53612yes—
385C4×C43C2×2−1+412yes—
386Dic43—22no—
387Dic43—22no—
388Dic43—22no—
389Dic43—42no—
390Dic43—42no—
391Dic43—42no—
392#3458—431no—
393C2×#542—431no—
394#3244—434no—
395#3244—434no—
396#3243—434no—
397#3243—434no—
398#3165—431no—
399#3165D4311yescharacteristic, complemented
400#3140—431no—
401#3140—431no—
402#3095—432no—
403#3094—432no—
404#3078—432no—
405#3077—432no—
406#2921—431no—
407C2×C43—22no—
408C2×C43C2×#53611yescharacteristic
409C2×C43#358511yescharacteristic
410C2×C43#358611yescharacteristic
411D43—42no—
412D43—82no—
413#544—432no—
414#544—432no—
415#544—432no—
416#544—432no—
417#544—861no—
418#544—861no—
419#543—861no—
420#543—861no—
421#542—434no—
422#542—434no—
423#542—862no—
424#542—862no—
425#533—432no—
426#533—431no—
427#533—862no—
428#533—862no—
429#533C2×D4311yescharacteristic
430C2×C4⋊Q8C2×D4311yescharacteristic
431C2×#126—861no—
432C2×#124—431no—
433C2×#124—861no—
434C2×#123—861no—
435C2×C22⋊Q8—431no—
436C2×C22⋊Q8—861no—
437C2×#121—431no—
438C2×C4×Q8—431no—
439C2×C4×D4—431no—
440C2×#117—431no—
441C2×#117—432no—
442#501—434no—
443#501C2×D4314yescomplemented
444#500—432no—
445#500C2×D4312yescomplemented
446#498—432no—
447#498C2×D4312yescomplemented
448#489—432no—
449#489—432no—
450#489—432no—
451#489—432no—
452#488—434no—
453#488—434no—
454#485—434no—
455#485—434no—
456#484—434no—
457#483—434no—
458#482—434no—
459#482—434no—
460#481—434no—
461#480—434no—
462#479—434no—
463#479—434no—
464#478—434no—
465#478—434no—
466#477—434no—
467#476—434no—
468#475—434no—
469#474—434no—
470#433—434no—
471#433—434no—
472#428—432no—
473#428—432no—
474#428C2×D4312yes—
475#428C2×D4312yes—
476#423—432no—
477#419—432no—
478#419—432no—
479#418—432no—
480#418—432no—
481#407—432no—
482C4×M16—431no—
483C4×M16C2×D4311yescharacteristic
484C43#6087011yescharacteristic, complemented, Sylow
485C22×Q8—21no—
486C22×Q8—431no—
487C22×D4—431no—
488C22×D4—861no—
489C23×C4—431no—
490C23×C4—861no—
491C2×M16—432no—
492C2×M16C22×D4312yes—
493C4⋊Q8—21no—
494C4⋊Q8—21no—
495C4⋊Q8—432no—
496C4⋊Q8—432no—
497C4⋊Q8—431no—
498C4⋊Q8—431no—
499C4⋊Q8—862no—
500C4⋊Q8—862no—
501C4⋊Q8—862no—
502C4⋊Q8—862no—
503C4⋊Q8C22×D4312yes—
504C4⋊Q8C22×D4312yes—
505C4⋊Q8C22×D4311yescharacteristic
506C4⋊Q8C22×D4311yescharacteristic
507#126—864no—
508#126—864no—
509#125—432no—
510#125—432no—
511#125—432no—
512#125—862no—
513#125—862no—
514#125—862no—
515#125—862no—
516#125C22×D4312yes—
517#124—432no—
518#124—432no—
519#124—864no—
520#124—864no—
521#124—861no—
522#124—861no—
523#123—864no—
524#123—864no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—434no—
528C22⋊Q8—862no—
529C22⋊Q8—862no—
530C22⋊Q8—862no—
531C22⋊Q8—862no—
532C22⋊Q8—862no—
533C22⋊Q8—862no—
534C22⋊Q8—862no—
535C22⋊Q8—862no—
536C22⋊Q8—862no—
537C22⋊Q8—862no—
538C22⋊Q8—862no—
539C22⋊Q8—864no—
540C22⋊Q8—864no—
541C22⋊Q8—861no—
542C22⋊Q8—861no—
543#121—434no—
544#121—862no—
545C4×Q8—21no—
546C4×Q8—21no—
547C4×Q8—434no—
548C4×Q8—862no—
549C4×Q8—862no—
550C4×Q8—862no—
551C4×Q8—861no—
552C4×Q8—861no—
553C4×D4—434no—
554C4×D4—862no—
555#117—432no—
556#117—432no—
557#117—432no—
558#117—432no—
559#117—432no—
560#117—432no—
561#117—432no—
562#117—862no—
563#117—862no—
564#117C22×D4312yes—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—432no—
569C2×C4⋊C4—432no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4C22×D4311yescharacteristic
573C2×C4⋊C4C22×D4311yescharacteristic
574C2×C22⋊C4—431no—
575C2×C22⋊C4—431no—
576C2×C22⋊C4—862no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C22⋊C4—861no—
582C2×C42—431no—
583C2×C42—862no—
584C2×C42—861no—
585C2×C42C22×D4311yescharacteristic
586#107—434no—
587#107—434no—
588#107C22×D4314yes—
589#107C22×D4314yes—
590#106—434no—
591#106—434no—
592#106C22×D4314yes—
593#106C22×D4314yes—
594C4⋊C8—434no—
595C4⋊C8—434no—
596#103—434no—
597#103—434no—
598#103—434no—
599#103—434no—
600#102—434no—
601#102—434no—
602#102—434no—
603#102—434no—
604C22⋊C8—434no—
605C22⋊C8—434no—
606#97—432no—
607#97C22×D4312yes—
608C4×C8—432no—
609C4×C8C22×D4312yes—
610C24—431no—
611C24—861no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—22no—
615C2×Q8—22no—
616C2×Q8—82no—
617C2×Q8—432no—
618C2×Q8—862no—
619C2×Q8—862no—
620C2×Q8—861no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—864no—
624C2×D4—432no—
625C2×D4—864no—
626C2×D4—861no—
627C2×D4—864no—
628C2×D4—3442no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—432no—
635C22×C4—432no—
636C22×C4—864no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—864no—
640C22×C4—861no—
641C22×C4—3442no—
642C22×C4D4×D4311yescharacteristic
643C22×C4D4×D4311yescharacteristic
644C22×C4C23×D4311yescharacteristic
645M16—24no—
646M16—864no—
647C2×C8—434no—
648C2×C8C23×D4314yes—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—432no—
658C4⋊C4—432no—
659C4⋊C4—432no—
660C4⋊C4—432no—
661C4⋊C4—432no—
662C4⋊C4—432no—
663C4⋊C4—862no—
664C4⋊C4—862no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4—862no—
668C4⋊C4—862no—
669C4⋊C4—862no—
670C4⋊C4—862no—
671C4⋊C4—862no—
672C4⋊C4—862no—
673C4⋊C4—862no—
674C4⋊C4—862no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4C23×D4312yes—
678C4⋊C4C23×D4312yes—
679C4⋊C4C23×D4312yes—
680C4⋊C4C23×D4312yes—
681C22⋊C4—22no—
682C22⋊C4—432no—
683C22⋊C4—432no—
684C22⋊C4—432no—
685C22⋊C4—432no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—862no—
689C22⋊C4—862no—
690C22⋊C4—864no—
691C22⋊C4—862no—
692C22⋊C4—862no—
693C22⋊C4—862no—
694C22⋊C4—862no—
695C22⋊C4—862no—
696C42—22no—
697C42—432no—
698C42—432no—
699C42—862no—
700C42—862no—
701C42—864no—
702C42—862no—
703C42D4×D4311yescharacteristic
704C42D4×D4311yescharacteristic
705C42C23×D4311yescharacteristic
706C42C23×D4311yescharacteristic
707C23—432no—
708C23—862no—
709C23—862no—
710C23—1721no—
711C23—1721no—
712C23—1722no—
713C23—1722no—
714C23—1722no—
715C23C2×D4×D4311yescharacteristic
716Q8—82no—
717Q8—82no—
718Q8—81no—
719Q8—81no—
720Q8—864no—
721Q8—3441no—
722Q8—3441no—
723Q8—3442no—
724Q8—3442no—
725Q8—1722no—
726D4—864no—
727D4—3444no—
728D4—1722no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—432no—
738C2×C4—432no—
739C2×C4—432no—
740C2×C4—862no—
741C2×C4—864no—
742C2×C4—864no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—3444no—
747C2×C4—3442no—
748C2×C4—3442no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1722no—
752C2×C4C2×D4×D4311yescharacteristic
753C2×C4C2×D4×D4311yescharacteristic
754C2×C4C2×D4×D4311yescharacteristic
755C2×C4C2×D4×D4311yescharacteristic
756C2×C4C2×D4×D4311yescharacteristic
757C2×C4#1306337314yes—
758C2×C4C24×D4311yescharacteristic
759C8—24no—
760C8—864no—
761C22—21no—
762C22—21no—
763C22—862no—
764C22—862no—
765C22—862no—
766C22—3444no—
767C22—3442no—
768C22—1722no—
769C22—1722no—
770C22—1722no—
771C22#1458347412yes—
772C22C22×D4×D4311yescharacteristic
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—862no—
782C4—862no—
783C4—862no—
784C4—1722no—
785C4—1722no—
786C4—1722no—
787C4#1458347412yes—
788C4C2×#1306337312yes—
789C2—22no—
790C2—3442no—
791C2—1722no—
792C2C2×#1458347411yescharacteristic
793C2#1914937111yescharacteristic
794C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3165C2
socleC22×C43C23×D4
prime radicalC2×#13063300C22
hypercenter#3165D43
hypocenterC43#60870
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. #19147998C2semidirect
3. #19145896C2semidirect
4. #19145894C2semidirect
5. #19145881C2semidirect
6. #19145879C2semidirect
7. #19145137C2semidirect
8. #19144984C2semidirect
9. #19144982C2semidirect
10. #19144545C2semidirect
12. #19144399C2semidirect
13. #19144391C2semidirect
14. #19143231C2semidirect
15. C43×#3165C2semidirect
16. #14583529C22semidirect
17. #14583529C22semidirect
20. #14583526C22semidirect
21. #14583526C22semidirect
43. #14583305C22semidirect
44. #14583302C22semidirect
45. #14583295C22semidirect
46. #14583261C22semidirect
47. #14583261C22semidirect
48. #14583259C22semidirect
49. #14583259C22semidirect
50. #14583256C22semidirect
51. #14583254C22semidirect
52. #14583243C22semidirect
53. #14583242C22semidirect
54. #14583236C22semidirect
55. #14583231C22semidirect
60. #14583209C22semidirect
61. #14583205C22semidirect
62. #14583202C22semidirect
63. #14583198C22semidirect
64. #14583193C22semidirect
65. #14583188C22semidirect
66. #14583183C22semidirect
67. #14583178C22semidirect
68. #14582961C22semidirect
69. #14582958C22semidirect
81. C43×#501C22semidirect
82. C43×#500C22semidirect
83. C43×#498C22semidirect
399. #3165D43semidirect
443. #501C2×D43semidirect
445. #500C2×D43semidirect
447. #498C2×D43semidirect
484. C43#60870semidirect

Maximal subgroups

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

subgroupindex
#191479982
C2×#145835232
#191458962
#191458942
#191458812
#191458792
#191451372
#191449842
#191449822
#191445452
#191445372
#191443992
#191443912
#191432312
C43×#31652
#6087043