Finite Group Databasebeta

← #25968963

Subgroups — #25968963

Order 11008.

1626 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147998C211yesmaximal, characteristic
2C2×#14583507C211yesmaximal, characteristic
3#19145870C214yesmaximal, complemented
4#19145868C214yesmaximal, complemented
5#19145862C214yesmaximal, complemented
6#19145860C214yesmaximal, complemented
7#19145145C212yesmaximal, complemented
8#19144973C212yesmaximal, complemented
9#19144545C212yesmaximal
10#19144541C212yesmaximal
11#19144402C211yesmaximal, characteristic, complemented
12#19144400C211yesmaximal, characteristic, complemented
13#19144396C211yesmaximal, characteristic, complemented
14#19143232C211yesmaximal, characteristic
15C43×#3078C211yesmaximal, characteristic, complemented
16#14583529C2212yes—
17#14583529C2212yes—
18#14583528—21no—
19#14583528—21no—
20#14583526C2212yes—
21#14583526C2212yes—
22#14583524—21no—
23#14583524—21no—
24#14583507—22no—
25#14583507—22no—
26#14583507C2214yes—
27#14583507C2214yes—
28#14583456C2211yescharacteristic
29#14583453—22no—
30#14583453—22no—
31#14583452C2212yes—
32C2×#13063323C2211yescharacteristic
33C2×#13063320—21no—
34C2×#13063319—21no—
35C2×#13063317—21no—
36C2×#13063316C2211yescharacteristic
37C2×#13063315—21no—
38C2×#13063305C2211yescharacteristic
39C2×#13063301C2211yescharacteristic
40C2×C4×Dic86C2211yescharacteristic
41C2×#13063282C2211yescharacteristic
42#117×D43C2212yes—
43#14583307C2214yescomplemented
44#14583306C2214yescomplemented
45#14583300C2214yescomplemented
46#14583299C2214yescomplemented
47#14583266C2214yescomplemented
48#14583266C2214yescomplemented
49#14583248C2214yescomplemented
50#14583248C2214yescomplemented
51#14583243C2214yes—
52#14583242C2214yes—
53#14583239C2214yes—
54#14583238C2214yes—
55#14583236C2214yes—
56#14583233C2214yes—
57#14583231C2214yes—
58#14583228C2214yes—
59#14583207C2214yescomplemented
60#14583206C2214yescomplemented
61#14583203C2214yescomplemented
62#14583195C2212yescomplemented
63#14583194C2212yescomplemented
64#14583191C2212yescomplemented
65#14583185C2212yescomplemented
66#14583184C2212yescomplemented
67#14583181C2212yescomplemented
68#14582959C2214yes—
69#14582959C2214yes—
70#14582942C2212yes—
71#14582941C2212yes—
72#14582939C2212yes—
73#14582923C2211yescharacteristic
74#14582909C2212yes—
75#14582908C2212yes—
76#14582907C2212yes—
77#14582862C2212yes—
78M16×Dic43C2212yes—
79C43×#533C2211yescharacteristic
80C2×C4×Q8×C43C2211yescharacteristic
81C43×#479C2214yescomplemented
82C43×#477C2212yescomplemented
83C43×#475C2212yescomplemented
84C43×#428C2212yes—
85C43×#423C2211yescharacteristic
86C43×#419C2212yes—
87C22×Dic86C2311yescharacteristic
88C22×C4×D43C2311yescharacteristic
89C2×#10621877C2312yes—
90#13063325C2311yescharacteristic
91#13063325C2311yescharacteristic
92#13063324—22no—
93#13063324—22no—
94#13063324C2312yes—
95#13063324C2312yes—
96#13063323—22no—
97#13063323—22no—
98#13063323—22no—
99#13063323C2314yes—
100#13063320—24no—
101#13063320—24no—
102#13063319—24no—
103#13063319—24no—
104#13063317—24no—
105#13063317—24no—
106#13063317C2312yes—
107#13063316—22no—
108#13063316C2312yes—
109#13063316C2314yes—
110#13063316C2312yes—
111#13063315—24no—
112#13063315—24no—
113#13063315—22no—
114#13063315—22no—
115#13063315—22no—
116#13063315—22no—
117#13063305—22no—
118#13063305—22no—
119#13063305—22no—
120#13063305C2314yes—
121#13063304—21no—
122#13063304—21no—
123#13063303—22no—
124#13063303—22no—
125#13063303—22no—
126#13063303—22no—
127#13063302—22no—
128#13063302—22no—
129#13063301—22no—
130#13063301—22no—
131#13063301—22no—
132#13063301C2314yes—
133C4×Dic86—21no—
134C4×Dic86—21no—
135C4×Dic86—21no—
136C4×Dic86—21no—
137C4×Dic86—22no—
138C4×Dic86—22no—
139C4×Dic86C2312yes—
140C4×Dic86C2312yes—
141#13063284C2312yes—
142#13063283C2312yes—
143#13063283C2312yes—
144#13063282—22no—
145#13063282D412yes—
146#13063282D412yes—
147#13063282C2312yes—
148#13063282C2312yes—
149#13063281—22no—
150C2×C4⋊Dic43—21no—
151C2×C4⋊Dic43—21no—
152C2×C4⋊Dic43C2311yescharacteristic
153C2×Dic43⋊C4—21no—
154C2×Dic43⋊C4—21no—
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4D411yescharacteristic
159C2×Dic43⋊C4D411yescharacteristic
160C4⋊C4×D43C2312yes—
161C4⋊C4×D43C2312yes—
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#13063259C2314yes—
171#13063258C2314yes—
172#13063258C2314yes—
173#13063257C2314yes—
174#13063256C2314yes—
175#13063256C2314yes—
176C4⋊(C43⋊C8)C2312yes—
177C4⋊(C43⋊C8)C2312yes—
178#13063250C2314yes—
179#13063250C2314yes—
180#13063249C2314yes—
181#13063249C2314yes—
182#13063248C2314yes—
183#13063248C2314yes—
184(C2×D43)⋊C8C2314yes—
185(C2×D43)⋊C8C2314yes—
186#13063235C2314yes—
187C8×Dic43C2314yes—
188C22×Q8×C43C2311yescharacteristic
189C2×M16×C43C2312yes—
190C4⋊Q8×C43C2311yescharacteristic
191C4⋊Q8×C43C2311yescharacteristic
192#125×C43C2312yes—
193C22⋊Q8×C43—21no—
194C22⋊Q8×C43—21no—
195C4×Q8×C43—21no—
196C4×Q8×C43—21no—
197C4×Q8×C43—21no—
198C4×Q8×C43—21no—
199C4×Q8×C43C2312yes—
200C4×Q8×C43C2312yes—
201#117×C43C2312yes—
202C2×C4⋊C4×C43—21no—
203C2×C4⋊C4×C43C2311yescharacteristic
204C2×C42×C43—21no—
205C2×C42×C43C2311yescharacteristic
206#107×C43C2314yes—
207#106×C43C2314yes—
208C4⋊C8×C43C2312yes—
209C4⋊C8×C43C2312yes—
210#103×C43C2314yes—
211#103×C43C2314yes—
212C23×D43C2×D411yescharacteristic
213C2×Q8×C43—21no—
214C2×Q8×C43—21no—
215C2×Q8×C43—21no—
216C2×Q8×C43—22no—
217C2×Q8×C43—22no—
218C2×Q8×C43C2412yes—
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—22no—
232C2×C4×D43—22no—
233C2×C4×D43C2×D412yes—
234C2×C4×D43C2412yes—
235C2×Dic86—22no—
236C2×Dic86—22no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—22no—
241C2×Dic86—22no—
242C2×Dic86C2412yes—
243M16×C43—24no—
244C2×C8×C43C2414yes—
245C4⋊C4×C43—22no—
246C4⋊C4×C43—22no—
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—
255C22⋊C4×C43—22no—
256C42×C43—22no—
257C42×C43—22no—
258C42×C43—22no—
259C42×C43C2×D411yescharacteristic
260C42×C43C2×D411yescharacteristic
261C42×C43C2411yescharacteristic
262C42×C43C2411yescharacteristic
263C22⋊Dic43—22no—
264(C2×D43)⋊C4—22no—
265(C2×D43)⋊C4—22no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4C2×D412yes—
269(C2×D43)⋊C4C2×D412yes—
270(C2×D43)⋊C4C2×D412yes—
271(C2×D43)⋊C4C2×D412yes—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—24no—
276C4⋊Dic43—24no—
277C4⋊Dic43—22no—
278C4⋊Dic43—22no—
279C4⋊Dic43C2412yes—
280C4⋊Dic43C2412yes—
281C4⋊Dic43C2412yes—
282Dic43⋊C4—22no—
283Dic43⋊C4—22no—
284Dic43⋊C4—22no—
285Dic43⋊C4—22no—
286Dic43⋊C4—22no—
287Dic43⋊C4—22no—
288Dic43⋊C4—24no—
289Dic43⋊C4—24no—
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—22no—
304C4×Dic43—22no—
305C4×Dic43C2×D412yes—
306C4×Dic43C2412yes—
307#10621877—24no—
308C2×C43⋊C8C2414yes—
309C23×C43C22×D411yescharacteristic
310C22×D43—22no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43C22×D412yes—
314Q8×C43—22no—
315Q8×C43—22no—
316Q8×C43—42no—
317Q8×C43—81no—
318Q8×C43—81no—
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×C432−1+412yes—
333C2×C4×C432−1+412yes—
334C2×C4×C43C2511yescharacteristic
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43C22×D412yes—
345C2×Dic43C22×D412yes—
346C2×Dic43C22×D412yes—
347C4×D43—24no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—82no—
351C4×D43—82no—
352Dic86—22no—
353Dic86—22no—
354Dic86—42no—
355Dic86—82no—
356Dic86—82no—
357Dic86—81no—
358Dic86—81no—
359C8×C43—24no—
360C43⋊C8—24no—
361#60869—431nomaximal, Sylow
362C22×C43—21no—
363C22×C43—21no—
364C22×C43#53612yes—
365C22×C43C23×D411yescharacteristic
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—82no—
370C4×C43—21no—
371C4×C43—21no—
372C4×C43—21no—
373C4×C43—21no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43#53612yes—
379C4×C43C2×2−1+411yescharacteristic
380C4×C43C2×2−1+411yescharacteristic
381Dic43—22no—
382Dic43—22no—
383Dic43—22no—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388#3458—431no—
389C2×#541—431no—
390#3242—434no—
391#3242—434no—
392#3242—434no—
393#3242—434no—
394#3166—432no—
395#3139—432no—
396#3095—432no—
397#3095—432no—
398#3078—431no—
399#3078—431no—
400#3078—431no—
401#3078D4311yescharacteristic, complemented
402#2921—431no—
403C2×C43—22no—
404C2×C43C2×#53611yescharacteristic
405C2×C43#358611yescharacteristic
406C2×C43#358611yescharacteristic
407D43—42no—
408#544—432no—
409#544—432no—
410#544—432no—
411#544—432no—
412#544—861no—
413#544—861no—
414#543—861no—
415#543—861no—
416#541—434no—
417#541—434no—
418#541—862no—
419#541—862no—
420#533—432no—
421#533—431no—
422#533—862no—
423#533—862no—
424#533C2×D4311yescharacteristic
425C2×C4⋊Q8—431no—
426C2×#126—861no—
427C2×#126—861no—
428C2×#125—431no—
429C2×#125—861no—
430C2×#125—861no—
431C2×C22⋊Q8—431no—
432C2×C22⋊Q8—431no—
433C2×C4×Q8—431no—
434C2×C4×Q8C2×D4311yescharacteristic
435C2×#117—431no—
436C2×#117—432no—
437#501—434no—
438#501—434no—
439#499—434no—
440#499—434no—
441#491—434no—
442#491—434no—
443#487—434no—
444#487—434no—
445#485—434no—
446#485—434no—
447#485—434no—
448#485—434no—
449#484—434no—
450#484—434no—
451#483—434no—
452#483—434no—
453#479—434no—
454#479—434no—
455#479—434no—
456#479C2×D4314yescomplemented
457#477—432no—
458#477—432no—
459#477—432no—
460#477C2×D4312yescomplemented
461#475—432no—
462#475—432no—
463#475—432no—
464#475C2×D4312yescomplemented
465#433—434no—
466#433—434no—
467#428—432no—
468#428—432no—
469#428—432no—
470#428C2×D4312yes—
471#423—431no—
472#423C2×D4311yescharacteristic
473#419—432no—
474#419—432no—
475#419—432no—
476#419C2×D4312yes—
477#407—432no—
478C4×M16—432no—
479C43#6086911yescharacteristic, complemented, Sylow
480C22×Q8—431no—
481C22×Q8C22×D4311yescharacteristic
482C23×C4—431no—
483C2×M16—432no—
484C2×M16C22×D4312yes—
485C4⋊Q8—432no—
486C4⋊Q8—432no—
487C4⋊Q8—434no—
488C4⋊Q8—431no—
489C4⋊Q8—431no—
490C4⋊Q8—862no—
491C4⋊Q8—862no—
492C4⋊Q8—862no—
493C4⋊Q8—862no—
494C4⋊Q8—862no—
495C4⋊Q8C22×D4311yescharacteristic
496C4⋊Q8C22×D4311yescharacteristic
497#126—864no—
498#126—864no—
499#126—864no—
500#126—864no—
501#125—434no—
502#125—432no—
503#125—432no—
504#125—432no—
505#125—864no—
506#125—864no—
507#125—862no—
508#125—864no—
509#125—864no—
510#125—862no—
511#125—862no—
512#125—862no—
513#125—862no—
514#125C22×D4312yes—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—434no—
518C22⋊Q8—434no—
519C22⋊Q8—862no—
520C22⋊Q8—862no—
521C22⋊Q8—862no—
522C22⋊Q8—862no—
523C22⋊Q8—862no—
524C22⋊Q8—862no—
525C22⋊Q8—862no—
526C22⋊Q8—862no—
527C22⋊Q8—862no—
528C22⋊Q8—862no—
529C22⋊Q8—862no—
530C22⋊Q8—862no—
531C22⋊Q8—861no—
532C22⋊Q8—861no—
533C4×Q8—21no—
534C4×Q8—21no—
535C4×Q8—21no—
536C4×Q8—21no—
537C4×Q8—432no—
538C4×Q8—432no—
539C4×Q8—862no—
540C4×Q8—862no—
541C4×Q8—861no—
542C4×Q8—861no—
543C4×Q8—861no—
544C4×Q8—861no—
545C4×Q8C22×D4312yes—
546C4×Q8C22×D4312yes—
547#117—432no—
548#117—432no—
549#117—432no—
550#117—432no—
551#117—432no—
552#117—432no—
553#117—432no—
554#117—862no—
555#117—862no—
556#117C22×D4312yes—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—432no—
562C2×C4⋊C4—432no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4C22×D4311yescharacteristic
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—862no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C42—21no—
577C2×C42—431no—
578C2×C42—862no—
579C2×C42—861no—
580C2×C42C22×D4311yescharacteristic
581#107—434no—
582#107—434no—
583#107—434no—
584#107C22×D4314yes—
585#106—434no—
586#106—434no—
587#106—434no—
588#106C22×D4314yes—
589C4⋊C8—432no—
590C4⋊C8—432no—
591C4⋊C8C22×D4312yes—
592C4⋊C8C22×D4312yes—
593#103—434no—
594#103—434no—
595#103—434no—
596#103—434no—
597#103—434no—
598#103—434no—
599#103C22×D4314yes—
600#103C22×D4314yes—
601C22⋊C8—434no—
602C22⋊C8—434no—
603#97—434no—
604C4×C8—434no—
605C24—431no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—432no—
612C2×Q8—862no—
613C2×Q8—862no—
614C2×Q8—861no—
615C2×Q8—861no—
616C2×Q8—861no—
617C2×Q8—862no—
618C2×Q8—862no—
619C2×Q8C23×D4312yes—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—432no—
626C22×C4—432no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4D4×D4311yescharacteristic
634C22×C4D4×D4311yescharacteristic
635C22×C4C23×D4311yescharacteristic
636M16—24no—
637M16—864no—
638C2×C8—434no—
639C2×C8C23×D4314yes—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—432no—
648C4⋊C4—432no—
649C4⋊C4—432no—
650C4⋊C4—432no—
651C4⋊C4—432no—
652C4⋊C4—432no—
653C4⋊C4—432no—
654C4⋊C4—862no—
655C4⋊C4—862no—
656C4⋊C4—864no—
657C4⋊C4—864no—
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—862no—
667C4⋊C4—862no—
668C4⋊C4—861no—
669C4⋊C4—862no—
670C4⋊C4—862no—
671C4⋊C4—862no—
672C4⋊C4—862no—
673C4⋊C4—861no—
674C4⋊C4—861no—
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—864no—
686C22⋊C4—864no—
687C22⋊C4—862no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—432no—
692C42—432no—
693C42—862no—
694C42—862no—
695C42—862no—
696C42—862no—
697C42—862no—
698C42D4×D4311yescharacteristic
699C42D4×D4311yescharacteristic
700C42C23×D4311yescharacteristic
701C42C23×D4311yescharacteristic
702C23—432no—
703C23—862no—
704C23—1721no—
705C23—1721no—
706C23C2×D4×D4311yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710Q8—81no—
711Q8—81no—
712Q8—862no—
713Q8—862no—
714Q8—3441no—
715Q8—3441no—
716Q8—3442no—
717Q8—3442no—
718Q8—1722no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—432no—
728C2×C4—432no—
729C2×C4—432no—
730C2×C4—862no—
731C2×C4—864no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—3442no—
739C2×C4—3442no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1722no—
743C2×C4—1722no—
744C2×C4C2×D4×D4311yescharacteristic
745C2×C4C2×D4×D4311yescharacteristic
746C2×C4C2×D4×D4311yescharacteristic
747C2×C4C2×D4×D4311yescharacteristic
748C2×C4C2×D4×D4311yescharacteristic
749C2×C4#1306337212yes—
750C2×C4#1306337312yes—
751C2×C4C24×D4311yescharacteristic
752C8—24no—
753C8—864no—
754C22—21no—
755C22—21no—
756C22—862no—
757C22—862no—
758C22—862no—
759C22—3442no—
760C22#1458347212yes—
761C22C22×D4×D4311yescharacteristic
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—862no—
771C4—862no—
772C4—862no—
773C4—1722no—
774C4—1722no—
775C4—1722no—
776C4—1722no—
777C4#1458347212yes—
778C4C2×#1306337211yescharacteristic
779C4C2×#1306337311yescharacteristic
780C2—22no—
781C2—1722no—
782C2C2×#1458347211yescharacteristic
783C2#1914937811yescharacteristic
784C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3078C2
socleC22×C43C23×D4
prime radicalC23×D43C2×D4
hypercenter#3078D43
hypocenterC43#60869
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #19145870C2semidirect
4. #19145868C2semidirect
5. #19145862C2semidirect
6. #19145860C2semidirect
7. #19145145C2semidirect
8. #19144973C2semidirect
11. #19144402C2semidirect
12. #19144400C2semidirect
13. #19144396C2semidirect
15. C43×#3078C2semidirect
43. #14583307C22semidirect
44. #14583306C22semidirect
45. #14583300C22semidirect
46. #14583299C22semidirect
47. #14583266C22semidirect
48. #14583266C22semidirect
49. #14583248C22semidirect
50. #14583248C22semidirect
59. #14583207C22semidirect
60. #14583206C22semidirect
61. #14583203C22semidirect
62. #14583195C22semidirect
63. #14583194C22semidirect
64. #14583191C22semidirect
65. #14583185C22semidirect
66. #14583184C22semidirect
67. #14583181C22semidirect
81. C43×#479C22semidirect
82. C43×#477C22semidirect
83. C43×#475C22semidirect
401. #3078D43semidirect
456. #479C2×D43semidirect
460. #477C2×D43semidirect
464. #475C2×D43semidirect
479. C43#60869semidirect

Maximal subgroups

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

subgroupindex
#191479982
C2×#145835072
#191458702
#191458682
#191458622
#191458602
#191451452
#191449732
#191445452
#191445412
#191444022
#191444002
#191443962
#191432322
C43×#30782
#6086943