Finite Group Databasebeta

← #7643456

Subgroups — #7643456

Order 512.

6818 conjugacy classes of subgroups.

The subgroup lattice has 1251 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C2×#3444C211yesmaximal, characteristic
3#39591C214yesmaximal, complemented
4#39463C214yesmaximal, complemented
5#39119C214yesmaximal, complemented
6#38915C214yesmaximal, complemented
7#38051C214yesmaximal, complemented
8#38048C214yesmaximal, complemented
9#37847C214yesmaximal, complemented
10#37844C214yesmaximal, complemented
11#37377C212yesmaximal, complemented
12#37376C212yesmaximal, complemented
13#37375C212yesmaximal, complemented
14#37374C212yesmaximal, complemented
15#36625C212yesmaximal, complemented
16#35663C214yesmaximal, complemented
17#35635C214yesmaximal, complemented
18#35297C212yesmaximal, complemented
19#35297C212yesmaximal, complemented
20#35297C212yesmaximal, complemented
21#35280C212yesmaximal, complemented
22#35279C212yesmaximal, complemented
23#34188C211yesmaximal, characteristic, complemented
24#3509—216no—
25C2×#557C2214yescomplemented
26C2×#556C2214yes—
27C2×#552C2214yes—
28C2×#552C2214yescomplemented
29C2×#541C2212yes—
30C2×#541C2212yescomplemented
31C2×#536C2212yes—
32#3444—216no—
33C2×#533C2211yescharacteristic
34C2×#533C2212yes—
35C2×#533C2212yes—
36C2×#533C2212yescomplemented
37C2×#533C2211yescharacteristic, complemented
38C2×#532C2211yescharacteristic
39C2×#532C2212yes—
40C22×C4⋊Q8C2211yescharacteristic, complemented
41C2×#529C2212yes—
42C2×#529C2212yes—
43C2×#529C2212yes—
44C2×#529C2212yes—
45C2×#529C2212yes—
46C2×#529C2212yes—
47C2×#525C2212yes—
48C2×#525C2212yes—
49C2×#525C2211yescharacteristic
50C2×#525C2211yescharacteristic
51C2×#519C2212yescomplemented
52C2×C4×#41C2212yes—
53C2×C4×#41C2212yes—
54C2×C4×#41C2211yescharacteristic
55C2×C4×#41C2211yescharacteristic
56C23×C42C2211yescharacteristic
57#2857C2212yes—
58#2857C2212yes—
59#2857C2212yes—
60#2857C2212yes—
61#2857C2212yescomplemented
62#2857C2212yescomplemented
63#2857C2212yescomplemented
64#2857C2212yescomplemented
65#2855C2214yes—
66#2855C2214yes—
67#2851C2214yes—
68#2851C2214yes—
69#2848C2214yes—
70#2848C2214yes—
71#2734C2214yescomplemented
72#2731C2214yescomplemented
73#2729C2218yes—
74#2724C2214yes—
75#2720C2218yes—
76#2719C2218yescomplemented
77#2718C2218yes—
78#2717C2214yes—
79#2717C2214yescomplemented
80#2713C2218yescomplemented
81#2711C2218yes—
82#2709C2214yescomplemented
83#2708C2218yes—
84#2701C2218yes—
85#2698C2218yes—
86#2697C2214yes—
87#2689C2218yes—
88#2686C2218yes—
89#2685C2218yes—
90#2684C2214yes—
91#2629C2214yes—
92#2629C2214yescomplemented
93#2628C2214yes—
94#2628C2214yescomplemented
95#2625C2214yes—
96#2625C2214yescomplemented
97#2625C2214yescomplemented
98#2616C2214yes—
99#2616C2214yes—
100#2616C2214yes—
101#2584C2214yescomplemented
102#2584C2214yescomplemented
103#2584C2214yescomplemented
104#2582C2214yescomplemented
105#2582C2214yescomplemented
106#2581C2214yescomplemented
107#2581C2214yescomplemented
108#2581C2214yescomplemented
109#2568C2214yescomplemented
110#2567C2214yescomplemented
111#2563C2214yes—
112#2562C2214yes—
113#2562C2214yes—
114#2562C2214yescomplemented
115#2559C2218yes—
116#2558C2218yes—
117#2556C2218yes—
118#2553C2218yes—
119#2542C2214yes—
120#2538C2214yes—
121#2538C2214yes—
122#2536C2214yes—
123#2536C2214yes—
124#2536C2214yescomplemented
125#2521C2218yescomplemented
126#2519C2218yescomplemented
127#2506C2218yescomplemented
128#2496C2218yescomplemented
129#2487C2214yes—
130#2487C2214yescomplemented
131#2485C2214yes—
132#2485C2214yes—
133#2485C2214yes—
134#2485C2214yes—
135#2485C2214yescomplemented
136#2485C2214yescomplemented
137#2478C2218yescomplemented
138#2476C2218yes—
139#2474C2218yescomplemented
140#2470C2218yes—
141#2469C2218yescomplemented
142#2465C2218yes—
143#2462C2218yescomplemented
144#2458C2218yes—
145#2417C2214yes—
146#2417C2214yes—
147#2417C2214yescomplemented
148#2417C2214yescomplemented
149#2415C2214yes—
150#2415C2214yes—
151#2415C2214yes—
152#2415C2214yes—
153#2415C2214yescomplemented
154#2415C2214yescomplemented
155#2409C2214yes—
156#2409C2214yescomplemented
157#2355C2214yescomplemented
158#2354C2214yes—
159#2352C2214yes—
160#2352C2214yescomplemented
161#2323C2214yes—
162#2323C2214yes—
163#2323C2214yescomplemented
164#2323C2214yescomplemented
165#2323C2214yescomplemented
166#2323C2214yescomplemented
167#2317C2214yescomplemented
168#2316C2214yescomplemented
169#2314C2212yes—
170#2314C2212yescomplemented
171#2311C2212yes—
172#2311C2214yes—
173#2311C2214yes—
174C4×C22⋊Q8C2214yes—
175C4×C22⋊Q8C2214yes—
176C4×C22⋊Q8C2214yes—
177C4×C22⋊Q8C2214yes—
178#2296C2214yes—
179#2285C2212yes—
180#2285C2212yescomplemented
181#2285C2211yescharacteristic, complemented
182C2×#384C2211yescharacteristic, complemented
183#2280C2214yes—
184#2274C2212yescomplemented
185C22×#41C2312yes—
186C22×#41C2312yes—
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2312yes—
190C24×C4C2312yes—
191C24×C4C2311yescharacteristic
192#557—232no—
193#556—232no—
194#552—232no—
195#552—232no—
196#541—216no—
197#541—216no—
198#536—216no—
199#533—216no—
200#533—28no—
201#533—216no—
202#533—28no—
203#533—216no—
204#532—28no—
205#532—216no—
206C2×C4⋊Q8—28no—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2314yes—
214C2×#127C2311yescharacteristic
215#529—216no—
216#529—216no—
217#529—216no—
218#529—216no—
219#529—216no—
220#529—216no—
221C2×#126C2312yes—
222C2×#126C2312yes—
223C2×#126C2312yes—
224C2×#126C2312yes—
225C2×#126C2318yes—
226C2×#126C2318yes—
227C2×#125C2312yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#125C2312yes—
231C2×#125C2312yes—
232C2×#125C2312yes—
233C2×#125C2318yes—
234C2×#125C2318yes—
235C2×#124C2311yescharacteristic
236C2×#124C2312yes—
237C2×#124C2311yescharacteristic
238C2×#124C2312yes—
239C2×#124C2314yes—
240#525—28no—
241#525—216no—
242#525—216no—
243#525—28no—
244C2×#123C2312yes—
245C2×#123C2311yescharacteristic
246C2×#123C2312yes—
247C2×#123C2311yescharacteristic
248C2×#123C2312yes—
249C2×#123C2312yes—
250C2×#123C2312yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×#121C2312yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#120C2311yescharacteristic
279C2×#120C2312yes—
280C2×#120C2311yescharacteristic
281#519—216no—
282C4×#41—28no—
283C4×#41—216no—
284C4×#41—216no—
285C4×#41D4116yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2314yes—
289C2×C4×Q8C2314yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2314yes—
294C2×C4×Q8C2314yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2318yes—
297C2×C4×Q8C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×#117C2314yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2312yes—
321C2×#117C2312yes—
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2311yescharacteristic
325C2×#117C2312yes—
326C2×#117C2318yes—
327C2×#117C2314yes—
328C2×#117C2314yes—
329C2×#117C2312yes—
330C2×#117C2314yes—
331C2×#117C2311yescharacteristic
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C22×C4⋊C4C2314yes—
335C22×C4⋊C4C2314yes—
336C22×C4⋊C4C2312yes—
337C22×C42—28no—
338C22×C42C2312yes—
339C22×C42C2312yes—
340C22×C42C2311yescharacteristic
341C22×C42C2312yes—
342C22×C42C2312yes—
343C22×C42C2312yes—
344C22×C42C2312yes—
345C22×C42C2311yescharacteristic
346C22×C42C2311yescharacteristic
347C22×C42C2311yescharacteristic
348#400C2318yes—
349#400C2318yes—
350#400C2318yes—
351#400C2318yes—
352#400C2318yes—
353#399C2318yes—
354#399C2318yes—
355#398C2318yes—
356#398C2318yes—
357#398C2318yes—
358#398C2318yes—
359#398C2318yes—
360#398C2318yes—
361#398C2318yes—
362#397C2318yes—
363#397C2318yes—
364#397C2318yes—
365#397C2318yes—
366#397C2318yes—
367#397C2318yes—
368#396C2318yes—
369#396C2318yes—
370#396C2318yes—
371#396C2318yes—
372#395C2318yes—
373#395C2318yes—
374#395C2318yes—
375#395C2318yes—
376#395C2318yes—
377#394C2318yes—
378#394C2318yes—
379#394C2318yes—
380#394C2318yes—
381#394C2318yes—
382#394C2318yes—
383#394C2318yes—
384#394C2318yes—
385#394C2318yes—
386#393C2318yes—
387#393C2318yes—
388#391C2318yes—
389#391C2318yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#390C2318yes—
400#390C2314yes—
401#390C2318yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2318yes—
410#389C2318yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2318yes—
416#389C2318yes—
417#389C2314yes—
418#389C2314yes—
419#389C2318yes—
420#389C2318yes—
421#389C2318yes—
422#389C2318yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#386C2314yes—
453#386C2314yes—
454#386C2318yes—
455#386C2318yes—
456#386C2318yes—
457#386C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#384C2318yes—
467#384C2312yes—
468#384C2314yes—
469#384C2312yes—
470#384C2312yes—
471#382C2318yes—
472#382C2312yes—
473#382C2314yes—
474#382C2314yes—
475#381C2318yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2314yes—
487#380C2314yes—
488#380C2314yes—
489#380C2314yes—
490#380C2314yes—
491#380C2314yes—
492#380C2314yes—
493#380C2314yes—
494#380C2318yes—
495#380C2318yes—
496#380C2314yes—
497#380C2314yes—
498#380C2314yes—
499#379C2318yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2318yes—
506C4×C4⋊C4C2318yes—
507C4×C4⋊C4C2318yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C25C2411yescharacteristic
512C2×#41—28no—
513C2×#41—28no—
514C2×#41—24no—
515C2×#41—28no—
516C2×#41—28no—
517C2×#41—42no—
518C2×#41—44no—
519C2×#41—42no—
520C2×#41—44no—
521C2×#41—42no—
522C2×#41—42no—
523C2×#41C2×D418yes—
524C22×Q8—28no—
525C22×Q8—44no—
526C22×Q8—44no—
527C22×Q8C2414yes—
528C22×Q8C2414yes—
529C22×Q8C2412yes—
530C22×Q8C2412yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2414yes—
533C22×Q8C2411yescharacteristic
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2412yes—
537C22×D4C2412yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2411yescharacteristic
542C22×D4C2411yescharacteristic
543C22×D4C2411yescharacteristic
544C22×D4C2411yescharacteristic
545C23×C4—28no—
546C23×C4—24no—
547C23×C4—28no—
548C23×C4—44no—
549C23×C4—42no—
550C23×C4—42no—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2411yescharacteristic
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2411yescharacteristic
564C23×C4C2411yescharacteristic
565C23×C4C2412yes—
566C23×C4C2414yes—
567C23×C4C2412yes—
568C23×C4C2411yescharacteristic
569C23×C4C2414yes—
570C4⋊Q8—24no—
571C4⋊Q8—216no—
572C4⋊Q8—28no—
573C4⋊Q8—28no—
574C4⋊Q8—28no—
575C4⋊Q8—216no—
576C4⋊Q8—28no—
577#127—24no—
578#126—28no—
579#126—28no—
580#126—28no—
581#126—28no—
582#126—232no—
583#126—232no—
584#125—28no—
585#125—28no—
586#125—28no—
587#125—232no—
588#125—232no—
589#125—28no—
590#125—216no—
591#125—216no—
592#124—24no—
593#124—24no—
594#124—216no—
595#124—28no—
596#124—28no—
597#123—24no—
598#123—24no—
599#123—216no—
600#123—216no—
601#123—28no—
602#123—28no—
603#123—28no—
604#123—28no—
605#123—28no—
606C22⋊Q8—28no—
607C22⋊Q8—216no—
608C22⋊Q8—216no—
609C22⋊Q8—216no—
610C22⋊Q8—216no—
611C22⋊Q8—216no—
612C22⋊Q8—216no—
613C22⋊Q8—28no—
614C22⋊Q8—28no—
615C22⋊Q8—28no—
616C22⋊Q8—28no—
617C22⋊Q8—28no—
618C22⋊Q8—48no—
619C22⋊Q8—48no—
620C22⋊Q8—48no—
621C22⋊Q8—48no—
622C22⋊Q8—48no—
623C22⋊Q8—48no—
624C22⋊Q8—48no—
625#121—28no—
626#121—28no—
627#121—28no—
628#121—28no—
629#121—28no—
630#121—28no—
631#120—24no—
632#120—24no—
633#120—28no—
634C4×Q8—232no—
635C4×Q8—28no—
636C4×Q8—28no—
637C4×Q8—28no—
638C4×Q8—28no—
639C4×Q8—28no—
640C4×Q8—216no—
641C4×Q8—216no—
642C4×Q8—216no—
643C4×Q8—216no—
644C4×Q8—216no—
645C4×Q8C2×D4116yes—
646C4×D4—28no—
647C4×D4—28no—
648C4×D4—28no—
649C4×D4—28no—
650C4×D4—28no—
651C4×D4—28no—
652C4×D4—28no—
653C4×D4—28no—
654C4×D4—28no—
655C4×D4—28no—
656C4×D4—28no—
657C4×D4—28no—
658C4×D4—28no—
659C4×D4—28no—
660C4×D4—28no—
661C4×D4C2×D4116yes—
662C4×D4C2×D4116yes—
663C4×D4C2×D4116yes—
664#117—24no—
665#117—28no—
666#117—28no—
667#117—28no—
668#117—216no—
669#117—216no—
670#117—232no—
671#117—28no—
672#117—28no—
673#117—28no—
674#117—28no—
675#117—28no—
676#117—48no—
677#117—48no—
678#117—44no—
679#117C2×D418yes—
680#117C2×D418yes—
681#117C2×D418yes—
682C2×C4⋊C4—216no—
683C2×C4⋊C4—48no—
684C2×C4⋊C4—44no—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2418yes—
710C2×C4⋊C4C2418yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2418yes—
713C2×C4⋊C4C2418yes—
714C2×C4⋊C4C2418yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2418yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2418yes—
719C2×C4⋊C4C2418yes—
720C2×C4⋊C4C2418yes—
721C2×C4⋊C4C2418yes—
722C2×C4⋊C4C2418yes—
723C2×C4⋊C4C2418yes—
724C2×C4⋊C4C2418yes—
725C2×C4⋊C4C2418yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2412yes—
731C2×C22⋊C4C2412yes—
732C2×C22⋊C4C2412yes—
733C2×C22⋊C4C2412yes—
734C2×C22⋊C4C2411yescharacteristic
735C2×C22⋊C4C2411yescharacteristic
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2412yes—
744C2×C22⋊C4C2412yes—
745C2×C22⋊C4C2412yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2418yes—
751C2×C22⋊C4C2418yes—
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2418yes—
754C2×C22⋊C4C2418yes—
755C2×C22⋊C4C2418yes—
756C2×C22⋊C4C2418yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2418yes—
759C2×C22⋊C4C2412yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2412yes—
762C2×C42—28no—
763C2×C42—24no—
764C2×C42—28no—
765C2×C42—28no—
766C2×C42—28no—
767C2×C42—28no—
768C2×C42—28no—
769C2×C42C2×D418yes—
770C2×C42C2×D418yes—
771C2×C42C2×D418yes—
772C2×C42C2412yes—
773C2×C42C2412yes—
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2418yes—
777C2×C42C2418yes—
778C2×C42C2414yes—
779C2×C42C2412yes—
780C2×C42C2412yes—
781C2×C42C2412yes—
782C2×C42C2411yescharacteristic
783C2×C42C2412yes—
784C2×C42C2411yescharacteristic
785C2×C42C2418yes—
786C2×C42C2418yes—
787C2×C42C2414yes—
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2411yescharacteristic
793C2×C42C2412yes—
794C2×C42C2411yescharacteristic
795#95C2418yes—
796#95C2418yes—
797#95C2418yes—
798#95C2418yes—
799#95C2418yes—
800#95C2418yes—
801#95C2418yes—
802#95C2418yes—
803#95C2418yes—
804#95C2418yes—
805#95C2418yes—
806#95C2418yes—
807#95C2418yes—
808#95C2418yes—
809#95C2418yes—
810#95C2418yes—
811#95C2418yes—
812#95C2418yes—
813#95C2418yes—
814#95C2418yes—
815#95C2418yes—
816C24—22no—
817C24—24no—
818C24—42no—
819C24—41no—
820C24—41no—
821C24C2512yes—
822C24C2511yescharacteristic
823C24C2511yescharacteristic
824C24C2511yescharacteristic
825C24C2512yes—
826#41—416no—
827#41—432no—
828#41—432no—
829#41—416no—
830C2×Q8—28no—
831C2×Q8—24no—
832C2×Q8—24no—
833C2×Q8—22no—
834C2×Q8—28no—
835C2×Q8—28no—
836C2×Q8—28no—
837C2×Q8—24no—
838C2×Q8—24no—
839C2×Q8—28no—
840C2×Q8—28no—
841C2×Q8—28no—
842C2×Q8—44no—
843C2×Q8—44no—
844C2×Q8—41no—
845C2×Q8—42no—
846C2×Q8—41no—
847C2×Q8—42no—
848C2×Q8—41no—
849C2×Q8—41no—
850C2×Q8—432no—
851C2×Q8C22×D414yes—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—24no—
860C2×D4—24no—
861C2×D4—24no—
862C2×D4—24no—
863C2×D4—22no—
864C2×D4—24no—
865C2×D4—24no—
866C2×D4—41no—
867C2×D4—42no—
868C2×D4—41no—
869C2×D4—42no—
870C2×D4—41no—
871C2×D4—41no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4C22×D414yes—
883C2×D4C22×D414yes—
884C2×D4C22×D414yes—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—22no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—22no—
893C22×C4—24no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—24no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—24no—
900C22×C4—22no—
901C22×C4—28no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—432no—
933C22×C4—48no—
934C22×C4—44no—
935C22×C4—416no—
936C22×C4C22×D418yes—
937C22×C4C22×D414yes—
938C22×C4C22×D418yes—
939C22×C4C22×D418yes—
940C22×C4C22×D414yes—
941C22×C4C22×D414yes—
942C22×C42−1+418yes—
943C22×C4C2518yes—
944C22×C4C2512yes—
945C22×C4C2518yes—
946C22×C4C2512yes—
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2518yes—
950C22×C4C2518yes—
951C22×C4C2512yes—
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2511yescharacteristic
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2511yescharacteristic
961C4⋊C4—28no—
962C4⋊C4—28no—
963C4⋊C4—216no—
964C4⋊C4—28no—
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—24no—
968C4⋊C4—24no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—28no—
981C4⋊C4—216no—
982C4⋊C4—216no—
983C4⋊C4—216no—
984C4⋊C4—216no—
985C4⋊C4—216no—
986C4⋊C4—28no—
987C4⋊C4—216no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—48no—
994C4⋊C4—44no—
995C4⋊C4—48no—
996C4⋊C4—48no—
997C4⋊C4—48no—
998C4⋊C4—48no—
999C4⋊C4—48no—
1000C4⋊C4—48no—
1001C4⋊C4—48no—
1002C4⋊C4C22×D418yes—
1003C4⋊C4C22×D418yes—
1004C4⋊C4C22×D418yes—
1005C22⋊C4—28no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—24no—
1009C22⋊C4—24no—
1010C22⋊C4—24no—
1011C22⋊C4—24no—
1012C22⋊C4—216no—
1013C22⋊C4—216no—
1014C22⋊C4—216no—
1015C22⋊C4—24no—
1016C22⋊C4—24no—
1017C22⋊C4—24no—
1018C22⋊C4—24no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—24no—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—48no—
1026C22⋊C4—48no—
1027C22⋊C4—44no—
1028C22⋊C4—48no—
1029C22⋊C4—48no—
1030C22⋊C4—48no—
1031C22⋊C4—48no—
1032C22⋊C4—48no—
1033C22⋊C4—48no—
1034C22⋊C4—48no—
1035C22⋊C4C22×D418yes—
1036C22⋊C4C22×D418yes—
1037C22⋊C4C22×D418yes—
1038C42—24no—
1039C42—24no—
1040C42—24no—
1041C42—24no—
1042C42—22no—
1043C42—24no—
1044C42—22no—
1045C42—24no—
1046C42—24no—
1047C42—24no—
1048C42—216no—
1049C42—216no—
1050C42—28no—
1051C42—48no—
1052C42—48no—
1053C42—44no—
1054C42C22×D414yes—
1055C42C22×D414yes—
1056C42C22×D418yes—
1057C42C22×D418yes—
1058C42C22×D418yes—
1059C42C22×D414yes—
1060C42C22×D414yes—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—21no—
1072C23—22no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—22no—
1077C23—21no—
1078C23—21no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—48no—
1087C23—44no—
1088C23—44no—
1089C23—48no—
1090C23—44no—
1091C23C23×D412yes—
1092C23C23×D412yes—
1093C23C23×D412yes—
1094C23C2×2−1+414yes—
1095C23C2611yescharacteristic
1096Q8—44no—
1097Q8—48no—
1098Q8—48no—
1099Q8—416no—
1100Q8—44no—
1101Q8—416no—
1102Q8—416no—
1103D4—44no—
1104D4—44no—
1105D4—44no—
1106D4—48no—
1107D4—48no—
1108D4—48no—
1109D4—48no—
1110D4—44no—
1111D4—48no—
1112D4—48no—
1113D4—48no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—28no—
1129C2×C4—28no—
1130C2×C4—28no—
1131C2×C4—216no—
1132C2×C4—216no—
1133C2×C4—216no—
1134C2×C4—216no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—28no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—28no—
1142C2×C4—28no—
1143C2×C4—28no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—28no—
1148C2×C4—28no—
1149C2×C4—28no—
1150C2×C4—28no—
1151C2×C4—28no—
1152C2×C4—28no—
1153C2×C4—28no—
1154C2×C4—28no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—48no—
1163C2×C4—48no—
1164C2×C4—48no—
1165C2×C4—48no—
1166C2×C4—44no—
1167C2×C4—416no—
1168C2×C4—48no—
1169C2×C4—48no—
1170C2×C4—48no—
1171C2×C4—48no—
1172C2×C4—48no—
1173C2×C4—164no—
1174C2×C4C23×D414yes—
1175C2×C4C23×D412yes—
1176C2×C4C23×D414yes—
1177C2×C4C23×D412yes—
1178C2×C4C23×D412yes—
1179C2×C4C23×D414yes—
1180C2×C4C23×D412yes—
1181C2×C4C23×D414yes—
1182C2×C4C2×2−1+414yes—
1183C2×C4C2×2−1+414yes—
1184C2×C4#58512yes—
1185C2×C4#58512yes—
1186C2×C4#58514yes—
1187C22—24no—
1188C22—24no—
1189C22—24no—
1190C22—24no—
1191C22—24no—
1192C22—24no—
1193C22—22no—
1194C22—22no—
1195C22—22no—
1196C22—416no—
1197C22—42no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—41no—
1206C22—41no—
1207C22—42no—
1208C22—41no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22C24×D411yescharacteristic
1218C22C22×2−1+412yes—
1219C22C2×#58512yes—
1220C22C2×#58511yescharacteristic
1221C22C2×#58511yescharacteristic
1222C4—24no—
1223C4—24no—
1224C4—24no—
1225C4—24no—
1226C4—22no—
1227C4—22no—
1228C4—22no—
1229C4—42no—
1230C4—42no—
1231C4—42no—
1232C4—48no—
1233C4—48no—
1234C4—48no—
1235C4—42no—
1236C4—42no—
1237C4—48no—
1238C4#344914yes—
1239C4#348918yes—
1240C2—42no—
1241C2—42no—
1242C2—44no—
1243C2—42no—
1244C2—82no—
1245C2C2×#344911yescharacteristic
1246C2C2×#348912yes—
1247C2#6283711yescharacteristic
1248C2#6283812yes—
1249C2#6283911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3444C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3509C2semidirect
3. #39591C2semidirect
4. #39463C2semidirect
5. #39119C2semidirect
6. #38915C2semidirect
7. #38051C2semidirect
8. #38048C2semidirect
9. #37847C2semidirect
10. #37844C2semidirect
11. #37377C2semidirect
12. #37376C2semidirect
13. #37375C2semidirect
14. #37374C2semidirect
15. #36625C2semidirect
16. #35663C2semidirect
17. #35635C2semidirect
18. #35297C2semidirect
19. #35297C2semidirect
20. #35297C2semidirect
21. #35280C2semidirect
22. #35279C2semidirect
23. #34188C2semidirect
25. C2×#557C22semidirect
28. C2×#552C22semidirect
30. C2×#541C22semidirect
36. C2×#533C22semidirect
37. C2×#533C22semidirect
40. C22×C4⋊Q8C22semidirect
51. C2×#519C22semidirect
61. #2857C22semidirect
62. #2857C22semidirect
63. #2857C22semidirect
64. #2857C22semidirect
71. #2734C22semidirect
72. #2731C22semidirect
76. #2719C22semidirect
79. #2717C22semidirect
80. #2713C22semidirect
82. #2709C22semidirect
92. #2629C22semidirect
94. #2628C22semidirect
96. #2625C22semidirect
97. #2625C22semidirect
101. #2584C22semidirect
102. #2584C22semidirect
103. #2584C22semidirect
104. #2582C22semidirect
105. #2582C22semidirect
106. #2581C22semidirect
107. #2581C22semidirect
108. #2581C22semidirect
109. #2568C22semidirect
110. #2567C22semidirect
114. #2562C22semidirect
124. #2536C22semidirect
125. #2521C22semidirect
126. #2519C22semidirect
127. #2506C22semidirect
128. #2496C22semidirect
130. #2487C22semidirect
135. #2485C22semidirect
136. #2485C22semidirect
137. #2478C22semidirect
139. #2474C22semidirect
141. #2469C22semidirect
143. #2462C22semidirect
147. #2417C22semidirect
148. #2417C22semidirect
153. #2415C22semidirect
154. #2415C22semidirect
156. #2409C22semidirect
157. #2355C22semidirect
160. #2352C22semidirect
163. #2323C22semidirect
164. #2323C22semidirect
165. #2323C22semidirect
166. #2323C22semidirect
167. #2317C22semidirect
168. #2316C22semidirect
170. #2314C22semidirect
180. #2285C22semidirect
181. #2285C22semidirect
182. C2×#384C22semidirect
184. #2274C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C2×#34442
#395912
#394632
#391192
#389152
#380512
#380482
#378472
#378442
#373772
#373762
#373752
#373742
#366252
#356632
#356352
#352972
#352802
#352792
#341882