Finite Group Databasebeta

← #7709551

Subgroups — #7709551

Order 512.

7466 conjugacy classes of subgroups.

The subgroup lattice has 1267 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3536C211yesmaximal, characteristic, complemented
2C22×#529C211yesmaximal, characteristic, complemented
3#59076C214yesmaximal, complemented
4#59046C214yesmaximal, complemented
5#45766C218yesmaximal, complemented
6#39135C212yesmaximal, complemented
7#38907C212yesmaximal, complemented
8#38023C214yesmaximal, complemented
9#37797C214yesmaximal, complemented
10#37785C214yesmaximal, complemented
11#37770C214yesmaximal, complemented
12#37754C214yesmaximal, complemented
13#37450C211yesmaximal, characteristic, complemented
14#37439C211yesmaximal, characteristic, complemented
15#36971C212yesmaximal, complemented
16#36961C212yesmaximal, complemented
17#36626C211yesmaximal, characteristic, complemented
18C2×#2854C211yesmaximal, characteristic, complemented
19#36578C212yesmaximal, complemented
20#36102C212yesmaximal, complemented
21#36099C214yesmaximal, complemented
22#35150C212yesmaximal, complemented
23#35094C212yesmaximal, complemented
24#34380C211yesmaximal, characteristic, complemented
25#3536—216no—
26C2×#562C2214yescomplemented
27C2×#554C2212yescomplemented
28C2×#548C2212yes—
29C2×#547C2212yes—
30C2×#546C2214yes—
31C2×#546C2212yescomplemented
32C2×#543C2212yescomplemented
33C2×#542C2212yescomplemented
34C2×#539C2212yes—
35C2×#538C2212yescomplemented
36C2×#537C2212yes—
37C2×#537C2212yescomplemented
38C2×#529—216no—
39C2×#529C2214yes—
40C2×#529C2214yes—
41C2×#529C2214yescomplemented
42C2×#529C2214yescomplemented
43C22×#126C2212yescomplemented
44C22×#125C2211yescharacteristic, complemented
45C22×#124C2211yescharacteristic, complemented
46C2×#525C2211yescharacteristic
47C2×#525C2214yescomplemented
48C22×#123C2212yes—
49C22×#123C2212yes—
50C22×C22⋊Q8C2211yescharacteristic
51C22×#121C2211yescharacteristic
52C22×#121C2211yescharacteristic
53C22×C4×Q8C2211yescharacteristic, complemented
54C22×C4×D4C2212yes—
55C22×C4×D4C2211yescharacteristic, complemented
56C22×#117C2212yescomplemented
57C23×C42C2211yescharacteristic
58#2855C2211yescharacteristic, complemented
59#2855C2211yescharacteristic, complemented
60#2855C2212yescomplemented
61#2854C2212yes—
62#2854C2212yes—
63#2854C2212yes—
64#2854C2212yes—
65#2854C2214yescomplemented
66#2854C2214yescomplemented
67#2854C2214yescomplemented
68#2854C2211yescharacteristic, complemented
69#2854C2211yescharacteristic, complemented
70#2854C2212yescomplemented
71#2853C2214yescomplemented
72#2849C2212yes—
73#2849C2212yes—
74#2849C2214yescomplemented
75#2815C2214yes—
76#2813C2214yescomplemented
77#2733C2218yescomplemented
78#2730C2218yescomplemented
79#2727C2218yescomplemented
80#2725C2218yescomplemented
81#2723C2218yescomplemented
82#2723C2218yescomplemented
83#2714C2218yescomplemented
84#2714C2218yescomplemented
85#2710C2218yescomplemented
86#2706C2218yescomplemented
87#2705C2218yescomplemented
88#2703C2218yescomplemented
89#2703C2218yescomplemented
90#2702C2218yescomplemented
91#2694C2218yescomplemented
92#2690C2218yescomplemented
93#2656C2212yes—
94#2639C2212yes—
95#2626C2212yescomplemented
96#2624C2212yescomplemented
97#2623C2214yescomplemented
98#2619C2214yes—
99#2617C2212yes—
100#2617C2212yes—
101#2617C2214yes—
102#2617C2212yescomplemented
103#2617C2214yescomplemented
104#2615C2212yescomplemented
105#2550C2214yescomplemented
106#2548C2214yescomplemented
107#2539C2214yescomplemented
108#2539C2218yescomplemented
109#2534C2214yescomplemented
110#2504C2212yes—
111#2504C2212yes—
112#2504C2214yescomplemented
113#2490C2214yescomplemented
114#2488C2218yescomplemented
115#2487C2212yescomplemented
116#2487C2214yescomplemented
117#2479C2218yescomplemented
118#2477C2218yescomplemented
119#2475C2218yescomplemented
120#2471C2218yescomplemented
121#2464C2218yescomplemented
122#2463C2218yescomplemented
123#2461C2218yescomplemented
124#2456C2218yescomplemented
125#2456C2218yescomplemented
126#2455C2218yescomplemented
127#2454C2214yescomplemented
128#2452C2214yescomplemented
129#2449C2218yescomplemented
130#2448C2218yescomplemented
131#2448C2214yescomplemented
132#2448C2214yescomplemented
133#2442C2214yescomplemented
134#2433C2212yes—
135#2433C2212yes—
136#2431C2214yescomplemented
137#2428C2214yescomplemented
138#2426C2214yescomplemented
139#2425C2218yescomplemented
140#2424C2218yescomplemented
141#2421C2218yescomplemented
142#2421C2214yescomplemented
143#2416C2214yes—
144#2415C2218yescomplemented
145#2415C2218yescomplemented
146#2414C2218yescomplemented
147#2414C2218yescomplemented
148#2413C2214yescomplemented
149#2412C2218yescomplemented
150#2411C2214yescomplemented
151#2410C2214yes—
152#2408C2212yescomplemented
153#2406C2214yescomplemented
154#2404C2214yescomplemented
155#2403C2214yes—
156#2378C2214yescomplemented
157#2366C2214yescomplemented
158#2361C2218yescomplemented
159#2361C2214yescomplemented
160#2360C2214yescomplemented
161#2358C2218yescomplemented
162#2351C2214yescomplemented
163#2344C2212yescomplemented
164#2342C2214yes—
165#2341C2214yescomplemented
166Q8×C22⋊C4C2212yescomplemented
167#2329C2214yescomplemented
168#2323C2214yescomplemented
169#2321C2214yescomplemented
170#2316C2212yescomplemented
171#2313C2212yescomplemented
172#2311C2214yescomplemented
173C4×#123C2214yescomplemented
174C4×#123C2212yescomplemented
175C4×#123C2214yescomplemented
176C4×#123C2212yescomplemented
177#2297C2212yescomplemented
178#2296C2212yescomplemented
179C2×#390C2212yescomplemented
180C2×#389C2212yescomplemented
181C2×#388C2214yescomplemented
182C2×#386C2212yes—
183#2280C2211yescharacteristic
184C2×#380C2211yescharacteristic
185C22×#41C2314yes—
186C22×#41C2312yes—
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×D4C2312yes—
190C23×D4C2311yescharacteristic
191C23×D4C2312yes—
192C23×D4C2311yescharacteristic
193C24×C4C2311yescharacteristic
194C24×C4C2312yes—
195C24×C4C2311yescharacteristic
196C24×C4C2311yescharacteristic
197#562—232no—
198#554—216no—
199#548—216no—
200#547—216no—
201#546—216no—
202#546—232no—
203#543—216no—
204#542—216no—
205#539—216no—
206#538—216no—
207#537—216no—
208#537—216no—
209C2×C4⋊Q8C2312yes—
210C2×#127C2314yes—
211#529—232no—
212#529—232no—
213#529—232no—
214#529—232no—
215C2×#126—216no—
216C2×#126C2318yes—
217C2×#126C2318yes—
218C2×#126C2314yes—
219C2×#125—28no—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#124—28no—
224C2×#124C2314yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2312yes—
229#525—28no—
230#525—416no—
231C2×#123—216no—
232C2×#123—48no—
233C2×#123C2312yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2312yes—
237C2×#123C2318yes—
238C2×#123C2318yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2312yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2318yes—
246C2×C22⋊Q8D4116yescomplemented
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2318yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×#121—28no—
262C2×#121—28no—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C2×#121C2311yescharacteristic
266C2×#121C2312yes—
267C2×#121C2311yescharacteristic
268C2×#121C2312yes—
269C2×#121C2314yes—
270C2×#121C2312yes—
271C2×#121C2312yes—
272C2×#121C2312yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2312yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2318yes—
281C2×#121C2318yes—
282C2×#120C2312yes—
283C2×#120C2314yes—
284C2×#120C2314yes—
285C2×#120C2318yes—
286C2×#120C2314yes—
287C2×#120C2314yes—
288C2×C4×Q8—28no—
289C2×C4×Q8C2314yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2314yes—
293C2×C4×D4—28no—
294C2×C4×D4—216no—
295C2×C4×D4C2314yes—
296C2×C4×D4C2318yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2318yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2318yes—
305C2×C4×D4C2318yes—
306C2×#117—216no—
307C2×#117C2311yescharacteristic
308C2×#117C2318yes—
309C2×#117C2318yes—
310C2×#117C2314yes—
311C2×#117C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2314yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2311yescharacteristic
322C22×C22⋊C4C2312yes—
323C22×C22⋊C4C2314yes—
324C22×C22⋊C4C2312yes—
325C22×C22⋊C4C2312yes—
326C22×C22⋊C4C2312yes—
327C22×C22⋊C4C2312yes—
328C22×C22⋊C4C2312yes—
329C22×C22⋊C4C2314yes—
330C22×C22⋊C4C2314yes—
331C22×C22⋊C4C2312yes—
332C22×C42—28no—
333C22×C42C2312yes—
334C22×C42C2311yescharacteristic
335C22×C42C2311yescharacteristic
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338C22×C42C2312yes—
339C22×C42C2312yes—
340C22×C42C2312yes—
341C22×C42C2312yes—
342#400C2318yes—
343#400C2314yes—
344#400C2318yes—
345#399C2318yes—
346#399C2314yes—
347#399C2314yes—
348#399C2318yes—
349#399C2318yes—
350#398C2318yes—
351#398C2318yes—
352#397C2314yes—
353#397C2318yes—
354#397C2314yes—
355#397C2314yes—
356#397C2318yes—
357#397C2318yes—
358#397C2318yes—
359#397C2318yes—
360#396C2318yes—
361#396C2318yes—
362#396C2318yes—
363#396C2318yes—
364#395C2318yes—
365#394C2318yes—
366#394C2318yes—
367#394C2318yes—
368#394C2318yes—
369#394C2318yes—
370#394C2318yes—
371#394C2314yes—
372#394C2318yes—
373#394C2318yes—
374#394C2318yes—
375#393C2314yes—
376#393C2318yes—
377#392C2314yes—
378#392C2318yes—
379#392C2314yes—
380#392C2318yes—
381#392C2314yes—
382#392C2318yes—
383#392C2318yes—
384#392C2318yes—
385#392C2314yes—
386#392C2318yes—
387#392C2318yes—
388#391C2318yes—
389#391C2314yes—
390#391C2318yes—
391#391C2312yes—
392#391C2312yes—
393#390C2318yes—
394#390C2318yes—
395#390C2314yes—
396#390C2318yes—
397#390C2314yes—
398#390C2318yes—
399#390C2314yes—
400#390C2314yes—
401#390C2314yes—
402#390C2312yes—
403#390C2312yes—
404#390C2318yes—
405#390C2314yes—
406#390C2318yes—
407#390C2314yes—
408#390C2318yes—
409#389C2318yes—
410#389C2318yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2318yes—
421#389C2314yes—
422#389C2318yes—
423#389C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2318yes—
440#388C2318yes—
441#388C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2318yes—
450#386C2312yes—
451#386C2314yes—
452#386C2314yes—
453#386C2314yes—
454#386C2318yes—
455#386C2314yes—
456#386C2314yes—
457#386C2314yes—
458#386C2312yes—
459#386C2318yes—
460#386C2318yes—
461#386C2314yes—
462#386C2318yes—
463#386C2318yes—
464#386C2318yes—
465#386C2318yes—
466#386C2318yes—
467#386C2314yes—
468#386C2318yes—
469#385C2312yes—
470#385C2318yes—
471#385C2314yes—
472#385C2314yes—
473#385C2314yes—
474#385C2312yes—
475#385C2318yes—
476#385C2318yes—
477#385C2318yes—
478#385C2318yes—
479#385C2314yes—
480#382C2314yes—
481#382C2318yes—
482#381C2314yes—
483#381C2312yes—
484#381C2314yes—
485#381C2312yes—
486#381C2312yes—
487#380C2318yes—
488#380C2318yes—
489#380C2311yescharacteristic
490#380C2312yes—
491#380C2311yescharacteristic
492#380C2314yes—
493#380C2312yes—
494#380C2312yes—
495#380C2312yes—
496#380C2314yes—
497#380C2318yes—
498#380C2312yes—
499#379C2314yes—
500#379C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2318yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C2×#95C2312yes—
513C2×#95C2314yes—
514C25C2411yescharacteristic
515C25C2412yes—
516C25C2412yes—
517C2×#41—28no—
518C2×#41—24no—
519C2×#41—216no—
520C2×#41—44no—
521C2×#41—48no—
522C2×#41—48no—
523C2×#41—48no—
524C22×Q8—44no—
525C22×Q8C2×D418yes—
526C22×Q8C2412yes—
527C22×Q8C2414yes—
528C22×Q8C2411yescharacteristic
529C22×Q8C2412yes—
530C22×D4—28no—
531C22×D4—28no—
532C22×D4—24no—
533C22×D4—24no—
534C22×D4—44no—
535C22×D4—44no—
536C22×D4—48no—
537C22×D4—44no—
538C22×D4—44no—
539C22×D4C2412yes—
540C22×D4C2414yes—
541C22×D4C2412yes—
542C22×D4C2412yes—
543C22×D4C2414yes—
544C22×D4C2412yes—
545C22×D4C2414yes—
546C22×D4C2412yes—
547C22×D4C2414yes—
548C22×D4C2412yes—
549C22×D4C2414yes—
550C22×D4C2411yescharacteristic
551C22×D4C2414yes—
552C22×D4C2412yes—
553C22×D4C2418yes—
554C22×D4C2418yes—
555C22×D4C2418yes—
556C23×C4—24no—
557C23×C4—24no—
558C23×C4—28no—
559C23×C4—24no—
560C23×C4—28no—
561C23×C4—44no—
562C23×C4—44no—
563C23×C4—42no—
564C23×C4—44no—
565C23×C4C2×D418yes—
566C23×C4C2411yescharacteristic
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2418yes—
571C23×C4C2412yes—
572C23×C4C2412yes—
573C23×C4C2411yescharacteristic
574C23×C4C2411yescharacteristic
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2414yes—
578C23×C4C2411yescharacteristic
579C23×C4C2411yescharacteristic
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2414yes—
583C23×C4C2414yes—
584C23×C4C2414yes—
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2411yescharacteristic
588C23×C4C2411yescharacteristic
589C23×C4C2411yescharacteristic
590C4⋊Q8—28no—
591#127—48no—
592#126—232no—
593#126—232no—
594#126—216no—
595#125—216no—
596#125—216no—
597#125—216no—
598#124—216no—
599#124—216no—
600#124—216no—
601#124—28no—
602#124—216no—
603#123—28no—
604#123—216no—
605#123—216no—
606#123—28no—
607#123—216no—
608#123—216no—
609#123—232no—
610#123—232no—
611#123—216no—
612#123—416no—
613#123—48no—
614#123—48no—
615#123—44no—
616C22⋊Q8—28no—
617C22⋊Q8—216no—
618C22⋊Q8—24no—
619C22⋊Q8—24no—
620C22⋊Q8—216no—
621C22⋊Q8—216no—
622C22⋊Q8—216no—
623C22⋊Q8—216no—
624C22⋊Q8—216no—
625C22⋊Q8—416no—
626C22⋊Q8C2×D4116yes—
627C22⋊Q8C2×D4116yes—
628C22⋊Q8C2×D4116yes—
629C22⋊Q8C2×D4116yes—
630#121—28no—
631#121—28no—
632#121—28no—
633#121—28no—
634#121—28no—
635#121—28no—
636#121—28no—
637#121—28no—
638#121—24no—
639#121—24no—
640#121—216no—
641#121—216no—
642#121—28no—
643#121—216no—
644#121—216no—
645#121—216no—
646#121—416no—
647#121—48no—
648#121—416no—
649#120—28no—
650#120—216no—
651#120—416no—
652#120—48no—
653#120—48no—
654#120—48no—
655C4×Q8—216no—
656C4×Q8—216no—
657C4×Q8—28no—
658C4×Q8—48no—
659C4×D4—28no—
660C4×D4—28no—
661C4×D4—216no—
662C4×D4—216no—
663C4×D4—216no—
664C4×D4—28no—
665C4×D4—232no—
666C4×D4—232no—
667C4×D4—216no—
668C4×D4—416no—
669C4×D4—416no—
670#117—24no—
671#117—232no—
672#117—232no—
673#117—44no—
674#117—48no—
675C2×C4⋊C4—28no—
676C2×C4⋊C4—28no—
677C2×C4⋊C4—24no—
678C2×C4⋊C4—28no—
679C2×C4⋊C4—24no—
680C2×C4⋊C4—28no—
681C2×C4⋊C4—44no—
682C2×C4⋊C4—48no—
683C2×C4⋊C4C2×D4116yes—
684C2×C4⋊C4C2×D418yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2418yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2418yes—
709C2×C4⋊C4C2418yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C22⋊C4—28no—
718C2×C22⋊C4—28no—
719C2×C22⋊C4—28no—
720C2×C22⋊C4—28no—
721C2×C22⋊C4—28no—
722C2×C22⋊C4—216no—
723C2×C22⋊C4—48no—
724C2×C22⋊C4—44no—
725C2×C22⋊C4—48no—
726C2×C22⋊C4C2×D4116yes—
727C2×C22⋊C4C2412yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2412yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2412yes—
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2418yes—
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2418yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2418yes—
756C2×C22⋊C4C2418yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2418yes—
759C2×C22⋊C4C2418yes—
760C2×C22⋊C4C2418yes—
761C2×C22⋊C4C2418yes—
762C2×C22⋊C4C2418yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C42—24no—
769C2×C42—28no—
770C2×C42—24no—
771C2×C42—24no—
772C2×C42—24no—
773C2×C42—28no—
774C2×C42—28no—
775C2×C42—28no—
776C2×C42—28no—
777C2×C42C2412yes—
778C2×C42C2412yes—
779C2×C42C2418yes—
780C2×C42C2412yes—
781C2×C42C2414yes—
782C2×C42C2412yes—
783C2×C42C2412yes—
784C2×C42C2414yes—
785C2×C42C2412yes—
786C2×C42C2412yes—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2418yes—
790C2×C42C2418yes—
791#95C2414yes—
792#95C2414yes—
793#95C2418yes—
794#95C2418yes—
795#95C2414yes—
796#95C2414yes—
797#95C2418yes—
798#95C2412yes—
799#95C2414yes—
800#95C2412yes—
801#95C2418yes—
802#95C2418yes—
803#95C2414yes—
804#95C2414yes—
805#95C2418yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2418yes—
810#95C2414yes—
811#95C2418yes—
812#95C2418yes—
813#95C2418yes—
814C24—22no—
815C24—24no—
816C24—22no—
817C24—24no—
818C24—24no—
819C24—24no—
820C24—28no—
821C24—24no—
822C24—42no—
823C24—44no—
824C24—44no—
825C24—42no—
826C24—44no—
827C24—42no—
828C24C22×D414yes—
829C24C2514yes—
830C24C2514yes—
831C24C2512yes—
832C24C2511yescharacteristic
833C24C2511yescharacteristic
834C24C2511yescharacteristic
835#41—88no—
836#41—832no—
837#41—816no—
838C2×Q8—22no—
839C2×Q8—28no—
840C2×Q8—28no—
841C2×Q8—44no—
842C2×Q8—44no—
843C2×Q8—42no—
844C2×Q8—44no—
845C2×Q8—416no—
846C2×Q8C22×D418yes—
847C2×Q8C22×D418yes—
848C2×D4—24no—
849C2×D4—28no—
850C2×D4—28no—
851C2×D4—24no—
852C2×D4—28no—
853C2×D4—24no—
854C2×D4—28no—
855C2×D4—216no—
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—24no—
859C2×D4—24no—
860C2×D4—28no—
861C2×D4—24no—
862C2×D4—24no—
863C2×D4—24no—
864C2×D4—28no—
865C2×D4—28no—
866C2×D4—22no—
867C2×D4—24no—
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—44no—
871C2×D4—48no—
872C2×D4—416no—
873C2×D4—48no—
874C2×D4—48no—
875C2×D4—48no—
876C2×D4—44no—
877C2×D4—48no—
878C2×D4—48no—
879C2×D4—44no—
880C2×D4—48no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—48no—
884C2×D4—42no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—48no—
888C2×D4—48no—
889C2×D4—48no—
890C2×D4—432no—
891C2×D4—88no—
892C2×D4—816no—
893C22×C4—22no—
894C22×C4—24no—
895C22×C4—22no—
896C22×C4—24no—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—22no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—22no—
912C22×C4—24no—
913C22×C4—28no—
914C22×C4—24no—
915C22×C4—216no—
916C22×C4—24no—
917C22×C4—216no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—28no—
923C22×C4—416no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—48no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—432no—
937C22×C4—44no—
938C22×C4—42no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—42no—
943C22×C4—48no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—416no—
947C22×C4—416no—
948C22×C4C22×D414yes—
949C22×C4C22×D414yes—
950C22×C4C22×D414yes—
951C22×C4C22×D418yes—
952C22×C4C22×D414yes—
953C22×C4C22×D414yes—
954C22×C4C22×D414yes—
955C22×C4C22×D418yes—
956C22×C4H(5,𝔽2)14yes—
957C22×C4C2514yes—
958C22×C4C2512yes—
959C22×C4C2514yes—
960C22×C4C2518yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2514yes—
964C22×C4C2512yes—
965C22×C4C2514yes—
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2511yescharacteristic
969C22×C4C2514yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2514yes—
973C22×C4C2512yes—
974C22×C4C2511yescharacteristic
975C4⋊C4—24no—
976C4⋊C4—216no—
977C4⋊C4—216no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—216no—
981C4⋊C4—24no—
982C4⋊C4—28no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—216no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—44no—
994C4⋊C4—48no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—48no—
998C4⋊C4—48no—
999C4⋊C4—48no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4C22×D418yes—
1004C4⋊C4C22×D4116yes—
1005C4⋊C4C22×D4116yes—
1006C4⋊C4C22×D418yes—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—24no—
1010C22⋊C4—28no—
1011C22⋊C4—24no—
1012C22⋊C4—28no—
1013C22⋊C4—24no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—216no—
1017C22⋊C4—216no—
1018C22⋊C4—216no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—24no—
1026C22⋊C4—28no—
1027C22⋊C4—24no—
1028C22⋊C4—216no—
1029C22⋊C4—28no—
1030C22⋊C4—48no—
1031C22⋊C4—48no—
1032C22⋊C4—44no—
1033C22⋊C4—48no—
1034C22⋊C4—44no—
1035C22⋊C4—48no—
1036C22⋊C4—48no—
1037C22⋊C4—48no—
1038C22⋊C4—48no—
1039C22⋊C4—48no—
1040C22⋊C4—48no—
1041C22⋊C4—48no—
1042C22⋊C4—48no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4C22×D4116yes—
1047C22⋊C4C22×D4116yes—
1048C42—24no—
1049C42—24no—
1050C42—24no—
1051C42—24no—
1052C42—24no—
1053C42—24no—
1054C42—24no—
1055C42—24no—
1056C42—216no—
1057C42—24no—
1058C42—28no—
1059C42—28no—
1060C42—48no—
1061C42—48no—
1062C23—21no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—21no—
1067C23—21no—
1068C23—22no—
1069C23—22no—
1070C23—21no—
1071C23—28no—
1072C23—28no—
1073C23—24no—
1074C23—24no—
1075C23—22no—
1076C23—24no—
1077C23—22no—
1078C23—24no—
1079C23—24no—
1080C23—28no—
1081C23—22no—
1082C23—24no—
1083C23—28no—
1084C23—28no—
1085C23—24no—
1086C23—28no—
1087C23—24no—
1088C23—44no—
1089C23—48no—
1090C23—48no—
1091C23—48no—
1092C23—48no—
1093C23—48no—
1094C23—48no—
1095C23—88no—
1096C23—88no—
1097C23—84no—
1098C23—84no—
1099C23—88no—
1100C23—88no—
1101C23C23×D412yes—
1102C23C23×D412yes—
1103C23C23×D412yes—
1104C23C2×H(5,𝔽2)12yes—
1105C23#58514yes—
1106C23#58512yes—
1107C23C2611yescharacteristic
1108Q8—216no—
1109Q8—48no—
1110Q8—82no—
1111Q8—88no—
1112D4—48no—
1113D4—416no—
1114D4—48no—
1115D4—416no—
1116D4—416no—
1117D4—48no—
1118D4—48no—
1119D4—48no—
1120D4—84no—
1121D4—82no—
1122D4—88no—
1123D4—88no—
1124D4—88no—
1125D4—84no—
1126D4—816no—
1127D4—816no—
1128D4—168no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—28no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—28no—
1138C2×C4—216no—
1139C2×C4—28no—
1140C2×C4—28no—
1141C2×C4—28no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—28no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—28no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—28no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—28no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—44no—
1173C2×C4—44no—
1174C2×C4—44no—
1175C2×C4—48no—
1176C2×C4—432no—
1177C2×C4—48no—
1178C2×C4—48no—
1179C2×C4—44no—
1180C2×C4—44no—
1181C2×C4—48no—
1182C2×C4—48no—
1183C2×C4—48no—
1184C2×C4—44no—
1185C2×C4—48no—
1186C2×C4—88no—
1187C2×C4—88no—
1188C2×C4—88no—
1189C2×C4—88no—
1190C2×C4—84no—
1191C2×C4C23×D412yes—
1192C2×C4C23×D412yes—
1193C2×C4C23×D412yes—
1194C2×C4C23×D418yes—
1195C2×C4C23×D418yes—
1196C2×C4C23×D412yes—
1197C2×C4C2×H(5,𝔽2)14yes—
1198C2×C4#58514yes—
1199C22—24no—
1200C22—24no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—24no—
1206C22—24no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—416no—
1211C22—42no—
1212C22—42no—
1213C22—44no—
1214C22—48no—
1215C22—48no—
1216C22—42no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—42no—
1221C22—44no—
1222C22—44no—
1223C22—42no—
1224C22—44no—
1225C22—48no—
1226C22—48no—
1227C22—44no—
1228C22—816no—
1229C22—168no—
1230C22#348714yes—
1231C22#348814yes—
1232C22C24×D411yescharacteristic
1233C22C22×H(5,𝔽2)11yescharacteristic
1234C22C2×#58512yes—
1235C22C2×#58512yes—
1236C22C2×#58511yescharacteristic
1237C4—22no—
1238C4—22no—
1239C4—22no—
1240C4—28no—
1241C4—24no—
1242C4—28no—
1243C4—48no—
1244C4—44no—
1245C4—42no—
1246C4—42no—
1247C4—42no—
1248C4—44no—
1249C4—42no—
1250C4—42no—
1251C4—44no—
1252C4—42no—
1253C4—44no—
1254C4#348514yes—
1255C2—24no—
1256C2—24no—
1257C2—42no—
1258C2—82no—
1259C2—84no—
1260C2—84no—
1261C2#6274812yes—
1262C2C2×#348511yescharacteristic
1263C2C2×#348711yescharacteristic
1264C2C2×#348811yescharacteristic
1265C2#6282912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3536C2semidirect
2. C22×#529C2semidirect
3. #59076C2semidirect
4. #59046C2semidirect
5. #45766C2semidirect
6. #39135C2semidirect
7. #38907C2semidirect
8. #38023C2semidirect
9. #37797C2semidirect
10. #37785C2semidirect
11. #37770C2semidirect
12. #37754C2semidirect
13. #37450C2semidirect
14. #37439C2semidirect
15. #36971C2semidirect
16. #36961C2semidirect
17. #36626C2semidirect
18. C2×#2854C2semidirect
19. #36578C2semidirect
20. #36102C2semidirect
21. #36099C2semidirect
22. #35150C2semidirect
23. #35094C2semidirect
24. #34380C2semidirect
26. C2×#562C22semidirect
27. C2×#554C22semidirect
31. C2×#546C22semidirect
32. C2×#543C22semidirect
33. C2×#542C22semidirect
35. C2×#538C22semidirect
37. C2×#537C22semidirect
41. C2×#529C22semidirect
42. C2×#529C22semidirect
43. C22×#126C22semidirect
44. C22×#125C22semidirect
45. C22×#124C22semidirect
47. C2×#525C22semidirect
53. C22×C4×Q8C22semidirect
55. C22×C4×D4C22semidirect
56. C22×#117C22semidirect
58. #2855C22semidirect
59. #2855C22semidirect
60. #2855C22semidirect
65. #2854C22semidirect
66. #2854C22semidirect
67. #2854C22semidirect
68. #2854C22semidirect
69. #2854C22semidirect
70. #2854C22semidirect
71. #2853C22semidirect
74. #2849C22semidirect
76. #2813C22semidirect
77. #2733C22semidirect
78. #2730C22semidirect
79. #2727C22semidirect
80. #2725C22semidirect
81. #2723C22semidirect
82. #2723C22semidirect
83. #2714C22semidirect
84. #2714C22semidirect
85. #2710C22semidirect
86. #2706C22semidirect
87. #2705C22semidirect
88. #2703C22semidirect
89. #2703C22semidirect
90. #2702C22semidirect
91. #2694C22semidirect
92. #2690C22semidirect
95. #2626C22semidirect
96. #2624C22semidirect
97. #2623C22semidirect
102. #2617C22semidirect
103. #2617C22semidirect
104. #2615C22semidirect
105. #2550C22semidirect
106. #2548C22semidirect
107. #2539C22semidirect
108. #2539C22semidirect
109. #2534C22semidirect
112. #2504C22semidirect
113. #2490C22semidirect
114. #2488C22semidirect
115. #2487C22semidirect
116. #2487C22semidirect
117. #2479C22semidirect
118. #2477C22semidirect
119. #2475C22semidirect
120. #2471C22semidirect
121. #2464C22semidirect
122. #2463C22semidirect
123. #2461C22semidirect
124. #2456C22semidirect
125. #2456C22semidirect
126. #2455C22semidirect
127. #2454C22semidirect
128. #2452C22semidirect
129. #2449C22semidirect
130. #2448C22semidirect
131. #2448C22semidirect
132. #2448C22semidirect
133. #2442C22semidirect
136. #2431C22semidirect
137. #2428C22semidirect
138. #2426C22semidirect
139. #2425C22semidirect
140. #2424C22semidirect
141. #2421C22semidirect
142. #2421C22semidirect
144. #2415C22semidirect
145. #2415C22semidirect
146. #2414C22semidirect
147. #2414C22semidirect
148. #2413C22semidirect
149. #2412C22semidirect
150. #2411C22semidirect
152. #2408C22semidirect
153. #2406C22semidirect
154. #2404C22semidirect
156. #2378C22semidirect
157. #2366C22semidirect
158. #2361C22semidirect
159. #2361C22semidirect
160. #2360C22semidirect
161. #2358C22semidirect
162. #2351C22semidirect
163. #2344C22semidirect
165. #2341C22semidirect
166. Q8×C22⋊C4C22semidirect
167. #2329C22semidirect
168. #2323C22semidirect
169. #2321C22semidirect
170. #2316C22semidirect
171. #2313C22semidirect
172. #2311C22semidirect
173. C4×#123C22semidirect
174. C4×#123C22semidirect
175. C4×#123C22semidirect
176. C4×#123C22semidirect
177. #2297C22semidirect
178. #2296C22semidirect
179. C2×#390C22semidirect
180. C2×#389C22semidirect
181. C2×#388C22semidirect
246. C2×C22⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35362
C22×#5292
#590762
#590462
#457662
#391352
#389072
#380232
#377972
#377852
#377702
#377542
#374502
#374392
#369712
#369612
#366262
C2×#28542
#365782
#361022
#360992
#351502
#350942
#343802