Finite Group Databasebeta

← #7633040

Subgroups — #7633040

Order 512.

11865 conjugacy classes of subgroups.

The subgroup lattice has 1273 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3488C211yesmaximal, characteristic, complemented
2C2×#3488C211yesmaximal, characteristic, complemented
3C2×D4×#41C211yesmaximal, characteristic, complemented
4C22×#520C211yesmaximal, characteristic, complemented
5#36576C212yesmaximal, complemented
6#36434C212yesmaximal, complemented
7#36214C216yesmaximal, complemented
8D4×#121C216yesmaximal, complemented
9#36029C212yesmaximal, complemented
10#35831C212yesmaximal, complemented
11#35821C216yesmaximal, complemented
12#35728C216yesmaximal, complemented
13#35564C213yesmaximal, complemented
14#35563C213yesmaximal, complemented
15#35533C213yesmaximal, complemented
16#35518C213yesmaximal, complemented
17#35252C213yesmaximal, complemented
18#35223C213yesmaximal, complemented
19#34737C213yesmaximal, complemented
20C2×#2416C213yesmaximal, complemented
21#34258C211yesmaximal, characteristic, complemented
22#34250C211yesmaximal, characteristic, complemented
23#34175C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic
25C23×#41C2211yescharacteristic
26C23×#41C2211yescharacteristic
27#3488—216no—
28#3488—216no—
29D4×#41—216no—
30C2×#550C2212yescomplemented
31C2×#550C2212yescomplemented
32C2×#550C2211yescharacteristic, complemented
33C2×D4×Q8C2211yescharacteristic, complemented
34C2×#548C2212yescomplemented
35C2×#548C2212yescomplemented
36C2×#548C2211yescharacteristic, complemented
37C2×#548C2211yescharacteristic, complemented
38C2×#547C2213yescomplemented
39C2×#546C2216yescomplemented
40C2×#546C2216yescomplemented
41C2×#546C2213yescomplemented
42C2×#546C2213yescomplemented
43C2×D42C2216yescomplemented
44C2×D42C2216yescomplemented
45C2×D42C2213yescomplemented
46C2×#537C2213yescomplemented
47C2×#537C2213yescomplemented
48C2×#535C2213yescomplemented
49C2×#535C2213yescomplemented
50C2×#532C2213yescomplemented
51C2×#525C2213yescomplemented
52C2×#525C2213yescomplemented
53C2×#525C2213yescomplemented
54C2×#525C2213yescomplemented
55C22×#121C2213yescomplemented
56C22×#121C2213yescomplemented
57C22×#121C2216yescomplemented
58C2×#520—216no—
59C2×#520C2211yescharacteristic
60C2×#520C2211yescharacteristic
61C2×#520C2211yescharacteristic
62C2×#520C2216yescomplemented
63C2×#520C2212yescomplemented
64C2×#520C2213yescomplemented
65C2×#520C2213yescomplemented
66C2×C4×#41C2211yescharacteristic
67C22×C4×Q8C2212yescomplemented
68C22×C4×D4C2213yescomplemented
69C22×C4×D4C2216yescomplemented
70C22×#117C2213yescomplemented
71C23×C4⋊C4C2213yescomplemented
72#2856C2216yescomplemented
73#2850C2216yescomplemented
74#2847C22112yescomplemented
75#2620C2216yescomplemented
76#2619C2216yescomplemented
77#2618C22112yescomplemented
78#2548C2216yescomplemented
79#2545C2216yescomplemented
80#2544C2216yescomplemented
81#2543C22112yescomplemented
82#2541C2216yescomplemented
83#2538C2216yescomplemented
84#2537C2216yescomplemented
85#2536C2216yescomplemented
86#2535C2216yescomplemented
87#2534C22112yescomplemented
88#2429C2216yescomplemented
89#2428C2216yescomplemented
90#2428C2216yescomplemented
91#2428C2216yescomplemented
92#2427C2216yescomplemented
93#2426C2216yescomplemented
94#2426C2216yescomplemented
95#2426C2216yescomplemented
96#2425C22112yescomplemented
97#2424C22112yescomplemented
98#2424C22112yescomplemented
99#2424C22112yescomplemented
100#2417C2216yescomplemented
101#2417C2213yescomplemented
102#2417C2216yescomplemented
103#2417C2216yescomplemented
104#2417C2211yescharacteristic, complemented
105#2416C2216yescomplemented
106#2416C2213yescomplemented
107#2416C2216yescomplemented
108#2416C2216yescomplemented
109#2416C2216yescomplemented
110#2416C2216yescomplemented
111#2416C2216yescomplemented
112#2416C2216yescomplemented
113#2416C2216yescomplemented
114#2416C2216yescomplemented
115#2416C2216yescomplemented
116#2416C2213yescomplemented
117#2416C22112yescomplemented
118#2415C2213yescomplemented
119#2415C2213yescomplemented
120#2414C2213yescomplemented
121#2414C2213yescomplemented
122#2414C2216yescomplemented
123#2414C2216yescomplemented
124#2413C2216yescomplemented
125#2412C2216yescomplemented
126#2411C2216yescomplemented
127#2411C22112yescomplemented
128#2410C22112yescomplemented
129#2410C2216yescomplemented
130#2408C22112yescomplemented
131#2392C2216yescomplemented
132#2392C2216yescomplemented
133C2×#396C2216yescomplemented
134C2×#394C2216yescomplemented
135#2351C2212yescomplemented
136Q8×C4⋊C4C2212yescomplemented
137#2349C2216yescomplemented
138D4×C4⋊C4C2216yescomplemented
139#2341C2212yescomplemented
140#2341C2212yescomplemented
141#2341C2212yescomplemented
142Q8×C22⋊C4C2212yescomplemented
143#2339C2216yescomplemented
144D4×C22⋊C4C2216yescomplemented
145D4×C22⋊C4C2216yescomplemented
146D4×C22⋊C4C2216yescomplemented
147#2317C2213yescomplemented
148#2316C2213yescomplemented
149#2311C2213yescomplemented
150#2311C2213yescomplemented
151#2311C2213yescomplemented
152#2309C2213yescomplemented
153C4×#121C2216yescomplemented
154C4×#121C2216yescomplemented
155#2297C2213yescomplemented
156#2296C2213yescomplemented
157C2×#390C2213yescomplemented
158C2×#389C2213yescomplemented
159C2×#386C2216yescomplemented
160#2280C2213yescomplemented
161C2×#380C2213yescomplemented
162C2×H(5,𝔽2)—28no—
163C2×H(5,𝔽2)—28no—
164C2×H(5,𝔽2)—28no—
165C22×#41—28no—
166C22×#41—28no—
167C22×#41—28no—
168C22×#41—28no—
169C22×#41—28no—
170C22×#41D4116yescomplemented
171C22×#41C2313yes—
172C22×#41C2313yes—
173C22×#41C2311yescharacteristic
174C22×#41C2313yes—
175C22×#41C2312yes—
176C22×#41C2313yes—
177C22×#41C2313yes—
178C22×#41C2311yescharacteristic
179C22×#41C2311yescharacteristic
180C23×Q8C2311yescharacteristic
181C23×Q8C2311yescharacteristic
182C23×D4C2313yes—
183C23×D4C2313yes—
184C23×D4C2316yes—
185C23×D4C2313yes—
186C23×D4C2313yes—
187C23×D4C2316yes—
188C23×D4C2316yes—
189C24×C4C2313yes—
190C24×C4C2313yes—
191C24×C4C2316yes—
192#550—28no—
193#550—216no—
194#550—216no—
195D4×Q8—28no—
196#548—28no—
197#548—28no—
198#548—216no—
199#548—216no—
200#547—224no—
201#546—224no—
202#546—248no—
203#546—224no—
204#546—248no—
205D42—224no—
206D42—248no—
207D42—248no—
208#537—224no—
209#537—224no—
210#535—224no—
211#535—224no—
212#532—224no—
213C2×C4⋊Q8C2313yes—
214C2×#127C2316yes—
215C2×#127C2313yes—
216C2×#127C2316yes—
217C2×#124C2316yes—
218C2×#124C2313yes—
219C2×#124C2313yes—
220C2×#124C2316yes—
221#525—224no—
222#525—224no—
223#525—224no—
224#525—224no—
225C2×#123C2316yes—
226C2×#123C2316yes—
227C2×#123C2316yes—
228C2×#123C2316yes—
229C2×C22⋊Q8C2313yes—
230C2×C22⋊Q8C2313yes—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2313yes—
234C2×C22⋊Q8C2313yes—
235C2×C22⋊Q8C2313yes—
236C2×C22⋊Q8C2313yes—
237C2×C22⋊Q8C2316yes—
238C2×C22⋊Q8C2316yes—
239C2×#121—224no—
240C2×#121—224no—
241C2×#121—424no—
242C2×#121C23112yes—
243C2×#121C2316yes—
244C2×#121C2313yes—
245C2×#121C2313yes—
246C2×#121C2316yes—
247C2×#121C2316yes—
248C2×#121C2313yes—
249C2×#121C2313yes—
250C2×#121C2316yes—
251C2×#121C2316yes—
252C2×#121C2316yes—
253C2×#121C2316yes—
254C2×#121C2313yes—
255C2×#121C2313yes—
256C2×#121C2313yes—
257C2×#121C2313yes—
258C2×#121C2316yes—
259C2×#121C2316yes—
260C2×#121C23112yes—
261C2×#121C2316yes—
262C2×#121C2316yes—
263C2×#121C23112yes—
264C2×#121C2316yes—
265C2×#121C23112yes—
266C2×#121C23112yes—
267C2×#121C23112yes—
268C2×#120C2316yes—
269C2×#120C2316yes—
270C2×#120C2316yes—
271C2×#120C23112yes—
272C2×#120C2316yes—
273C2×#120C23112yes—
274#520—28no—
275#520—28no—
276#520—216no—
277#520—248no—
278#520—224no—
279#520—224no—
280#520D4116yescomplemented
281C4×#41—28no—
282C2×C4×Q8—216no—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2316yes—
288C2×C4×Q8C2316yes—
289C2×C4×Q8C2312yes—
290C2×C4×D4—224no—
291C2×C4×D4—248no—
292C2×C4×D4C2316yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2316yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2316yes—
299C2×C4×D4C2316yes—
300C2×C4×D4C2316yes—
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C23112yes—
303C2×C4×D4C23112yes—
304C2×C4×D4C2316yes—
305C2×C4×D4C2316yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2316yes—
312C2×C4×D4C2316yes—
313C2×C4×D4C2316yes—
314C2×#117—224no—
315C2×#117C2313yes—
316C2×#117C2313yes—
317C2×#117C2313yes—
318C2×#117C2316yes—
319C2×#117C2316yes—
320C2×#117C2313yes—
321C2×#117C2313yes—
322C2×#117C2313yes—
323C22×C4⋊C4—224no—
324C22×C4⋊C4C2313yes—
325C22×C4⋊C4C2313yes—
326C22×C4⋊C4C2316yes—
327C22×C4⋊C4C2313yes—
328C22×C4⋊C4C2313yes—
329C22×C4⋊C4C2316yes—
330C22×C4⋊C4C2316yes—
331C22×C4⋊C4C2316yes—
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2316yes—
334C22×C4⋊C4C2313yes—
335C22×C22⋊C4C2313yes—
336C22×C22⋊C4C2316yes—
337C22×C22⋊C4C2316yes—
338C22×C22⋊C4C2316yes—
339C22×C22⋊C4C2313yes—
340C22×C22⋊C4C2316yes—
341C22×C22⋊C4C2316yes—
342C22×C22⋊C4C2316yes—
343C22×C42C2316yes—
344C22×C42C2313yes—
345#398C2316yes—
346#398C23112yes—
347#398C2312yes—
348#397C2316yes—
349#397C2316yes—
350#396C2316yes—
351#396C23112yes—
352#396C23112yes—
353#396C23112yes—
354#396C2316yes—
355#396C2316yes—
356#396C23112yes—
357#396C23112yes—
358#396C2312yes—
359#394C23112yes—
360#394C23112yes—
361#394C2316yes—
362#394C23112yes—
363#394C23112yes—
364#394C2316yes—
365#394C23112yes—
366#394C23112yes—
367#394C2316yes—
368#394C2316yes—
369#394C2316yes—
370#394C2316yes—
371#392C23112yes—
372#392C23112yes—
373#392C2316yes—
374#392C2316yes—
375#391C2313yes—
376#391C2316yes—
377#391C2316yes—
378#391C2311yescharacteristic
379#390C2313yes—
380#390C2316yes—
381#390C2316yes—
382#390C2316yes—
383#390C2316yes—
384#390C2316yes—
385#390C2316yes—
386#390C2316yes—
387#390C23112yes—
388#390C23112yes—
389#390C2316yes—
390#390C2316yes—
391#390C2313yes—
392#389C2313yes—
393#389C2316yes—
394#389C2316yes—
395#389C2316yes—
396#389C2313yes—
397#389C2316yes—
398#389C2316yes—
399#389C2316yes—
400#389C2316yes—
401#389C2311yescharacteristic
402#389C2313yes—
403#388C23112yes—
404#388C23112yes—
405#388C2316yes—
406#388C2316yes—
407#388C2316yes—
408#388C2316yes—
409#386C23112yes—
410#386C23112yes—
411#386C23112yes—
412#386C2316yes—
413#386C23112yes—
414#386C23112yes—
415#386C23112yes—
416#386C2316yes—
417#386C2316yes—
418#386C2316yes—
419#386C2312yes—
420#386C2316yes—
421#386C23112yes—
422#386C23112yes—
423#385C23112yes—
424#385C2316yes—
425#385C2316yes—
426#384C2316yes—
427#382C2316yes—
428#381C2316yes—
429#380C2313yes—
430#380C2316yes—
431#380C2313yes—
432#380C2316yes—
433#380C2316yes—
434#380C23112yes—
435#380C2316yes—
436#380C23112yes—
437#380C2316yes—
438#380C2316yes—
439#380C2312yes—
440#380C2311yescharacteristic
441#380C2313yes—
442#379C23112yes—
443#379C2316yes—
444C4×C4⋊C4C2316yes—
445C4×C4⋊C4C2316yes—
446C4×C22⋊C4C2316yes—
447C4×C22⋊C4C2316yes—
448C4×C22⋊C4C2316yes—
449C4×C22⋊C4C2316yes—
450C2×#95C2316yes—
451C2×#95C2316yes—
452C25C2413yes—
453C25C2413yes—
454C25C2416yes—
455H(5,𝔽2)—464no—
456C2×#41—2128no—
457C2×#41—24no—
458C2×#41—24no—
459C2×#41—28no—
460C2×#41—28no—
461C2×#41—24no—
462C2×#41—24no—
463C2×#41—24no—
464C2×#41—28no—
465C2×#41—212no—
466C2×#41—212no—
467C2×#41—212no—
468C2×#41—212no—
469C2×#41—212no—
470C2×#41—212no—
471C2×#41—212no—
472C2×#41—212no—
473C2×#41—212no—
474C2×#41—212no—
475C2×#41—212no—
476C2×#41—212no—
477C2×#41—212no—
478C2×#41—464no—
479C2×#41C2×D418yes—
480C2×#41C2×D418yes—
481C2×#41C2×D4124yescomplemented
482C2×#41C2×D4124yescomplemented
483C2×#41C2×D418yescomplemented
484C2×#41#4118yes—
485C22×Q8—24no—
486C22×Q8—24no—
487C22×Q8—24no—
488C22×Q8—24no—
489C22×Q8—24no—
490C22×Q8C2×D418yescomplemented
491C22×Q8C2411yescharacteristic
492C22×Q8C2413yes—
493C22×Q8C2413yes—
494C22×Q8C2411yescharacteristic
495C22×D4—212no—
496C22×D4—212no—
497C22×D4—212no—
498C22×D4—224no—
499C22×D4—212no—
500C22×D4—212no—
501C22×D4—224no—
502C22×D4—224no—
503C22×D4—212no—
504C22×D4—224no—
505C22×D4—212no—
506C22×D4—212no—
507C22×D4—212no—
508C22×D4—224no—
509C22×D4—212no—
510C22×D4—46no—
511C22×D4—412no—
512C22×D4—412no—
513C22×D4—412no—
514C22×D4—86no—
515C22×D4C2×D4124yescomplemented
516C22×D4C2413yes—
517C22×D4C2416yes—
518C22×D4C2416yes—
519C22×D4C2416yes—
520C22×D4C2413yes—
521C22×D4C2416yes—
522C22×D4C2413yes—
523C22×D4C2413yes—
524C22×D4C2413yes—
525C22×D4C2416yes—
526C22×D4C2416yes—
527C22×D4C2413yes—
528C22×D4C2411yescharacteristic
529C22×D4C2416yes—
530C22×D4C2416yes—
531C22×D4C2416yes—
532C22×D4C24112yes—
533C22×D4C24112yes—
534C22×D4C2413yes—
535C23×C4—212no—
536C23×C4—212no—
537C23×C4—212no—
538C23×C4—212no—
539C23×C4—212no—
540C23×C4—224no—
541C23×C4—412no—
542C23×C4—86no—
543C23×C4C2×D4124yescomplemented
544C23×C4C2413yes—
545C23×C4C2411yescharacteristic
546C23×C4C2413yes—
547C23×C4C2413yes—
548C23×C4C2413yes—
549C23×C4C2416yes—
550C23×C4C2412yes—
551C23×C4C2413yes—
552C23×C4C2416yes—
553C23×C4C2413yes—
554C23×C4C2411yescharacteristic
555C23×C4C2413yes—
556C23×C4C2413yes—
557C23×C4C2413yes—
558C23×C4C2413yes—
559C23×C4C2416yes—
560C23×C4C2416yes—
561C23×C4C24112yes—
562C23×C4C2416yes—
563C23×C4C2413yes—
564C4⋊Q8—212no—
565#127—212no—
566#127—224no—
567#127—224no—
568#124—212no—
569#124—224no—
570#124—212no—
571#124—224no—
572#123—224no—
573#123—224no—
574#123—224no—
575#123—224no—
576C22⋊Q8—212no—
577C22⋊Q8—212no—
578C22⋊Q8—224no—
579C22⋊Q8—24no—
580C22⋊Q8—212no—
581C22⋊Q8—212no—
582C22⋊Q8—212no—
583C22⋊Q8—24no—
584C22⋊Q8—212no—
585C22⋊Q8—224no—
586#121—212no—
587#121—212no—
588#121—224no—
589#121—224no—
590#121—248no—
591#121—224no—
592#121—224no—
593#121—212no—
594#121—224no—
595#121—224no—
596#121—224no—
597#121—212no—
598#121—212no—
599#121—212no—
600#121—248no—
601#121—212no—
602#121—224no—
603#121—224no—
604#121—224no—
605#121—212no—
606#121—224no—
607#121—424no—
608#121—424no—
609#121—424no—
610#121—412no—
611#121—812no—
612#120—224no—
613#120—224no—
614#120—224no—
615#120—248no—
616#120—224no—
617#120—248no—
618C4×Q8—28no—
619C4×Q8—24no—
620C4×Q8—24no—
621C4×Q8—28no—
622C4×Q8—224no—
623C4×Q8—224no—
624C4×Q8C2×D4116yescomplemented
625C4×D4—224no—
626C4×D4—212no—
627C4×D4—212no—
628C4×D4—224no—
629C4×D4—24no—
630C4×D4—248no—
631C4×D4—212no—
632C4×D4—212no—
633C4×D4—212no—
634C4×D4—212no—
635C4×D4—212no—
636C4×D4—212no—
637C4×D4—212no—
638C4×D4—224no—
639C4×D4—224no—
640C4×D4—224no—
641C4×D4—224no—
642C4×D4—248no—
643C4×D4—224no—
644C4×D4—224no—
645C4×D4—224no—
646C4×D4C2×D4148yescomplemented
647#117—212no—
648#117—212no—
649#117—212no—
650#117—212no—
651#117—212no—
652#117—224no—
653#117—224no—
654#117C2×D4124yescomplemented
655C2×C4⋊C4—224no—
656C2×C4⋊C4—212no—
657C2×C4⋊C4—212no—
658C2×C4⋊C4—212no—
659C2×C4⋊C4—212no—
660C2×C4⋊C4—224no—
661C2×C4⋊C4—224no—
662C2×C4⋊C4—224no—
663C2×C4⋊C4—24no—
664C2×C4⋊C4—412no—
665C2×C4⋊C4C2×D4124yescomplemented
666C2×C4⋊C4C2413yes—
667C2×C4⋊C4C2416yes—
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2416yes—
670C2×C4⋊C4C24112yes—
671C2×C4⋊C4C2413yes—
672C2×C4⋊C4C2416yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2413yes—
676C2×C4⋊C4C2413yes—
677C2×C4⋊C4C2413yes—
678C2×C4⋊C4C2416yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2413yes—
681C2×C4⋊C4C2413yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2416yes—
685C2×C4⋊C4C2416yes—
686C2×C4⋊C4C2416yes—
687C2×C4⋊C4C24112yes—
688C2×C4⋊C4C2416yes—
689C2×C4⋊C4C2416yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2416yes—
693C2×C4⋊C4C2411yescharacteristic
694C2×C22⋊C4—212no—
695C2×C22⋊C4—212no—
696C2×C22⋊C4—224no—
697C2×C22⋊C4—224no—
698C2×C22⋊C4—224no—
699C2×C22⋊C4—412no—
700C2×C22⋊C4—412no—
701C2×C22⋊C4—86no—
702C2×C22⋊C4C2411yescharacteristic
703C2×C22⋊C4C2411yescharacteristic
704C2×C22⋊C4C2416yes—
705C2×C22⋊C4C2416yes—
706C2×C22⋊C4C2416yes—
707C2×C22⋊C4C2416yes—
708C2×C22⋊C4C2416yes—
709C2×C22⋊C4C2416yes—
710C2×C22⋊C4C2416yes—
711C2×C22⋊C4C2413yes—
712C2×C22⋊C4C2413yes—
713C2×C22⋊C4C2413yes—
714C2×C22⋊C4C2413yes—
715C2×C22⋊C4C2413yes—
716C2×C22⋊C4C2413yes—
717C2×C22⋊C4C24112yes—
718C2×C22⋊C4C24112yes—
719C2×C22⋊C4C2416yes—
720C2×C22⋊C4C2416yes—
721C2×C22⋊C4C2412yes—
722C2×C22⋊C4C2412yes—
723C2×C22⋊C4C2416yes—
724C2×C22⋊C4C2416yes—
725C2×C22⋊C4C2416yes—
726C2×C22⋊C4C2416yes—
727C2×C22⋊C4C2416yes—
728C2×C22⋊C4C2416yes—
729C2×C22⋊C4C2416yes—
730C2×C22⋊C4C24112yes—
731C2×C22⋊C4C24112yes—
732C2×C22⋊C4C24112yes—
733C2×C22⋊C4C2416yes—
734C2×C22⋊C4C2416yes—
735C2×C22⋊C4C2416yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2416yes—
738C2×C22⋊C4C2416yes—
739C2×C42—212no—
740C2×C42—224no—
741C2×C42C2413yes—
742C2×C42C2416yes—
743C2×C42C2416yes—
744C2×C42C2416yes—
745C2×C42C2416yes—
746C2×C42C2411yescharacteristic
747C2×C42C2413yes—
748C2×C42C2413yes—
749C2×C42C2416yes—
750#95C2416yes—
751#95C2416yes—
752#95C24112yes—
753#95C24112yes—
754#95C2412yes—
755#95C2412yes—
756#95C2412yes—
757#95C2416yes—
758#95C2416yes—
759#95C2416yes—
760#95C2416yes—
761#95C2412yes—
762#95C2416yes—
763#95C2416yes—
764C24—26no—
765C24—26no—
766C24—26no—
767C24—26no—
768C24—26no—
769C24—26no—
770C24—26no—
771C24—26no—
772C24—212no—
773C24—212no—
774C24—212no—
775C24—43no—
776C24—43no—
777C24—43no—
778C24—43no—
779C24—43no—
780C24—46no—
781C24—46no—
782C24—46no—
783C24—46no—
784C24C22×D4112yes—
785C24C2516yes—
786C24C2513yes—
787C24C2513yes—
788C24C2511yescharacteristic
789C24C2513yes—
790C24C2511yescharacteristic
791#41—232no—
792#41—296no—
793#41—296no—
794#41—416no—
795#41—432no—
796#41—448no—
797#41—448no—
798#41—448no—
799#41#121164yescomplemented
800C2×Q8—232no—
801C2×Q8—26no—
802C2×Q8—22no—
803C2×Q8—22no—
804C2×Q8—26no—
805C2×Q8—26no—
806C2×Q8—26no—
807C2×Q8—26no—
808C2×Q8—22no—
809C2×Q8—416no—
810C2×Q8C22×D4112yes—
811C2×Q8C22×D414yes—
812C2×Q8C22×D414yes—
813C2×Q8C2×#4114yes—
814C2×D4—22no—
815C2×D4—212no—
816C2×D4—212no—
817C2×D4—22no—
818C2×D4—296no—
819C2×D4—26no—
820C2×D4—26no—
821C2×D4—26no—
822C2×D4—212no—
823C2×D4—212no—
824C2×D4—212no—
825C2×D4—212no—
826C2×D4—212no—
827C2×D4—212no—
828C2×D4—212no—
829C2×D4—212no—
830C2×D4—212no—
831C2×D4—26no—
832C2×D4—26no—
833C2×D4—26no—
834C2×D4—212no—
835C2×D4—212no—
836C2×D4—212no—
837C2×D4—224no—
838C2×D4—26no—
839C2×D4—212no—
840C2×D4—26no—
841C2×D4—26no—
842C2×D4—212no—
843C2×D4—212no—
844C2×D4—26no—
845C2×D4—26no—
846C2×D4—212no—
847C2×D4—224no—
848C2×D4—26no—
849C2×D4—26no—
850C2×D4—212no—
851C2×D4—26no—
852C2×D4—26no—
853C2×D4—43no—
854C2×D4—43no—
855C2×D4—46no—
856C2×D4—412no—
857C2×D4—412no—
858C2×D4—46no—
859C2×D4—46no—
860C2×D4—46no—
861C2×D4—412no—
862C2×D4—412no—
863C2×D4—46no—
864C2×D4—46no—
865C2×D4—46no—
866C2×D4—448no—
867C2×D4—448no—
868C2×D4—496no—
869C2×D4—448no—
870C2×D4—848no—
871C2×D4—848no—
872C2×D4C22×D4124yes—
873C2×D4C22×D4112yes—
874C2×D4C22×D4112yes—
875C2×D4C22×D4112yes—
876C2×D4C2×#41112yes—
877C2×D4H(5,𝔽2)14yescomplemented
878C22×C4—26no—
879C22×C4—26no—
880C22×C4—296no—
881C22×C4—26no—
882C22×C4—22no—
883C22×C4—26no—
884C22×C4—26no—
885C22×C4—22no—
886C22×C4—26no—
887C22×C4—26no—
888C22×C4—26no—
889C22×C4—26no—
890C22×C4—26no—
891C22×C4—26no—
892C22×C4—26no—
893C22×C4—212no—
894C22×C4—24no—
895C22×C4—26no—
896C22×C4—212no—
897C22×C4—212no—
898C22×C4—24no—
899C22×C4—212no—
900C22×C4—22no—
901C22×C4—26no—
902C22×C4—26no—
903C22×C4—26no—
904C22×C4—26no—
905C22×C4—26no—
906C22×C4—212no—
907C22×C4—212no—
908C22×C4—22no—
909C22×C4—26no—
910C22×C4—22no—
911C22×C4—26no—
912C22×C4—26no—
913C22×C4—26no—
914C22×C4—212no—
915C22×C4—26no—
916C22×C4—224no—
917C22×C4—46no—
918C22×C4—46no—
919C22×C4—46no—
920C22×C4—42no—
921C22×C4—43no—
922C22×C4—46no—
923C22×C4—46no—
924C22×C4—43no—
925C22×C4—46no—
926C22×C4—412no—
927C22×C4—412no—
928C22×C4—43no—
929C22×C4—46no—
930C22×C4—448no—
931C22×C4—848no—
932C22×C4C22×D4112yes—
933C22×C4C22×D414yes—
934C22×C4C22×D4112yes—
935C22×C4C22×D4112yes—
936C22×C4C22×D4112yes—
937C22×C4C22×D4124yes—
938C22×C4C22×D4112yes—
939C22×C4C22×D4112yes—
940C22×C4C2×#41112yes—
941C22×C4C2511yescharacteristic
942C22×C4C2512yes—
943C22×C4C2513yes—
944C22×C4C2516yes—
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2516yes—
950C22×C4C2513yes—
951C22×C4C2512yes—
952C22×C4C2516yes—
953C22×C4C2513yes—
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2513yes—
957C22×C4C2511yescharacteristic
958C4⋊C4—212no—
959C4⋊C4—26no—
960C4⋊C4—22no—
961C4⋊C4—224no—
962C4⋊C4—212no—
963C4⋊C4—26no—
964C4⋊C4—24no—
965C4⋊C4—22no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—212no—
970C4⋊C4—22no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—212no—
976C4⋊C4—212no—
977C4⋊C4—212no—
978C4⋊C4—212no—
979C4⋊C4—412no—
980C4⋊C4—42no—
981C4⋊C4—46no—
982C4⋊C4—46no—
983C4⋊C4C22×D4112yes—
984C4⋊C4C22×D4124yes—
985C4⋊C4C22×D414yes—
986C22⋊C4—22no—
987C22⋊C4—212no—
988C22⋊C4—26no—
989C22⋊C4—26no—
990C22⋊C4—26no—
991C22⋊C4—212no—
992C22⋊C4—212no—
993C22⋊C4—24no—
994C22⋊C4—212no—
995C22⋊C4—212no—
996C22⋊C4—212no—
997C22⋊C4—22no—
998C22⋊C4—212no—
999C22⋊C4—212no—
1000C22⋊C4—212no—
1001C22⋊C4—212no—
1002C22⋊C4—26no—
1003C22⋊C4—26no—
1004C22⋊C4—26no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
1007C22⋊C4—24no—
1008C22⋊C4—212no—
1009C22⋊C4—212no—
1010C22⋊C4—212no—
1011C22⋊C4—212no—
1012C22⋊C4—212no—
1013C22⋊C4—412no—
1014C22⋊C4—412no—
1015C22⋊C4—46no—
1016C22⋊C4—412no—
1017C22⋊C4—46no—
1018C22⋊C4—42no—
1019C22⋊C4—46no—
1020C22⋊C4—46no—
1021C22⋊C4—46no—
1022C22⋊C4C22×D4124yes—
1023C42—22no—
1024C42—26no—
1025C42—212no—
1026C42—212no—
1027C42—212no—
1028C42—26no—
1029C42—26no—
1030C42—212no—
1031C42C22×D4124yes—
1032C23—21no—
1033C23—21no—
1034C23—23no—
1035C23—23no—
1036C23—21no—
1037C23—23no—
1038C23—21no—
1039C23—23no—
1040C23—23no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—23no—
1045C23—23no—
1046C23—21no—
1047C23—23no—
1048C23—23no—
1049C23—21no—
1050C23—21no—
1051C23—23no—
1052C23—224no—
1053C23—224no—
1054C23—23no—
1055C23—26no—
1056C23—26no—
1057C23—23no—
1058C23—23no—
1059C23—26no—
1060C23—26no—
1061C23—23no—
1062C23—23no—
1063C23—26no—
1064C23—26no—
1065C23—23no—
1066C23—26no—
1067C23—23no—
1068C23—412no—
1069C23—412no—
1070C23—412no—
1071C23—412no—
1072C23—412no—
1073C23—412no—
1074C23—412no—
1075C23—412no—
1076C23—412no—
1077C23—424no—
1078C23—86no—
1079C23—86no—
1080C23—86no—
1081C23—812no—
1082C23—812no—
1083C23—812no—
1084C23—812no—
1085C23—812no—
1086C23—812no—
1087C23C23×D416yes—
1088C23C23×D416yes—
1089C23C23×D416yes—
1090C23C23×D412yes—
1091C23C22×#4116yes—
1092C23C2×H(5,𝔽2)12yes—
1093C23C2×H(5,𝔽2)12yes—
1094C23#58512yes—
1095C23C2611yescharacteristic
1096Q8—224no—
1097Q8—412no—
1098Q8—44no—
1099Q8C2×#121116yescomplemented
1100D4—248no—
1101D4—28no—
1102D4—224no—
1103D4—412no—
1104D4—424no—
1105D4—412no—
1106D4—424no—
1107D4—424no—
1108D4—412no—
1109D4—424no—
1110D4—412no—
1111D4—424no—
1112D4—412no—
1113D4—812no—
1114D4—824no—
1115D4—812no—
1116D4—812no—
1117D4—824no—
1118D4C2×#121148yescomplemented
1119C2×C4—21no—
1120C2×C4—23no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—23no—
1124C2×C4—26no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—26no—
1128C2×C4—22no—
1129C2×C4—224no—
1130C2×C4—28no—
1131C2×C4—224no—
1132C2×C4—224no—
1133C2×C4—224no—
1134C2×C4—22no—
1135C2×C4—21no—
1136C2×C4—22no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—26no—
1140C2×C4—26no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—23no—
1150C2×C4—26no—
1151C2×C4—26no—
1152C2×C4—23no—
1153C2×C4—22no—
1154C2×C4—23no—
1155C2×C4—26no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—26no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—23no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—424no—
1165C2×C4—48no—
1166C2×C4—424no—
1167C2×C4—412no—
1168C2×C4—412no—
1169C2×C4—44no—
1170C2×C4—412no—
1171C2×C4—412no—
1172C2×C4—412no—
1173C2×C4—424no—
1174C2×C4—824no—
1175C2×C4—86no—
1176C2×C4—812no—
1177C2×C4—812no—
1178C2×C4C2×#121148yescomplemented
1179C2×C4C23×D414yes—
1180C2×C4C23×D4112yes—
1181C2×C4C23×D412yes—
1182C2×C4C23×D416yes—
1183C2×C4C23×D412yes—
1184C2×C4C23×D416yes—
1185C2×C4C23×D416yes—
1186C2×C4C23×D412yes—
1187C2×C4C22×#4112yes—
1188C2×C4C22×#4116yes—
1189C2×C4C2×H(5,𝔽2)12yes—
1190C22—22no—
1191C22—26no—
1192C22—22no—
1193C22—26no—
1194C22—22no—
1195C22—26no—
1196C22—22no—
1197C22—26no—
1198C22—26no—
1199C22—26no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—26no—
1206C22—26no—
1207C22—26no—
1208C22—448no—
1209C22—43no—
1210C22—43no—
1211C22—43no—
1212C22—41no—
1213C22—43no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—46no—
1218C22—43no—
1219C22—43no—
1220C22—46no—
1221C22—43no—
1222C22—46no—
1223C22—43no—
1224C22—46no—
1225C22—43no—
1226C22—46no—
1227C22—43no—
1228C22—46no—
1229C22—43no—
1230C22—46no—
1231C22—824no—
1232C22—1624no—
1233C22C22×#121112yes—
1234C22#348814yescomplemented
1235C22C24×D411yescharacteristic
1236C22C24×D411yescharacteristic
1237C22C23×#4111yescharacteristic
1238C22C22×H(5,𝔽2)11yescharacteristic
1239C22C2×#58511yescharacteristic
1240C22H(7,𝔽2)11yescharacteristic
1241C222−1+611yescharacteristic
1242C4—212no—
1243C4—24no—
1244C4—22no—
1245C4—22no—
1246C4—26no—
1247C4—46no—
1248C4—42no—
1249C4—43no—
1250C4—46no—
1251C4—41no—
1252C4—43no—
1253C4—42no—
1254C4—41no—
1255C4—42no—
1256C4—43no—
1257C4C22×#12114yes—
1258C4C22×#121112yes—
1259C2—24no—
1260C2—212no—
1261C2—46no—
1262C2—42no—
1263C2—83no—
1264C2—86no—
1265C2C23×#12111yescharacteristic
1266C2C2×#348811yescharacteristic
1267C2#6285311yescharacteristic
1268C2D4×H(5,𝔽2)11yescharacteristic
1269C2#6298511yescharacteristic
1270C2#6300211yescharacteristic
1271C2#6300811yescharacteristic
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×#3488C2semidirect
2. C2×#3488C2semidirect
3. C2×D4×#41C2semidirect
4. C22×#520C2semidirect
5. #36576C2semidirect
6. #36434C2semidirect
7. #36214C2semidirect
8. D4×#121C2semidirect
9. #36029C2semidirect
10. #35831C2semidirect
11. #35821C2semidirect
12. #35728C2semidirect
13. #35564C2semidirect
14. #35563C2semidirect
15. #35533C2semidirect
16. #35518C2semidirect
17. #35252C2semidirect
18. #35223C2semidirect
19. #34737C2semidirect
20. C2×#2416C2semidirect
21. #34258C2semidirect
22. #34250C2semidirect
23. #34175C2semidirect
30. C2×#550C22semidirect
31. C2×#550C22semidirect
32. C2×#550C22semidirect
33. C2×D4×Q8C22semidirect
34. C2×#548C22semidirect
35. C2×#548C22semidirect
36. C2×#548C22semidirect
37. C2×#548C22semidirect
38. C2×#547C22semidirect
39. C2×#546C22semidirect
40. C2×#546C22semidirect
41. C2×#546C22semidirect
42. C2×#546C22semidirect
43. C2×D42C22semidirect
44. C2×D42C22semidirect
45. C2×D42C22semidirect
46. C2×#537C22semidirect
47. C2×#537C22semidirect
48. C2×#535C22semidirect
49. C2×#535C22semidirect
50. C2×#532C22semidirect
51. C2×#525C22semidirect
52. C2×#525C22semidirect
53. C2×#525C22semidirect
54. C2×#525C22semidirect
55. C22×#121C22semidirect
56. C22×#121C22semidirect
57. C22×#121C22semidirect
62. C2×#520C22semidirect
63. C2×#520C22semidirect
64. C2×#520C22semidirect
65. C2×#520C22semidirect
67. C22×C4×Q8C22semidirect
68. C22×C4×D4C22semidirect
69. C22×C4×D4C22semidirect
70. C22×#117C22semidirect
71. C23×C4⋊C4C22semidirect
72. #2856C22semidirect
73. #2850C22semidirect
74. #2847C22semidirect
75. #2620C22semidirect
76. #2619C22semidirect
77. #2618C22semidirect
78. #2548C22semidirect
79. #2545C22semidirect
80. #2544C22semidirect
81. #2543C22semidirect
82. #2541C22semidirect
83. #2538C22semidirect
84. #2537C22semidirect
85. #2536C22semidirect
86. #2535C22semidirect
87. #2534C22semidirect
88. #2429C22semidirect
89. #2428C22semidirect
90. #2428C22semidirect
91. #2428C22semidirect
92. #2427C22semidirect
93. #2426C22semidirect
94. #2426C22semidirect
95. #2426C22semidirect
96. #2425C22semidirect
97. #2424C22semidirect
98. #2424C22semidirect
99. #2424C22semidirect
100. #2417C22semidirect
101. #2417C22semidirect
102. #2417C22semidirect
103. #2417C22semidirect
104. #2417C22semidirect
105. #2416C22semidirect
106. #2416C22semidirect
107. #2416C22semidirect
108. #2416C22semidirect
109. #2416C22semidirect
110. #2416C22semidirect
111. #2416C22semidirect
112. #2416C22semidirect
113. #2416C22semidirect
114. #2416C22semidirect
115. #2416C22semidirect
116. #2416C22semidirect
117. #2416C22semidirect
118. #2415C22semidirect
119. #2415C22semidirect
120. #2414C22semidirect
121. #2414C22semidirect
122. #2414C22semidirect
123. #2414C22semidirect
124. #2413C22semidirect
125. #2412C22semidirect
126. #2411C22semidirect
127. #2411C22semidirect
128. #2410C22semidirect
129. #2410C22semidirect
130. #2408C22semidirect
131. #2392C22semidirect
132. #2392C22semidirect
133. C2×#396C22semidirect
134. C2×#394C22semidirect
135. #2351C22semidirect
136. Q8×C4⋊C4C22semidirect
137. #2349C22semidirect
138. D4×C4⋊C4C22semidirect
139. #2341C22semidirect
140. #2341C22semidirect
141. #2341C22semidirect
142. Q8×C22⋊C4C22semidirect
143. #2339C22semidirect
144. D4×C22⋊C4C22semidirect
145. D4×C22⋊C4C22semidirect
146. D4×C22⋊C4C22semidirect
147. #2317C22semidirect
148. #2316C22semidirect
149. #2311C22semidirect
150. #2311C22semidirect
151. #2311C22semidirect
152. #2309C22semidirect
153. C4×#121C22semidirect
154. C4×#121C22semidirect
155. #2297C22semidirect
156. #2296C22semidirect
157. C2×#390C22semidirect
158. C2×#389C22semidirect
159. C2×#386C22semidirect
160. #2280C22semidirect
161. C2×#380C22semidirect
170. C22×#41D4semidirect
280. #520D4semidirect
481. C2×#41C2×D4semidirect
482. C2×#41C2×D4semidirect
483. C2×#41C2×D4semidirect
490. C22×Q8C2×D4semidirect
515. C22×D4C2×D4semidirect
543. C23×C4C2×D4semidirect
624. C4×Q8C2×D4semidirect
646. C4×D4C2×D4semidirect
654. #117C2×D4semidirect
665. C2×C4⋊C4C2×D4semidirect
799. #41#121semidirect
877. C2×D4H(5,𝔽2)semidirect
1099. Q8C2×#121semidirect
1118. D4C2×#121semidirect
1178. C2×C4C2×#121semidirect
1234. C22#3488semidirect

Maximal subgroups

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

subgroupindex
C2×#34882
C2×D4×#412
C22×#5202
#365762
#364342
#362142
D4×#1212
#360292
#358312
#358212
#357282
#355642
#355632
#355332
#355182
#352522
#352232
#347372
C2×#24162
#342582
#342502
#341752