Finite Group Databasebeta

← #7632628

Subgroups — #7632628

Order 512.

8308 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×#3428C211yesmaximal, characteristic, complemented
3#36442C216yesmaximal, complemented
4#36438C216yesmaximal, complemented
5#36433C212yesmaximal, complemented
6#36429C212yesmaximal, complemented
7#36040C211yesmaximal, characteristic, complemented
8#36029C211yesmaximal, characteristic, complemented
9#36018C211yesmaximal, characteristic, complemented
10#35845C211yesmaximal, characteristic, complemented
11#35741C213yesmaximal, complemented
12#35730C213yesmaximal, complemented
13#35704C213yesmaximal, complemented
14#35693C213yesmaximal, complemented
15#35601C216yesmaximal, complemented
16#35538C216yesmaximal, complemented
17#35301C213yesmaximal, complemented
18#35210C213yesmaximal, complemented
19#34977C213yesmaximal, complemented
20#34877C213yesmaximal, complemented
21#34313C212yesmaximal, complemented
22#34312C212yesmaximal, complemented
23#34125C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25#3517—216no—
26C2×#557C2211yescharacteristic, complemented
27C2×#553C2216yescomplemented
28C2×#550C2212yes—
29C2×#550C2212yes—
30C2×#550C2213yescomplemented
31C2×#550C2211yescharacteristic, complemented
32C2×#548C2212yes—
33C2×#547C2213yescomplemented
34C2×#540C2216yescomplemented
35C2×#532C2213yescomplemented
36C2×#529C2213yescomplemented
37#3428—216no—
38C2×#520C2211yescharacteristic
39C2×#520C2213yes—
40C2×#520C2213yes—
41C2×#520C2211yescharacteristic
42C2×#520C2212yescomplemented
43C2×#519C2211yescharacteristic
44C2×#519C2211yescharacteristic
45C2×#518C2213yes—
46C2×#518C2213yes—
47C2×C4×#41C2211yescharacteristic
48C2×C4×#41C2213yes—
49C2×C4×#41C2213yes—
50C2×C4×#41C2211yescharacteristic
51C22×#117C2213yes—
52C22×#117C2213yes—
53#2854C2216yescomplemented
54#2852C22112yescomplemented
55#2847C2216yes—
56#2638C2216yescomplemented
57#2635C2216yescomplemented
58#2628C2213yes—
59#2628C2213yescomplemented
60#2619C2213yes—
61#2619C2213yescomplemented
62#2611C2211yescharacteristic
63#2611C2213yescomplemented
64#2610C2213yes—
65#2610C2213yescomplemented
66#2610C2216yescomplemented
67#2602C22112yescomplemented
68#2601C2216yes—
69#2601C2216yescomplemented
70#2598C2216yes—
71#2598C2216yescomplemented
72#2591C2216yescomplemented
73#2591C2213yescomplemented
74#2583C2213yescomplemented
75#2581C2213yescomplemented
76#2580C2213yescomplemented
77#2567C2213yescomplemented
78#2563C2213yescomplemented
79#2561C2213yes—
80#2548C2213yescomplemented
81#2541C2213yescomplemented
82#2539C2213yes—
83#2539C2216yes—
84#2536C2213yescomplemented
85#2535C2213yescomplemented
86#2500C2216yescomplemented
87#2485C2216yescomplemented
88#2476C22112yescomplemented
89#2470C22112yescomplemented
90#2464C22112yescomplemented
91#2457C22112yescomplemented
92#2456C22112yescomplemented
93#2455C22112yescomplemented
94#2454C2216yescomplemented
95#2453C2216yescomplemented
96#2445C2216yescomplemented
97#2445C2216yescomplemented
98#2442C2216yescomplemented
99#2441C2216yes—
100#2433C2216yes—
101#2431C2216yes—
102#2431C2216yes—
103#2428C2216yescomplemented
104#2426C2216yescomplemented
105#2424C22112yes—
106#2422C2216yescomplemented
107#2420C2216yescomplemented
108#2418C22112yes—
109#2416C2216yescomplemented
110#2414C2216yes—
111#2414C22112yescomplemented
112#2413C2216yescomplemented
113#2411C2216yes—
114#2408C2216yes—
115#2407C2216yes—
116#2407C2216yes—
117#2406C2216yescomplemented
118#2404C2216yes—
119#2396C2213yes—
120#2396C2213yescomplemented
121#2392C2213yes—
122#2392C2213yescomplemented
123#2388C2216yescomplemented
124#2388C2216yescomplemented
125#2367C2216yescomplemented
126#2366C2216yescomplemented
127#2363C2216yes—
128#2361C2216yescomplemented
129#2361C2216yescomplemented
130#2360C2216yescomplemented
131#2357C2213yescomplemented
132#2357C2213yescomplemented
133#2352C2216yes—
134#2351C2211yescharacteristic, complemented
135#2351C2212yescomplemented
136#2351C2211yescharacteristic, complemented
137Q8×C4⋊C4C2212yescomplemented
138D4×C4⋊C4C2216yescomplemented
139#2347C2216yescomplemented
140#2341C2212yes—
141#2341C2212yes—
142#2341C2212yescomplemented
143#2341C2212yescomplemented
144Q8×C22⋊C4C2212yes—
145#2324C2216yes—
146#2324C2216yescomplemented
147#2324C2216yescomplemented
148#2323C2216yescomplemented
149C4×#127C2216yescomplemented
150C4×#124C2216yescomplemented
151C4×#123C2216yescomplemented
152C4×#121C22112yescomplemented
153C4×#120C2216yes—
154#2293C2216yes—
155#2293C2216yescomplemented
156#2293C2216yescomplemented
157#2283C2213yescomplemented
158C42×Q8C2212yescomplemented
159C4×#117C2213yescomplemented
160C22×#41—28no—
161C22×#41—28no—
162C22×#41—28no—
163C22×#41C2313yes—
164C22×#41C2313yes—
165C22×#41C2312yes—
166C22×#41C2311yescharacteristic
167C22×#41C2311yescharacteristic
168C22×#41C2316yes—
169C23×Q8C2311yescharacteristic
170C23×D4C2313yes—
171C24×C4C2313yes—
172#557—28no—
173#553—248no—
174#550—216no—
175#550—216no—
176#550—28no—
177#550—224no—
178#548—216no—
179#547—224no—
180#540—248no—
181#532—224no—
182C2×C4⋊Q8C2313yes—
183C2×#127C2316yes—
184C2×#127C2313yes—
185C2×#127C2316yes—
186#529—224no—
187C2×#126C2316yes—
188C2×#125C2311yescharacteristic
189C2×#125C2316yes—
190C2×#124C2313yes—
191C2×#124C2316yes—
192C2×#123C2316yes—
193C2×#123C23112yes—
194C2×#123C2316yes—
195C2×#123C23112yes—
196C2×C22⋊Q8C2313yes—
197C2×C22⋊Q8C2316yes—
198C2×#121C2316yes—
199C2×#121C2316yes—
200C2×#121C2316yes—
201C2×#121C2313yes—
202C2×#121C2316yes—
203C2×#121C2316yes—
204C2×#121C2316yes—
205C2×#121C2316yes—
206C2×#121C23112yes—
207C2×#121C23112yes—
208C2×#120C2316yes—
209C2×#120C23112yes—
210#520—28no—
211#520—28no—
212#520—216no—
213#520—224no—
214#520—224no—
215#519—28no—
216#519—28no—
217#518—224no—
218#518—224no—
219C4×#41—28no—
220C4×#41—224no—
221C4×#41—224no—
222C4×#41D4116yescomplemented
223C2×C4×Q8C2313yes—
224C2×C4×Q8C2313yes—
225C2×C4×Q8C2313yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2313yes—
232C2×C4×Q8C2313yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4C2313yes—
236C2×C4×D4C2316yes—
237C2×C4×D4C2313yes—
238C2×C4×D4C2316yes—
239C2×C4×D4C2316yes—
240C2×C4×D4C2316yes—
241C2×C4×D4C2316yes—
242C2×C4×D4C2313yes—
243C2×C4×D4C2316yes—
244C2×C4×D4C2316yes—
245C2×C4×D4C2313yes—
246C2×C4×D4C2313yes—
247C2×C4×D4C2313yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2316yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C23112yes—
253C2×C4×D4C23112yes—
254C2×C4×D4C2313yes—
255C2×C4×D4C2313yes—
256C2×#117—224no—
257C2×#117—224no—
258C2×#117C2316yes—
259C2×#117C2313yes—
260C2×#117C2313yes—
261C2×#117C2313yes—
262C2×#117C2313yes—
263C2×#117C2313yes—
264C2×#117C2311yescharacteristic
265C2×#117C2313yes—
266C2×#117C2313yes—
267C2×#117C2313yes—
268C2×#117C2313yes—
269C2×#117C2313yes—
270C2×#117C2316yes—
271C2×#117C2316yes—
272C2×#117C2313yes—
273C22×C4⋊C4C2313yes—
274C22×C4⋊C4C2313yes—
275C22×C4⋊C4C2313yes—
276C22×C4⋊C4C2316yes—
277C22×C4⋊C4C2313yes—
278C22×C22⋊C4C2313yes—
279C22×C22⋊C4C2313yes—
280C22×C22⋊C4C2316yes—
281C22×C42C2316yes—
282C22×C42C2313yes—
283C22×C42C2313yes—
284#400C2313yes—
285#400C2311yescharacteristic
286#400C2316yes—
287#400C2316yes—
288#399C2313yes—
289#399C2316yes—
290#399C2316yes—
291#399C2311yescharacteristic
292#398C2311yescharacteristic
293#398C2313yes—
294#398C2316yes—
295#398C2316yes—
296#397C2311yescharacteristic
297#397C2313yes—
298#397C23112yes—
299#396C2316yes—
300#396C2316yes—
301#396C2316yes—
302#396C2316yes—
303#395C2313yes—
304#395C2316yes—
305#395C2313yes—
306#394C2316yes—
307#394C2316yes—
308#394C2313yes—
309#394C2313yes—
310#394C2316yes—
311#394C2316yes—
312#394C23112yes—
313#394C23112yes—
314#394C2316yes—
315#394C23112yes—
316#394C23112yes—
317#393C2313yes—
318#393C2313yes—
319#393C2316yes—
320#392C2316yes—
321#392C2316yes—
322#392C23112yes—
323#392C2313yes—
324#392C2316yes—
325#392C2313yes—
326#392C23112yes—
327#392C23112yes—
328#391C2316yes—
329#391C2316yes—
330#390C2316yes—
331#390C2316yes—
332#390C23112yes—
333#390C2316yes—
334#390C2316yes—
335#390C2316yes—
336#390C2316yes—
337#390C2316yes—
338#390C2316yes—
339#390C2316yes—
340#390C2316yes—
341#390C2316yes—
342#390C2316yes—
343#390C23112yes—
344#389C23112yes—
345#389C2316yes—
346#389C2316yes—
347#389C2316yes—
348#389C2316yes—
349#389C2316yes—
350#389C2316yes—
351#389C2316yes—
352#389C2316yes—
353#389C2316yes—
354#389C2312yes—
355#388C2316yes—
356#388C2316yes—
357#388C23112yes—
358#388C23112yes—
359#388C2316yes—
360#388C2316yes—
361#388C2316yes—
362#388C2316yes—
363#388C23112yes—
364#388C23112yes—
365#388C2316yes—
366#388C2316yes—
367#388C23112yes—
368#388C23112yes—
369#388C2316yes—
370#388C2312yes—
371#387C23112yes—
372#387C23112yes—
373#387C2316yes—
374#387C2312yes—
375#386C23112yes—
376#386C23112yes—
377#386C23112yes—
378#386C23112yes—
379#386C23112yes—
380#386C2316yes—
381#386C2316yes—
382#386C2316yes—
383#386C23112yes—
384#386C23112yes—
385#386C2316yes—
386#385C23112yes—
387#385C23112yes—
388#385C23112yes—
389#385C23112yes—
390#385C2316yes—
391#385C2316yes—
392#385C2316yes—
393#385C2312yes—
394#384C2316yes—
395#383C2316yes—
396#382C2316yes—
397#382C2313yes—
398#382C2313yes—
399#381C2316yes—
400#381C2316yes—
401#380C23112yes—
402#380C2316yes—
403#380C2316yes—
404#380C2316yes—
405#380C2316yes—
406#380C2316yes—
407#379C2316yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2316yes—
411C4×C4⋊C4C2316yes—
412C4×C4⋊C4C2316yes—
413C4×C4⋊C4C2316yes—
414C4×C4⋊C4C2316yes—
415C4×C4⋊C4C2316yes—
416C4×C22⋊C4C2313yes—
417C4×C22⋊C4C2313yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C23112yes—
425C4×C22⋊C4C23112yes—
426#376C2313yes—
427#376C2311yescharacteristic
428C43C2316yes—
429C25C2413yes—
430C2×#41—2128no—
431C2×#41—24no—
432C2×#41—28no—
433C2×#41—212no—
434C2×#41—212no—
435C2×#41—24no—
436C2×#41—24no—
437C2×#41—24no—
438C2×#41—28no—
439C2×#41—28no—
440C2×#41—212no—
441C2×#41—212no—
442C2×#41—212no—
443C2×#41—224no—
444C2×#41—212no—
445C2×#41—812no—
446C2×#41C2×D418yes—
447C2×#41#4118yescomplemented
448C22×Q8—24no—
449C22×Q8—24no—
450C22×Q8#4118yescomplemented
451C22×Q8C2413yes—
452C22×Q8C2413yes—
453C22×Q8C2411yescharacteristic
454C22×D4—212no—
455C22×D4—212no—
456C22×D4—212no—
457C22×D4C2416yes—
458C22×D4C2416yes—
459C22×D4C2416yes—
460C22×D4C2413yes—
461C22×D4C2413yes—
462C22×D4C2416yes—
463C22×D4C2416yes—
464C22×D4C24112yes—
465C22×D4C2416yes—
466C22×D4C2413yes—
467C22×D4C24112yes—
468C23×C4—212no—
469C23×C4—212no—
470C23×C4—212no—
471C23×C4C2413yes—
472C23×C4C2416yes—
473C23×C4C2411yescharacteristic
474C23×C4C2413yes—
475C23×C4C2413yes—
476C23×C4C2413yes—
477C23×C4C2413yes—
478C23×C4C2416yes—
479C23×C4C2416yes—
480C23×C4C2413yes—
481C23×C4C2413yes—
482C23×C4C24112yes—
483C23×C4C2413yes—
484C23×C4C2413yes—
485C4⋊Q8—212no—
486#127—224no—
487#127—224no—
488#127—212no—
489#126—224no—
490#125—224no—
491#125—24no—
492#124—224no—
493#124—212no—
494#123—224no—
495#123—248no—
496#123—412no—
497#123—812no—
498C22⋊Q8—224no—
499C22⋊Q8—212no—
500#121—224no—
501#121—224no—
502#121—212no—
503#121—224no—
504#121—224no—
505#121—224no—
506#121—224no—
507#121—224no—
508#121—248no—
509#121—424no—
510#120—412no—
511#120—812no—
512C4×Q8—24no—
513C4×Q8—24no—
514C4×Q8—28no—
515C4×Q8—28no—
516C4×Q8—28no—
517C4×Q8—212no—
518C4×Q8—212no—
519C4×Q8—212no—
520C4×Q8—212no—
521C4×Q8—212no—
522C4×Q8C2×D418yes—
523C4×Q8C2×D418yes—
524C4×D4—212no—
525C4×D4—212no—
526C4×D4—224no—
527C4×D4—224no—
528C4×D4—224no—
529C4×D4—224no—
530C4×D4—224no—
531C4×D4—212no—
532C4×D4—212no—
533C4×D4—224no—
534C4×D4—224no—
535C4×D4—224no—
536C4×D4—212no—
537C4×D4—212no—
538C4×D4—224no—
539C4×D4—212no—
540C4×D4—224no—
541C4×D4—812no—
542C4×D4—812no—
543C4×D4C2×D4124yes—
544C4×D4C2×D4124yes—
545#117—212no—
546#117—212no—
547#117—212no—
548#117—224no—
549#117—212no—
550#117—24no—
551#117—212no—
552#117—212no—
553#117—212no—
554#117—212no—
555#117—212no—
556#117—212no—
557#117—224no—
558#117—412no—
559#117C2×D4124yes—
560C2×C4⋊C4—212no—
561C2×C4⋊C4—212no—
562C2×C4⋊C4—212no—
563C2×C4⋊C4—212no—
564C2×C4⋊C4—224no—
565C2×C4⋊C4C2413yes—
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2413yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2413yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C24112yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C2416yes—
594C2×C4⋊C4C2413yes—
595C2×C4⋊C4C2413yes—
596C2×C22⋊C4—212no—
597C2×C22⋊C4—212no—
598C2×C22⋊C4—224no—
599C2×C22⋊C4C2413yes—
600C2×C22⋊C4C2411yescharacteristic
601C2×C22⋊C4C2411yescharacteristic
602C2×C22⋊C4C2413yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2413yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C24112yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C24112yes—
625C2×C22⋊C4C24112yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C24112yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C24112yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C42—212no—
634C2×C42—224no—
635C2×C42C2×D4124yes—
636C2×C42C2413yes—
637C2×C42C2411yescharacteristic
638C2×C42C2412yes—
639C2×C42C2416yes—
640C2×C42C2413yes—
641C2×C42C2413yes—
642C2×C42C2416yes—
643C2×C42C2416yes—
644C2×C42C2416yes—
645C2×C42C2416yes—
646C2×C42C2416yes—
647C2×C42C2416yes—
648C2×C42C2416yes—
649C2×C42C2413yes—
650C2×C42C2413yes—
651C2×C42C2411yescharacteristic
652C2×C42C2413yes—
653#95C2412yes—
654#95C2411yescharacteristic
655#95C2411yescharacteristic
656#95C2416yes—
657#95C2413yes—
658#95C2413yes—
659#95C2412yes—
660#95C2412yes—
661#95C2412yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C24112yes—
668#95C24112yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C24112yes—
673#95C2412yes—
674#95C2416yes—
675#95C2416yes—
676C24—26no—
677C24—26no—
678C24—26no—
679C24—46no—
680C24—46no—
681C24C2516yes—
682C24C2513yes—
683C24C2511yescharacteristic
684C24C2513yes—
685#41—296no—
686#41—296no—
687#41—232no—
688#41—232no—
689#41—432no—
690#41—848no—
691C2×Q8—232no—
692C2×Q8—26no—
693C2×Q8—26no—
694C2×Q8—26no—
695C2×Q8—46no—
696C2×Q8C22×D414yes—
697C2×Q8C2×#41112yes—
698C2×Q8C2×#4114yes—
699C2×Q8C2×#4114yes—
700C2×D4—296no—
701C2×D4—212no—
702C2×D4—212no—
703C2×D4—212no—
704C2×D4—212no—
705C2×D4—224no—
706C2×D4—212no—
707C2×D4—224no—
708C2×D4—26no—
709C2×D4—212no—
710C2×D4—26no—
711C2×D4—212no—
712C2×D4—212no—
713C2×D4—26no—
714C2×D4—26no—
715C2×D4—26no—
716C2×D4—212no—
717C2×D4—212no—
718C2×D4—212no—
719C2×D4—46no—
720C2×D4—46no—
721C2×D4—412no—
722C2×D4—46no—
723C2×D4—46no—
724C2×D4—46no—
725C2×D4—412no—
726C2×D4—412no—
727C2×D4—412no—
728C2×D4—46no—
729C2×D4—412no—
730C2×D4C22×D4112yes—
731C2×D4C2×#41112yes—
732C22×C4—296no—
733C22×C4—26no—
734C22×C4—22no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—26no—
738C22×C4—22no—
739C22×C4—26no—
740C22×C4—22no—
741C22×C4—26no—
742C22×C4—26no—
743C22×C4—26no—
744C22×C4—26no—
745C22×C4—26no—
746C22×C4—26no—
747C22×C4—26no—
748C22×C4—26no—
749C22×C4—26no—
750C22×C4—212no—
751C22×C4—212no—
752C22×C4—212no—
753C22×C4—212no—
754C22×C4—212no—
755C22×C4—224no—
756C22×C4—46no—
757C22×C4—46no—
758C22×C4—412no—
759C22×C4—412no—
760C22×C4—412no—
761C22×C4—412no—
762C22×C4—46no—
763C22×C4—46no—
764C22×C4C22×D4112yes—
765C22×C4C22×D4112yes—
766C22×C4C22×D4112yes—
767C22×C4C2×#41112yes—
768C22×C4C2×#41112yes—
769C22×C4C2516yes—
770C22×C4C2516yes—
771C22×C4C2512yes—
772C22×C4C2513yes—
773C22×C4C2511yescharacteristic
774C22×C4C2512yes—
775C22×C4C2516yes—
776C22×C4C2512yes—
777C22×C4C2511yescharacteristic
778C22×C4C2513yes—
779C22×C4C2511yescharacteristic
780C22×C4C2511yescharacteristic
781C22×C4C2513yes—
782C22×C4C2513yes—
783C22×C4C2511yescharacteristic
784C22×C4C2513yes—
785C22×C4C2511yescharacteristic
786C22×C4C2512yes—
787C22×C4C2513yes—
788C4⋊C4—26no—
789C4⋊C4—26no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—212no—
793C4⋊C4—26no—
794C4⋊C4—26no—
795C4⋊C4—26no—
796C4⋊C4—26no—
797C4⋊C4—26no—
798C4⋊C4—26no—
799C4⋊C4—212no—
800C4⋊C4—24no—
801C4⋊C4—22no—
802C4⋊C4—24no—
803C4⋊C4—212no—
804C4⋊C4—22no—
805C4⋊C4—212no—
806C4⋊C4—24no—
807C4⋊C4—212no—
808C4⋊C4—212no—
809C4⋊C4—212no—
810C4⋊C4—212no—
811C4⋊C4—24no—
812C4⋊C4—46no—
813C4⋊C4—46no—
814C4⋊C4—412no—
815C4⋊C4—46no—
816C4⋊C4—46no—
817C4⋊C4C22×D4112yes—
818C4⋊C4C22×D4112yes—
819C22⋊C4—212no—
820C22⋊C4—212no—
821C22⋊C4—24no—
822C22⋊C4—212no—
823C22⋊C4—26no—
824C22⋊C4—26no—
825C22⋊C4—22no—
826C22⋊C4—22no—
827C22⋊C4—26no—
828C22⋊C4—26no—
829C22⋊C4—26no—
830C22⋊C4—26no—
831C22⋊C4—212no—
832C22⋊C4—212no—
833C22⋊C4—212no—
834C22⋊C4—212no—
835C22⋊C4—212no—
836C22⋊C4—212no—
837C22⋊C4—224no—
838C22⋊C4—212no—
839C22⋊C4—24no—
840C22⋊C4—212no—
841C22⋊C4—46no—
842C22⋊C4—46no—
843C22⋊C4—46no—
844C22⋊C4—412no—
845C22⋊C4—412no—
846C22⋊C4—46no—
847C22⋊C4—46no—
848C22⋊C4—412no—
849C22⋊C4—412no—
850C22⋊C4—46no—
851C22⋊C4—46no—
852C22⋊C4C22×D4124yes—
853C42—22no—
854C42—26no—
855C42—212no—
856C42—212no—
857C42—26no—
858C42—26no—
859C42—212no—
860C42—212no—
861C42—212no—
862C42—24no—
863C42—46no—
864C42—46no—
865C42—46no—
866C42C22×D4112yes—
867C42C22×D414yes—
868C42C22×D4112yes—
869C42C22×D4112yes—
870C23—224no—
871C23—21no—
872C23—23no—
873C23—21no—
874C23—23no—
875C23—23no—
876C23—23no—
877C23—26no—
878C23—22no—
879C23—26no—
880C23—26no—
881C23—22no—
882C23—26no—
883C23—26no—
884C23—26no—
885C23—26no—
886C23—26no—
887C23—26no—
888C23—26no—
889C23—26no—
890C23—812no—
891C23—812no—
892C23—86no—
893C23—86no—
894C23C23×D416yes—
895C23C22×#4112yes—
896C23C22×#4116yes—
897C23C2611yescharacteristic
898Q8—224no—
899Q8—412no—
900Q8#525116yes—
901D4—248no—
902D4—224no—
903D4—224no—
904D4—424no—
905D4—412no—
906D4—424no—
907D4—812no—
908D4—812no—
909D4—824no—
910D4—812no—
911D4—824no—
912C2×C4—28no—
913C2×C4—224no—
914C2×C4—224no—
915C2×C4—23no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—23no—
922C2×C4—22no—
923C2×C4—26no—
924C2×C4—22no—
925C2×C4—26no—
926C2×C4—22no—
927C2×C4—224no—
928C2×C4—224no—
929C2×C4—224no—
930C2×C4—23no—
931C2×C4—21no—
932C2×C4—23no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—26no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—26no—
939C2×C4—26no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—26no—
944C2×C4—26no—
945C2×C4—22no—
946C2×C4—26no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—26no—
951C2×C4—26no—
952C2×C4—26no—
953C2×C4—22no—
954C2×C4—26no—
955C2×C4—26no—
956C2×C4—412no—
957C2×C4—412no—
958C2×C4—424no—
959C2×C4—812no—
960C2×C4—812no—
961C2×C4—824no—
962C2×C4—86no—
963C2×C4—86no—
964C2×C4C23×D412yes—
965C2×C4C23×D416yes—
966C2×C4C23×D416yes—
967C2×C4C23×D412yes—
968C2×C4C23×D412yes—
969C2×C4C23×D416yes—
970C2×C4C22×#4112yes—
971C2×C4C22×#4116yes—
972C2×C4C22×#4116yes—
973C2×C4C22×#4116yes—
974C2×C4#58514yes—
975C22—24no—
976C22—212no—
977C22—26no—
978C22—26no—
979C22—22no—
980C22—26no—
981C22—26no—
982C22—46no—
983C22—46no—
984C22—46no—
985C22—42no—
986C22—43no—
987C22—41no—
988C22—43no—
989C22—41no—
990C22—46no—
991C22—46no—
992C22—46no—
993C22—46no—
994C22—46no—
995C22—46no—
996C22—46no—
997C22—824no—
998C22C24×D411yescharacteristic
999C22C23×#4111yescharacteristic
1000C22C23×#4111yescharacteristic
1001C22C2×#58512yes—
1002C22H(7,𝔽2)12yes—
1003C4—24no—
1004C4—22no—
1005C4—26no—
1006C4—22no—
1007C4—26no—
1008C4—22no—
1009C4—22no—
1010C4—26no—
1011C4—42no—
1012C4—46no—
1013C4—46no—
1014C4—43no—
1015C4—41no—
1016C4—42no—
1017C4—43no—
1018C4—41no—
1019C4—46no—
1020C4—42no—
1021C4C2×#525112yes—
1022C2—46no—
1023C2—46no—
1024C2—42no—
1025C2—86no—
1026C2C22×#52511yescharacteristic
1027C2#6281211yescharacteristic
1028C2#6285211yescharacteristic
1029C2#6300612yes—
1030C2#6300812yes—
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×#3517C2semidirect
2. C2×#3428C2semidirect
3. #36442C2semidirect
4. #36438C2semidirect
5. #36433C2semidirect
6. #36429C2semidirect
7. #36040C2semidirect
8. #36029C2semidirect
9. #36018C2semidirect
10. #35845C2semidirect
11. #35741C2semidirect
12. #35730C2semidirect
13. #35704C2semidirect
14. #35693C2semidirect
15. #35601C2semidirect
16. #35538C2semidirect
17. #35301C2semidirect
18. #35210C2semidirect
19. #34977C2semidirect
20. #34877C2semidirect
21. #34313C2semidirect
22. #34312C2semidirect
23. #34125C2semidirect
26. C2×#557C22semidirect
27. C2×#553C22semidirect
30. C2×#550C22semidirect
31. C2×#550C22semidirect
33. C2×#547C22semidirect
34. C2×#540C22semidirect
35. C2×#532C22semidirect
36. C2×#529C22semidirect
42. C2×#520C22semidirect
53. #2854C22semidirect
54. #2852C22semidirect
56. #2638C22semidirect
57. #2635C22semidirect
59. #2628C22semidirect
61. #2619C22semidirect
63. #2611C22semidirect
65. #2610C22semidirect
66. #2610C22semidirect
67. #2602C22semidirect
69. #2601C22semidirect
71. #2598C22semidirect
72. #2591C22semidirect
73. #2591C22semidirect
74. #2583C22semidirect
75. #2581C22semidirect
76. #2580C22semidirect
77. #2567C22semidirect
78. #2563C22semidirect
80. #2548C22semidirect
81. #2541C22semidirect
84. #2536C22semidirect
85. #2535C22semidirect
86. #2500C22semidirect
87. #2485C22semidirect
88. #2476C22semidirect
89. #2470C22semidirect
90. #2464C22semidirect
91. #2457C22semidirect
92. #2456C22semidirect
93. #2455C22semidirect
94. #2454C22semidirect
95. #2453C22semidirect
96. #2445C22semidirect
97. #2445C22semidirect
98. #2442C22semidirect
103. #2428C22semidirect
104. #2426C22semidirect
106. #2422C22semidirect
107. #2420C22semidirect
109. #2416C22semidirect
111. #2414C22semidirect
112. #2413C22semidirect
117. #2406C22semidirect
120. #2396C22semidirect
122. #2392C22semidirect
123. #2388C22semidirect
124. #2388C22semidirect
125. #2367C22semidirect
126. #2366C22semidirect
128. #2361C22semidirect
129. #2361C22semidirect
130. #2360C22semidirect
131. #2357C22semidirect
132. #2357C22semidirect
134. #2351C22semidirect
135. #2351C22semidirect
136. #2351C22semidirect
137. Q8×C4⋊C4C22semidirect
138. D4×C4⋊C4C22semidirect
139. #2347C22semidirect
142. #2341C22semidirect
143. #2341C22semidirect
146. #2324C22semidirect
147. #2324C22semidirect
148. #2323C22semidirect
149. C4×#127C22semidirect
150. C4×#124C22semidirect
151. C4×#123C22semidirect
152. C4×#121C22semidirect
155. #2293C22semidirect
156. #2293C22semidirect
157. #2283C22semidirect
158. C42×Q8C22semidirect
159. C4×#117C22semidirect
222. C4×#41D4semidirect
447. C2×#41#41semidirect
450. C22×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×#34282
#364422
#364382
#364332
#364292
#360402
#360292
#360182
#358452
#357412
#357302
#357042
#356932
#356012
#355382
#353012
#352102
#349772
#348772
#343132
#343122
#341252