Finite Group Databasebeta

← #7658159

Subgroups — #7658159

Order 512.

8816 conjugacy classes of subgroups.

The subgroup lattice has 1101 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3488C211yesmaximal, characteristic, complemented
2C2×#3487C211yesmaximal, characteristic, complemented
3#42985C213yesmaximal, complemented
4#42984C213yesmaximal, complemented
5#42979C213yesmaximal, complemented
6#42969C213yesmaximal, complemented
7#42422C216yesmaximal, complemented
8#42420C216yesmaximal, complemented
9#39960C216yesmaximal, complemented
10#39957C216yesmaximal, complemented
11#37445C213yesmaximal, complemented
12#37437C213yesmaximal, complemented
13#36455C212yesmaximal, complemented
14#36430C212yesmaximal, complemented
15#36091C211yesmaximal, characteristic, complemented
16#36082C211yesmaximal, characteristic, complemented
17#36076C211yesmaximal, characteristic, complemented
18#35996C211yesmaximal, characteristic, complemented
19#35801C212yesmaximal, complemented
20#35757C212yesmaximal, complemented
21#35078C213yesmaximal, complemented
22#34575C213yesmaximal, complemented
23C22⋊C4×#41C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic, complemented
25C22×H(5,𝔽2)C2211yescharacteristic
26C23×#41C2211yescharacteristic
27#3488—216no—
28#3487—216no—
29C2×#550C2211yescharacteristic
30C2×#550C2212yes—
31C2×#550C2213yescomplemented
32C2×#550C2211yescharacteristic, complemented
33C2×#550C2213yescomplemented
34C2×#550C2212yescomplemented
35C2×#548C2211yescharacteristic
36C2×#548C2212yes—
37C2×#548C2213yescomplemented
38C2×#548C2211yescharacteristic, complemented
39C2×#548C2213yescomplemented
40C2×#548C2212yescomplemented
41C2×#546C2216yes—
42C2×D42C2216yes—
43C2×#537C2213yes—
44C2×#535C2213yes—
45C2×#535C2213yescomplemented
46C2×#535C2213yescomplemented
47C2×#525C2213yes—
48C2×#525C2213yescomplemented
49C2×#525C2213yescomplemented
50C22×#121C2213yes—
51C2×#520C2211yescharacteristic
52C2×#519C2211yescharacteristic, complemented
53C2×C4×#41C2212yescomplemented
54#2856C2216yescomplemented
55#2850C2216yescomplemented
56#2816C2216yescomplemented
57#2815C2216yescomplemented
58#2812C22112yescomplemented
59#2688C22112yescomplemented
60#2686C22112yescomplemented
61#2684C22112yescomplemented
62#2673C22112yescomplemented
63#2671C22112yescomplemented
64#2669C22112yescomplemented
65#2668C22112yescomplemented
66#2668C22112yescomplemented
67#2663C2211yescharacteristic, complemented
68#2663C2216yescomplemented
69#2663C2213yescomplemented
70#2661C2213yescomplemented
71#2661C2216yescomplemented
72#2661C2216yescomplemented
73#2661C2213yescomplemented
74#2659C2213yescomplemented
75#2656C2213yescomplemented
76#2639C2213yescomplemented
77#2639C2213yescomplemented
78#2638C2216yescomplemented
79#2635C2216yescomplemented
80#2625C2213yescomplemented
81#2624C2216yescomplemented
82#2624C2213yescomplemented
83#2617C2216yescomplemented
84#2617C2216yescomplemented
85#2616C2213yescomplemented
86#2615C2216yescomplemented
87#2615C2213yescomplemented
88#2613C2216yescomplemented
89#2613C2216yescomplemented
90#2602C22112yescomplemented
91#2561C2216yescomplemented
92#2544C2216yescomplemented
93#2543C2216yescomplemented
94#2543C2216yescomplemented
95#2541C2216yescomplemented
96#2539C2216yescomplemented
97#2537C2216yescomplemented
98#2535C2216yescomplemented
99#2504C2213yescomplemented
100#2502C2213yescomplemented
101#2500C2216yescomplemented
102#2486C2213yescomplemented
103#2486C2213yescomplemented
104#2485C2216yescomplemented
105#2448C2216yescomplemented
106#2448C2216yescomplemented
107#2447C2216yescomplemented
108#2445C2216yescomplemented
109#2436C2216yescomplemented
110#2435C2213yescomplemented
111#2435C2216yescomplemented
112#2433C2213yescomplemented
113#2433C2216yescomplemented
114#2431C2216yescomplemented
115#2431C2216yescomplemented
116#2428C2216yescomplemented
117#2428C2216yescomplemented
118#2428C2216yescomplemented
119#2427C2216yescomplemented
120#2423C2216yescomplemented
121#2422C2216yescomplemented
122#2421C2216yescomplemented
123#2420C2216yescomplemented
124#2415C2216yescomplemented
125#2414C2216yescomplemented
126#2414C2216yescomplemented
127#2414C2216yescomplemented
128#2410C22112yescomplemented
129#2409C2216yescomplemented
130#2408C2216yescomplemented
131#2408C2216yescomplemented
132#2408C2213yescomplemented
133#2408C2213yescomplemented
134#2407C2216yescomplemented
135#2407C2216yescomplemented
136#2395C2213yescomplemented
137#2395C2216yescomplemented
138#2395C2213yescomplemented
139#2388C2216yescomplemented
140#2388C2213yescomplemented
141#2388C2213yescomplemented
142#2351C2212yescomplemented
143Q8×C4⋊C4C2212yescomplemented
144#2341C2211yescharacteristic
145#2341C2211yescharacteristic
146#2341C2212yescomplemented
147#2341C2212yescomplemented
148#2341C2212yescomplemented
149Q8×C22⋊C4C2212yescomplemented
150Q8×C22⋊C4C2212yescomplemented
151#2339C2213yescomplemented
152#2339C2213yescomplemented
153D4×C22⋊C4C2216yescomplemented
154#2321C22112yescomplemented
155C4×#121C2216yescomplemented
156C4×#121C2216yescomplemented
157#2297C2216yescomplemented
158#2280C2213yescomplemented
159C2×C4×C22⋊C4C2213yescomplemented
160C2×2−1+4—28no—
161C2×2−1+4—48no—
162C2×H(5,𝔽2)—28no—
163C2×H(5,𝔽2)—48no—
164C22×#41—48no—
165C22×#41D4116yescomplemented
166C22×#41C2312yes—
167C22×#41C2311yescharacteristic
168C22×#41C2311yescharacteristic
169C22×#41C2311yescharacteristic
170C22×#41C2313yes—
171C22×#41C2313yes—
172C22×#41C2313yes—
173C22×#41C2313yes—
174C22×#41C2313yes—
175C22×#41C2313yes—
176C23×Q8C2311yescharacteristic
177C23×Q8C2311yescharacteristic
178C23×Q8C2313yes—
179C23×D4C2313yes—
180C23×D4C2316yes—
181C23×D4C2316yes—
182C23×D4C2313yes—
183C24×C4C2313yes—
184#550—28no—
185#550—216no—
186#550—28no—
187#550—224no—
188#550—224no—
189#550—48no—
190#548—28no—
191#548—28no—
192#548—224no—
193#548—224no—
194#548—216no—
195#548—48no—
196#546—248no—
197D42—248no—
198#537—224no—
199#535—224no—
200#535—224no—
201#535—224no—
202C2×#127C2316yes—
203C2×#127C2316yes—
204C2×#127C2313yes—
205C2×#127C2313yes—
206C2×#127C2316yes—
207C2×#124C2316yes—
208C2×#124C2313yes—
209C2×#124C2316yes—
210C2×#124C2313yes—
211C2×#124C2316yes—
212#525—224no—
213#525—224no—
214#525—224no—
215C2×#123C2316yes—
216C2×#123C2313yes—
217C2×#123C2311yescharacteristic
218C2×#123C2316yes—
219C2×#123C2316yes—
220C2×C22⋊Q8C2313yes—
221C2×C22⋊Q8C2313yes—
222C2×C22⋊Q8C2313yes—
223C2×C22⋊Q8C2313yes—
224C2×C22⋊Q8C2313yes—
225C2×C22⋊Q8C2316yes—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2316yes—
228C2×#121—224no—
229C2×#121C2316yes—
230C2×#121C2316yes—
231C2×#121C2313yes—
232C2×#121C2316yes—
233C2×#121C2313yes—
234C2×#121C2313yes—
235C2×#121C2313yes—
236C2×#121C2313yes—
237C2×#121C2313yes—
238C2×#121C2313yes—
239C2×#121C2313yes—
240C2×#121C2316yes—
241C2×#121C2316yes—
242C2×#121C23112yes—
243C2×#121C2313yes—
244C2×#121C2313yes—
245C2×#121C2316yes—
246C2×#121C2316yes—
247C2×#121C2316yes—
248C2×#121C2316yes—
249C2×#121C2316yes—
250C2×#121C2316yes—
251C2×#121C23112yes—
252C2×#121C23112yes—
253C2×#120C2313yes—
254C2×#120C2313yes—
255C2×#120C2316yes—
256C2×#120C2316yes—
257C2×#120C23112yes—
258C2×#120C23112yes—
259C2×#120C2316yes—
260C2×#120C2316yes—
261#520—28no—
262#519—28no—
263C4×#41—48no—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2313yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2316yes—
273C2×C4×D4C2316yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2316yes—
277C2×C4×D4C2316yes—
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×C4×D4C2316yes—
281C2×C4×D4C2316yes—
282C2×C4×D4C2316yes—
283C2×C4×D4C2316yes—
284C2×#117C2313yes—
285C2×#117C2313yes—
286C2×#117C2313yes—
287C2×#117C2316yes—
288C22×C4⋊C4C2313yes—
289C22×C22⋊C4C2316yes—
290C22×C22⋊C4C2316yes—
291C22×C42C2316yes—
292#400C2313yes—
293#400C2311yescharacteristic
294#400C2316yes—
295#399C23112yes—
296#399C2313yes—
297#399C2311yescharacteristic
298#399C2316yes—
299#398C2313yes—
300#398C2316yes—
301#398C2316yes—
302#398C2313yes—
303#397C23112yes—
304#397C23112yes—
305#397C2312yes—
306#397C2316yes—
307#397C2316yes—
308#397C2316yes—
309#397C2316yes—
310#397C23112yes—
311#397C2316yes—
312#397C2313yes—
313#397C2313yes—
314#395C2313yes—
315#395C2311yescharacteristic
316#395C2316yes—
317#394C2313yes—
318#394C23112yes—
319#394C23112yes—
320#394C2316yes—
321#394C23112yes—
322#394C23112yes—
323#394C2316yes—
324#394C23112yes—
325#394C2312yes—
326#394C2316yes—
327#394C2316yes—
328#394C2316yes—
329#394C2316yes—
330#394C2316yes—
331#394C2316yes—
332#394C23112yes—
333#394C23112yes—
334#394C2316yes—
335#394C2313yes—
336#393C23112yes—
337#393C2313yes—
338#393C2311yescharacteristic
339#393C2316yes—
340#392C23112yes—
341#392C2316yes—
342#392C23112yes—
343#392C23112yes—
344#392C23112yes—
345#392C2316yes—
346#392C23112yes—
347#392C2316yes—
348#392C2316yes—
349#392C2316yes—
350#392C23112yes—
351#392C2313yes—
352#392C2316yes—
353#392C2313yes—
354#391C2316yes—
355#391C2316yes—
356#391C2316yes—
357#391C2316yes—
358#390C2316yes—
359#390C23112yes—
360#390C2316yes—
361#390C2316yes—
362#390C2316yes—
363#390C2316yes—
364#390C2316yes—
365#390C2316yes—
366#390C2316yes—
367#390C2316yes—
368#390C2316yes—
369#389C2316yes—
370#389C2316yes—
371#389C2316yes—
372#389C2316yes—
373#389C2316yes—
374#389C2312yes—
375#388C2316yes—
376#388C23112yes—
377#388C2316yes—
378#388C23112yes—
379#388C23112yes—
380#388C2316yes—
381#388C23112yes—
382#388C2312yes—
383#387C23112yes—
384#386C23112yes—
385#386C23112yes—
386#386C23112yes—
387#386C23112yes—
388#386C23112yes—
389#386C23112yes—
390#386C23112yes—
391#386C23112yes—
392#386C2316yes—
393#386C2316yes—
394#386C2316yes—
395#386C2316yes—
396#385C23112yes—
397#385C23112yes—
398#384C2316yes—
399#382C2316yes—
400#381C2316yes—
401#381C2316yes—
402#381C2316yes—
403#380C2316yes—
404#380C2313yes—
405#380C2313yes—
406#380C2316yes—
407#380C2316yes—
408#380C2316yes—
409#380C2316yes—
410#380C2316yes—
411#380C2316yes—
412#379C2316yes—
413#379C2316yes—
414#379C23112yes—
415#379C2316yes—
416C4×C4⋊C4C2316yes—
417C4×C4⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2313yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2311yescharacteristic
428C4×C22⋊C4C2313yes—
429C2×#95C2313yes—
430C2×#95C2313yes—
431C25C2416yes—
432C25C2413yes—
4332−1+4—464no—
434H(5,𝔽2)—464no—
435C2×#41—28no—
436C2×#41—212no—
437C2×#41—24no—
438C2×#41—28no—
439C2×#41—28no—
440C2×#41—28no—
441C2×#41—28no—
442C2×#41—28no—
443C2×#41—212no—
444C2×#41—212no—
445C2×#41—212no—
446C2×#41—412no—
447C2×#41—412no—
448C2×#41—412no—
449C2×#41—412no—
450C2×#41—412no—
451C2×#41—412no—
452C2×#41—464no—
453C2×#41C2×D418yes—
454C2×#41C2×D418yes—
455C2×#41C2×D4124yes—
456C2×#41C2×D4124yes—
457C22×Q8—28no—
458C22×Q8—212no—
459C22×Q8—24no—
460C22×Q8—28no—
461C22×Q8—412no—
462C22×Q8C2×D418yes—
463C22×Q8C2413yes—
464C22×Q8C2413yes—
465C22×Q8C2411yescharacteristic
466C22×Q8C2413yes—
467C22×Q8C2411yescharacteristic
468C22×D4—224no—
469C22×D4—224no—
470C22×D4—212no—
471C22×D4—412no—
472C22×D4—412no—
473C22×D4—412no—
474C22×D4—412no—
475C22×D4—86no—
476C22×D4—86no—
477C22×D4C2×D4124yes—
478C22×D4C2416yes—
479C22×D4C2413yes—
480C22×D4C2413yes—
481C22×D4C2413yes—
482C22×D4C2413yes—
483C22×D4C2413yes—
484C22×D4C2416yes—
485C22×D4C2416yes—
486C22×D4C2416yes—
487C22×D4C2416yes—
488C22×D4C2413yes—
489C22×D4C2413yes—
490C22×D4C2416yes—
491C22×D4C2411yescharacteristic
492C22×D4C2413yes—
493C22×D4C24112yes—
494C22×D4C2416yes—
495C22×D4C2413yes—
496C22×D4C2413yes—
497C22×D4C2416yes—
498C22×D4C24112yes—
499C22×D4C2416yes—
500C23×C4—412no—
501C23×C4C2×D4124yes—
502C23×C4C2413yes—
503C23×C4C2413yes—
504C23×C4C2416yes—
505C23×C4C2413yes—
506C23×C4C2413yes—
507C23×C4C2413yes—
508C23×C4C2416yes—
509C23×C4C2416yes—
510C23×C4C2416yes—
511C23×C4C2416yes—
512C23×C4C2413yes—
513C23×C4C2413yes—
514C23×C4C2411yescharacteristic
515#127—224no—
516#127—212no—
517#127—212no—
518#127—224no—
519#127—412no—
520#124—224no—
521#124—212no—
522#124—212no—
523#124—224no—
524#124—412no—
525#123—212no—
526#123—24no—
527#123—224no—
528#123—86no—
529#123—86no—
530C22⋊Q8—224no—
531C22⋊Q8—24no—
532C22⋊Q8—212no—
533C22⋊Q8—212no—
534C22⋊Q8—212no—
535C22⋊Q8—212no—
536C22⋊Q8—212no—
537C22⋊Q8—412no—
538#121—212no—
539#121—212no—
540#121—212no—
541#121—212no—
542#121—224no—
543#121—224no—
544#121—248no—
545#121—224no—
546#121—212no—
547#121—224no—
548#121—224no—
549#121—224no—
550#121—212no—
551#121—212no—
552#121—212no—
553#121—212no—
554#121—212no—
555#121—412no—
556#121—412no—
557#121—412no—
558#121—412no—
559#121—412no—
560#121—812no—
561#121—812no—
562#120—212no—
563#120—212no—
564#120—224no—
565#120—224no—
566#120—248no—
567#120—424no—
568#120—86no—
569#120—86no—
570C4×Q8—212no—
571C4×Q8—212no—
572C4×Q8—24no—
573C4×Q8—24no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×Q8—28no—
577C4×D4—224no—
578C4×D4—224no—
579C4×D4—224no—
580C4×D4—212no—
581C4×D4—212no—
582C4×D4—212no—
583C4×D4—212no—
584C4×D4—224no—
585C4×D4—224no—
586C4×D4—412no—
587C4×D4—412no—
588C4×D4—412no—
589C4×D4—412no—
590#117—212no—
591#117—212no—
592#117—212no—
593#117—412no—
594C2×C4⋊C4—212no—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2416yes—
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C2413yes—
601C2×C4⋊C4C2413yes—
602C2×C4⋊C4C2413yes—
603C2×C4⋊C4C2413yes—
604C2×C4⋊C4C2413yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2413yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2416yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2416yes—
613C2×C4⋊C4C2416yes—
614C2×C4⋊C4C24112yes—
615C2×C4⋊C4C2416yes—
616C2×C4⋊C4C2416yes—
617C2×C22⋊C4—224no—
618C2×C22⋊C4—412no—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C24112yes—
623C2×C22⋊C4C2411yescharacteristic
624C2×C22⋊C4C2413yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2413yes—
628C2×C22⋊C4C2411yescharacteristic
629C2×C22⋊C4C2413yes—
630C2×C22⋊C4C2411yescharacteristic
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2413yes—
634C2×C22⋊C4C2413yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C2413yes—
637C2×C22⋊C4C2413yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C2416yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2416yes—
642C2×C22⋊C4C2416yes—
643C2×C22⋊C4C24112yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2416yes—
646C2×C22⋊C4C2416yes—
647C2×C22⋊C4C2416yes—
648C2×C22⋊C4C2416yes—
649C2×C22⋊C4C24112yes—
650C2×C22⋊C4C2416yes—
651C2×C22⋊C4C2416yes—
652C2×C22⋊C4C24112yes—
653C2×C22⋊C4C2416yes—
654C2×C22⋊C4C2416yes—
655C2×C22⋊C4C24112yes—
656C2×C22⋊C4C24112yes—
657C2×C22⋊C4C2416yes—
658C2×C22⋊C4C2416yes—
659C2×C22⋊C4C2416yes—
660C2×C42—412no—
661C2×C42C2416yes—
662C2×C42C2413yes—
663C2×C42C2413yes—
664C2×C42C2416yes—
665C2×C42C2416yes—
666C2×C42C2416yes—
667C2×C42C2416yes—
668C2×C42C2412yes—
669#95C2411yescharacteristic
670#95C2411yescharacteristic
671#95C2413yes—
672#95C2413yes—
673#95C2416yes—
674#95C2416yes—
675#95C2412yes—
676#95C2412yes—
677#95C2412yes—
678#95C2416yes—
679#95C2416yes—
680#95C2416yes—
681#95C24112yes—
682#95C2416yes—
683#95C2416yes—
684#95C2412yes—
685#95C2416yes—
686#95C2416yes—
687#95C2416yes—
688#95C24112yes—
689#95C24112yes—
690C24—212no—
691C24—46no—
692C24—46no—
693C24—43no—
694C24—43no—
695C24—412no—
696C24—412no—
697C24—46no—
698C24—46no—
699C24C22×D4112yes—
700C24C2516yes—
701C24C2511yescharacteristic
702C24C2513yes—
703C24C2511yescharacteristic
704C24C2513yes—
705C24C2513yes—
706#41—232no—
707#41—232no—
708#41—448no—
709#41—448no—
710#41—448no—
711#41—448no—
712#41—448no—
713#41—448no—
714#41—432no—
715#41—416no—
716C2×Q8—232no—
717C2×Q8—22no—
718C2×Q8—26no—
719C2×Q8—26no—
720C2×Q8—212no—
721C2×Q8—212no—
722C2×Q8—46no—
723C2×Q8—42no—
724C2×Q8—448no—
725C2×Q8—416no—
726C2×Q8C22×D4112yes—
727C2×Q8C22×D414yes—
728C2×Q8H(5,𝔽2)18yes—
729C2×D4—212no—
730C2×D4—22no—
731C2×D4—26no—
732C2×D4—212no—
733C2×D4—212no—
734C2×D4—26no—
735C2×D4—26no—
736C2×D4—212no—
737C2×D4—212no—
738C2×D4—26no—
739C2×D4—26no—
740C2×D4—224no—
741C2×D4—26no—
742C2×D4—212no—
743C2×D4—26no—
744C2×D4—26no—
745C2×D4—212no—
746C2×D4—212no—
747C2×D4—212no—
748C2×D4—212no—
749C2×D4—212no—
750C2×D4—212no—
751C2×D4—448no—
752C2×D4—46no—
753C2×D4—46no—
754C2×D4—46no—
755C2×D4—412no—
756C2×D4—46no—
757C2×D4—46no—
758C2×D4—46no—
759C2×D4—42no—
760C2×D4—46no—
761C2×D4—448no—
762C2×D4—46no—
763C2×D4—46no—
764C2×D4—412no—
765C2×D4—46no—
766C2×D4—43no—
767C2×D4—43no—
768C2×D4—46no—
769C2×D4—46no—
770C2×D4—46no—
771C2×D4—46no—
772C2×D4—46no—
773C2×D4—46no—
774C2×D4—46no—
775C2×D4—46no—
776C2×D4—412no—
777C2×D4—412no—
778C2×D4—43no—
779C2×D4—43no—
780C2×D4—412no—
781C2×D4—412no—
782C2×D4—412no—
783C2×D4—496no—
784C2×D4—848no—
785C2×D4C22×D4112yes—
786C2×D4C22×D4112yes—
787C2×D4C22×D4124yes—
788C22×C4—212no—
789C22×C4—212no—
790C22×C4—212no—
791C22×C4—212no—
792C22×C4—212no—
793C22×C4—26no—
794C22×C4—26no—
795C22×C4—212no—
796C22×C4—212no—
797C22×C4—212no—
798C22×C4—212no—
799C22×C4—212no—
800C22×C4—212no—
801C22×C4—448no—
802C22×C4—42no—
803C22×C4—46no—
804C22×C4—46no—
805C22×C4—412no—
806C22×C4—46no—
807C22×C4—46no—
808C22×C4—46no—
809C22×C4—46no—
810C22×C4—46no—
811C22×C4—46no—
812C22×C4—46no—
813C22×C4C22×D4112yes—
814C22×C4C22×D4112yes—
815C22×C4C22×D4112yes—
816C22×C4C22×D4112yes—
817C22×C4C22×D4112yes—
818C22×C4C22×D414yes—
819C22×C4C2512yes—
820C22×C4C2516yes—
821C22×C4C2512yes—
822C22×C4C2513yes—
823C22×C4C2511yescharacteristic
824C22×C4C2516yes—
825C22×C4C2516yes—
826C22×C4C2511yescharacteristic
827C22×C4C2513yes—
828C22×C4C2512yes—
829C22×C4C2511yescharacteristic
830C22×C4C2513yes—
831C22×C4C2513yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2512yes—
835C22×C4C2513yes—
836C4⋊C4—26no—
837C4⋊C4—212no—
838C4⋊C4—22no—
839C4⋊C4—26no—
840C4⋊C4—26no—
841C4⋊C4—26no—
842C4⋊C4—26no—
843C4⋊C4—26no—
844C4⋊C4—22no—
845C4⋊C4—26no—
846C4⋊C4—22no—
847C4⋊C4—24no—
848C4⋊C4—212no—
849C4⋊C4—212no—
850C4⋊C4—212no—
851C4⋊C4—24no—
852C4⋊C4—42no—
853C4⋊C4—46no—
854C4⋊C4—46no—
855C4⋊C4—46no—
856C4⋊C4—412no—
857C4⋊C4—46no—
858C22⋊C4—22no—
859C22⋊C4—26no—
860C22⋊C4—212no—
861C22⋊C4—24no—
862C22⋊C4—212no—
863C22⋊C4—26no—
864C22⋊C4—26no—
865C22⋊C4—212no—
866C22⋊C4—26no—
867C22⋊C4—26no—
868C22⋊C4—212no—
869C22⋊C4—212no—
870C22⋊C4—224no—
871C22⋊C4—26no—
872C22⋊C4—22no—
873C22⋊C4—26no—
874C22⋊C4—22no—
875C22⋊C4—212no—
876C22⋊C4—24no—
877C22⋊C4—212no—
878C22⋊C4—212no—
879C22⋊C4—24no—
880C22⋊C4—46no—
881C22⋊C4—46no—
882C22⋊C4—412no—
883C22⋊C4—42no—
884C22⋊C4—46no—
885C22⋊C4—46no—
886C22⋊C4—46no—
887C22⋊C4—412no—
888C22⋊C4—46no—
889C22⋊C4—412no—
890C22⋊C4—46no—
891C22⋊C4—46no—
892C22⋊C4—46no—
893C22⋊C4—46no—
894C22⋊C4—412no—
895C22⋊C4—46no—
896C22⋊C4—46no—
897C22⋊C4—412no—
898C22⋊C4—46no—
899C42—212no—
900C42—212no—
901C42—26no—
902C42—26no—
903C42—212no—
904C42—212no—
905C42—42no—
906C42—46no—
907C23—26no—
908C23—22no—
909C23—26no—
910C23—22no—
911C23—26no—
912C23—26no—
913C23—23no—
914C23—23no—
915C23—23no—
916C23—23no—
917C23—21no—
918C23—21no—
919C23—26no—
920C23—21no—
921C23—23no—
922C23—26no—
923C23—22no—
924C23—26no—
925C23—26no—
926C23—22no—
927C23—26no—
928C23—26no—
929C23—26no—
930C23—21no—
931C23—23no—
932C23—23no—
933C23—26no—
934C23—26no—
935C23—21no—
936C23—412no—
937C23—412no—
938C23—412no—
939C23—424no—
940C23—812no—
941C23—812no—
942C23—812no—
943C23—812no—
944C23—1612no—
945C23—1612no—
946C23C23×D416yes—
947C23C23×D412yes—
948C23C23×D416yes—
949C23C2611yescharacteristic
950Q8—224no—
951Q8—412no—
952Q8—44no—
953Q8—412no—
954Q8#534116yes—
955D4—224no—
956D4—224no—
957D4—424no—
958D4—412no—
959D4—412no—
960D4—424no—
961D4—424no—
962D4—44no—
963D4—412no—
964D4—424no—
965D4—412no—
966D4—812no—
967D4—86no—
968D4—86no—
969D4—812no—
970D4—812no—
971D4—86no—
972D4—86no—
973D4—812no—
974D4—824no—
975D4—812no—
976D4—1612no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—26no—
981C2×C4—22no—
982C2×C4—224no—
983C2×C4—224no—
984C2×C4—224no—
985C2×C4—22no—
986C2×C4—23no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—23no—
990C2×C4—26no—
991C2×C4—21no—
992C2×C4—23no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—26no—
996C2×C4—26no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—26no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—26no—
1003C2×C4—26no—
1004C2×C4—22no—
1005C2×C4—26no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—26no—
1009C2×C4—22no—
1010C2×C4—21no—
1011C2×C4—26no—
1012C2×C4—23no—
1013C2×C4—23no—
1014C2×C4—26no—
1015C2×C4—26no—
1016C2×C4—21no—
1017C2×C4—44no—
1018C2×C4—412no—
1019C2×C4—412no—
1020C2×C4—424no—
1021C2×C4—424no—
1022C2×C4—412no—
1023C2×C4—412no—
1024C2×C4—812no—
1025C2×C4—812no—
1026C2×C4—812no—
1027C2×C4C23×D416yes—
1028C2×C4C23×D412yes—
1029C2×C4C23×D412yes—
1030C2×C4C23×D416yes—
1031C2×C4C2×H(5,𝔽2)112yes—
1032C2×C4#58514yes—
1033C22—26no—
1034C22—26no—
1035C22—22no—
1036C22—26no—
1037C22—22no—
1038C22—26no—
1039C22—22no—
1040C22—26no—
1041C22—26no—
1042C22—46no—
1043C22—42no—
1044C22—46no—
1045C22—46no—
1046C22—42no—
1047C22—46no—
1048C22—41no—
1049C22—43no—
1050C22—46no—
1051C22—46no—
1052C22—41no—
1053C22—43no—
1054C22—42no—
1055C22—46no—
1056C22—46no—
1057C22—46no—
1058C22—46no—
1059C22—46no—
1060C22—42no—
1061C22—46no—
1062C22—43no—
1063C22—41no—
1064C22—46no—
1065C22—824no—
1066C22—1624no—
1067C22C24×D411yescharacteristic
1068C22C22×H(5,𝔽2)12yes—
1069C22C2×#58512yes—
1070C22H(7,𝔽2)11yescharacteristic
1071C22H(7,𝔽2)11yescharacteristic
1072C4—24no—
1073C4—22no—
1074C4—22no—
1075C4—26no—
1076C4—42no—
1077C4—43no—
1078C4—41no—
1079C4—46no—
1080C4—41no—
1081C4—43no—
1082C4—46no—
1083C4—42no—
1084C4—46no—
1085C4—42no—
1086C4—41no—
1087C4—43no—
1088C4C2×#534112yes—
1089C2—46no—
1090C2—42no—
1091C2—46no—
1092C2—81no—
1093C2—83no—
1094C2—86no—
1095C2C22×#53411yescharacteristic
1096C2#6281211yescharacteristic
1097C2#6285211yescharacteristic
1098C2#6289912yes—
1099C2#6292312yes—
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×#3487C2semidirect
3. #42985C2semidirect
4. #42984C2semidirect
5. #42979C2semidirect
6. #42969C2semidirect
7. #42422C2semidirect
8. #42420C2semidirect
9. #39960C2semidirect
10. #39957C2semidirect
11. #37445C2semidirect
12. #37437C2semidirect
13. #36455C2semidirect
14. #36430C2semidirect
15. #36091C2semidirect
16. #36082C2semidirect
17. #36076C2semidirect
18. #35996C2semidirect
19. #35801C2semidirect
20. #35757C2semidirect
21. #35078C2semidirect
22. #34575C2semidirect
23. C22⋊C4×#41C2semidirect
24. C22×2−1+4C22semidirect
31. C2×#550C22semidirect
32. C2×#550C22semidirect
33. C2×#550C22semidirect
34. C2×#550C22semidirect
37. C2×#548C22semidirect
38. C2×#548C22semidirect
39. C2×#548C22semidirect
40. C2×#548C22semidirect
45. C2×#535C22semidirect
46. C2×#535C22semidirect
48. C2×#525C22semidirect
49. C2×#525C22semidirect
52. C2×#519C22semidirect
53. C2×C4×#41C22semidirect
54. #2856C22semidirect
55. #2850C22semidirect
56. #2816C22semidirect
57. #2815C22semidirect
58. #2812C22semidirect
59. #2688C22semidirect
60. #2686C22semidirect
61. #2684C22semidirect
62. #2673C22semidirect
63. #2671C22semidirect
64. #2669C22semidirect
65. #2668C22semidirect
66. #2668C22semidirect
67. #2663C22semidirect
68. #2663C22semidirect
69. #2663C22semidirect
70. #2661C22semidirect
71. #2661C22semidirect
72. #2661C22semidirect
73. #2661C22semidirect
74. #2659C22semidirect
75. #2656C22semidirect
76. #2639C22semidirect
77. #2639C22semidirect
78. #2638C22semidirect
79. #2635C22semidirect
80. #2625C22semidirect
81. #2624C22semidirect
82. #2624C22semidirect
83. #2617C22semidirect
84. #2617C22semidirect
85. #2616C22semidirect
86. #2615C22semidirect
87. #2615C22semidirect
88. #2613C22semidirect
89. #2613C22semidirect
90. #2602C22semidirect
91. #2561C22semidirect
92. #2544C22semidirect
93. #2543C22semidirect
94. #2543C22semidirect
95. #2541C22semidirect
96. #2539C22semidirect
97. #2537C22semidirect
98. #2535C22semidirect
99. #2504C22semidirect
100. #2502C22semidirect
101. #2500C22semidirect
102. #2486C22semidirect
103. #2486C22semidirect
104. #2485C22semidirect
105. #2448C22semidirect
106. #2448C22semidirect
107. #2447C22semidirect
108. #2445C22semidirect
109. #2436C22semidirect
110. #2435C22semidirect
111. #2435C22semidirect
112. #2433C22semidirect
113. #2433C22semidirect
114. #2431C22semidirect
115. #2431C22semidirect
116. #2428C22semidirect
117. #2428C22semidirect
118. #2428C22semidirect
119. #2427C22semidirect
120. #2423C22semidirect
121. #2422C22semidirect
122. #2421C22semidirect
123. #2420C22semidirect
124. #2415C22semidirect
125. #2414C22semidirect
126. #2414C22semidirect
127. #2414C22semidirect
128. #2410C22semidirect
129. #2409C22semidirect
130. #2408C22semidirect
131. #2408C22semidirect
132. #2408C22semidirect
133. #2408C22semidirect
134. #2407C22semidirect
135. #2407C22semidirect
136. #2395C22semidirect
137. #2395C22semidirect
138. #2395C22semidirect
139. #2388C22semidirect
140. #2388C22semidirect
141. #2388C22semidirect
142. #2351C22semidirect
143. Q8×C4⋊C4C22semidirect
146. #2341C22semidirect
147. #2341C22semidirect
148. #2341C22semidirect
149. Q8×C22⋊C4C22semidirect
150. Q8×C22⋊C4C22semidirect
151. #2339C22semidirect
152. #2339C22semidirect
153. D4×C22⋊C4C22semidirect
154. #2321C22semidirect
155. C4×#121C22semidirect
156. C4×#121C22semidirect
157. #2297C22semidirect
158. #2280C22semidirect
159. C2×C4×C22⋊C4C22semidirect
165. C22×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34882
C2×#34872
#429852
#429842
#429792
#429692
#424222
#424202
#399602
#399572
#374452
#374372
#364552
#364302
#360912
#360822
#360762
#359962
#358012
#357572
#350782
#345752
C22⋊C4×#412