Finite Group Databasebeta

← #7658148

Subgroups — #7658148

Order 512.

8935 conjugacy classes of subgroups.

The subgroup lattice has 1107 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3488C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#42992C213yesmaximal, complemented
4#42988C213yesmaximal, complemented
5#42967C213yesmaximal, complemented
6#42966C213yesmaximal, complemented
7#42475C216yesmaximal, complemented
8#42474C216yesmaximal, complemented
9#39888C216yesmaximal, complemented
10#39885C216yesmaximal, complemented
11#37448C213yesmaximal, complemented
12#37445C213yesmaximal, complemented
13#36433C212yesmaximal, complemented
14#36429C212yesmaximal, complemented
15#36091C211yesmaximal, characteristic, complemented
16#36082C211yesmaximal, characteristic, complemented
17#36018C212yesmaximal, complemented
18#36005C211yesmaximal, characteristic, complemented
19#35983C211yesmaximal, characteristic, complemented
20#35771C212yesmaximal, complemented
21#35076C213yesmaximal, complemented
22#34562C213yesmaximal, complemented
23#34174C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic, complemented
25C23×#41C2211yescharacteristic
26C23×#41C2211yescharacteristic, complemented
27#3488—216no—
28D4×#41—216no—
29C2×#550C2212yes—
30C2×#550C2211yescharacteristic
31C2×#550C2212yescomplemented
32C2×D4×Q8C2211yescharacteristic, complemented
33C2×#548C2211yescharacteristic
34C2×#548C2212yescomplemented
35C2×#548C2211yescharacteristic, complemented
36C2×#548C2212yescomplemented
37C2×#547C2213yescomplemented
38C2×#546C2216yescomplemented
39C2×#546C2213yescomplemented
40C2×#546C2213yescomplemented
41C2×D42C2216yescomplemented
42C2×D42C2213yescomplemented
43C2×#537C2213yescomplemented
44C2×#535C2213yescomplemented
45C2×#532C2213yescomplemented
46C2×#525C2213yescomplemented
47C2×#525C2213yescomplemented
48C2×#525C2213yescomplemented
49C22×#121C2213yescomplemented
50C2×#520C2211yescharacteristic, complemented
51C2×#519C2212yescomplemented
52C2×C4×#41C2211yescharacteristic, complemented
53C22×C4×D4C2213yescomplemented
54#2854C2216yescomplemented
55#2847C2216yescomplemented
56#2813C2216yescomplemented
57#2813C2216yescomplemented
58#2812C22112yescomplemented
59#2701C22112yescomplemented
60#2699C22112yescomplemented
61#2697C22112yescomplemented
62#2682C22112yescomplemented
63#2679C22112yescomplemented
64#2678C22112yescomplemented
65#2678C22112yescomplemented
66#2678C22112yescomplemented
67#2663C2216yescomplemented
68#2661C2216yescomplemented
69#2638C2211yescharacteristic, complemented
70#2638C2213yescomplemented
71#2635C2213yescomplemented
72#2635C2213yescomplemented
73#2635C2216yescomplemented
74#2630C2216yescomplemented
75#2630C2216yescomplemented
76#2627C2213yescomplemented
77#2626C2213yescomplemented
78#2625C2213yescomplemented
79#2624C2213yescomplemented
80#2622C2216yescomplemented
81#2620C2216yescomplemented
82#2619C2216yescomplemented
83#2618C2213yescomplemented
84#2617C2213yescomplemented
85#2616C2213yescomplemented
86#2615C2213yescomplemented
87#2613C2216yescomplemented
88#2613C22112yescomplemented
89#2602C22112yescomplemented
90#2591C2216yescomplemented
91#2548C2216yescomplemented
92#2545C2216yescomplemented
93#2539C2216yescomplemented
94#2538C2216yescomplemented
95#2536C2216yescomplemented
96#2534C22112yescomplemented
97#2503C2213yescomplemented
98#2501C2213yescomplemented
99#2500C2216yescomplemented
100#2487C2213yescomplemented
101#2487C2213yescomplemented
102#2485C2216yescomplemented
103#2447C2216yescomplemented
104#2445C2216yescomplemented
105#2445C2216yescomplemented
106#2445C2216yescomplemented
107#2435C2213yescomplemented
108#2435C2216yescomplemented
109#2433C2213yescomplemented
110#2433C2216yescomplemented
111#2433C2216yescomplemented
112#2431C2216yescomplemented
113#2431C2216yescomplemented
114#2429C2216yescomplemented
115#2426C2216yescomplemented
116#2426C2216yescomplemented
117#2426C2216yescomplemented
118#2422C2216yescomplemented
119#2422C2216yescomplemented
120#2420C2216yescomplemented
121#2420C2216yescomplemented
122#2415C2216yescomplemented
123#2414C2216yescomplemented
124#2414C2216yescomplemented
125#2414C2216yescomplemented
126#2408C2213yescomplemented
127#2408C2213yescomplemented
128#2408C2216yescomplemented
129#2408C2216yescomplemented
130#2408C2216yescomplemented
131#2407C2216yescomplemented
132#2407C2216yescomplemented
133#2405C2216yescomplemented
134#2403C2216yescomplemented
135#2395C2213yescomplemented
136#2395C2213yescomplemented
137#2392C2216yescomplemented
138#2392C2216yescomplemented
139#2388C2213yescomplemented
140#2388C2213yescomplemented
141#2351C2212yescomplemented
142Q8×C4⋊C4C2212yescomplemented
143#2341C2212yescomplemented
144#2341C2212yescomplemented
145#2341C2212yescomplemented
146#2341C2212yescomplemented
147#2341C2211yescharacteristic, complemented
148#2341C2211yescharacteristic, complemented
149#2341C2216yescomplemented
150#2341C2213yescomplemented
151#2341C2213yescomplemented
152Q8×C22⋊C4C2212yescomplemented
153#2321C2216yescomplemented
154#2321C2216yescomplemented
155#2309C2216yescomplemented
156C4×#123C2216yescomplemented
157C4×#120C2216yescomplemented
158#2280C2213yescomplemented
159#2280C2213yescomplemented
160C2×H(5,𝔽2)—28no—
161C2×H(5,𝔽2)—48no—
162C22×#41—28no—
163C22×#41—48no—
164C22×#41—48no—
165C22×#41D4116yescomplemented
166C22×#41C2311yescharacteristic
167C22×#41C2312yes—
168C22×#41C2311yescharacteristic
169C22×#41C2311yescharacteristic
170C22×#41C2313yes—
171C22×#41C2313yes—
172C22×#41C2313yes—
173C22×#41C2313yes—
174C22×#41C2313yes—
175C23×Q8C2311yescharacteristic
176C23×Q8C2311yescharacteristic
177C23×D4C2313yes—
178C23×D4C2313yes—
179C23×D4C2316yes—
180C23×D4C2313yes—
181C23×D4C2316yes—
182C23×D4C2313yes—
183C24×C4C2313yes—
184C24×C4C2313yes—
185#550—28no—
186#550—216no—
187#550—48no—
188D4×Q8—28no—
189#548—28no—
190#548—28no—
191#548—216no—
192#548—48no—
193#547—224no—
194#546—224no—
195#546—248no—
196#546—224no—
197D42—224no—
198D42—248no—
199#537—224no—
200#535—224no—
201#532—224no—
202C2×C4⋊Q8C2313yes—
203C2×#127C2313yes—
204C2×#127C2316yes—
205C2×#127C2316yes—
206C2×#124C2313yes—
207C2×#124C2313yes—
208C2×#124C2316yes—
209C2×#124C2316yes—
210#525—224no—
211#525—224no—
212#525—224no—
213C2×#123C2316yes—
214C2×#123C2316yes—
215C2×#123C2316yes—
216C2×#123C2316yes—
217C2×#123C23112yes—
218C2×#123C23112yes—
219C2×C22⋊Q8C2313yes—
220C2×C22⋊Q8C2313yes—
221C2×C22⋊Q8C2313yes—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2313yes—
224C2×C22⋊Q8C2313yes—
225C2×C22⋊Q8C2316yes—
226C2×C22⋊Q8C2316yes—
227C2×#121—224no—
228C2×#121C2316yes—
229C2×#121C2316yes—
230C2×#121C2313yes—
231C2×#121C2313yes—
232C2×#121C2313yes—
233C2×#121C2316yes—
234C2×#121C2313yes—
235C2×#121C2316yes—
236C2×#121C2313yes—
237C2×#121C2313yes—
238C2×#121C2316yes—
239C2×#121C2316yes—
240C2×#121C23112yes—
241C2×#121C2316yes—
242C2×#121C2316yes—
243C2×#121C2316yes—
244C2×#120C2316yes—
245C2×#120C2316yes—
246C2×#120C2316yes—
247C2×#120C23112yes—
248C2×#120C2316yes—
249C2×#120C2316yes—
250C2×#120C2316yes—
251C2×#120C23112yes—
252C2×#120C23112yes—
253#520—28no—
254#519—48no—
255C4×#41—28no—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2316yes—
262C2×C4×Q8C2316yes—
263C2×C4×D4—224no—
264C2×C4×D4C2313yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2313yes—
269C2×C4×D4C2313yes—
270C2×C4×D4C2313yes—
271C2×C4×D4C2313yes—
272C2×C4×D4C2313yes—
273C2×C4×D4C2316yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2316yes—
277C2×C4×D4C2316yes—
278C2×C4×D4C2316yes—
279C2×C4×D4C2316yes—
280C2×#117C2313yes—
281C2×#117C2313yes—
282C2×#117C2316yes—
283C2×#117C2316yes—
284C22×C4⋊C4C2313yes—
285C22×C4⋊C4C2313yes—
286C22×C22⋊C4C2316yes—
287C22×C22⋊C4C2313yes—
288C22×C22⋊C4C2313yes—
289C22×C42C2313yes—
290#400C2313yes—
291#400C2316yes—
292#400C2313yes—
293#399C2316yes—
294#399C2313yes—
295#399C2313yes—
296#398C2311yescharacteristic
297#398C2313yes—
298#398C2316yes—
299#398C2316yes—
300#397C23112yes—
301#397C2311yescharacteristic
302#397C2313yes—
303#397C2312yes—
304#397C2316yes—
305#397C2316yes—
306#397C2316yes—
307#397C23112yes—
308#396C2316yes—
309#396C2316yes—
310#396C23112yes—
311#396C23112yes—
312#396C2316yes—
313#396C2316yes—
314#395C2313yes—
315#395C2311yescharacteristic
316#394C2313yes—
317#394C2316yes—
318#394C23112yes—
319#394C23112yes—
320#394C2312yes—
321#394C2316yes—
322#394C23112yes—
323#394C2316yes—
324#394C2316yes—
325#394C2316yes—
326#394C23112yes—
327#394C23112yes—
328#394C2316yes—
329#394C2316yes—
330#394C2313yes—
331#394C23112yes—
332#394C23112yes—
333#394C2316yes—
334#394C2316yes—
335#394C2316yes—
336#394C23112yes—
337#394C23112yes—
338#393C2313yes—
339#393C2311yescharacteristic
340#392C23112yes—
341#392C2316yes—
342#392C23112yes—
343#392C2316yes—
344#392C2316yes—
345#392C2316yes—
346#392C23112yes—
347#392C23112yes—
348#392C2316yes—
349#392C2313yes—
350#392C2313yes—
351#392C23112yes—
352#391C2316yes—
353#391C2316yes—
354#390C2316yes—
355#390C2316yes—
356#390C2316yes—
357#390C2316yes—
358#390C23112yes—
359#390C23112yes—
360#390C23112yes—
361#390C23112yes—
362#390C2316yes—
363#390C2316yes—
364#390C2316yes—
365#390C2316yes—
366#390C2316yes—
367#390C2316yes—
368#390C23112yes—
369#389C2316yes—
370#389C2316yes—
371#389C23112yes—
372#389C2316yes—
373#389C2316yes—
374#388C2316yes—
375#388C23112yes—
376#388C23112yes—
377#388C23112yes—
378#388C23112yes—
379#388C23112yes—
380#388C2316yes—
381#387C2316yes—
382#387C2312yes—
383#386C2316yes—
384#386C23112yes—
385#386C2316yes—
386#386C2316yes—
387#386C23112yes—
388#386C23112yes—
389#386C2316yes—
390#386C2316yes—
391#386C2316yes—
392#385C2316yes—
393#385C2316yes—
394#385C2316yes—
395#385C2316yes—
396#385C2316yes—
397#385C2312yes—
398#384C2316yes—
399#382C2316yes—
400#381C2316yes—
401#381C23112yes—
402#381C2311yescharacteristic
403#381C2313yes—
404#380C2316yes—
405#380C2316yes—
406#380C2316yes—
407#380C2313yes—
408#380C2313yes—
409#380C2313yes—
410#380C2313yes—
411#380C2316yes—
412#380C2316yes—
413#380C2316yes—
414#379C2316yes—
415#379C2316yes—
416#379C2316yes—
417#379C2316yes—
418#379C2316yes—
419#379C23112yes—
420C4×C4⋊C4C2316yes—
421C4×C4⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2313yes—
426C4×C22⋊C4C2313yes—
427C4×C22⋊C4C2316yes—
428C4×C22⋊C4C2316yes—
429C4×C22⋊C4C2316yes—
430C4×C22⋊C4C2316yes—
431C25C2413yes—
432C25C2416yes—
433C25C2413yes—
434H(5,𝔽2)—464no—
435C2×#41—24no—
436C2×#41—28no—
437C2×#41—28no—
438C2×#41—28no—
439C2×#41—28no—
440C2×#41—28no—
441C2×#41—28no—
442C2×#41—212no—
443C2×#41—212no—
444C2×#41—212no—
445C2×#41—412no—
446C2×#41—412no—
447C2×#41—412no—
448C2×#41—412no—
449C2×#41—412no—
450C2×#41—464no—
451C2×#41—464no—
452C2×#41C2×D418yes—
453C2×#41C2×D418yes—
454C2×#41C2×D4124yes—
455C2×#41C2×D4124yes—
456C22×Q8—28no—
457C22×Q8—24no—
458C22×Q8—28no—
459C22×Q8C2×D418yes—
460C22×Q8C2413yes—
461C22×Q8C2413yes—
462C22×Q8C2411yescharacteristic
463C22×Q8C2411yescharacteristic
464C22×D4—212no—
465C22×D4—224no—
466C22×D4—212no—
467C22×D4—224no—
468C22×D4—212no—
469C22×D4—46no—
470C22×D4—412no—
471C22×D4—412no—
472C22×D4—412no—
473C22×D4—412no—
474C22×D4—412no—
475C22×D4—46no—
476C22×D4—812no—
477C22×D4C2×D4124yes—
478C22×D4C2411yescharacteristic
479C22×D4C2416yes—
480C22×D4C2413yes—
481C22×D4C2413yes—
482C22×D4C2413yes—
483C22×D4C2413yes—
484C22×D4C2413yes—
485C22×D4C2413yes—
486C22×D4C2416yes—
487C22×D4C2416yes—
488C22×D4C2416yes—
489C22×D4C2416yes—
490C22×D4C24112yes—
491C22×D4C2416yes—
492C22×D4C2416yes—
493C22×D4C2413yes—
494C22×D4C2416yes—
495C22×D4C24112yes—
496C22×D4C2416yes—
497C23×C4—212no—
498C23×C4—412no—
499C23×C4—412no—
500C23×C4C2×D4124yes—
501C23×C4C2413yes—
502C23×C4C2413yes—
503C23×C4C2416yes—
504C23×C4C2413yes—
505C23×C4C2413yes—
506C23×C4C2413yes—
507C23×C4C2413yes—
508C23×C4C2413yes—
509C23×C4C2416yes—
510C23×C4C2413yes—
511C23×C4C2411yescharacteristic
512C23×C4C2413yes—
513C23×C4C2413yes—
514C23×C4C2413yes—
515C23×C4C2411yescharacteristic
516C4⋊Q8—212no—
517#127—212no—
518#127—224no—
519#127—412no—
520#124—212no—
521#124—224no—
522#124—212no—
523#124—412no—
524#123—224no—
525#123—224no—
526#123—224no—
527#123—412no—
528#123—812no—
529#123—812no—
530C22⋊Q8—212no—
531C22⋊Q8—212no—
532C22⋊Q8—224no—
533C22⋊Q8—24no—
534C22⋊Q8—212no—
535C22⋊Q8—212no—
536C22⋊Q8—212no—
537C22⋊Q8—412no—
538#121—212no—
539#121—212no—
540#121—224no—
541#121—224no—
542#121—248no—
543#121—224no—
544#121—212no—
545#121—224no—
546#121—224no—
547#121—224no—
548#121—212no—
549#121—212no—
550#121—212no—
551#121—412no—
552#121—412no—
553#121—412no—
554#120—224no—
555#120—224no—
556#120—224no—
557#120—248no—
558#120—412no—
559#120—412no—
560#120—412no—
561#120—812no—
562#120—812no—
563C4×Q8—24no—
564C4×Q8—24no—
565C4×Q8—28no—
566C4×Q8—28no—
567C4×Q8—28no—
568C4×Q8—412no—
569C4×Q8—412no—
570C4×D4—212no—
571C4×D4—212no—
572C4×D4—224no—
573C4×D4—24no—
574C4×D4—212no—
575C4×D4—212no—
576C4×D4—212no—
577C4×D4—212no—
578C4×D4—212no—
579C4×D4—212no—
580C4×D4—212no—
581C4×D4—224no—
582C4×D4—224no—
583C4×D4—224no—
584C4×D4—412no—
585C4×D4—412no—
586#117—212no—
587#117—212no—
588#117—412no—
589#117—412no—
590C2×C4⋊C4—212no—
591C2×C4⋊C4—212no—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2413yes—
594C2×C4⋊C4C2413yes—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2413yes—
597C2×C4⋊C4C2416yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2413yes—
600C2×C4⋊C4C2413yes—
601C2×C4⋊C4C2416yes—
602C2×C4⋊C4C2416yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2416yes—
605C2×C4⋊C4C2416yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2416yes—
608C2×C4⋊C4C2416yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2416yes—
611C2×C4⋊C4C2416yes—
612C2×C4⋊C4C2416yes—
613C2×C4⋊C4C24112yes—
614C2×C4⋊C4C2416yes—
615C2×C22⋊C4—212no—
616C2×C22⋊C4—212no—
617C2×C22⋊C4—224no—
618C2×C22⋊C4C2411yescharacteristic
619C2×C22⋊C4C2411yescharacteristic
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2413yes—
622C2×C22⋊C4C2413yes—
623C2×C22⋊C4C2413yes—
624C2×C22⋊C4C2413yes—
625C2×C22⋊C4C2413yes—
626C2×C22⋊C4C2413yes—
627C2×C22⋊C4C24112yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2416yes—
641C2×C22⋊C4C2416yes—
642C2×C22⋊C4C2416yes—
643C2×C22⋊C4C2416yes—
644C2×C22⋊C4C2416yes—
645C2×C22⋊C4C2416yes—
646C2×C22⋊C4C24112yes—
647C2×C22⋊C4C24112yes—
648C2×C22⋊C4C24112yes—
649C2×C22⋊C4C2416yes—
650C2×C22⋊C4C2416yes—
651C2×C22⋊C4C2416yes—
652C2×C22⋊C4C2416yes—
653C2×C22⋊C4C24112yes—
654C2×C22⋊C4C24112yes—
655C2×C22⋊C4C2416yes—
656C2×C22⋊C4C2416yes—
657C2×C22⋊C4C2416yes—
658C2×C22⋊C4C2416yes—
659C2×C22⋊C4C2416yes—
660C2×C42—212no—
661C2×C42C2413yes—
662C2×C42C2416yes—
663C2×C42C2416yes—
664C2×C42C2416yes—
665C2×C42C2411yescharacteristic
666C2×C42C2413yes—
667C2×C42C2413yes—
668C2×C42C24112yes—
669#95C2412yes—
670#95C2416yes—
671#95C2411yescharacteristic
672#95C2413yes—
673#95C2413yes—
674#95C2411yescharacteristic
675#95C2412yes—
676#95C2412yes—
677#95C2412yes—
678#95C2416yes—
679#95C2416yes—
680#95C2416yes—
681#95C2416yes—
682#95C2416yes—
683#95C2412yes—
684#95C2416yes—
685#95C2416yes—
686#95C2416yes—
687#95C24112yes—
688#95C24112yes—
689C24—26no—
690C24—212no—
691C24—26no—
692C24—46no—
693C24—46no—
694C24—43no—
695C24—43no—
696C24—43no—
697C24—46no—
698C24—412no—
699C24—46no—
700C24—46no—
701C24—46no—
702C24—412no—
703C24C22×D4112yes—
704C24C2516yes—
705C24C2513yes—
706C24C2511yescharacteristic
707C24C2513yes—
708C24C2513yes—
709C24C2511yescharacteristic
710#41—232no—
711#41—232no—
712#41—448no—
713#41—448no—
714#41—448no—
715#41—448no—
716#41—448no—
717#41—416no—
718#41—432no—
719C2×Q8—232no—
720C2×Q8—22no—
721C2×Q8—26no—
722C2×Q8—212no—
723C2×Q8—212no—
724C2×Q8—42no—
725C2×Q8—416no—
726C2×Q8C22×D4112yes—
727C2×Q8C22×D414yes—
728C2×Q8H(5,𝔽2)18yes—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—26no—
732C2×D4—26no—
733C2×D4—26no—
734C2×D4—212no—
735C2×D4—212no—
736C2×D4—212no—
737C2×D4—26no—
738C2×D4—212no—
739C2×D4—212no—
740C2×D4—224no—
741C2×D4—212no—
742C2×D4—26no—
743C2×D4—212no—
744C2×D4—26no—
745C2×D4—212no—
746C2×D4—212no—
747C2×D4—212no—
748C2×D4—212no—
749C2×D4—212no—
750C2×D4—22no—
751C2×D4—26no—
752C2×D4—448no—
753C2×D4—46no—
754C2×D4—46no—
755C2×D4—46no—
756C2×D4—43no—
757C2×D4—43no—
758C2×D4—43no—
759C2×D4—43no—
760C2×D4—412no—
761C2×D4—412no—
762C2×D4—46no—
763C2×D4—46no—
764C2×D4—448no—
765C2×D4—46no—
766C2×D4—46no—
767C2×D4—46no—
768C2×D4—46no—
769C2×D4—46no—
770C2×D4—46no—
771C2×D4—412no—
772C2×D4—412no—
773C2×D4—46no—
774C2×D4—412no—
775C2×D4—412no—
776C2×D4—412no—
777C2×D4—412no—
778C2×D4—448no—
779C2×D4—448no—
780C2×D4—496no—
781C2×D4—848no—
782C2×D4C22×D4112yes—
783C2×D4C22×D4112yes—
784C2×D4C22×D4124yes—
785C22×C4—212no—
786C22×C4—212no—
787C22×C4—212no—
788C22×C4—26no—
789C22×C4—26no—
790C22×C4—26no—
791C22×C4—212no—
792C22×C4—22no—
793C22×C4—26no—
794C22×C4—26no—
795C22×C4—26no—
796C22×C4—212no—
797C22×C4—212no—
798C22×C4—212no—
799C22×C4—212no—
800C22×C4—212no—
801C22×C4—26no—
802C22×C4—448no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—46no—
806C22×C4—46no—
807C22×C4—46no—
808C22×C4—46no—
809C22×C4—43no—
810C22×C4—46no—
811C22×C4—412no—
812C22×C4—448no—
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×C4C2516yes—
824C22×C4C2511yescharacteristic
825C22×C4C2513yes—
826C22×C4C2512yes—
827C22×C4C2516yes—
828C22×C4C2511yescharacteristic
829C22×C4C2512yes—
830C22×C4C2513yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2513yes—
834C22×C4C2511yescharacteristic
835C22×C4C2513yes—
836C4⋊C4—22no—
837C4⋊C4—26no—
838C4⋊C4—26no—
839C4⋊C4—26no—
840C4⋊C4—26no—
841C4⋊C4—212no—
842C4⋊C4—22no—
843C4⋊C4—26no—
844C4⋊C4—26no—
845C4⋊C4—24no—
846C4⋊C4—212no—
847C4⋊C4—212no—
848C4⋊C4—212no—
849C4⋊C4—212no—
850C4⋊C4—24no—
851C4⋊C4—46no—
852C4⋊C4—46no—
853C4⋊C4—42no—
854C4⋊C4—46no—
855C4⋊C4—46no—
856C4⋊C4—46no—
857C4⋊C4—412no—
858C4⋊C4—46no—
859C22⋊C4—22no—
860C22⋊C4—26no—
861C22⋊C4—26no—
862C22⋊C4—26no—
863C22⋊C4—212no—
864C22⋊C4—212no—
865C22⋊C4—24no—
866C22⋊C4—212no—
867C22⋊C4—212no—
868C22⋊C4—24no—
869C22⋊C4—22no—
870C22⋊C4—212no—
871C22⋊C4—26no—
872C22⋊C4—26no—
873C22⋊C4—26no—
874C22⋊C4—224no—
875C22⋊C4—212no—
876C22⋊C4—212no—
877C22⋊C4—212no—
878C22⋊C4—42no—
879C22⋊C4—46no—
880C22⋊C4—42no—
881C22⋊C4—46no—
882C22⋊C4—46no—
883C22⋊C4—46no—
884C22⋊C4—46no—
885C22⋊C4—46no—
886C22⋊C4—46no—
887C22⋊C4—46no—
888C22⋊C4—412no—
889C22⋊C4—46no—
890C22⋊C4—46no—
891C22⋊C4—46no—
892C22⋊C4—412no—
893C22⋊C4—412no—
894C22⋊C4—412no—
895C22⋊C4—412no—
896C22⋊C4—46no—
897C22⋊C4—46no—
898C22⋊C4—46no—
899C22⋊C4—46no—
900C22⋊C4—46no—
901C42—22no—
902C42—26no—
903C42—26no—
904C42—26no—
905C42—212no—
906C42—212no—
907C42—212no—
908C42—412no—
909C23—21no—
910C23—22no—
911C23—22no—
912C23—26no—
913C23—26no—
914C23—23no—
915C23—23no—
916C23—23no—
917C23—23no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—22no—
922C23—26no—
923C23—26no—
924C23—22no—
925C23—23no—
926C23—26no—
927C23—26no—
928C23—26no—
929C23—26no—
930C23—26no—
931C23—26no—
932C23—23no—
933C23—23no—
934C23—26no—
935C23—26no—
936C23—26no—
937C23—412no—
938C23—412no—
939C23—412no—
940C23—412no—
941C23—412no—
942C23—424no—
943C23—86no—
944C23—812no—
945C23—812no—
946C23—812no—
947C23—812no—
948C23—812no—
949C23—812no—
950C23—1612no—
951C23—1612no—
952C23C23×D416yes—
953C23C23×D412yes—
954C23C23×D416yes—
955C23#58512yes—
956C23C2611yescharacteristic
957Q8—224no—
958Q8—44no—
959Q8—412no—
960Q8#534116yes—
961D4—28no—
962D4—224no—
963D4—224no—
964D4—424no—
965D4—412no—
966D4—412no—
967D4—412no—
968D4—412no—
969D4—424no—
970D4—424no—
971D4—424no—
972D4—424no—
973D4—412no—
974D4—812no—
975D4—812no—
976D4—812no—
977D4—824no—
978D4—812no—
979D4—1612no—
980C2×C4—21no—
981C2×C4—26no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—224no—
986C2×C4—224no—
987C2×C4—224no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—23no—
991C2×C4—23no—
992C2×C4—26no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—23no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—26no—
999C2×C4—26no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—26no—
1003C2×C4—22no—
1004C2×C4—26no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—26no—
1009C2×C4—23no—
1010C2×C4—23no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—26no—
1014C2×C4—26no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—26no—
1018C2×C4—26no—
1019C2×C4—26no—
1020C2×C4—44no—
1021C2×C4—412no—
1022C2×C4—412no—
1023C2×C4—412no—
1024C2×C4—44no—
1025C2×C4—412no—
1026C2×C4—412no—
1027C2×C4—412no—
1028C2×C4—412no—
1029C2×C4—424no—
1030C2×C4—86no—
1031C2×C4—812no—
1032C2×C4C23×D412yes—
1033C2×C4C23×D416yes—
1034C2×C4C23×D412yes—
1035C2×C4C23×D416yes—
1036C2×C4C2×H(5,𝔽2)112yes—
1037C2×C4#58512yes—
1038C22—26no—
1039C22—22no—
1040C22—22no—
1041C22—26no—
1042C22—26no—
1043C22—26no—
1044C22—22no—
1045C22—24no—
1046C22—22no—
1047C22—26no—
1048C22—26no—
1049C22—41no—
1050C22—46no—
1051C22—42no—
1052C22—46no—
1053C22—46no—
1054C22—42no—
1055C22—42no—
1056C22—46no—
1057C22—41no—
1058C22—43no—
1059C22—46no—
1060C22—46no—
1061C22—43no—
1062C22—46no—
1063C22—46no—
1064C22—46no—
1065C22—46no—
1066C22—46no—
1067C22—46no—
1068C22—43no—
1069C22—46no—
1070C22—824no—
1071C22—824no—
1072C22—1624no—
1073C22C24×D411yescharacteristic
1074C22C22×H(5,𝔽2)12yes—
1075C22C2×#58511yescharacteristic
1076C22C2×#58511yescharacteristic
1077C22H(7,𝔽2)12yes—
1078C4—22no—
1079C4—22no—
1080C4—22no—
1081C4—26no—
1082C4—43no—
1083C4—42no—
1084C4—41no—
1085C4—46no—
1086C4—43no—
1087C4—46no—
1088C4—42no—
1089C4—42no—
1090C4—46no—
1091C4—41no—
1092C4—42no—
1093C4—43no—
1094C4C2×#534112yes—
1095C2—46no—
1096C2—42no—
1097C2—42no—
1098C2—46no—
1099C2—83no—
1100C2—86no—
1101C2C22×#53411yescharacteristic
1102C2#6281111yescharacteristic
1103C2#6285211yescharacteristic
1104C2#6289912yes—
1105C2#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×D4×#41C2semidirect
3. #42992C2semidirect
4. #42988C2semidirect
5. #42967C2semidirect
6. #42966C2semidirect
7. #42475C2semidirect
8. #42474C2semidirect
9. #39888C2semidirect
10. #39885C2semidirect
11. #37448C2semidirect
12. #37445C2semidirect
13. #36433C2semidirect
14. #36429C2semidirect
15. #36091C2semidirect
16. #36082C2semidirect
17. #36018C2semidirect
18. #36005C2semidirect
19. #35983C2semidirect
20. #35771C2semidirect
21. #35076C2semidirect
22. #34562C2semidirect
23. #34174C2semidirect
24. C22×H(5,𝔽2)C22semidirect
26. C23×#41C22semidirect
31. C2×#550C22semidirect
32. C2×D4×Q8C22semidirect
34. C2×#548C22semidirect
35. C2×#548C22semidirect
36. C2×#548C22semidirect
37. C2×#547C22semidirect
38. C2×#546C22semidirect
39. C2×#546C22semidirect
40. C2×#546C22semidirect
41. C2×D42C22semidirect
42. C2×D42C22semidirect
43. C2×#537C22semidirect
44. C2×#535C22semidirect
45. C2×#532C22semidirect
46. C2×#525C22semidirect
47. C2×#525C22semidirect
48. C2×#525C22semidirect
49. C22×#121C22semidirect
50. C2×#520C22semidirect
51. C2×#519C22semidirect
52. C2×C4×#41C22semidirect
53. C22×C4×D4C22semidirect
54. #2854C22semidirect
55. #2847C22semidirect
56. #2813C22semidirect
57. #2813C22semidirect
58. #2812C22semidirect
59. #2701C22semidirect
60. #2699C22semidirect
61. #2697C22semidirect
62. #2682C22semidirect
63. #2679C22semidirect
64. #2678C22semidirect
65. #2678C22semidirect
66. #2678C22semidirect
67. #2663C22semidirect
68. #2661C22semidirect
69. #2638C22semidirect
70. #2638C22semidirect
71. #2635C22semidirect
72. #2635C22semidirect
73. #2635C22semidirect
74. #2630C22semidirect
75. #2630C22semidirect
76. #2627C22semidirect
77. #2626C22semidirect
78. #2625C22semidirect
79. #2624C22semidirect
80. #2622C22semidirect
81. #2620C22semidirect
82. #2619C22semidirect
83. #2618C22semidirect
84. #2617C22semidirect
85. #2616C22semidirect
86. #2615C22semidirect
87. #2613C22semidirect
88. #2613C22semidirect
89. #2602C22semidirect
90. #2591C22semidirect
91. #2548C22semidirect
92. #2545C22semidirect
93. #2539C22semidirect
94. #2538C22semidirect
95. #2536C22semidirect
96. #2534C22semidirect
97. #2503C22semidirect
98. #2501C22semidirect
99. #2500C22semidirect
100. #2487C22semidirect
101. #2487C22semidirect
102. #2485C22semidirect
103. #2447C22semidirect
104. #2445C22semidirect
105. #2445C22semidirect
106. #2445C22semidirect
107. #2435C22semidirect
108. #2435C22semidirect
109. #2433C22semidirect
110. #2433C22semidirect
111. #2433C22semidirect
112. #2431C22semidirect
113. #2431C22semidirect
114. #2429C22semidirect
115. #2426C22semidirect
116. #2426C22semidirect
117. #2426C22semidirect
118. #2422C22semidirect
119. #2422C22semidirect
120. #2420C22semidirect
121. #2420C22semidirect
122. #2415C22semidirect
123. #2414C22semidirect
124. #2414C22semidirect
125. #2414C22semidirect
126. #2408C22semidirect
127. #2408C22semidirect
128. #2408C22semidirect
129. #2408C22semidirect
130. #2408C22semidirect
131. #2407C22semidirect
132. #2407C22semidirect
133. #2405C22semidirect
134. #2403C22semidirect
135. #2395C22semidirect
136. #2395C22semidirect
137. #2392C22semidirect
138. #2392C22semidirect
139. #2388C22semidirect
140. #2388C22semidirect
141. #2351C22semidirect
142. Q8×C4⋊C4C22semidirect
143. #2341C22semidirect
144. #2341C22semidirect
145. #2341C22semidirect
146. #2341C22semidirect
147. #2341C22semidirect
148. #2341C22semidirect
149. #2341C22semidirect
150. #2341C22semidirect
151. #2341C22semidirect
152. Q8×C22⋊C4C22semidirect
153. #2321C22semidirect
154. #2321C22semidirect
155. #2309C22semidirect
156. C4×#123C22semidirect
157. C4×#120C22semidirect
158. #2280C22semidirect
159. #2280C22semidirect
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×D4×#412
#429922
#429882
#429672
#429662
#424752
#424742
#398882
#398852
#374482
#374452
#364332
#364292
#360912
#360822
#360182
#360052
#359832
#357712
#350762
#345622
#341742