Finite Group Databasebeta

← #7654944

Subgroups — #7654944

Order 512.

9243 conjugacy classes of subgroups.

The subgroup lattice has 1122 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#42967C213yesmaximal, complemented
4#42966C213yesmaximal, complemented
5#42942C213yesmaximal, complemented
6#42916C213yesmaximal, complemented
7#39888C216yesmaximal, complemented
8#39885C216yesmaximal, complemented
9#39358C216yesmaximal, complemented
10#38949C216yesmaximal, complemented
11#37444C213yesmaximal, complemented
12#36576C212yesmaximal, complemented
13#36434C212yesmaximal, complemented
14#36433C212yesmaximal, complemented
15#36429C212yesmaximal, complemented
16#36091C211yesmaximal, characteristic, complemented
17#36082C211yesmaximal, characteristic, complemented
18#36076C211yesmaximal, characteristic, complemented
19#35996C211yesmaximal, characteristic, complemented
20#35078C213yesmaximal, complemented
21#35000C213yesmaximal, complemented
22#34957C213yesmaximal, complemented
23C2×#2341C211yesmaximal, 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×#546C2213yescomplemented
39C2×#546C2216yescomplemented
40C2×#546C2213yescomplemented
41C2×D42C2216yescomplemented
42C2×D42C2213yescomplemented
43C2×#537C2213yescomplemented
44C2×#535C2213yescomplemented
45C2×#534C2216yescomplemented
46C2×#532C2213yescomplemented
47C2×#525C2213yescomplemented
48C2×#525C2213yescomplemented
49C2×#525C2213yescomplemented
50C22×#121C2213yescomplemented
51C2×#520C2211yescharacteristic, complemented
52C2×C4×#41C2211yescharacteristic, complemented
53C22×C4×Q8C2212yescomplemented
54C22×C4×D4C2213yescomplemented
55#2856C2216yescomplemented
56#2854C2216yescomplemented
57#2850C2216yescomplemented
58#2847C2216yescomplemented
59#2814C2216yescomplemented
60#2813C2216yescomplemented
61#2701C22112yescomplemented
62#2699C22112yescomplemented
63#2697C22112yescomplemented
64#2682C22112yescomplemented
65#2679C22112yescomplemented
66#2678C22112yescomplemented
67#2678C22112yescomplemented
68#2678C22112yescomplemented
69#2661C2216yescomplemented
70#2661C2216yescomplemented
71#2630C22112yescomplemented
72#2625C2213yescomplemented
73#2624C2213yescomplemented
74#2618C2216yescomplemented
75#2617C22112yescomplemented
76#2617C2216yescomplemented
77#2616C2213yescomplemented
78#2615C2213yescomplemented
79#2602C2216yescomplemented
80#2602C2216yescomplemented
81#2591C2213yescomplemented
82#2583C2213yescomplemented
83#2564C2213yescomplemented
84#2564C2211yescharacteristic, complemented
85#2561C2213yescomplemented
86#2548C2216yescomplemented
87#2545C2216yescomplemented
88#2543C2213yescomplemented
89#2543C2216yescomplemented
90#2543C2213yescomplemented
91#2539C2213yescomplemented
92#2538C2216yescomplemented
93#2536C2216yescomplemented
94#2534C2216yescomplemented
95#2534C2216yescomplemented
96#2504C2213yescomplemented
97#2502C2213yescomplemented
98#2500C2216yescomplemented
99#2486C2213yescomplemented
100#2486C2213yescomplemented
101#2485C2216yescomplemented
102#2447C2216yescomplemented
103#2445C2216yescomplemented
104#2445C2216yescomplemented
105#2445C2216yescomplemented
106#2435C2213yescomplemented
107#2435C2216yescomplemented
108#2433C2213yescomplemented
109#2433C2216yescomplemented
110#2433C2216yescomplemented
111#2431C2216yescomplemented
112#2431C2216yescomplemented
113#2429C2216yescomplemented
114#2426C2216yescomplemented
115#2426C2216yescomplemented
116#2426C2216yescomplemented
117#2422C2216yescomplemented
118#2422C2216yescomplemented
119#2420C2216yescomplemented
120#2420C2216yescomplemented
121#2417C2216yescomplemented
122#2416C2216yescomplemented
123#2416C2216yescomplemented
124#2416C2216yescomplemented
125#2412C2216yescomplemented
126#2410C22112yescomplemented
127#2410C2216yescomplemented
128#2408C2216yescomplemented
129#2408C2216yescomplemented
130#2408C2213yescomplemented
131#2408C2213yescomplemented
132#2408C2216yescomplemented
133#2407C2216yescomplemented
134#2407C2216yescomplemented
135#2395C2213yescomplemented
136#2395C2213yescomplemented
137#2388C2213yescomplemented
138#2388C2213yescomplemented
139#2351C2212yescomplemented
140Q8×C4⋊C4C2212yescomplemented
141#2341C2212yescomplemented
142#2341C2211yescharacteristic, complemented
143#2341C2213yescomplemented
144#2341C2213yescomplemented
145#2341C2216yescomplemented
146#2341C2211yescharacteristic, complemented
147#2341C2212yescomplemented
148#2341C2212yescomplemented
149#2341C2212yescomplemented
150Q8×C22⋊C4C2212yescomplemented
151#2321C22112yescomplemented
152#2308C2216yescomplemented
153C4×#123C2216yescomplemented
154C4×#121C2216yescomplemented
155C4×#121C2216yescomplemented
156C4×#120C2216yescomplemented
157C2×#390C2216yescomplemented
158C2×#380C2213yescomplemented
159C2×C4×C22⋊C4C2213yescomplemented
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×D4C2316yes—
179C23×D4C2313yes—
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#534—424no—
202#532—224no—
203C2×C4⋊Q8C2313yes—
204C2×#127C2313yes—
205C2×#127C2316yes—
206C2×#127C2316yes—
207C2×#124C2313yes—
208C2×#124C2313yes—
209C2×#124C2316yes—
210C2×#124C2316yes—
211#525—224no—
212#525—224no—
213#525—224no—
214C2×#123C2316yes—
215C2×#123C2316yes—
216C2×#123C2316yes—
217C2×#123C23112yes—
218C2×#123C2316yes—
219C2×#123C2316yes—
220C2×#123C2316yes—
221C2×C22⋊Q8C2313yes—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2313yes—
224C2×C22⋊Q8C2313yes—
225C2×C22⋊Q8C2313yes—
226C2×C22⋊Q8C2313yes—
227C2×C22⋊Q8C2316yes—
228C2×C22⋊Q8C2316yes—
229C2×#121—224no—
230C2×#121C2313yes—
231C2×#121C2316yes—
232C2×#121C2316yes—
233C2×#121C2313yes—
234C2×#121C2313yes—
235C2×#121C2316yes—
236C2×#121C2316yes—
237C2×#121C2313yes—
238C2×#121C2313yes—
239C2×#121C2313yes—
240C2×#121C2316yes—
241C2×#121C2316yes—
242C2×#121C2316yes—
243C2×#121C23112yes—
244C2×#121C2316yes—
245C2×#121C2316yes—
246C2×#121C2316yes—
247C2×#121C23112yes—
248C2×#121C2316yes—
249C2×#120C2316yes—
250C2×#120C2316yes—
251C2×#120C2316yes—
252C2×#120C23112yes—
253C2×#120C23112yes—
254C2×#120C23112yes—
255C2×#120C2316yes—
256C2×#120C2316yes—
257C2×#120C2316yes—
258#520—28no—
259C4×#41—28no—
260C2×C4×Q8—48no—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2316yes—
267C2×C4×Q8C2316yes—
268C2×C4×D4—224no—
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2313yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2313yes—
273C2×C4×D4C2313yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2313yes—
277C2×C4×D4C2313yes—
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×C4×D4C2316yes—
281C2×C4×D4C2316yes—
282C2×C4×D4C2316yes—
283C2×C4×D4C2316yes—
284C2×C4×D4C2316yes—
285C2×#117C2313yes—
286C2×#117C2313yes—
287C22×C4⋊C4C2313yes—
288C22×C4⋊C4C2313yes—
289C22×C4⋊C4C2316yes—
290C22×C22⋊C4C2313yes—
291C22×C22⋊C4C2313yes—
292C22×C22⋊C4C2316yes—
293C22×C22⋊C4C2316yes—
294C22×C22⋊C4C2316yes—
295C22×C42C2313yes—
296C22×C42C2316yes—
297#400C2311yescharacteristic
298#400C2313yes—
299#399C2313yes—
300#399C2311yescharacteristic
301#398C2313yes—
302#398C2313yes—
303#398C2316yes—
304#398C23112yes—
305#397C2313yes—
306#397C2313yes—
307#397C2316yes—
308#397C2316yes—
309#397C2316yes—
310#397C23112yes—
311#397C23112yes—
312#396C23112yes—
313#396C23112yes—
314#396C23112yes—
315#396C23112yes—
316#395C2311yescharacteristic
317#395C2313yes—
318#394C2313yes—
319#394C2313yes—
320#394C2316yes—
321#394C2316yes—
322#394C2316yes—
323#394C2316yes—
324#394C23112yes—
325#394C2316yes—
326#394C23112yes—
327#394C23112yes—
328#394C23112yes—
329#394C23112yes—
330#394C23112yes—
331#394C23112yes—
332#394C23112yes—
333#394C23112yes—
334#393C2311yescharacteristic
335#393C2313yes—
336#392C2316yes—
337#392C2316yes—
338#392C23112yes—
339#392C2316yes—
340#392C2313yes—
341#392C23112yes—
342#392C2313yes—
343#392C23112yes—
344#392C23112yes—
345#391C2316yes—
346#391C2316yes—
347#390C23112yes—
348#390C23112yes—
349#390C2316yes—
350#390C2316yes—
351#390C2316yes—
352#390C2316yes—
353#390C2316yes—
354#390C23112yes—
355#390C23112yes—
356#390C2316yes—
357#390C2316yes—
358#390C2316yes—
359#390C2316yes—
360#390C2316yes—
361#390C2316yes—
362#390C2316yes—
363#389C2316yes—
364#389C2316yes—
365#389C2316yes—
366#389C2316yes—
367#389C2316yes—
368#389C2316yes—
369#388C2316yes—
370#388C2316yes—
371#388C2316yes—
372#388C23112yes—
373#388C23112yes—
374#388C23112yes—
375#388C2316yes—
376#388C2316yes—
377#388C2316yes—
378#387C2312yes—
379#387C2316yes—
380#386C2316yes—
381#386C23112yes—
382#386C23112yes—
383#386C23112yes—
384#386C2316yes—
385#386C2312yes—
386#386C2316yes—
387#386C23112yes—
388#386C23112yes—
389#386C2316yes—
390#386C2316yes—
391#386C2316yes—
392#386C2316yes—
393#385C2312yes—
394#385C2316yes—
395#385C23112yes—
396#385C2316yes—
397#385C2316yes—
398#384C2316yes—
399#382C2316yes—
400#381C2316yes—
401#381C2316yes—
402#381C2316yes—
403#380C2316yes—
404#380C2312yes—
405#380C2316yes—
406#380C2316yes—
407#380C2316yes—
408#380C2313yes—
409#380C2313yes—
410#380C2316yes—
411#380C2316yes—
412#380C2316yes—
413#380C2316yes—
414#379C2316yes—
415#379C2316yes—
416#379C2316yes—
417#379C23112yes—
418C4×C4⋊C4C2316yes—
419C4×C4⋊C4C2316yes—
420C4×C22⋊C4C2313yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2313yes—
425C4×C22⋊C4C2313yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428C4×C22⋊C4C2316yes—
429C4×C22⋊C4C2316yes—
430C2×#95C2311yescharacteristic
431C2×#95C2313yes—
432C25C2413yes—
433C25C2413yes—
434C25C2416yes—
435H(5,𝔽2)—464no—
436C2×#41—24no—
437C2×#41—28no—
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—464no—
452C2×#41—464no—
453C2×#41C2×D418yes—
454C2×#41C2×D418yes—
455C2×#41C2×D4124yes—
456C2×#41C2×D4124yes—
457C22×Q8—28no—
458C22×Q8—24no—
459C22×Q8—28no—
460C22×Q8C2×D418yes—
461C22×Q8C2413yes—
462C22×Q8C2413yes—
463C22×Q8C2411yescharacteristic
464C22×Q8C2411yescharacteristic
465C22×D4—212no—
466C22×D4—224no—
467C22×D4—212no—
468C22×D4—224no—
469C22×D4—212no—
470C22×D4—212no—
471C22×D4—412no—
472C22×D4—412no—
473C22×D4—412no—
474C22×D4—412no—
475C22×D4—412no—
476C22×D4—46no—
477C22×D4—412no—
478C22×D4—412no—
479C22×D4C2×D4124yes—
480C22×D4C2413yes—
481C22×D4C2416yes—
482C22×D4C2416yes—
483C22×D4C2413yes—
484C22×D4C2413yes—
485C22×D4C2413yes—
486C22×D4C2413yes—
487C22×D4C2413yes—
488C22×D4C2411yescharacteristic
489C22×D4C2416yes—
490C22×D4C2416yes—
491C22×D4C2416yes—
492C22×D4C2416yes—
493C22×D4C24112yes—
494C22×D4C2416yes—
495C22×D4C2416yes—
496C22×D4C2413yes—
497C22×D4C24112yes—
498C22×D4C2416yes—
499C23×C4—212no—
500C23×C4—412no—
501C23×C4—412no—
502C23×C4C2×D4124yes—
503C23×C4C2413yes—
504C23×C4C2413yes—
505C23×C4C2416yes—
506C23×C4C2412yes—
507C23×C4C2413yes—
508C23×C4C2413yes—
509C23×C4C2413yes—
510C23×C4C2413yes—
511C23×C4C2416yes—
512C23×C4C2413yes—
513C23×C4C2416yes—
514C23×C4C2413yes—
515C23×C4C2411yescharacteristic
516C23×C4C2413yes—
517C23×C4C2413yes—
518C23×C4C2413yes—
519C23×C4C2411yescharacteristic
520C4⋊Q8—212no—
521#127—212no—
522#127—224no—
523#127—412no—
524#124—212no—
525#124—224no—
526#124—212no—
527#124—412no—
528#123—224no—
529#123—224no—
530#123—224no—
531#123—412no—
532#123—412no—
533#123—424no—
534#123—412no—
535C22⋊Q8—212no—
536C22⋊Q8—212no—
537C22⋊Q8—224no—
538C22⋊Q8—24no—
539C22⋊Q8—212no—
540C22⋊Q8—212no—
541C22⋊Q8—212no—
542C22⋊Q8—412no—
543#121—212no—
544#121—212no—
545#121—224no—
546#121—224no—
547#121—248no—
548#121—224no—
549#121—224no—
550#121—212no—
551#121—224no—
552#121—224no—
553#121—224no—
554#121—212no—
555#121—212no—
556#121—212no—
557#121—412no—
558#121—412no—
559#121—412no—
560#121—412no—
561#121—424no—
562#120—224no—
563#120—224no—
564#120—224no—
565#120—248no—
566#120—424no—
567#120—412no—
568#120—412no—
569#120—424no—
570#120—412no—
571C4×Q8—24no—
572C4×Q8—24no—
573C4×Q8—28no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×Q8—412no—
577C4×Q8—412no—
578C4×D4—212no—
579C4×D4—212no—
580C4×D4—224no—
581C4×D4—24no—
582C4×D4—212no—
583C4×D4—212no—
584C4×D4—212no—
585C4×D4—212no—
586C4×D4—212no—
587C4×D4—212no—
588C4×D4—212no—
589C4×D4—224no—
590C4×D4—224no—
591C4×D4—224no—
592C4×D4—412no—
593C4×D4—412no—
594#117—212no—
595#117—212no—
596C2×C4⋊C4—212no—
597C2×C4⋊C4—212no—
598C2×C4⋊C4—412no—
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2413yes—
601C2×C4⋊C4C2413yes—
602C2×C4⋊C4C2413yes—
603C2×C4⋊C4C2413yes—
604C2×C4⋊C4C2416yes—
605C2×C4⋊C4C2416yes—
606C2×C4⋊C4C2416yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2413yes—
609C2×C4⋊C4C2413yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2416yes—
612C2×C4⋊C4C2416yes—
613C2×C4⋊C4C2416yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C24112yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2416yes—
618C2×C4⋊C4C24112yes—
619C2×C4⋊C4C2416yes—
620C2×C4⋊C4C2416yes—
621C2×C22⋊C4—212no—
622C2×C22⋊C4—212no—
623C2×C22⋊C4—224no—
624C2×C22⋊C4—412no—
625C2×C22⋊C4—412no—
626C2×C22⋊C4C2411yescharacteristic
627C2×C22⋊C4C2411yescharacteristic
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2413yes—
630C2×C22⋊C4C2413yes—
631C2×C22⋊C4C2413yes—
632C2×C22⋊C4C2413yes—
633C2×C22⋊C4C2413yes—
634C2×C22⋊C4C2413yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C24112yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C2416yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2416yes—
642C2×C22⋊C4C2416yes—
643C2×C22⋊C4C2416yes—
644C2×C22⋊C4C2416yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2416yes—
647C2×C22⋊C4C2416yes—
648C2×C22⋊C4C2416yes—
649C2×C22⋊C4C2416yes—
650C2×C22⋊C4C2416yes—
651C2×C22⋊C4C24112yes—
652C2×C22⋊C4C2416yes—
653C2×C22⋊C4C2416yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2416yes—
656C2×C22⋊C4C2416yes—
657C2×C22⋊C4C2416yes—
658C2×C22⋊C4C24112yes—
659C2×C22⋊C4C24112yes—
660C2×C22⋊C4C2416yes—
661C2×C22⋊C4C24112yes—
662C2×C22⋊C4C24112yes—
663C2×C22⋊C4C2416yes—
664C2×C22⋊C4C2416yes—
665C2×C22⋊C4C2416yes—
666C2×C42—212no—
667C2×C42—412no—
668C2×C42C2413yes—
669C2×C42C2416yes—
670C2×C42C2411yescharacteristic
671C2×C42C2413yes—
672C2×C42C2413yes—
673C2×C42C2416yes—
674C2×C42C2416yes—
675C2×C42C2416yes—
676C2×C42C2416yes—
677#95C2412yes—
678#95C2411yescharacteristic
679#95C2411yescharacteristic
680#95C2416yes—
681#95C2413yes—
682#95C2413yes—
683#95C2412yes—
684#95C2412yes—
685#95C2412yes—
686#95C2416yes—
687#95C2416yes—
688#95C2416yes—
689#95C2416yes—
690#95C2416yes—
691#95C2412yes—
692#95C2416yes—
693#95C2416yes—
694#95C2416yes—
695#95C24112yes—
696#95C24112yes—
697C24—26no—
698C24—26no—
699C24—26no—
700C24—212no—
701C24—26no—
702C24—46no—
703C24—46no—
704C24—46no—
705C24—43no—
706C24—412no—
707C24—46no—
708C24—46no—
709C24—412no—
710C24—46no—
711C24C22×D4112yes—
712C24C2516yes—
713C24C2513yes—
714C24C2513yes—
715C24C2513yes—
716C24C2511yescharacteristic
717C24C2511yescharacteristic
718#41—232no—
719#41—232no—
720#41—448no—
721#41—448no—
722#41—448no—
723#41—448no—
724#41—448no—
725#41—416no—
726#41—432no—
727C2×Q8—232no—
728C2×Q8—22no—
729C2×Q8—26no—
730C2×Q8—212no—
731C2×Q8—212no—
732C2×Q8—42no—
733C2×Q8—416no—
734C2×Q8C22×D4112yes—
735C2×Q8C22×D414yes—
736C2×Q8H(5,𝔽2)18yes—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—26no—
740C2×D4—26no—
741C2×D4—26no—
742C2×D4—212no—
743C2×D4—212no—
744C2×D4—212no—
745C2×D4—26no—
746C2×D4—212no—
747C2×D4—26no—
748C2×D4—26no—
749C2×D4—212no—
750C2×D4—212no—
751C2×D4—212no—
752C2×D4—224no—
753C2×D4—212no—
754C2×D4—26no—
755C2×D4—212no—
756C2×D4—26no—
757C2×D4—212no—
758C2×D4—212no—
759C2×D4—26no—
760C2×D4—212no—
761C2×D4—212no—
762C2×D4—212no—
763C2×D4—212no—
764C2×D4—448no—
765C2×D4—46no—
766C2×D4—46no—
767C2×D4—46no—
768C2×D4—43no—
769C2×D4—43no—
770C2×D4—412no—
771C2×D4—412no—
772C2×D4—448no—
773C2×D4—46no—
774C2×D4—46no—
775C2×D4—412no—
776C2×D4—46no—
777C2×D4—46no—
778C2×D4—412no—
779C2×D4—46no—
780C2×D4—46no—
781C2×D4—412no—
782C2×D4—412no—
783C2×D4—412no—
784C2×D4—412no—
785C2×D4—448no—
786C2×D4—448no—
787C2×D4—496no—
788C2×D4—848no—
789C2×D4C22×D4112yes—
790C2×D4C22×D4112yes—
791C2×D4C22×D4124yes—
792C2×D4H(5,𝔽2)14yescomplemented
793C22×C4—212no—
794C22×C4—212no—
795C22×C4—212no—
796C22×C4—26no—
797C22×C4—26no—
798C22×C4—24no—
799C22×C4—26no—
800C22×C4—212no—
801C22×C4—212no—
802C22×C4—22no—
803C22×C4—26no—
804C22×C4—26no—
805C22×C4—26no—
806C22×C4—212no—
807C22×C4—212no—
808C22×C4—212no—
809C22×C4—212no—
810C22×C4—212no—
811C22×C4—26no—
812C22×C4—24no—
813C22×C4—448no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—46no—
818C22×C4—46no—
819C22×C4—46no—
820C22×C4—46no—
821C22×C4—43no—
822C22×C4—46no—
823C22×C4—46no—
824C22×C4—46no—
825C22×C4—46no—
826C22×C4—46no—
827C22×C4—448no—
828C22×C4C22×D4112yes—
829C22×C4C22×D4112yes—
830C22×C4C22×D4112yes—
831C22×C4C22×D4112yes—
832C22×C4C22×D4112yes—
833C22×C4C22×D414yes—
834C22×C4C2512yes—
835C22×C4C2511yescharacteristic
836C22×C4C2512yes—
837C22×C4C2513yes—
838C22×C4C2516yes—
839C22×C4C2516yes—
840C22×C4C2511yescharacteristic
841C22×C4C2513yes—
842C22×C4C2512yes—
843C22×C4C2516yes—
844C22×C4C2513yes—
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C22×C4C2513yes—
848C22×C4C2511yescharacteristic
849C22×C4C2512yes—
850C22×C4C2513yes—
851C4⋊C4—22no—
852C4⋊C4—26no—
853C4⋊C4—26no—
854C4⋊C4—26no—
855C4⋊C4—26no—
856C4⋊C4—212no—
857C4⋊C4—22no—
858C4⋊C4—26no—
859C4⋊C4—26no—
860C4⋊C4—24no—
861C4⋊C4—212no—
862C4⋊C4—212no—
863C4⋊C4—212no—
864C4⋊C4—212no—
865C4⋊C4—212no—
866C4⋊C4—24no—
867C4⋊C4—412no—
868C4⋊C4—42no—
869C4⋊C4—46no—
870C4⋊C4—46no—
871C4⋊C4—412no—
872C4⋊C4—46no—
873C22⋊C4—22no—
874C22⋊C4—26no—
875C22⋊C4—26no—
876C22⋊C4—26no—
877C22⋊C4—212no—
878C22⋊C4—212no—
879C22⋊C4—24no—
880C22⋊C4—212no—
881C22⋊C4—212no—
882C22⋊C4—212no—
883C22⋊C4—22no—
884C22⋊C4—212no—
885C22⋊C4—26no—
886C22⋊C4—26no—
887C22⋊C4—26no—
888C22⋊C4—224no—
889C22⋊C4—212no—
890C22⋊C4—212no—
891C22⋊C4—212no—
892C22⋊C4—212no—
893C22⋊C4—212no—
894C22⋊C4—24no—
895C22⋊C4—212no—
896C22⋊C4—46no—
897C22⋊C4—46no—
898C22⋊C4—46no—
899C22⋊C4—412no—
900C22⋊C4—46no—
901C22⋊C4—42no—
902C22⋊C4—46no—
903C22⋊C4—46no—
904C22⋊C4—46no—
905C22⋊C4—46no—
906C22⋊C4—412no—
907C22⋊C4—412no—
908C22⋊C4—412no—
909C22⋊C4—46no—
910C22⋊C4—46no—
911C22⋊C4—412no—
912C22⋊C4—46no—
913C42—22no—
914C42—26no—
915C42—26no—
916C42—26no—
917C42—212no—
918C42—212no—
919C42—212no—
920C42—46no—
921C42—46no—
922C23—22no—
923C23—22no—
924C23—21no—
925C23—23no—
926C23—23no—
927C23—22no—
928C23—26no—
929C23—26no—
930C23—26no—
931C23—26no—
932C23—22no—
933C23—23no—
934C23—23no—
935C23—21no—
936C23—224no—
937C23—23no—
938C23—26no—
939C23—26no—
940C23—23no—
941C23—26no—
942C23—26no—
943C23—26no—
944C23—26no—
945C23—23no—
946C23—26no—
947C23—26no—
948C23—26no—
949C23—412no—
950C23—412no—
951C23—412no—
952C23—412no—
953C23—424no—
954C23—812no—
955C23—812no—
956C23—812no—
957C23—86no—
958C23—812no—
959C23—812no—
960C23—812no—
961C23—1612no—
962C23—1612no—
963C23C23×D416yes—
964C23C23×D416yes—
965C23C23×D412yes—
966C23C2×H(5,𝔽2)12yes—
967C23C2×H(5,𝔽2)12yes—
968C23#58512yes—
969C23C2611yescharacteristic
970Q8—224no—
971Q8—44no—
972Q8—412no—
973Q8#534116yescomplemented
974D4—28no—
975D4—224no—
976D4—224no—
977D4—424no—
978D4—412no—
979D4—412no—
980D4—412no—
981D4—424no—
982D4—424no—
983D4—412no—
984D4—424no—
985D4—424no—
986D4—412no—
987D4—812no—
988D4—812no—
989D4—812no—
990D4—812no—
991D4—824no—
992D4—1612no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—26no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—224no—
1001C2×C4—224no—
1002C2×C4—224no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—23no—
1006C2×C4—23no—
1007C2×C4—26no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—23no—
1011C2×C4—22no—
1012C2×C4—26no—
1013C2×C4—26no—
1014C2×C4—26no—
1015C2×C4—26no—
1016C2×C4—26no—
1017C2×C4—23no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—26no—
1021C2×C4—22no—
1022C2×C4—26no—
1023C2×C4—26no—
1024C2×C4—22no—
1025C2×C4—26no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—23no—
1030C2×C4—26no—
1031C2×C4—22no—
1032C2×C4—44no—
1033C2×C4—412no—
1034C2×C4—412no—
1035C2×C4—48no—
1036C2×C4—412no—
1037C2×C4—44no—
1038C2×C4—412no—
1039C2×C4—412no—
1040C2×C4—412no—
1041C2×C4—412no—
1042C2×C4—424no—
1043C2×C4—812no—
1044C2×C4—86no—
1045C2×C4—812no—
1046C2×C4C23×D412yes—
1047C2×C4C23×D416yes—
1048C2×C4C23×D412yes—
1049C2×C4C23×D416yes—
1050C2×C4C2×H(5,𝔽2)12yes—
1051C2×C4C2×H(5,𝔽2)112yes—
1052C2×C4#58514yes—
1053C22—24no—
1054C22—24no—
1055C22—22no—
1056C22—22no—
1057C22—24no—
1058C22—26no—
1059C22—26no—
1060C22—22no—
1061C22—26no—
1062C22—26no—
1063C22—26no—
1064C22—26no—
1065C22—46no—
1066C22—46no—
1067C22—46no—
1068C22—42no—
1069C22—46no—
1070C22—41no—
1071C22—41no—
1072C22—46no—
1073C22—46no—
1074C22—46no—
1075C22—46no—
1076C22—46no—
1077C22—46no—
1078C22—43no—
1079C22—46no—
1080C22—43no—
1081C22—46no—
1082C22—43no—
1083C22—46no—
1084C22—824no—
1085C22—824no—
1086C22—1624no—
1087C22#348814yes—
1088C22C24×D411yescharacteristic
1089C22C22×H(5,𝔽2)11yescharacteristic
1090C22C22×H(5,𝔽2)12yes—
1091C22C2×#58512yes—
1092C22C2×#58511yescharacteristic
1093C4—24no—
1094C4—22no—
1095C4—22no—
1096C4—22no—
1097C4—26no—
1098C4—46no—
1099C4—46no—
1100C4—42no—
1101C4—43no—
1102C4—46no—
1103C4—41no—
1104C4—43no—
1105C4—42no—
1106C4—41no—
1107C4—42no—
1108C4—43no—
1109C4C2×#534112yes—
1110C2—24no—
1111C2—46no—
1112C2—42no—
1113C2—46no—
1114C2—83no—
1115C2—86no—
1116C2C22×#53411yescharacteristic
1117C2C2×#348811yescharacteristic
1118C2#6281211yescharacteristic
1119C2#6301412yes—
1120C2#6302012yes—
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. #42967C2semidirect
4. #42966C2semidirect
5. #42942C2semidirect
6. #42916C2semidirect
7. #39888C2semidirect
8. #39885C2semidirect
9. #39358C2semidirect
10. #38949C2semidirect
11. #37444C2semidirect
12. #36576C2semidirect
13. #36434C2semidirect
14. #36433C2semidirect
15. #36429C2semidirect
16. #36091C2semidirect
17. #36082C2semidirect
18. #36076C2semidirect
19. #35996C2semidirect
20. #35078C2semidirect
21. #35000C2semidirect
22. #34957C2semidirect
23. C2×#2341C2semidirect
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×#534C22semidirect
46. C2×#532C22semidirect
47. C2×#525C22semidirect
48. C2×#525C22semidirect
49. C2×#525C22semidirect
50. C22×#121C22semidirect
51. C2×#520C22semidirect
52. C2×C4×#41C22semidirect
53. C22×C4×Q8C22semidirect
54. C22×C4×D4C22semidirect
55. #2856C22semidirect
56. #2854C22semidirect
57. #2850C22semidirect
58. #2847C22semidirect
59. #2814C22semidirect
60. #2813C22semidirect
61. #2701C22semidirect
62. #2699C22semidirect
63. #2697C22semidirect
64. #2682C22semidirect
65. #2679C22semidirect
66. #2678C22semidirect
67. #2678C22semidirect
68. #2678C22semidirect
69. #2661C22semidirect
70. #2661C22semidirect
71. #2630C22semidirect
72. #2625C22semidirect
73. #2624C22semidirect
74. #2618C22semidirect
75. #2617C22semidirect
76. #2617C22semidirect
77. #2616C22semidirect
78. #2615C22semidirect
79. #2602C22semidirect
80. #2602C22semidirect
81. #2591C22semidirect
82. #2583C22semidirect
83. #2564C22semidirect
84. #2564C22semidirect
85. #2561C22semidirect
86. #2548C22semidirect
87. #2545C22semidirect
88. #2543C22semidirect
89. #2543C22semidirect
90. #2543C22semidirect
91. #2539C22semidirect
92. #2538C22semidirect
93. #2536C22semidirect
94. #2534C22semidirect
95. #2534C22semidirect
96. #2504C22semidirect
97. #2502C22semidirect
98. #2500C22semidirect
99. #2486C22semidirect
100. #2486C22semidirect
101. #2485C22semidirect
102. #2447C22semidirect
103. #2445C22semidirect
104. #2445C22semidirect
105. #2445C22semidirect
106. #2435C22semidirect
107. #2435C22semidirect
108. #2433C22semidirect
109. #2433C22semidirect
110. #2433C22semidirect
111. #2431C22semidirect
112. #2431C22semidirect
113. #2429C22semidirect
114. #2426C22semidirect
115. #2426C22semidirect
116. #2426C22semidirect
117. #2422C22semidirect
118. #2422C22semidirect
119. #2420C22semidirect
120. #2420C22semidirect
121. #2417C22semidirect
122. #2416C22semidirect
123. #2416C22semidirect
124. #2416C22semidirect
125. #2412C22semidirect
126. #2410C22semidirect
127. #2410C22semidirect
128. #2408C22semidirect
129. #2408C22semidirect
130. #2408C22semidirect
131. #2408C22semidirect
132. #2408C22semidirect
133. #2407C22semidirect
134. #2407C22semidirect
135. #2395C22semidirect
136. #2395C22semidirect
137. #2388C22semidirect
138. #2388C22semidirect
139. #2351C22semidirect
140. Q8×C4⋊C4C22semidirect
141. #2341C22semidirect
142. #2341C22semidirect
143. #2341C22semidirect
144. #2341C22semidirect
145. #2341C22semidirect
146. #2341C22semidirect
147. #2341C22semidirect
148. #2341C22semidirect
149. #2341C22semidirect
150. Q8×C22⋊C4C22semidirect
151. #2321C22semidirect
152. #2308C22semidirect
153. C4×#123C22semidirect
154. C4×#121C22semidirect
155. C4×#121C22semidirect
156. C4×#120C22semidirect
157. C2×#390C22semidirect
158. C2×#380C22semidirect
159. C2×C4×C22⋊C4C22semidirect
165. C22×#41D4semidirect
792. C2×D4H(5,𝔽2)semidirect
973. Q8#534semidirect

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
#429672
#429662
#429422
#429162
#398882
#398852
#393582
#389492
#374442
#365762
#364342
#364332
#364292
#360912
#360822
#360762
#359962
#350782
#350002
#349572
C2×#23412