Finite Group Databasebeta

← #7699552

Subgroups — #7699552

Order 512.

9330 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×#3483C211yesmaximal, characteristic, complemented
2C22×#550C211yesmaximal, characteristic, complemented
3#59810C216yesmaximal, complemented
4#59419C213yesmaximal, complemented
5#59124C213yesmaximal, complemented
6#59097C216yesmaximal, complemented
7#59039C213yesmaximal, complemented
8#59026C216yesmaximal, complemented
9Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
10#36457C211yesmaximal, characteristic, complemented
11#36455C211yesmaximal, characteristic, complemented
12#36455C212yesmaximal, complemented
13#36433C212yesmaximal, complemented
14#36429C212yesmaximal, complemented
15#36412C213yesmaximal, complemented
16#36410C213yesmaximal, complemented
17#36160C213yesmaximal, complemented
18#36123C216yesmaximal, complemented
19#36121C213yesmaximal, complemented
20C4×#550C211yesmaximal, characteristic, complemented
21C4×#548C211yesmaximal, characteristic, complemented
22C4×#546C213yesmaximal, complemented
23C22⋊C4×#41C212yesmaximal, complemented
24C23×#41C2212yes—
25#3483—216no—
26C2×Q82C2211yescharacteristic, complemented
27C2×#555C2213yescomplemented
28C2×#555C2216yescomplemented
29C2×#550—216no—
30C2×#550C2213yes—
31C2×#550C2213yes—
32C2×#550C2212yes—
33C2×#550C2211yescharacteristic
34C2×#550C2216yes—
35C2×#550C2211yescharacteristic
36C2×#550C2213yescomplemented
37C2×#550C2212yescomplemented
38C2×#550C2212yescomplemented
39C2×#548C2211yescharacteristic
40C2×#546C2213yes—
41C2×#546C2216yes—
42C2×#532C2213yescomplemented
43C2×#532C2216yescomplemented
44C22×#127C2213yes—
45C22×#121C2216yes—
46C2×C4×#41C2212yescomplemented
47C2×C4×#41C2213yescomplemented
48C2×C4×#41C2211yescharacteristic, complemented
49C2×C4×#41C2212yescomplemented
50C22×C4×Q8C2211yescharacteristic
51C22×C4×D4C2213yes—
52#2858C2213yescomplemented
53#2857C2213yes—
54#2856C2213yescomplemented
55#2856C2216yescomplemented
56#2854C2216yescomplemented
57#2847C2216yes—
58#2699C22112yescomplemented
59#2686C22112yescomplemented
60#2673C22112yescomplemented
61#2582C2213yescomplemented
62#2567C2213yescomplemented
63#2563C2213yescomplemented
64#2555C22112yescomplemented
65#2555C22112yescomplemented
66#2548C2213yescomplemented
67#2544C2216yescomplemented
68#2543C22112yescomplemented
69#2541C2213yescomplemented
70#2541C2216yescomplemented
71#2537C2213yescomplemented
72#2537C2216yescomplemented
73#2500C2216yescomplemented
74#2491C2216yescomplemented
75#2491C2216yescomplemented
76#2485C2216yescomplemented
77#2476C22112yescomplemented
78#2472C22112yes—
79#2464C22112yescomplemented
80#2459C22112yescomplemented
81#2451C2216yescomplemented
82#2445C2216yescomplemented
83#2445C2216yescomplemented
84#2445C2216yescomplemented
85#2440C2216yes—
86#2435C2216yes—
87#2433C2216yes—
88#2431C2216yescomplemented
89#2431C2216yescomplemented
90#2431C2216yescomplemented
91#2431C2216yescomplemented
92#2430C22112yescomplemented
93#2428C2216yescomplemented
94#2428C2216yescomplemented
95#2428C2216yescomplemented
96#2428C2216yescomplemented
97#2428C2216yescomplemented
98#2422C2216yescomplemented
99#2420C2216yescomplemented
100#2420C2216yescomplemented
101#2414C2216yescomplemented
102#2414C2216yescomplemented
103#2414C2216yescomplemented
104#2410C22112yes—
105#2408C2216yes—
106#2408C2216yes—
107#2407C2216yescomplemented
108#2407C2216yescomplemented
109#2367C2213yescomplemented
110#2367C2213yescomplemented
111#2366C2213yescomplemented
112#2364C2216yescomplemented
113#2363C2216yescomplemented
114#2363C2213yescomplemented
115#2363C2216yescomplemented
116#2362C2213yescomplemented
117#2361C2213yes—
118#2360C2211yescharacteristic
119#2359C2216yescomplemented
120#2358C2216yes—
121#2354C2213yescomplemented
122#2352C2213yes—
123#2352C2213yes—
124#2351C2211yescharacteristic, complemented
125Q8×C4⋊C4C2212yescomplemented
126Q8×C4⋊C4C2211yescharacteristic, complemented
127#2349C2213yescomplemented
128#2342C2216yes—
129#2341C2212yescomplemented
130#2341C2212yescomplemented
131#2341C2212yescomplemented
132#2341C2212yescomplemented
133#2341C2211yescharacteristic, complemented
134Q8×C22⋊C4C2211yescharacteristic
135Q8×C22⋊C4C2212yes—
136#2339C2213yescomplemented
137#2339C2216yescomplemented
138#2339C2216yescomplemented
139D4×C22⋊C4C2213yes—
140D4×C22⋊C4C2216yes—
141D4×C22⋊C4C2216yes—
142C4×#127C2213yescomplemented
143C4×#124C2213yescomplemented
144C4×#124C2213yescomplemented
145C4×C22⋊Q8C2213yes—
146C4×C22⋊Q8C2213yescomplemented
147C4×#123C2216yescomplemented
148C4×#121C2213yes—
149C4×#121C2216yescomplemented
150C4×#121C2213yescomplemented
151C4×#121C2216yescomplemented
152C4×#120C2216yes—
153#2297C2216yescomplemented
154#2297C2216yescomplemented
155#2280C2216yes—
156C42×Q8C2211yescharacteristic, complemented
157C42×D4C2213yes—
158C42×D4C2213yescomplemented
159C2×C4×C22⋊C4C2216yes—
160C22×#41—216no—
161C22×#41—216no—
162C22×#41—48no—
163C22×#41C2312yes—
164C22×#41C2311yescharacteristic
165C22×#41C2316yes—
166C22×#41C2316yes—
167C22×#41C2313yes—
168C22×#41C2312yes—
169C22×#41C2316yes—
170C23×Q8C2311yescharacteristic
171C23×D4C2316yes—
172C23×D4C2313yes—
173C23×D4C2316yes—
174C24×C4C2316yes—
175Q82—28no—
176#555—248no—
177#555—224no—
178#550—216no—
179#550—216no—
180#550—224no—
181#550—224no—
182#550—248no—
183#550—28no—
184#550—224no—
185#550—48no—
186#550D4116yescomplemented
187#548—28no—
188#546—224no—
189#546—424no—
190#532—224no—
191#532—248no—
192C2×C4⋊Q8C2313yes—
193C2×C4⋊Q8C2316yes—
194C2×#127—224no—
195C2×#127C2313yes—
196C2×#127C2316yes—
197C2×#127C2316yes—
198C2×#127C2316yes—
199C2×#127C2316yes—
200C2×#127C2316yes—
201C2×#127C2313yes—
202C2×#124C2313yes—
203C2×#124C2313yes—
204C2×#124C2316yes—
205C2×#124C23112yes—
206C2×#124C2316yes—
207C2×#124C2316yes—
208C2×#123C2316yes—
209C2×#123C23112yes—
210C2×C22⋊Q8C2313yes—
211C2×C22⋊Q8C2316yes—
212C2×C22⋊Q8C2311yescharacteristic
213C2×#121—248no—
214C2×#121C2313yes—
215C2×#121C2316yes—
216C2×#121C2316yes—
217C2×#121C2313yes—
218C2×#121C2316yes—
219C2×#121C2316yes—
220C2×#121C2316yes—
221C2×#121C2316yes—
222C2×#121C2316yes—
223C2×#121C23112yes—
224C2×#121C23112yes—
225C2×#121C23112yes—
226C2×#121C2316yes—
227C2×#121C2316yes—
228C2×#121C2316yes—
229C2×#121C23112yes—
230C2×#121C2316yes—
231C2×#121C23112yes—
232C2×#121C2316yes—
233C2×#120C2316yes—
234C2×#120C23112yes—
235C4×#41—216no—
236C4×#41—28no—
237C4×#41—224no—
238C4×#41—48no—
239C2×C4×Q8—28no—
240C2×C4×Q8C2313yes—
241C2×C4×Q8C2313yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2313yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4—224no—
252C2×C4×D4C2313yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2313yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2313yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2316yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2313yes—
264C2×C4×D4C2313yes—
265C2×C4×D4C2316yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2313yes—
268C2×C4×D4C2313yes—
269C2×C4×D4C2316yes—
270C2×C4×D4C2316yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2316yes—
273C2×C4×D4C2313yes—
274C2×#117C2316yes—
275C2×#117C2313yes—
276C2×#117C2313yes—
277C2×#117C2316yes—
278C2×#117C2316yes—
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2313yes—
281C22×C22⋊C4C2316yes—
282C22×C22⋊C4C2316yes—
283C22×C22⋊C4C2316yes—
284C22×C42C2316yes—
285C22×C42C2313yes—
286C22×C42C2313yes—
287C22×C42C2316yes—
288#398C23112yes—
289#397C23112yes—
290#395C23112yes—
291#394C23112yes—
292#394C23112yes—
293#394C23112yes—
294#394C23112yes—
295#394C23112yes—
296#394C23112yes—
297#394C23112yes—
298#394C23112yes—
299#393C23112yes—
300#392C23112yes—
301#392C23112yes—
302#392C23112yes—
303#392C23112yes—
304#392C23112yes—
305#392C23112yes—
306#391C2316yes—
307#391C2313yes—
308#391C2316yes—
309#391C2311yescharacteristic
310#391C2313yes—
311#391C2313yes—
312#391C2316yes—
313#390C2316yes—
314#390C2316yes—
315#390C2316yes—
316#390C2316yes—
317#390C2316yes—
318#390C2316yes—
319#390C2316yes—
320#390C2316yes—
321#390C2313yes—
322#390C2313yes—
323#390C2316yes—
324#390C2313yes—
325#390C2316yes—
326#390C2316yes—
327#390C2313yes—
328#390C2316yes—
329#390C23112yes—
330#390C2316yes—
331#389C2313yes—
332#389C2316yes—
333#389C2316yes—
334#389C2313yes—
335#389C2316yes—
336#389C2311yescharacteristic
337#389C2316yes—
338#389C2313yes—
339#389C2312yes—
340#388C2316yes—
341#388C2316yes—
342#388C2316yes—
343#388C2316yes—
344#388C2316yes—
345#388C23112yes—
346#388C2316yes—
347#388C2316yes—
348#388C23112yes—
349#388C2316yes—
350#388C2316yes—
351#388C2316yes—
352#387C2316yes—
353#387C2316yes—
354#387C2316yes—
355#387C2312yes—
356#386C2316yes—
357#386C23112yes—
358#386C23112yes—
359#386C23112yes—
360#386C23112yes—
361#386C23112yes—
362#386C23112yes—
363#386C2316yes—
364#386C2316yes—
365#386C2316yes—
366#386C2316yes—
367#386C23112yes—
368#386C2316yes—
369#386C2316yes—
370#386C2316yes—
371#386C23112yes—
372#385C2312yes—
373#385C2316yes—
374#385C2316yes—
375#385C2316yes—
376#385C2316yes—
377#385C2316yes—
378#384C2313yes—
379#384C2316yes—
380#382C2313yes—
381#382C2313yes—
382#381C23112yes—
383#381C2316yes—
384#380C2316yes—
385#380C2316yes—
386#380C2316yes—
387#380C2316yes—
388#380C2313yes—
389#380C2313yes—
390#380C2316yes—
391#380C2313yes—
392#380C2313yes—
393#380C2316yes—
394#379C23112yes—
395#379C2316yes—
396C4×C4⋊C4C2313yes—
397C4×C4⋊C4C2313yes—
398C4×C4⋊C4C2313yes—
399C4×C4⋊C4C2316yes—
400C4×C4⋊C4C2313yes—
401C4×C4⋊C4C2313yes—
402C4×C4⋊C4C2313yes—
403C4×C4⋊C4C2313yes—
404C4×C4⋊C4C2311yescharacteristic
405C4×C4⋊C4C2313yes—
406C4×C22⋊C4C2311yescharacteristic
407C4×C22⋊C4C2313yes—
408C4×C22⋊C4C2316yes—
409C4×C22⋊C4C2316yes—
410C4×C22⋊C4C2316yes—
411C4×C22⋊C4C2313yes—
412C4×C22⋊C4C2313yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2313yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2312yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C23112yes—
423C4×C22⋊C4C2313yes—
424C4×C22⋊C4C2316yes—
425C2×#95C2316yes—
426C2×#95C2316yes—
427C43C2313yes—
428C25C2416yes—
429C2×#41—24no—
430C2×#41—28no—
431C2×#41—28no—
432C2×#41—24no—
433C2×#41—224no—
434C2×#41—224no—
435C2×#41—28no—
436C2×#41—212no—
437C2×#41—28no—
438C2×#41—24no—
439C2×#41—28no—
440C2×#41—212no—
441C2×#41—224no—
442C2×#41—224no—
443C2×#41—224no—
444C2×#41—412no—
445C2×#41—412no—
446C2×#41—412no—
447C2×#41—46no—
448C2×#41—4128no—
449C2×#41—86no—
450C2×#41C2×D4116yes—
451C22×Q8—24no—
452C22×Q8—24no—
453C22×Q8#4118yescomplemented
454C22×Q8C2413yes—
455C22×Q8C2411yescharacteristic
456C22×Q8C2416yes—
457C22×Q8C2411yescharacteristic
458C22×D4—212no—
459C22×D4—224no—
460C22×D4—224no—
461C22×D4—212no—
462C22×D4—224no—
463C22×D4—46no—
464C22×D4—412no—
465C22×D4—412no—
466C22×D4—86no—
467C22×D4C2413yes—
468C22×D4C2413yes—
469C22×D4C2413yes—
470C22×D4C2416yes—
471C22×D4C2416yes—
472C22×D4C2416yes—
473C22×D4C24112yes—
474C22×D4C2413yes—
475C22×D4C2416yes—
476C22×D4C2416yes—
477C22×D4C24112yes—
478C22×D4C24112yes—
479C22×D4C2416yes—
480C22×D4C24112yes—
481C22×D4C2416yes—
482C23×C4—224no—
483C23×C4—224no—
484C23×C4—412no—
485C23×C4C2413yes—
486C23×C4C2413yes—
487C23×C4C2416yes—
488C23×C4C2412yes—
489C23×C4C2413yes—
490C23×C4C2416yes—
491C23×C4C2416yes—
492C23×C4C2413yes—
493C23×C4C2416yes—
494C23×C4C2416yes—
495C23×C4C2416yes—
496C23×C4C2411yescharacteristic
497C23×C4C2413yes—
498C23×C4C2416yes—
499C23×C4C2416yes—
500C4⋊Q8—224no—
501C4⋊Q8—212no—
502#127—224no—
503#127—224no—
504#127—224no—
505#127—224no—
506#127—212no—
507#127—412no—
508#127C2×D4124yes—
509#124—212no—
510#124—212no—
511#124—224no—
512#124—248no—
513#124—412no—
514#124—86no—
515#123—224no—
516#123—424no—
517C22⋊Q8—212no—
518C22⋊Q8—412no—
519C22⋊Q8#4118yescomplemented
520#121—224no—
521#121—248no—
522#121—224no—
523#121—224no—
524#121—248no—
525#121—224no—
526#121—224no—
527#121—212no—
528#121—224no—
529#121—212no—
530#121—224no—
531#121—248no—
532#121—412no—
533#121—424no—
534#121—412no—
535#121—412no—
536#121—412no—
537#121—812no—
538#121C2×D4148yes—
539#120—224no—
540#120—424no—
541C4×Q8—24no—
542C4×Q8—24no—
543C4×Q8—28no—
544C4×Q8—24no—
545C4×Q8—24no—
546C4×Q8—28no—
547C4×Q8—212no—
548C4×Q8—24no—
549C4×Q8—212no—
550C4×Q8—212no—
551C4×Q8C2×D418yes—
552C4×D4—212no—
553C4×D4—212no—
554C4×D4—224no—
555C4×D4—224no—
556C4×D4—224no—
557C4×D4—224no—
558C4×D4—212no—
559C4×D4—212no—
560C4×D4—212no—
561C4×D4—212no—
562C4×D4—212no—
563C4×D4—224no—
564C4×D4—224no—
565C4×D4—212no—
566C4×D4—212no—
567C4×D4—212no—
568C4×D4—46no—
569C4×D4—412no—
570C4×D4—412no—
571C4×D4—412no—
572C4×D4—412no—
573C4×D4C2×D4124yes—
574#117—224no—
575#117—212no—
576#117—212no—
577#117—224no—
578#117—412no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—212no—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2413yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2413yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2413yes—
593C2×C4⋊C4C2413yes—
594C2×C4⋊C4C2413yes—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2413yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C24112yes—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2413yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2412yes—
605C2×C22⋊C4—224no—
606C2×C22⋊C4—224no—
607C2×C22⋊C4—224no—
608C2×C22⋊C4C2413yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C24112yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2411yescharacteristic
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2413yes—
624C2×C22⋊C4C2413yes—
625C2×C22⋊C4C2413yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C24112yes—
629C2×C22⋊C4C24112yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C24112yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C24112yes—
636C2×C22⋊C4C24112yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2411yescharacteristic
641C2×C42—224no—
642C2×C42—212no—
643C2×C42—212no—
644C2×C42—412no—
645C2×C42C2416yes—
646C2×C42C2413yes—
647C2×C42C2412yes—
648C2×C42C2413yes—
649C2×C42C2411yescharacteristic
650C2×C42C2413yes—
651C2×C42C2411yescharacteristic
652C2×C42C2413yes—
653C2×C42C2413yes—
654C2×C42C2413yes—
655C2×C42C2416yes—
656C2×C42C2416yes—
657C2×C42C2413yes—
658C2×C42C2413yes—
659C2×C42C2413yes—
660C2×C42C2416yes—
661C2×C42C2413yes—
662C2×C42C2412yes—
663C2×C42C2413yes—
664#95C2412yes—
665#95C2412yes—
666#95C2413yes—
667#95C2413yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2412yes—
673#95C2411yescharacteristic
674#95C2411yescharacteristic
675#95C2416yes—
676#95C2412yes—
677#95C2413yes—
678#95C2416yes—
679#95C2413yes—
680#95C2416yes—
681#95C2416yes—
682#95C24112yes—
683#95C2416yes—
684#95C2416yes—
685#95C2416yes—
686#95C2416yes—
687C24—212no—
688C24—212no—
689C24—212no—
690C24—212no—
691C24—46no—
692C24—46no—
693C24—46no—
694C24C2516yes—
695C24C2513yes—
696C24C2516yes—
697C24C2511yescharacteristic
698#41—264no—
699#41—496no—
700#41—448no—
701#41—496no—
702#41—416no—
703#41—432no—
704#41—848no—
705C2×Q8—232no—
706C2×Q8—22no—
707C2×Q8—26no—
708C2×Q8—212no—
709C2×Q8—26no—
710C2×Q8—22no—
711C2×Q8—46no—
712C2×Q8—46no—
713C2×Q8C22×D414yes—
714C2×Q8C2×#41112yes—
715C2×Q8C2×#4114yes—
716C2×Q8C2×#4114yescomplemented
717C2×Q8H(5,𝔽2)14yes—
718C2×D4—212no—
719C2×D4—212no—
720C2×D4—224no—
721C2×D4—26no—
722C2×D4—26no—
723C2×D4—26no—
724C2×D4—224no—
725C2×D4—224no—
726C2×D4—26no—
727C2×D4—26no—
728C2×D4—212no—
729C2×D4—212no—
730C2×D4—26no—
731C2×D4—212no—
732C2×D4—212no—
733C2×D4—212no—
734C2×D4—26no—
735C2×D4—26no—
736C2×D4—224no—
737C2×D4—212no—
738C2×D4—212no—
739C2×D4—212no—
740C2×D4—26no—
741C2×D4—212no—
742C2×D4—26no—
743C2×D4—26no—
744C2×D4—448no—
745C2×D4—496no—
746C2×D4—46no—
747C2×D4—46no—
748C2×D4—412no—
749C2×D4—46no—
750C2×D4—46no—
751C2×D4—46no—
752C2×D4—412no—
753C2×D4—412no—
754C2×D4—46no—
755C2×D4—46no—
756C2×D4—412no—
757C2×D4—412no—
758C2×D4—46no—
759C2×D4—412no—
760C2×D4—412no—
761C2×D4—412no—
762C2×D4—848no—
763C2×D4C22×D4112yes—
764C2×D4C22×D4124yes—
765C2×D4C22×D4124yes—
766C22×C4—22no—
767C22×C4—26no—
768C22×C4—212no—
769C22×C4—212no—
770C22×C4—26no—
771C22×C4—22no—
772C22×C4—212no—
773C22×C4—212no—
774C22×C4—212no—
775C22×C4—24no—
776C22×C4—26no—
777C22×C4—26no—
778C22×C4—26no—
779C22×C4—26no—
780C22×C4—26no—
781C22×C4—24no—
782C22×C4—212no—
783C22×C4—212no—
784C22×C4—212no—
785C22×C4—26no—
786C22×C4—26no—
787C22×C4—212no—
788C22×C4—212no—
789C22×C4—212no—
790C22×C4—212no—
791C22×C4—26no—
792C22×C4—26no—
793C22×C4—212no—
794C22×C4—26no—
795C22×C4—212no—
796C22×C4—212no—
797C22×C4—42no—
798C22×C4—46no—
799C22×C4—46no—
800C22×C4—43no—
801C22×C4—46no—
802C22×C4—43no—
803C22×C4—46no—
804C22×C4—496no—
805C22×C4—46no—
806C22×C4—46no—
807C22×C4—46no—
808C22×C4—46no—
809C22×C4C22×D4124yes—
810C22×C4C2×#4114yes—
811C22×C4C2×#41112yes—
812C22×C4C2512yes—
813C22×C4C2511yescharacteristic
814C22×C4C2513yes—
815C22×C4C2513yes—
816C22×C4C2513yes—
817C22×C4C2516yes—
818C22×C4C2516yes—
819C22×C4C2513yes—
820C22×C4C2511yescharacteristic
821C22×C4C2512yes—
822C22×C4C2513yes—
823C22×C4C2513yes—
824C22×C4C2511yescharacteristic
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C22×C4C2513yes—
830C22×C4C2511yescharacteristic
831C4⋊C4—24no—
832C4⋊C4—22no—
833C4⋊C4—212no—
834C4⋊C4—26no—
835C4⋊C4—24no—
836C4⋊C4—26no—
837C4⋊C4—212no—
838C4⋊C4—212no—
839C4⋊C4—26no—
840C4⋊C4—26no—
841C4⋊C4—26no—
842C4⋊C4—26no—
843C4⋊C4—26no—
844C4⋊C4—212no—
845C4⋊C4—26no—
846C4⋊C4—26no—
847C4⋊C4—42no—
848C4⋊C4—46no—
849C4⋊C4—412no—
850C4⋊C4—46no—
851C4⋊C4C22×D414yes—
852C4⋊C4C22×D4112yes—
853C4⋊C4C2×#4114yescomplemented
854C4⋊C4C2×#4118yescomplemented
855C22⋊C4—212no—
856C22⋊C4—212no—
857C22⋊C4—224no—
858C22⋊C4—26no—
859C22⋊C4—22no—
860C22⋊C4—212no—
861C22⋊C4—212no—
862C22⋊C4—212no—
863C22⋊C4—212no—
864C22⋊C4—212no—
865C22⋊C4—212no—
866C22⋊C4—212no—
867C22⋊C4—212no—
868C22⋊C4—26no—
869C22⋊C4—26no—
870C22⋊C4—212no—
871C22⋊C4—212no—
872C22⋊C4—212no—
873C22⋊C4—212no—
874C22⋊C4—26no—
875C22⋊C4—412no—
876C22⋊C4—46no—
877C22⋊C4—412no—
878C22⋊C4—46no—
879C22⋊C4—46no—
880C22⋊C4—412no—
881C22⋊C4—412no—
882C22⋊C4—46no—
883C22⋊C4—412no—
884C22⋊C4—46no—
885C22⋊C4C22×D4124yes—
886C22⋊C4C2×#4118yes—
887C22⋊C4H(5,𝔽2)14yes—
888C42—24no—
889C42—26no—
890C42—22no—
891C42—26no—
892C42—212no—
893C42—26no—
894C42—26no—
895C42—26no—
896C42—212no—
897C42—26no—
898C42—26no—
899C42—26no—
900C42—212no—
901C42—26no—
902C42—22no—
903C42—42no—
904C42—46no—
905C42—43no—
906C42C22×D4112yes—
907C23—21no—
908C23—21no—
909C23—21no—
910C23—21no—
911C23—26no—
912C23—26no—
913C23—26no—
914C23—26no—
915C23—26no—
916C23—26no—
917C23—23no—
918C23—26no—
919C23—23no—
920C23—26no—
921C23—23no—
922C23—26no—
923C23—26no—
924C23—23no—
925C23—23no—
926C23—26no—
927C23—26no—
928C23—23no—
929C23—26no—
930C23—23no—
931C23—424no—
932C23—424no—
933C23—424no—
934C23—424no—
935C23—812no—
936C23—812no—
937C23—812no—
938C23C23×D4112yes—
939C23C22×#4112yes—
940C23C22×#4112yes—
941C23C2×H(5,𝔽2)12yes—
942C23C2611yescharacteristic
943Q8—224no—
944Q8—28no—
945Q8—812no—
946Q8#546116yescomplemented
947D4—248no—
948D4—224no—
949D4—424no—
950D4—424no—
951D4—448no—
952D4—424no—
953D4—412no—
954D4—424no—
955D4—412no—
956D4—412no—
957D4—812no—
958D4—812no—
959D4—824no—
960D4—824no—
961D4—1612no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—23no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—23no—
970C2×C4—22no—
971C2×C4—23no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—23no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—224no—
979C2×C4—248no—
980C2×C4—28no—
981C2×C4—21no—
982C2×C4—23no—
983C2×C4—23no—
984C2×C4—26no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—23no—
988C2×C4—23no—
989C2×C4—23no—
990C2×C4—23no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—23no—
994C2×C4—26no—
995C2×C4—23no—
996C2×C4—26no—
997C2×C4—26no—
998C2×C4—23no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—23no—
1003C2×C4—26no—
1004C2×C4—21no—
1005C2×C4—23no—
1006C2×C4—26no—
1007C2×C4—23no—
1008C2×C4—424no—
1009C2×C4—412no—
1010C2×C4—48no—
1011C2×C4—424no—
1012C2×C4—412no—
1013C2×C4—424no—
1014C2×C4—424no—
1015C2×C4—424no—
1016C2×C4—412no—
1017C2×C4—412no—
1018C2×C4—812no—
1019C2×C4—812no—
1020C2×C4C23×D414yes—
1021C2×C4C23×D416yes—
1022C2×C4C23×D416yes—
1023C2×C4C23×D412yes—
1024C2×C4C22×#4114yes—
1025C2×C4C22×#4114yes—
1026C2×C4C22×#4112yes—
1027C2×C4C22×#4116yes—
1028C2×C4C22×#4116yes—
1029C2×C4C22×#4112yes—
1030C2×C4C2×H(5,𝔽2)12yes—
1031C2×C4C2×H(5,𝔽2)12yes—
1032C2×C4C2×H(5,𝔽2)16yes—
1033C2×C4#58512yes—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—212no—
1041C22—212no—
1042C22—212no—
1043C22—46no—
1044C22—46no—
1045C22—46no—
1046C22—46no—
1047C22—43no—
1048C22—46no—
1049C22—43no—
1050C22—46no—
1051C22—43no—
1052C22—46no—
1053C22—43no—
1054C22—46no—
1055C22—46no—
1056C22—43no—
1057C22—43no—
1058C22—46no—
1059C22—43no—
1060C22—46no—
1061C22—848no—
1062C22#348314yescomplemented
1063C22C24×D411yescharacteristic
1064C22C23×#4111yescharacteristic
1065C22C23×#4111yescharacteristic
1066C22C22×H(5,𝔽2)11yescharacteristic
1067C22C22×H(5,𝔽2)11yescharacteristic
1068C22C2×#58511yescharacteristic
1069C22H(7,𝔽2)11yescharacteristic
1070C4—22no—
1071C4—26no—
1072C4—24no—
1073C4—22no—
1074C4—24no—
1075C4—26no—
1076C4—22no—
1077C4—24no—
1078C4—43no—
1079C4—46no—
1080C4—43no—
1081C4—41no—
1082C4—46no—
1083C4—41no—
1084C4—42no—
1085C4—43no—
1086C4—43no—
1087C4C2×#546112yes—
1088C4D4×#4114yes—
1089C2—24no—
1090C2—412no—
1091C2—83no—
1092C2—86no—
1093C2C22×#54611yescharacteristic
1094C2C2×D4×#4111yescharacteristic
1095C2C2×#348311yescharacteristic
1096C2D4×H(5,𝔽2)11yescharacteristic
1097C2#6298611yescharacteristic
1098C2#6300611yescharacteristic
1099C2#6301411yescharacteristic
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×#3483C2semidirect
2. C22×#550C2semidirect
3. #59810C2semidirect
4. #59419C2semidirect
5. #59124C2semidirect
6. #59097C2semidirect
7. #59039C2semidirect
8. #59026C2semidirect
9. Q8×C22⋊Q8C2semidirect
10. #36457C2semidirect
11. #36455C2semidirect
12. #36455C2semidirect
13. #36433C2semidirect
14. #36429C2semidirect
15. #36412C2semidirect
16. #36410C2semidirect
17. #36160C2semidirect
18. #36123C2semidirect
19. #36121C2semidirect
20. C4×#550C2semidirect
21. C4×#548C2semidirect
22. C4×#546C2semidirect
23. C22⋊C4×#41C2semidirect
26. C2×Q82C22semidirect
27. C2×#555C22semidirect
28. C2×#555C22semidirect
36. C2×#550C22semidirect
37. C2×#550C22semidirect
38. C2×#550C22semidirect
42. C2×#532C22semidirect
43. C2×#532C22semidirect
46. C2×C4×#41C22semidirect
47. C2×C4×#41C22semidirect
48. C2×C4×#41C22semidirect
49. C2×C4×#41C22semidirect
52. #2858C22semidirect
54. #2856C22semidirect
55. #2856C22semidirect
56. #2854C22semidirect
58. #2699C22semidirect
59. #2686C22semidirect
60. #2673C22semidirect
61. #2582C22semidirect
62. #2567C22semidirect
63. #2563C22semidirect
64. #2555C22semidirect
65. #2555C22semidirect
66. #2548C22semidirect
67. #2544C22semidirect
68. #2543C22semidirect
69. #2541C22semidirect
70. #2541C22semidirect
71. #2537C22semidirect
72. #2537C22semidirect
73. #2500C22semidirect
74. #2491C22semidirect
75. #2491C22semidirect
76. #2485C22semidirect
77. #2476C22semidirect
79. #2464C22semidirect
80. #2459C22semidirect
81. #2451C22semidirect
82. #2445C22semidirect
83. #2445C22semidirect
84. #2445C22semidirect
88. #2431C22semidirect
89. #2431C22semidirect
90. #2431C22semidirect
91. #2431C22semidirect
92. #2430C22semidirect
93. #2428C22semidirect
94. #2428C22semidirect
95. #2428C22semidirect
96. #2428C22semidirect
97. #2428C22semidirect
98. #2422C22semidirect
99. #2420C22semidirect
100. #2420C22semidirect
101. #2414C22semidirect
102. #2414C22semidirect
103. #2414C22semidirect
107. #2407C22semidirect
108. #2407C22semidirect
109. #2367C22semidirect
110. #2367C22semidirect
111. #2366C22semidirect
112. #2364C22semidirect
113. #2363C22semidirect
114. #2363C22semidirect
115. #2363C22semidirect
116. #2362C22semidirect
119. #2359C22semidirect
121. #2354C22semidirect
124. #2351C22semidirect
125. Q8×C4⋊C4C22semidirect
126. Q8×C4⋊C4C22semidirect
127. #2349C22semidirect
129. #2341C22semidirect
130. #2341C22semidirect
131. #2341C22semidirect
132. #2341C22semidirect
133. #2341C22semidirect
136. #2339C22semidirect
137. #2339C22semidirect
138. #2339C22semidirect
142. C4×#127C22semidirect
143. C4×#124C22semidirect
144. C4×#124C22semidirect
146. C4×C22⋊Q8C22semidirect
147. C4×#123C22semidirect
149. C4×#121C22semidirect
150. C4×#121C22semidirect
151. C4×#121C22semidirect
153. #2297C22semidirect
154. #2297C22semidirect
156. C42×Q8C22semidirect
158. C42×D4C22semidirect
186. #550D4semidirect
453. C22×Q8#41semidirect
519. C22⋊Q8#41semidirect
716. C2×Q8C2×#41semidirect
853. C4⋊C4C2×#41semidirect
854. C4⋊C4C2×#41semidirect
946. Q8#546semidirect
1062. C22#3483semidirect

Maximal subgroups

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

subgroupindex
C2×#34832
C22×#5502
#598102
#594192
#591242
#590972
#590392
#590262
Q8×C22⋊Q82
#364572
#364552
#364332
#364292
#364122
#364102
#361602
#361232
#361212
C4×#5502
C4×#5482
C4×#5462
C22⋊C4×#412