Finite Group Databasebeta

← #7686632

Subgroups — #7686632

Order 512.

9290 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3498C211yesmaximal, characteristic, complemented
2C2×#3517C211yesmaximal, characteristic, complemented
3#59412C213yesmaximal, complemented
4#59408C216yesmaximal, complemented
5#59124C213yesmaximal, complemented
6#59035C213yesmaximal, complemented
7#44899C216yesmaximal, complemented
8#44872C216yesmaximal, complemented
9#39471C213yesmaximal, complemented
10#39434C216yesmaximal, complemented
11#38910C213yesmaximal, complemented
12#36583C211yesmaximal, characteristic, complemented
13#36455C212yesmaximal, complemented
14#36455C211yesmaximal, characteristic, complemented
15#36445C211yesmaximal, characteristic, complemented
16#36260C213yesmaximal, complemented
17#36121C213yesmaximal, complemented
18#36091C212yesmaximal, complemented
19#36005C212yesmaximal, complemented
20#34889C213yesmaximal, complemented
21#34258C212yesmaximal, complemented
22C4×#550C211yesmaximal, characteristic, complemented
23C4×#550C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2212yes—
25#3517—216no—
26#3498—216no—
27C2×#557C2211yescharacteristic, complemented
28C2×#553C2216yescomplemented
29C2×#550C2212yes—
30C2×#550C2211yescharacteristic
31C2×#550C2211yescharacteristic
32C2×#550C2211yescharacteristic
33C2×#550C2213yescomplemented
34C2×#550C2212yescomplemented
35C2×#550C2212yescomplemented
36C2×#547C2213yescomplemented
37C2×#546C2216yescomplemented
38C2×#546C2216yescomplemented
39C2×D42C2216yes—
40C2×D42C2213yes—
41C2×D42C2213yes—
42C2×#540C2216yescomplemented
43C2×#535C2216yes—
44C2×#532C2213yes—
45C2×#532C2213yescomplemented
46C22×#127C2213yes—
47C2×#529C2213yescomplemented
48C2×#520C2212yescomplemented
49C2×C4×#41C2211yescharacteristic
50C2×C4×#41C2211yescharacteristic, complemented
51C2×C4×#41C2212yescomplemented
52#2858C2213yescomplemented
53#2857C2213yescomplemented
54#2856C2216yescomplemented
55#2856C2213yescomplemented
56#2710C22112yescomplemented
57#2703C22112yescomplemented
58#2685C22112yescomplemented
59#2678C22112yescomplemented
60#2678C22112yescomplemented
61#2673C22112yescomplemented
62#2668C22112yescomplemented
63#2624C2216yescomplemented
64#2615C2216yescomplemented
65#2559C2216yescomplemented
66#2557C2216yescomplemented
67#2550C2211yescharacteristic, complemented
68#2548C2213yescomplemented
69#2547C2213yescomplemented
70#2544C2213yescomplemented
71#2542C2213yescomplemented
72#2541C2216yescomplemented
73#2541C2213yescomplemented
74#2540C2216yescomplemented
75#2540C2213yescomplemented
76#2539C22112yescomplemented
77#2539C22112yescomplemented
78#2538C2213yescomplemented
79#2537C2213yescomplemented
80#2537C2216yescomplemented
81#2535C2213yescomplemented
82#2521C2216yescomplemented
83#2501C2216yescomplemented
84#2492C2213yescomplemented
85#2490C2216yescomplemented
86#2490C2216yescomplemented
87#2490C2213yescomplemented
88#2487C2216yescomplemented
89#2464C2216yescomplemented
90#2454C2216yescomplemented
91#2445C2216yescomplemented
92#2445C2216yescomplemented
93#2445C2216yescomplemented
94#2441C2216yescomplemented
95#2435C2216yescomplemented
96#2433C2216yescomplemented
97#2433C2216yescomplemented
98#2433C2216yescomplemented
99#2431C2216yescomplemented
100#2428C2216yescomplemented
101#2428C2216yescomplemented
102#2428C2216yescomplemented
103#2428C2216yescomplemented
104#2428C2213yescomplemented
105#2427C2213yescomplemented
106#2424C22112yescomplemented
107#2422C2216yescomplemented
108#2422C2216yescomplemented
109#2418C22112yescomplemented
110#2414C2216yescomplemented
111#2414C2216yescomplemented
112#2414C2216yescomplemented
113#2410C22112yescomplemented
114#2408C2216yescomplemented
115#2408C2216yescomplemented
116#2408C2216yescomplemented
117#2408C2216yescomplemented
118#2408C2216yescomplemented
119#2407C2216yescomplemented
120#2395C2216yescomplemented
121#2388C2216yescomplemented
122#2366C2213yescomplemented
123#2366C2213yescomplemented
124#2363C2213yescomplemented
125#2363C2213yescomplemented
126#2363C2216yescomplemented
127#2354C2213yescomplemented
128#2354C2213yescomplemented
129Q8×C4⋊C4C2211yescharacteristic, complemented
130Q8×C4⋊C4C2212yescomplemented
131Q8×C4⋊C4C2211yescharacteristic, complemented
132#2341C2212yes—
133#2341C2211yescharacteristic
134#2341C2211yescharacteristic, complemented
135#2341C2212yescomplemented
136#2341C2212yescomplemented
137#2341C2212yescomplemented
138#2341C2212yescomplemented
139D4×C22⋊C4C2216yescomplemented
140D4×C22⋊C4C2216yescomplemented
141D4×C22⋊C4C2216yescomplemented
142D4×C22⋊C4C2216yescomplemented
143D4×C22⋊C4C2216yescomplemented
144#2311C2216yescomplemented
145#2309C2216yescomplemented
146C4×#127C2213yescomplemented
147C4×#127C2213yescomplemented
148C4×#124C2213yescomplemented
149C4×C22⋊Q8C2213yescomplemented
150C4×#121C2216yescomplemented
151C4×#121C2216yescomplemented
152C4×#121C2213yescomplemented
153C4×#121C2213yescomplemented
154C4×#121C2213yescomplemented
155#2297C2216yescomplemented
156C2×#390C2216yescomplemented
157C42×Q8C2211yescharacteristic, complemented
158C42×D4C2213yescomplemented
159C42×D4C2213yescomplemented
160C2×H(5,𝔽2)—216no—
161C2×H(5,𝔽2)—216no—
162C2×H(5,𝔽2)—48no—
163C22×#41C2312yes—
164C22×#41C2311yescharacteristic
165C22×#41C2316yes—
166C22×#41C2312yes—
167C22×#41C2311yescharacteristic
168C22×#41C2316yes—
169C23×D4C2316yes—
170C23×D4C2316yes—
171C23×D4C2316yes—
172C23×D4C2316yes—
173C23×D4C2316yes—
174#557—28no—
175#553—248no—
176#550—216no—
177#550—216no—
178#550—28no—
179#550—224no—
180#550—28no—
181#550—48no—
182#550D4116yescomplemented
183#547—224no—
184#546—424no—
185#546—424no—
186D42—224no—
187D42—248no—
188D42—224no—
189#540—248no—
190#535—248no—
191#532—224no—
192#532—224no—
193C2×C4⋊Q8C2313yes—
194C2×C4⋊Q8C2311yescharacteristic
195C2×#127—224no—
196C2×#127C2313yes—
197C2×#127C2313yes—
198C2×#127C2313yes—
199C2×#127C2316yes—
200C2×#127C2316yes—
201C2×#127C2316yes—
202C2×#127C2316yes—
203C2×#127C2313yes—
204#529—224no—
205C2×#126C2316yes—
206C2×#125C2311yescharacteristic
207C2×#125C2316yes—
208C2×#124C2313yes—
209C2×#124C2313yes—
210C2×#124C2316yes—
211C2×#124C2316yes—
212C2×#123C2316yes—
213C2×#123C23112yes—
214C2×#123C23112yes—
215C2×#123C23112yes—
216C2×C22⋊Q8C2313yes—
217C2×C22⋊Q8C2313yes—
218C2×C22⋊Q8C2316yes—
219C2×#121C2316yes—
220C2×#121C2316yes—
221C2×#121C2313yes—
222C2×#121C2313yes—
223C2×#121C2313yes—
224C2×#121C2313yes—
225C2×#121C2316yes—
226C2×#121C2316yes—
227C2×#121C23112yes—
228C2×#121C2316yes—
229C2×#121C2316yes—
230C2×#121C2313yes—
231C2×#121C2316yes—
232C2×#121C2313yes—
233C2×#121C2316yes—
234C2×#121C2316yes—
235C2×#121C23112yes—
236C2×#121C23112yes—
237C2×#121C2316yes—
238C2×#121C2316yes—
239C2×#121C2316yes—
240C2×#121C2316yes—
241C2×#120C23112yes—
242C2×#120C23112yes—
243C2×#120C23112yes—
244C2×#120C23112yes—
245C2×#120C23112yes—
246#520—216no—
247C4×#41—28no—
248C4×#41—28no—
249C4×#41—48no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2313yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×D4C2313yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2316yes—
264C2×C4×D4C2316yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2313yes—
267C2×C4×D4C2313yes—
268C2×C4×D4C2313yes—
269C2×C4×D4C2316yes—
270C2×C4×D4C2316yes—
271C2×C4×D4C2313yes—
272C2×C4×D4C2316yes—
273C2×C4×D4C2316yes—
274C2×C4×D4C2316yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2316yes—
277C2×C4×D4C2316yes—
278C2×C4×D4C2313yes—
279C2×#117C2316yes—
280C2×#117C2313yes—
281C2×#117C2313yes—
282C2×#117C2316yes—
283C22×C4⋊C4C2316yes—
284C22×C22⋊C4C23112yes—
285C22×C22⋊C4C23112yes—
286C22×C42C2313yes—
287C22×C42C2313yes—
288C22×C42C2316yes—
289#400C2316yes—
290#399C23112yes—
291#399C2316yes—
292#399C23112yes—
293#398C2312yes—
294#397C2316yes—
295#397C2316yes—
296#397C2316yes—
297#397C23112yes—
298#396C23112yes—
299#395C2312yes—
300#394C23112yes—
301#394C23112yes—
302#394C2316yes—
303#394C2316yes—
304#394C2316yes—
305#394C2316yes—
306#394C2316yes—
307#394C23112yes—
308#394C23112yes—
309#394C23112yes—
310#394C23112yes—
311#393C2316yes—
312#392C23112yes—
313#392C23112yes—
314#392C23112yes—
315#392C2316yes—
316#392C2316yes—
317#392C2316yes—
318#392C23112yes—
319#392C23112yes—
320#392C23112yes—
321#391C2316yes—
322#391C2313yes—
323#391C2313yes—
324#391C2312yes—
325#390C2313yes—
326#390C2313yes—
327#390C2316yes—
328#390C2316yes—
329#390C2316yes—
330#390C2316yes—
331#390C2316yes—
332#390C2313yes—
333#390C2316yes—
334#390C23112yes—
335#390C2316yes—
336#390C2316yes—
337#390C2316yes—
338#390C2316yes—
339#390C2316yes—
340#390C2316yes—
341#390C2316yes—
342#390C2316yes—
343#390C2316yes—
344#390C2316yes—
345#390C2313yes—
346#390C2316yes—
347#390C2313yes—
348#390C2316yes—
349#390C23112yes—
350#390C2316yes—
351#390C2313yes—
352#390C2316yes—
353#389C2316yes—
354#389C2316yes—
355#389C2313yes—
356#389C2316yes—
357#389C2313yes—
358#389C2316yes—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2312yes—
362#388C2316yes—
363#388C2316yes—
364#388C23112yes—
365#388C2316yes—
366#388C2316yes—
367#388C2316yes—
368#388C2316yes—
369#388C2316yes—
370#387C2316yes—
371#386C23112yes—
372#386C23112yes—
373#386C2316yes—
374#386C2316yes—
375#386C2316yes—
376#386C2316yes—
377#386C2316yes—
378#386C23112yes—
379#386C2316yes—
380#386C23112yes—
381#386C2316yes—
382#386C2316yes—
383#386C2316yes—
384#385C23112yes—
385#385C2316yes—
386#384C2313yes—
387#384C2313yes—
388#384C2316yes—
389#382C2311yescharacteristic
390#380C2313yes—
391#380C2316yes—
392#380C2316yes—
393#380C2316yes—
394#380C2316yes—
395#380C2316yes—
396#380C2313yes—
397#380C2316yes—
398#380C2313yes—
399#380C2313yes—
400#380C2316yes—
401#379C23112yes—
402#379C23112yes—
403#379C23112yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C4⋊C4C2313yes—
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C22⋊C4C2313yes—
415C4×C22⋊C4C2313yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2313yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2313yes—
425C4×C22⋊C4C2313yes—
426C4×C22⋊C4C2316yes—
427C43C2313yes—
428C25C24112yes—
429H(5,𝔽2)—4128no—
430C2×#41—24no—
431C2×#41—24no—
432C2×#41—28no—
433C2×#41—28no—
434C2×#41—24no—
435C2×#41—28no—
436C2×#41—28no—
437C2×#41—24no—
438C2×#41—24no—
439C2×#41—28no—
440C2×#41—224no—
441C2×#41—224no—
442C2×#41—224no—
443C2×#41—412no—
444C2×#41—412no—
445C2×#41—412no—
446C2×#41C2×D4116yes—
447C2×#41#4118yescomplemented
448C22×Q8C2413yes—
449C22×Q8C2412yes—
450C22×Q8C2411yescharacteristic
451C22×D4—224no—
452C22×D4—224no—
453C22×D4—224no—
454C22×D4—224no—
455C22×D4—224no—
456C22×D4—224no—
457C22×D4—224no—
458C22×D4—224no—
459C22×D4—412no—
460C22×D4—412no—
461C22×D4—412no—
462C22×D4—412no—
463C22×D4—412no—
464C22×D4—412no—
465C22×D4—86no—
466C22×D4C2413yes—
467C22×D4C2413yes—
468C22×D4C2416yes—
469C22×D4C2413yes—
470C22×D4C2416yes—
471C22×D4C2416yes—
472C22×D4C2416yes—
473C22×D4C2416yes—
474C22×D4C2416yes—
475C22×D4C2413yes—
476C22×D4C2413yes—
477C22×D4C2416yes—
478C22×D4C2416yes—
479C22×D4C2416yes—
480C22×D4C24112yes—
481C22×D4C24112yes—
482C22×D4C2416yes—
483C22×D4C24112yes—
484C22×D4C2416yes—
485C23×C4C2413yes—
486C23×C4C2413yes—
487C23×C4C2413yes—
488C23×C4C2416yes—
489C23×C4C2413yes—
490C23×C4C2416yes—
491C23×C4C2413yes—
492C23×C4C24112yes—
493C23×C4C2416yes—
494C23×C4C2416yes—
495C23×C4C2413yes—
496C4⋊Q8—24no—
497C4⋊Q8—212no—
498#127—212no—
499#127—224no—
500#127—224no—
501#127—224no—
502#127—212no—
503#127—212no—
504#127—412no—
505#127C2×D4124yes—
506#126—224no—
507#125—24no—
508#125—224no—
509#124—212no—
510#124—224no—
511#124—212no—
512#124—412no—
513#123—224no—
514#123—248no—
515#123—424no—
516#123—424no—
517C22⋊Q8—212no—
518C22⋊Q8—212no—
519C22⋊Q8—412no—
520#121—212no—
521#121—224no—
522#121—212no—
523#121—224no—
524#121—224no—
525#121—248no—
526#121—212no—
527#121—224no—
528#121—224no—
529#121—212no—
530#121—212no—
531#121—224no—
532#121—212no—
533#121—224no—
534#121—424no—
535#121—412no—
536#121—412no—
537#121—424no—
538#121—412no—
539#121—412no—
540#121—86no—
541#121C2×D4148yes—
542#120—248no—
543#120—248no—
544#120—424no—
545#120—424no—
546#120—812no—
547C4×Q8—24no—
548C4×Q8—24no—
549C4×Q8—28no—
550C4×Q8—24no—
551C4×Q8—24no—
552C4×Q8—28no—
553C4×Q8—212no—
554C4×Q8C2×D418yes—
555C4×D4—224no—
556C4×D4—224no—
557C4×D4—224no—
558C4×D4—224no—
559C4×D4—224no—
560C4×D4—212no—
561C4×D4—212no—
562C4×D4—212no—
563C4×D4—212no—
564C4×D4—212no—
565C4×D4—212no—
566C4×D4—212no—
567C4×D4—212no—
568C4×D4—212no—
569C4×D4—412no—
570C4×D4—412no—
571C4×D4—412no—
572C4×D4—412no—
573C4×D4—46no—
574C4×D4—86no—
575C4×D4C2×D4124yes—
576#117—224no—
577#117—212no—
578#117—212no—
579#117—412no—
580C2×C4⋊C4—224no—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2413yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2416yes—
598C2×C4⋊C4C2413yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2416yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2416yes—
603C2×C4⋊C4C2416yes—
604C2×C4⋊C4C24112yes—
605C2×C4⋊C4C2413yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C22⋊C4—424no—
609C2×C22⋊C4—424no—
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2413yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2413yes—
627C2×C22⋊C4C2413yes—
628C2×C22⋊C4C2413yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C24112yes—
632C2×C22⋊C4C24112yes—
633C2×C22⋊C4C24112yes—
634C2×C22⋊C4C24112yes—
635C2×C22⋊C4C24112yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C2413yes—
640C2×C22⋊C4C2416yes—
641C2×C22⋊C4C2416yes—
642C2×C22⋊C4C24112yes—
643C2×C22⋊C4C2416yes—
644C2×C22⋊C4C2416yes—
645C2×C22⋊C4C2416yes—
646C2×C42—212no—
647C2×C42—212no—
648C2×C42—412no—
649C2×C42C2413yes—
650C2×C42C2413yes—
651C2×C42C2413yes—
652C2×C42C2416yes—
653C2×C42C2413yes—
654C2×C42C2413yes—
655C2×C42C2416yes—
656C2×C42C2413yes—
657C2×C42C2413yes—
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2416yes—
661C2×C42C2413yes—
662C2×C42C2413yes—
663C2×C42C2412yes—
664C2×C42C2413yes—
665C2×C42C2411yescharacteristic
666#95C2411yescharacteristic
667#95C2411yescharacteristic
668#95C2412yes—
669#95C2412yes—
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2413yes—
674#95C2413yes—
675#95C2416yes—
676#95C2416yes—
677#95C2413yes—
678#95C2413yes—
679#95C2416yes—
680#95C2416yes—
681#95C2416yes—
682#95C2416yes—
683#95C2416yes—
684#95C2416yes—
685#95C2416yes—
686C24—224no—
687C24—224no—
688C24—412no—
689C24—412no—
690C24—412no—
691C24—412no—
692C24—412no—
693C24C2516yes—
694C24C2513yes—
695C24C2516yes—
696C24C2513yes—
697#41—264no—
698#41—232no—
699#41—496no—
700#41—416no—
701#41—432no—
702#41—848no—
703C2×Q8—26no—
704C2×Q8—24no—
705C2×Q8—24no—
706C2×Q8—26no—
707C2×Q8—26no—
708C2×Q8—42no—
709C2×Q8C22×D414yes—
710C2×Q8C2×#4114yes—
711C2×Q8H(5,𝔽2)14yes—
712C2×D4—212no—
713C2×D4—212no—
714C2×D4—212no—
715C2×D4—26no—
716C2×D4—212no—
717C2×D4—212no—
718C2×D4—212no—
719C2×D4—224no—
720C2×D4—224no—
721C2×D4—212no—
722C2×D4—26no—
723C2×D4—26no—
724C2×D4—26no—
725C2×D4—212no—
726C2×D4—212no—
727C2×D4—212no—
728C2×D4—212no—
729C2×D4—26no—
730C2×D4—212no—
731C2×D4—212no—
732C2×D4—26no—
733C2×D4—26no—
734C2×D4—212no—
735C2×D4—26no—
736C2×D4—26no—
737C2×D4—26no—
738C2×D4—26no—
739C2×D4—26no—
740C2×D4—212no—
741C2×D4—212no—
742C2×D4—212no—
743C2×D4—496no—
744C2×D4—496no—
745C2×D4—43no—
746C2×D4—46no—
747C2×D4—46no—
748C2×D4—46no—
749C2×D4—46no—
750C2×D4—46no—
751C2×D4—46no—
752C2×D4—46no—
753C2×D4—46no—
754C2×D4—412no—
755C2×D4—412no—
756C2×D4—46no—
757C2×D4—46no—
758C2×D4—412no—
759C2×D4—412no—
760C2×D4—46no—
761C2×D4—46no—
762C2×D4—46no—
763C2×D4—46no—
764C2×D4—412no—
765C2×D4—412no—
766C2×D4—412no—
767C2×D4—496no—
768C2×D4—848no—
769C2×D4—848no—
770C2×D4C22×D4124yes—
771C2×D4C22×D4112yes—
772C2×D4C22×D4124yes—
773C2×D4C2×#41112yes—
774C22×C4—26no—
775C22×C4—212no—
776C22×C4—212no—
777C22×C4—26no—
778C22×C4—224no—
779C22×C4—26no—
780C22×C4—26no—
781C22×C4—26no—
782C22×C4—26no—
783C22×C4—212no—
784C22×C4—26no—
785C22×C4—212no—
786C22×C4—26no—
787C22×C4—26no—
788C22×C4—26no—
789C22×C4—26no—
790C22×C4—26no—
791C22×C4—212no—
792C22×C4—26no—
793C22×C4—26no—
794C22×C4—212no—
795C22×C4—212no—
796C22×C4—43no—
797C22×C4—46no—
798C22×C4—46no—
799C22×C4—412no—
800C22×C4—412no—
801C22×C4—43no—
802C22×C4—46no—
803C22×C4—46no—
804C22×C4—43no—
805C22×C4C22×D4124yes—
806C22×C4C2×#41112yes—
807C22×C4C2512yes—
808C22×C4C2513yes—
809C22×C4C2513yes—
810C22×C4C2511yescharacteristic
811C22×C4C2512yes—
812C22×C4C2516yes—
813C22×C4C2511yescharacteristic
814C22×C4C2513yes—
815C22×C4C2513yes—
816C22×C4C2516yes—
817C22×C4C2513yes—
818C22×C4C2512yes—
819C22×C4C2511yescharacteristic
820C22×C4C2512yes—
821C22×C4C2511yescharacteristic
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2513yes—
825C22×C4C2511yescharacteristic
826C4⋊C4—26no—
827C4⋊C4—212no—
828C4⋊C4—212no—
829C4⋊C4—24no—
830C4⋊C4—26no—
831C4⋊C4—24no—
832C4⋊C4—22no—
833C4⋊C4—24no—
834C4⋊C4—212no—
835C4⋊C4—22no—
836C4⋊C4—212no—
837C4⋊C4—22no—
838C4⋊C4—26no—
839C4⋊C4—26no—
840C4⋊C4—212no—
841C4⋊C4—26no—
842C4⋊C4—26no—
843C4⋊C4—212no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—42no—
847C4⋊C4—46no—
848C4⋊C4—46no—
849C4⋊C4—412no—
850C4⋊C4C22×D4112yes—
851C4⋊C4C22×D414yes—
852C4⋊C4H(5,𝔽2)14yescomplemented
853C22⋊C4—212no—
854C22⋊C4—212no—
855C22⋊C4—212no—
856C22⋊C4—212no—
857C22⋊C4—26no—
858C22⋊C4—212no—
859C22⋊C4—212no—
860C22⋊C4—212no—
861C22⋊C4—212no—
862C22⋊C4—212no—
863C22⋊C4—26no—
864C22⋊C4—26no—
865C22⋊C4—212no—
866C22⋊C4—212no—
867C22⋊C4—212no—
868C22⋊C4—212no—
869C22⋊C4—212no—
870C22⋊C4—26no—
871C22⋊C4—212no—
872C22⋊C4—26no—
873C22⋊C4—46no—
874C22⋊C4—412no—
875C22⋊C4—412no—
876C22⋊C4—412no—
877C22⋊C4—412no—
878C22⋊C4—43no—
879C22⋊C4—46no—
880C22⋊C4—46no—
881C22⋊C4—46no—
882C22⋊C4—412no—
883C22⋊C4—412no—
884C22⋊C4—46no—
885C22⋊C4—46no—
886C22⋊C4—46no—
887C22⋊C4—46no—
888C22⋊C4C22×D4124yes—
889C42—22no—
890C42—22no—
891C42—26no—
892C42—26no—
893C42—26no—
894C42—26no—
895C42—212no—
896C42—26no—
897C42—26no—
898C42—212no—
899C42—26no—
900C42—42no—
901C42—46no—
902C42—43no—
903C42—43no—
904C42C22×D4112yes—
905C42H(5,𝔽2)14yescomplemented
906C23—23no—
907C23—26no—
908C23—23no—
909C23—23no—
910C23—26no—
911C23—26no—
912C23—26no—
913C23—23no—
914C23—23no—
915C23—26no—
916C23—26no—
917C23—23no—
918C23—23no—
919C23—26no—
920C23—23no—
921C23—26no—
922C23—26no—
923C23—26no—
924C23—23no—
925C23—23no—
926C23—23no—
927C23—26no—
928C23—23no—
929C23—26no—
930C23—26no—
931C23—23no—
932C23—448no—
933C23—824no—
934C23—824no—
935C23—824no—
936C23—824no—
937C23—1612no—
938C23—1612no—
939C23C23×D4112yes—
940C23C22×#4116yes—
941C23C2611yescharacteristic
942Q8—48no—
943Q8—412no—
944Q8#546116yescomplemented
945D4—224no—
946D4—248no—
947D4—224no—
948D4—424no—
949D4—412no—
950D4—424no—
951D4—424no—
952D4—424no—
953D4—424no—
954D4—424no—
955D4—412no—
956D4—412no—
957D4—812no—
958D4—812no—
959D4—812no—
960D4—812no—
961D4—824no—
962D4—824no—
963D4—1612no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—23no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—23no—
977C2×C4—21no—
978C2×C4—248no—
979C2×C4—224no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—23no—
984C2×C4—23no—
985C2×C4—26no—
986C2×C4—22no—
987C2×C4—23no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—23no—
991C2×C4—26no—
992C2×C4—23no—
993C2×C4—23no—
994C2×C4—23no—
995C2×C4—26no—
996C2×C4—26no—
997C2×C4—23no—
998C2×C4—26no—
999C2×C4—23no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—23no—
1003C2×C4—23no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—23no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—26no—
1010C2×C4—412no—
1011C2×C4—424no—
1012C2×C4—412no—
1013C2×C4—412no—
1014C2×C4—412no—
1015C2×C4—86no—
1016C2×C4—812no—
1017C2×C4—812no—
1018C2×C4—824no—
1019C2×C4C23×D416yes—
1020C2×C4C23×D414yes—
1021C2×C4C23×D416yes—
1022C2×C4C23×D412yes—
1023C2×C4C22×#4112yes—
1024C2×C4C22×#4116yes—
1025C2×C4C2×H(5,𝔽2)12yes—
1026C2×C4C2×H(5,𝔽2)12yes—
1027C2×C4C2×H(5,𝔽2)14yes—
1028C2×C4C2×H(5,𝔽2)16yes—
1029C2×C4C2×H(5,𝔽2)12yes—
1030C2×C4C2×H(5,𝔽2)12yes—
1031C2×C4#58512yes—
1032C22—26no—
1033C22—212no—
1034C22—212no—
1035C22—26no—
1036C22—26no—
1037C22—212no—
1038C22—46no—
1039C22—43no—
1040C22—46no—
1041C22—43no—
1042C22—43no—
1043C22—46no—
1044C22—46no—
1045C22—43no—
1046C22—43no—
1047C22—46no—
1048C22—43no—
1049C22—46no—
1050C22—43no—
1051C22—46no—
1052C22—43no—
1053C22—46no—
1054C22—43no—
1055C22—46no—
1056C22—43no—
1057C22—46no—
1058C22—46no—
1059C22—43no—
1060C22—1648no—
1061C22C24×D411yescharacteristic
1062C22C23×#4111yescharacteristic
1063C22C22×H(5,𝔽2)11yescharacteristic
1064C22C22×H(5,𝔽2)11yescharacteristic
1065C22C22×H(5,𝔽2)11yescharacteristic
1066C22C2×#58511yescharacteristic
1067C22H(7,𝔽2)11yescharacteristic
1068C4—22no—
1069C4—26no—
1070C4—24no—
1071C4—22no—
1072C4—22no—
1073C4—24no—
1074C4—22no—
1075C4—43no—
1076C4—41no—
1077C4—42no—
1078C4—43no—
1079C4—43no—
1080C4—43no—
1081C4—46no—
1082C4—46no—
1083C4—41no—
1084C4—42no—
1085C4C2×#546112yes—
1086C4#349814yes—
1087C2—412no—
1088C2—46no—
1089C2—83no—
1090C2—86no—
1091C2C22×#54611yescharacteristic
1092C2C2×#349811yescharacteristic
1093C2#6280011yescharacteristic
1094C2#6291611yescharacteristic
1095C2#6298611yescharacteristic
1096C2#6298711yescharacteristic
1097C2#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×#3498C2semidirect
2. C2×#3517C2semidirect
3. #59412C2semidirect
4. #59408C2semidirect
5. #59124C2semidirect
6. #59035C2semidirect
7. #44899C2semidirect
8. #44872C2semidirect
9. #39471C2semidirect
10. #39434C2semidirect
11. #38910C2semidirect
12. #36583C2semidirect
13. #36455C2semidirect
14. #36455C2semidirect
15. #36445C2semidirect
16. #36260C2semidirect
17. #36121C2semidirect
18. #36091C2semidirect
19. #36005C2semidirect
20. #34889C2semidirect
21. #34258C2semidirect
22. C4×#550C2semidirect
23. C4×#550C2semidirect
27. C2×#557C22semidirect
28. C2×#553C22semidirect
33. C2×#550C22semidirect
34. C2×#550C22semidirect
35. C2×#550C22semidirect
36. C2×#547C22semidirect
37. C2×#546C22semidirect
38. C2×#546C22semidirect
42. C2×#540C22semidirect
45. C2×#532C22semidirect
47. C2×#529C22semidirect
48. C2×#520C22semidirect
50. C2×C4×#41C22semidirect
51. C2×C4×#41C22semidirect
52. #2858C22semidirect
53. #2857C22semidirect
54. #2856C22semidirect
55. #2856C22semidirect
56. #2710C22semidirect
57. #2703C22semidirect
58. #2685C22semidirect
59. #2678C22semidirect
60. #2678C22semidirect
61. #2673C22semidirect
62. #2668C22semidirect
63. #2624C22semidirect
64. #2615C22semidirect
65. #2559C22semidirect
66. #2557C22semidirect
67. #2550C22semidirect
68. #2548C22semidirect
69. #2547C22semidirect
70. #2544C22semidirect
71. #2542C22semidirect
72. #2541C22semidirect
73. #2541C22semidirect
74. #2540C22semidirect
75. #2540C22semidirect
76. #2539C22semidirect
77. #2539C22semidirect
78. #2538C22semidirect
79. #2537C22semidirect
80. #2537C22semidirect
81. #2535C22semidirect
82. #2521C22semidirect
83. #2501C22semidirect
84. #2492C22semidirect
85. #2490C22semidirect
86. #2490C22semidirect
87. #2490C22semidirect
88. #2487C22semidirect
89. #2464C22semidirect
90. #2454C22semidirect
91. #2445C22semidirect
92. #2445C22semidirect
93. #2445C22semidirect
94. #2441C22semidirect
95. #2435C22semidirect
96. #2433C22semidirect
97. #2433C22semidirect
98. #2433C22semidirect
99. #2431C22semidirect
100. #2428C22semidirect
101. #2428C22semidirect
102. #2428C22semidirect
103. #2428C22semidirect
104. #2428C22semidirect
105. #2427C22semidirect
106. #2424C22semidirect
107. #2422C22semidirect
108. #2422C22semidirect
109. #2418C22semidirect
110. #2414C22semidirect
111. #2414C22semidirect
112. #2414C22semidirect
113. #2410C22semidirect
114. #2408C22semidirect
115. #2408C22semidirect
116. #2408C22semidirect
117. #2408C22semidirect
118. #2408C22semidirect
119. #2407C22semidirect
120. #2395C22semidirect
121. #2388C22semidirect
122. #2366C22semidirect
123. #2366C22semidirect
124. #2363C22semidirect
125. #2363C22semidirect
126. #2363C22semidirect
127. #2354C22semidirect
128. #2354C22semidirect
129. Q8×C4⋊C4C22semidirect
130. Q8×C4⋊C4C22semidirect
131. Q8×C4⋊C4C22semidirect
134. #2341C22semidirect
135. #2341C22semidirect
136. #2341C22semidirect
137. #2341C22semidirect
138. #2341C22semidirect
139. D4×C22⋊C4C22semidirect
140. D4×C22⋊C4C22semidirect
141. D4×C22⋊C4C22semidirect
142. D4×C22⋊C4C22semidirect
143. D4×C22⋊C4C22semidirect
144. #2311C22semidirect
145. #2309C22semidirect
146. C4×#127C22semidirect
147. C4×#127C22semidirect
148. C4×#124C22semidirect
149. C4×C22⋊Q8C22semidirect
150. C4×#121C22semidirect
151. C4×#121C22semidirect
152. C4×#121C22semidirect
153. C4×#121C22semidirect
154. C4×#121C22semidirect
155. #2297C22semidirect
156. C2×#390C22semidirect
157. C42×Q8C22semidirect
158. C42×D4C22semidirect
159. C42×D4C22semidirect
182. #550D4semidirect
447. C2×#41#41semidirect
852. C4⋊C4H(5,𝔽2)semidirect
905. C42H(5,𝔽2)semidirect
944. Q8#546semidirect

Maximal subgroups

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

subgroupindex
C2×#34982
C2×#35172
#594122
#594082
#591242
#590352
#448992
#448722
#394712
#394342
#389102
#365832
#364552
#364452
#362602
#361212
#360912
#360052
#348892
#342582
C4×#5502