Finite Group Databasebeta

← #7690107

Subgroups — #7690107

Order 512.

9376 conjugacy classes of subgroups.

The subgroup lattice has 1103 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3498C211yesmaximal, characteristic, complemented
2C2×#3483C211yesmaximal, characteristic, complemented
3#59412C213yesmaximal, complemented
4#59124C213yesmaximal, complemented
5#59095C216yesmaximal, complemented
6#59041C213yesmaximal, complemented
7#44929C216yesmaximal, complemented
8#44887C216yesmaximal, complemented
9#39469C213yesmaximal, complemented
10#38953C213yesmaximal, complemented
11#37782C216yesmaximal, complemented
12#36457C211yesmaximal, characteristic, complemented
13#36456C211yesmaximal, characteristic, complemented
14#36455C211yesmaximal, characteristic, complemented
15#36433C212yesmaximal, complemented
16#36258C213yesmaximal, complemented
17#36121C213yesmaximal, complemented
18#36091C212yesmaximal, complemented
19#36029C212yesmaximal, complemented
20#34715C213yesmaximal, complemented
21#34313C211yesmaximal, characteristic, complemented
22#34258C212yesmaximal, complemented
23C4×#550C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2212yes—
25#3498—216no—
26#3483—216no—
27C2×Q82C2211yescharacteristic, complemented
28C2×#555C2213yescomplemented
29C2×#555C2216yescomplemented
30C2×#550C2212yes—
31C2×#550C2211yescharacteristic
32C2×#550C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2213yescomplemented
35C2×#550C2212yescomplemented
36C2×#550C2212yescomplemented
37C2×#546C2216yescomplemented
38C2×#546C2216yescomplemented
39C2×D42C2213yes—
40C2×D42C2213yes—
41C2×D42C2216yes—
42C2×#535C2216yes—
43C2×#532C2213yes—
44C2×#532C2213yescomplemented
45C2×#532C2216yescomplemented
46C22×#127C2213yes—
47C2×#520C2212yescomplemented
48C2×C4×#41C2211yescharacteristic
49C2×C4×#41C2212yescomplemented
50C2×C4×#41C2211yescharacteristic, complemented
51C2×C4×#41C2213yescomplemented
52#2858C2213yescomplemented
53#2857C2213yescomplemented
54#2856C2213yescomplemented
55#2854C2216yescomplemented
56#2712C22112yescomplemented
57#2684C22112yescomplemented
58#2678C22112yescomplemented
59#2676C22112yescomplemented
60#2673C22112yescomplemented
61#2670C22112yescomplemented
62#2670C22112yescomplemented
63#2619C2216yescomplemented
64#2615C2216yescomplemented
65#2563C2213yescomplemented
66#2563C2213yescomplemented
67#2548C2213yescomplemented
68#2544C2216yescomplemented
69#2541C2213yescomplemented
70#2541C2216yescomplemented
71#2538C2213yescomplemented
72#2537C2213yescomplemented
73#2535C2216yescomplemented
74#2535C2216yescomplemented
75#2500C2216yescomplemented
76#2491C2216yescomplemented
77#2491C2216yescomplemented
78#2485C2216yescomplemented
79#2476C2216yescomplemented
80#2474C2216yescomplemented
81#2459C2216yescomplemented
82#2456C2216yescomplemented
83#2452C2216yescomplemented
84#2451C2211yescharacteristic, complemented
85#2445C2213yescomplemented
86#2445C2216yescomplemented
87#2445C2216yescomplemented
88#2439C2213yescomplemented
89#2439C2216yescomplemented
90#2435C2216yescomplemented
91#2433C2216yescomplemented
92#2433C2216yescomplemented
93#2433C2216yescomplemented
94#2431C2216yescomplemented
95#2431C2213yescomplemented
96#2428C2216yescomplemented
97#2428C2216yescomplemented
98#2428C2216yescomplemented
99#2428C2216yescomplemented
100#2426C2213yescomplemented
101#2424C22112yescomplemented
102#2424C22112yescomplemented
103#2422C2216yescomplemented
104#2420C2216yescomplemented
105#2420C2213yescomplemented
106#2416C2216yescomplemented
107#2416C2216yescomplemented
108#2414C2213yescomplemented
109#2414C2216yescomplemented
110#2414C2216yescomplemented
111#2411C22112yescomplemented
112#2410C22112yescomplemented
113#2408C2216yescomplemented
114#2408C2216yescomplemented
115#2408C2216yescomplemented
116#2408C2216yescomplemented
117#2408C2216yescomplemented
118#2407C2213yescomplemented
119#2404C22112yescomplemented
120#2392C2216yescomplemented
121#2388C2216yescomplemented
122#2366C2213yescomplemented
123#2366C2213yescomplemented
124#2363C2213yescomplemented
125#2363C2213yescomplemented
126#2361C2216yescomplemented
127#2354C2213yescomplemented
128#2351C2212yescomplemented
129Q8×C4⋊C4C2211yescharacteristic, complemented
130Q8×C4⋊C4C2211yescharacteristic, complemented
131D4×C4⋊C4C2213yescomplemented
132#2341C2212yes—
133#2341C2211yescharacteristic
134#2341C2212yescomplemented
135#2341C2212yescomplemented
136#2341C2212yescomplemented
137#2341C2212yescomplemented
138#2341C2211yescharacteristic, complemented
139D4×C22⋊C4C2216yescomplemented
140D4×C22⋊C4C2216yescomplemented
141D4×C22⋊C4C2216yescomplemented
142D4×C22⋊C4C2216yescomplemented
143D4×C22⋊C4C2216yescomplemented
144#2324C2216yescomplemented
145#2311C2216yescomplemented
146#2309C2216yescomplemented
147C4×#127C2213yescomplemented
148C4×#127C2213yescomplemented
149C4×#124C2213yescomplemented
150C4×C22⋊Q8C2213yescomplemented
151C4×#123C2216yescomplemented
152C4×#121C2213yescomplemented
153C4×#121C2213yescomplemented
154C4×#121C2213yescomplemented
155#2297C2216yescomplemented
156#2293C2213yescomplemented
157C2×#390C2216yescomplemented
158C42×Q8C2211yescharacteristic, complemented
159C42×D4C2213yescomplemented
160C2×H(5,𝔽2)—216no—
161C2×H(5,𝔽2)—216no—
162C2×H(5,𝔽2)—48no—
163C22×#41C2312yes—
164C22×#41C2311yescharacteristic
165C22×#41C2316yes—
166C22×#41C2313yes—
167C22×#41C2312yes—
168C22×#41C2311yescharacteristic
169C22×#41C2316yes—
170C23×D4C2316yes—
171C23×D4C2316yes—
172C23×D4C2316yes—
173C23×D4C2316yes—
174C23×D4C2316yes—
175Q82—28no—
176#555—248no—
177#555—224no—
178#550—216no—
179#550—216no—
180#550—28no—
181#550—224no—
182#550—28no—
183#550—48no—
184#550D4116yescomplemented
185#546—424no—
186#546—424no—
187D42—224no—
188D42—248no—
189D42—224no—
190#535—248no—
191#532—224no—
192#532—248no—
193#532—224no—
194C2×C4⋊Q8C2313yes—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2316yes—
197C2×#127—224no—
198C2×#127C2313yes—
199C2×#127C2313yes—
200C2×#127C2313yes—
201C2×#127C2316yes—
202C2×#127C2316yes—
203C2×#127C2316yes—
204C2×#127C2316yes—
205C2×#127C2313yes—
206C2×#124C23112yes—
207C2×#124C2316yes—
208C2×#124C2316yes—
209C2×#124C2313yes—
210C2×#124C2316yes—
211C2×#124C2316yes—
212C2×#123C2316yes—
213C2×#123C23112yes—
214C2×C22⋊Q8C2313yes—
215C2×C22⋊Q8C2316yes—
216C2×#121C2316yes—
217C2×#121C2313yes—
218C2×#121C2316yes—
219C2×#121C2313yes—
220C2×#121C2313yes—
221C2×#121C2316yes—
222C2×#121C2316yes—
223C2×#121C23112yes—
224C2×#121C2313yes—
225C2×#121C2316yes—
226C2×#121C2316yes—
227C2×#121C2316yes—
228C2×#121C2316yes—
229C2×#121C2316yes—
230C2×#121C2316yes—
231C2×#121C2316yes—
232C2×#121C2313yes—
233C2×#121C23112yes—
234C2×#121C23112yes—
235C2×#121C2316yes—
236C2×#120C23112yes—
237C2×#120C23112yes—
238C2×#120C23112yes—
239C2×#120C23112yes—
240C2×#120C23112yes—
241#520—48no—
242C4×#41—216no—
243C4×#41—28no—
244C4×#41—28no—
245C4×#41—224no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2313yes—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4C2313yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2313yes—
258C2×C4×D4C2316yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2313yes—
263C2×C4×D4C2313yes—
264C2×C4×D4C2313yes—
265C2×C4×D4C2316yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2313yes—
269C2×C4×D4C2316yes—
270C2×C4×D4C2316yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2316yes—
273C2×C4×D4C2316yes—
274C2×C4×D4C2316yes—
275C2×C4×D4C2313yes—
276C2×#117C2316yes—
277C2×#117C2313yes—
278C2×#117C2313yes—
279C2×#117C2316yes—
280C2×#117C2313yes—
281C2×#117C2316yes—
282C22×C4⋊C4C2316yes—
283C22×C22⋊C4C23112yes—
284C22×C22⋊C4C23112yes—
285C22×C42C2316yes—
286C22×C42C2313yes—
287C22×C42C2313yes—
288#398C2312yes—
289#397C2316yes—
290#397C23112yes—
291#396C2316yes—
292#396C2316yes—
293#396C23112yes—
294#395C2312yes—
295#394C2316yes—
296#394C23112yes—
297#394C2316yes—
298#394C2316yes—
299#394C2316yes—
300#394C2316yes—
301#394C2316yes—
302#394C23112yes—
303#394C23112yes—
304#394C23112yes—
305#394C23112yes—
306#394C23112yes—
307#393C23112yes—
308#393C23112yes—
309#393C2316yes—
310#392C23112yes—
311#392C23112yes—
312#392C23112yes—
313#392C23112yes—
314#392C23112yes—
315#392C2316yes—
316#392C2316yes—
317#392C2316yes—
318#392C2316yes—
319#392C23112yes—
320#391C2316yes—
321#391C2316yes—
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2312yes—
325#390C2313yes—
326#390C2313yes—
327#390C2316yes—
328#390C2316yes—
329#390C2313yes—
330#390C2316yes—
331#390C2316yes—
332#390C2316yes—
333#390C2316yes—
334#390C2316yes—
335#390C23112yes—
336#390C2316yes—
337#390C2316yes—
338#390C2316yes—
339#390C2313yes—
340#390C2313yes—
341#390C2316yes—
342#390C2316yes—
343#390C2316yes—
344#390C2316yes—
345#390C2316yes—
346#390C2313yes—
347#390C2316yes—
348#390C2313yes—
349#390C2313yes—
350#390C2316yes—
351#389C2316yes—
352#389C2313yes—
353#389C2316yes—
354#389C2313yes—
355#389C2316yes—
356#389C2313yes—
357#389C2313yes—
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#388C2316yes—
361#388C2316yes—
362#388C23112yes—
363#388C2316yes—
364#388C2316yes—
365#388C2316yes—
366#388C2316yes—
367#388C2316yes—
368#388C2316yes—
369#388C2316yes—
370#387C2316yes—
371#387C2316yes—
372#387C2312yes—
373#386C23112yes—
374#386C23112yes—
375#386C23112yes—
376#386C2316yes—
377#386C2316yes—
378#386C2316yes—
379#386C2316yes—
380#386C23112yes—
381#386C23112yes—
382#386C2316yes—
383#386C2316yes—
384#386C2316yes—
385#386C23112yes—
386#386C2316yes—
387#385C23112yes—
388#385C2316yes—
389#385C2316yes—
390#384C2313yes—
391#384C2313yes—
392#382C2313yes—
393#382C2316yes—
394#381C2316yes—
395#380C2313yes—
396#380C2316yes—
397#380C2316yes—
398#380C2316yes—
399#380C2313yes—
400#380C2316yes—
401#380C2316yes—
402#380C2316yes—
403#380C2313yes—
404#380C2313yes—
405#379C23112yes—
406#379C23112yes—
407#379C23112yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C4⋊C4C2313yes—
412C4×C4⋊C4C2316yes—
413C4×C4⋊C4C2313yes—
414C4×C4⋊C4C2313yes—
415C4×C4⋊C4C2311yescharacteristic
416C4×C22⋊C4C2313yes—
417C4×C22⋊C4C2313yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2313yes—
425C4×C22⋊C4C2313yes—
426C4×C22⋊C4C2313yes—
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—212no—
441C2×#41—212no—
442C2×#41—224no—
443C2×#41—224no—
444C2×#41—224no—
445C2×#41—412no—
446C2×#41—412no—
447C2×#41—46no—
448C2×#41—86no—
449C2×#41C2×D4116yes—
450C2×#41#4118yescomplemented
451C22×Q8C2412yes—
452C22×Q8C2411yescharacteristic
453C22×Q8C2416yes—
454C22×Q8C2411yescharacteristic
455C22×D4—224no—
456C22×D4—224no—
457C22×D4—224no—
458C22×D4—224no—
459C22×D4—224no—
460C22×D4—224no—
461C22×D4—224no—
462C22×D4—224no—
463C22×D4—412no—
464C22×D4—412no—
465C22×D4—412no—
466C22×D4—412no—
467C22×D4—412no—
468C22×D4—412no—
469C22×D4—86no—
470C22×D4C2413yes—
471C22×D4C2413yes—
472C22×D4C2416yes—
473C22×D4C2413yes—
474C22×D4C2416yes—
475C22×D4C2416yes—
476C22×D4C2416yes—
477C22×D4C2416yes—
478C22×D4C2416yes—
479C22×D4C2416yes—
480C22×D4C2413yes—
481C22×D4C2413yes—
482C22×D4C2416yes—
483C22×D4C24112yes—
484C22×D4C24112yes—
485C22×D4C2416yes—
486C22×D4C2416yes—
487C22×D4C24112yes—
488C22×D4C2416yes—
489C23×C4C2413yes—
490C23×C4C2413yes—
491C23×C4C2413yes—
492C23×C4C2416yes—
493C23×C4C2416yes—
494C23×C4C2416yes—
495C23×C4C2413yes—
496C23×C4C2413yes—
497C23×C4C2416yes—
498C23×C4C2413yes—
499C23×C4C24112yes—
500C4⋊Q8—24no—
501C4⋊Q8—224no—
502C4⋊Q8—212no—
503#127—212no—
504#127—224no—
505#127—224no—
506#127—224no—
507#127—212no—
508#127—212no—
509#127—412no—
510#127C2×D4124yes—
511#124—212no—
512#124—224no—
513#124—224no—
514#124—248no—
515#124—412no—
516#124—86no—
517#123—224no—
518#123—424no—
519C22⋊Q8—212no—
520C22⋊Q8—412no—
521#121—212no—
522#121—224no—
523#121—224no—
524#121—248no—
525#121—224no—
526#121—212no—
527#121—224no—
528#121—224no—
529#121—212no—
530#121—212no—
531#121—224no—
532#121—224no—
533#121—412no—
534#121—424no—
535#121—424no—
536#121—46no—
537#121—412no—
538#121—412no—
539#121—412no—
540#121C2×D4148yes—
541#120—248no—
542#120—248no—
543#120—424no—
544#120—424no—
545#120—812no—
546C4×Q8—24no—
547C4×Q8—24no—
548C4×Q8—28no—
549C4×Q8—24no—
550C4×Q8—24no—
551C4×Q8—28no—
552C4×Q8—24no—
553C4×Q8—212no—
554C4×Q8C2×D418yes—
555C4×D4—224no—
556C4×D4—212no—
557C4×D4—224no—
558C4×D4—224no—
559C4×D4—224no—
560C4×D4—212no—
561C4×D4—212no—
562C4×D4—212no—
563C4×D4—212no—
564C4×D4—224no—
565C4×D4—212no—
566C4×D4—212no—
567C4×D4—212no—
568C4×D4—412no—
569C4×D4—412no—
570C4×D4—412no—
571C4×D4—412no—
572C4×D4—46no—
573C4×D4—412no—
574C4×D4—412no—
575C4×D4C2×D4124yes—
576#117—224no—
577#117—212no—
578#117—212no—
579#117—212no—
580#117—224no—
581#117—412no—
582C2×C4⋊C4—412no—
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⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2413yes—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2416yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2416yes—
603C2×C4⋊C4C2416yes—
604C2×C4⋊C4C2413yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2413yes—
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⋊C4C24112yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2413yes—
624C2×C22⋊C4C2413yes—
625C2×C22⋊C4C2413yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C24112yes—
630C2×C22⋊C4C24112yes—
631C2×C22⋊C4C24112yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C24112yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C2413yes—
639C2×C22⋊C4C2413yes—
640C2×C22⋊C4C2416yes—
641C2×C22⋊C4C2416yes—
642C2×C22⋊C4C24112yes—
643C2×C22⋊C4C2416yes—
644C2×C22⋊C4C2416yes—
645C2×C22⋊C4C2416yes—
646C2×C42—224no—
647C2×C42—212no—
648C2×C42—212no—
649C2×C42C2413yes—
650C2×C42C2416yes—
651C2×C42C2413yes—
652C2×C42C2413yes—
653C2×C42C2416yes—
654C2×C42C2413yes—
655C2×C42C2413yes—
656C2×C42C2413yes—
657C2×C42C2411yescharacteristic
658C2×C42C2412yes—
659C2×C42C2413yes—
660C2×C42C2411yescharacteristic
661C2×C42C2416yes—
662C2×C42C2413yes—
663C2×C42C2411yescharacteristic
664C2×C42C2413yes—
665C2×C42C2413yes—
666#95C2411yescharacteristic
667#95C2411yescharacteristic
668#95C2412yes—
669#95C2412yes—
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2413yes—
674#95C2413yes—
675#95C2413yes—
676#95C2413yes—
677#95C2416yes—
678#95C2416yes—
679#95C2416yes—
680#95C2416yes—
681#95C2416yes—
682#95C2412yes—
683#95C2416yes—
684#95C2416yes—
685#95C2416yes—
686#95C24112yes—
687C24—224no—
688C24—224no—
689C24—412no—
690C24—412no—
691C24—412no—
692C24—412no—
693C24—412no—
694C24C2516yes—
695C24C2513yes—
696C24C2516yes—
697C24C2513yes—
698#41—264no—
699#41—232no—
700#41—496no—
701#41—448no—
702#41—416no—
703#41—432no—
704#41—848no—
705C2×Q8—22no—
706C2×Q8—24no—
707C2×Q8—212no—
708C2×Q8—24no—
709C2×Q8—22no—
710C2×Q8—42no—
711C2×Q8—46no—
712C2×Q8—46no—
713C2×Q8C22×D414yes—
714C2×Q8C2×#4114yes—
715C2×Q8H(5,𝔽2)14yes—
716C2×Q8H(5,𝔽2)14yescomplemented
717C2×D4—212no—
718C2×D4—212no—
719C2×D4—212no—
720C2×D4—212no—
721C2×D4—26no—
722C2×D4—212no—
723C2×D4—212no—
724C2×D4—224no—
725C2×D4—224no—
726C2×D4—212no—
727C2×D4—26no—
728C2×D4—26no—
729C2×D4—26no—
730C2×D4—212no—
731C2×D4—212no—
732C2×D4—212no—
733C2×D4—212no—
734C2×D4—26no—
735C2×D4—212no—
736C2×D4—212no—
737C2×D4—212no—
738C2×D4—26no—
739C2×D4—26no—
740C2×D4—26no—
741C2×D4—212no—
742C2×D4—212no—
743C2×D4—26no—
744C2×D4—26no—
745C2×D4—212no—
746C2×D4—26no—
747C2×D4—26no—
748C2×D4—496no—
749C2×D4—496no—
750C2×D4—46no—
751C2×D4—43no—
752C2×D4—46no—
753C2×D4—46no—
754C2×D4—46no—
755C2×D4—46no—
756C2×D4—46no—
757C2×D4—46no—
758C2×D4—46no—
759C2×D4—46no—
760C2×D4—412no—
761C2×D4—46no—
762C2×D4—46no—
763C2×D4—412no—
764C2×D4—412no—
765C2×D4—46no—
766C2×D4—46no—
767C2×D4—46no—
768C2×D4—412no—
769C2×D4—412no—
770C2×D4—412no—
771C2×D4—412no—
772C2×D4—496no—
773C2×D4—848no—
774C2×D4—848no—
775C2×D4C22×D4124yes—
776C2×D4C22×D4112yes—
777C2×D4C22×D4124yes—
778C2×D4C2×#41112yes—
779C22×C4—26no—
780C22×C4—212no—
781C22×C4—212no—
782C22×C4—26no—
783C22×C4—212no—
784C22×C4—212no—
785C22×C4—26no—
786C22×C4—26no—
787C22×C4—26no—
788C22×C4—26no—
789C22×C4—26no—
790C22×C4—212no—
791C22×C4—26no—
792C22×C4—212no—
793C22×C4—212no—
794C22×C4—212no—
795C22×C4—26no—
796C22×C4—26no—
797C22×C4—26no—
798C22×C4—26no—
799C22×C4—26no—
800C22×C4—212no—
801C22×C4—26no—
802C22×C4—26no—
803C22×C4—43no—
804C22×C4—46no—
805C22×C4—43no—
806C22×C4—46no—
807C22×C4—412no—
808C22×C4—412no—
809C22×C4—412no—
810C22×C4C22×D4124yes—
811C22×C4C2×#41112yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2513yes—
815C22×C4C2513yes—
816C22×C4C2513yes—
817C22×C4C2516yes—
818C22×C4C2516yes—
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C22×C4C2513yes—
822C22×C4C2513yes—
823C22×C4C2512yes—
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C22×C4C2512yes—
829C22×C4C2513yes—
830C22×C4C2511yescharacteristic
831C4⋊C4—24no—
832C4⋊C4—26no—
833C4⋊C4—26no—
834C4⋊C4—212no—
835C4⋊C4—212no—
836C4⋊C4—26no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—26no—
841C4⋊C4—26no—
842C4⋊C4—212no—
843C4⋊C4—26no—
844C4⋊C4—212no—
845C4⋊C4—212no—
846C4⋊C4—22no—
847C4⋊C4—46no—
848C4⋊C4—42no—
849C4⋊C4—43no—
850C4⋊C4—42no—
851C4⋊C4—46no—
852C4⋊C4—46no—
853C4⋊C4C22×D414yes—
854C4⋊C4C22×D4112yes—
855C4⋊C4H(5,𝔽2)14yescomplemented
856C22⋊C4—224no—
857C22⋊C4—212no—
858C22⋊C4—212no—
859C22⋊C4—26no—
860C22⋊C4—212no—
861C22⋊C4—212no—
862C22⋊C4—212no—
863C22⋊C4—212no—
864C22⋊C4—212no—
865C22⋊C4—26no—
866C22⋊C4—26no—
867C22⋊C4—212no—
868C22⋊C4—212no—
869C22⋊C4—212no—
870C22⋊C4—26no—
871C22⋊C4—212no—
872C22⋊C4—212no—
873C22⋊C4—212no—
874C22⋊C4—46no—
875C22⋊C4—412no—
876C22⋊C4—412no—
877C22⋊C4—412no—
878C22⋊C4—46no—
879C22⋊C4—46no—
880C22⋊C4—43no—
881C22⋊C4—43no—
882C22⋊C4—412no—
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⋊C4C22×D4124yes—
892C42—24no—
893C42—26no—
894C42—22no—
895C42—22no—
896C42—26no—
897C42—212no—
898C42—26no—
899C42—26no—
900C42—212no—
901C42—26no—
902C42—26no—
903C42—212no—
904C42—26no—
905C42—26no—
906C42—22no—
907C42—43no—
908C42C22×D4112yes—
909C23—23no—
910C23—26no—
911C23—23no—
912C23—23no—
913C23—26no—
914C23—26no—
915C23—26no—
916C23—23no—
917C23—23no—
918C23—26no—
919C23—23no—
920C23—26no—
921C23—23no—
922C23—26no—
923C23—23no—
924C23—26no—
925C23—26no—
926C23—26no—
927C23—23no—
928C23—23no—
929C23—23no—
930C23—26no—
931C23—23no—
932C23—26no—
933C23—26no—
934C23—23no—
935C23—448no—
936C23—824no—
937C23—824no—
938C23—824no—
939C23—824no—
940C23—1612no—
941C23—1612no—
942C23C23×D4112yes—
943C23C22×#4116yes—
944C23C2611yescharacteristic
945Q8—28no—
946Q8—48no—
947Q8—812no—
948Q8#546116yescomplemented
949D4—224no—
950D4—248no—
951D4—224no—
952D4—424no—
953D4—412no—
954D4—424no—
955D4—424no—
956D4—424no—
957D4—424no—
958D4—424no—
959D4—424no—
960D4—412no—
961D4—412no—
962D4—812no—
963D4—812no—
964D4—824no—
965D4—824no—
966D4—812no—
967D4—1612no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—23no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—23no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—248no—
983C2×C4—224no—
984C2×C4—23no—
985C2×C4—21no—
986C2×C4—23no—
987C2×C4—26no—
988C2×C4—22no—
989C2×C4—23no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—23no—
995C2×C4—23no—
996C2×C4—23no—
997C2×C4—26no—
998C2×C4—23no—
999C2×C4—26no—
1000C2×C4—26no—
1001C2×C4—26no—
1002C2×C4—23no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—23no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—23no—
1009C2×C4—23no—
1010C2×C4—21no—
1011C2×C4—23no—
1012C2×C4—22no—
1013C2×C4—26no—
1014C2×C4—412no—
1015C2×C4—412no—
1016C2×C4—424no—
1017C2×C4—424no—
1018C2×C4—424no—
1019C2×C4—412no—
1020C2×C4—412no—
1021C2×C4—412no—
1022C2×C4—1612no—
1023C2×C4C23×D414yes—
1024C2×C4C23×D416yes—
1025C2×C4C23×D416yes—
1026C2×C4C23×D412yes—
1027C2×C4C22×#4112yes—
1028C2×C4C22×#4116yes—
1029C2×C4C2×H(5,𝔽2)12yes—
1030C2×C4C2×H(5,𝔽2)14yes—
1031C2×C4C2×H(5,𝔽2)12yes—
1032C2×C4C2×H(5,𝔽2)12yes—
1033C2×C4C2×H(5,𝔽2)16yes—
1034C2×C4C2×H(5,𝔽2)12yes—
1035C2×C4#58512yes—
1036C22—212no—
1037C22—26no—
1038C22—212no—
1039C22—26no—
1040C22—26no—
1041C22—212no—
1042C22—43no—
1043C22—46no—
1044C22—46no—
1045C22—43no—
1046C22—43no—
1047C22—46no—
1048C22—46no—
1049C22—43no—
1050C22—43no—
1051C22—46no—
1052C22—43no—
1053C22—46no—
1054C22—43no—
1055C22—46no—
1056C22—43no—
1057C22—46no—
1058C22—43no—
1059C22—46no—
1060C22—43no—
1061C22—46no—
1062C22—46no—
1063C22—43no—
1064C22—1648no—
1065C22C24×D411yescharacteristic
1066C22C23×#4111yescharacteristic
1067C22C22×H(5,𝔽2)11yescharacteristic
1068C22C22×H(5,𝔽2)11yescharacteristic
1069C22C22×H(5,𝔽2)11yescharacteristic
1070C22C2×#58511yescharacteristic
1071C22H(7,𝔽2)11yescharacteristic
1072C4—22no—
1073C4—22no—
1074C4—26no—
1075C4—24no—
1076C4—22no—
1077C4—24no—
1078C4—22no—
1079C4—46no—
1080C4—43no—
1081C4—43no—
1082C4—46no—
1083C4—43no—
1084C4—43no—
1085C4—41no—
1086C4—42no—
1087C4—41no—
1088C4—42no—
1089C4C2×#546112yes—
1090C4#348814yes—
1091C2—412no—
1092C2—46no—
1093C2—83no—
1094C2—86no—
1095C2C22×#54611yescharacteristic
1096C2C2×#348811yescharacteristic
1097C2#6280011yescharacteristic
1098C2#6292311yescharacteristic
1099C2D4×H(5,𝔽2)11yescharacteristic
1100C2#6298611yescharacteristic
1101C2#6304011yescharacteristic
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×#3483C2semidirect
3. #59412C2semidirect
4. #59124C2semidirect
5. #59095C2semidirect
6. #59041C2semidirect
7. #44929C2semidirect
8. #44887C2semidirect
9. #39469C2semidirect
10. #38953C2semidirect
11. #37782C2semidirect
12. #36457C2semidirect
13. #36456C2semidirect
14. #36455C2semidirect
15. #36433C2semidirect
16. #36258C2semidirect
17. #36121C2semidirect
18. #36091C2semidirect
19. #36029C2semidirect
20. #34715C2semidirect
21. #34313C2semidirect
22. #34258C2semidirect
23. C4×#550C2semidirect
27. C2×Q82C22semidirect
28. C2×#555C22semidirect
29. C2×#555C22semidirect
34. C2×#550C22semidirect
35. C2×#550C22semidirect
36. C2×#550C22semidirect
37. C2×#546C22semidirect
38. C2×#546C22semidirect
44. C2×#532C22semidirect
45. C2×#532C22semidirect
47. C2×#520C22semidirect
49. C2×C4×#41C22semidirect
50. C2×C4×#41C22semidirect
51. C2×C4×#41C22semidirect
52. #2858C22semidirect
53. #2857C22semidirect
54. #2856C22semidirect
55. #2854C22semidirect
56. #2712C22semidirect
57. #2684C22semidirect
58. #2678C22semidirect
59. #2676C22semidirect
60. #2673C22semidirect
61. #2670C22semidirect
62. #2670C22semidirect
63. #2619C22semidirect
64. #2615C22semidirect
65. #2563C22semidirect
66. #2563C22semidirect
67. #2548C22semidirect
68. #2544C22semidirect
69. #2541C22semidirect
70. #2541C22semidirect
71. #2538C22semidirect
72. #2537C22semidirect
73. #2535C22semidirect
74. #2535C22semidirect
75. #2500C22semidirect
76. #2491C22semidirect
77. #2491C22semidirect
78. #2485C22semidirect
79. #2476C22semidirect
80. #2474C22semidirect
81. #2459C22semidirect
82. #2456C22semidirect
83. #2452C22semidirect
84. #2451C22semidirect
85. #2445C22semidirect
86. #2445C22semidirect
87. #2445C22semidirect
88. #2439C22semidirect
89. #2439C22semidirect
90. #2435C22semidirect
91. #2433C22semidirect
92. #2433C22semidirect
93. #2433C22semidirect
94. #2431C22semidirect
95. #2431C22semidirect
96. #2428C22semidirect
97. #2428C22semidirect
98. #2428C22semidirect
99. #2428C22semidirect
100. #2426C22semidirect
101. #2424C22semidirect
102. #2424C22semidirect
103. #2422C22semidirect
104. #2420C22semidirect
105. #2420C22semidirect
106. #2416C22semidirect
107. #2416C22semidirect
108. #2414C22semidirect
109. #2414C22semidirect
110. #2414C22semidirect
111. #2411C22semidirect
112. #2410C22semidirect
113. #2408C22semidirect
114. #2408C22semidirect
115. #2408C22semidirect
116. #2408C22semidirect
117. #2408C22semidirect
118. #2407C22semidirect
119. #2404C22semidirect
120. #2392C22semidirect
121. #2388C22semidirect
122. #2366C22semidirect
123. #2366C22semidirect
124. #2363C22semidirect
125. #2363C22semidirect
126. #2361C22semidirect
127. #2354C22semidirect
128. #2351C22semidirect
129. Q8×C4⋊C4C22semidirect
130. Q8×C4⋊C4C22semidirect
131. D4×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. #2324C22semidirect
145. #2311C22semidirect
146. #2309C22semidirect
147. C4×#127C22semidirect
148. C4×#127C22semidirect
149. C4×#124C22semidirect
150. C4×C22⋊Q8C22semidirect
151. C4×#123C22semidirect
152. C4×#121C22semidirect
153. C4×#121C22semidirect
154. C4×#121C22semidirect
155. #2297C22semidirect
156. #2293C22semidirect
157. C2×#390C22semidirect
158. C42×Q8C22semidirect
159. C42×D4C22semidirect
184. #550D4semidirect
450. C2×#41#41semidirect
716. C2×Q8H(5,𝔽2)semidirect
855. C4⋊C4H(5,𝔽2)semidirect
948. 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×#34832
#594122
#591242
#590952
#590412
#449292
#448872
#394692
#389532
#377822
#364572
#364562
#364552
#364332
#362582
#361212
#360912
#360292
#347152
#343132
#342582
C4×#5502