Finite Group Databasebeta

← #7691292

Subgroups — #7691292

Order 512.

8941 conjugacy classes of subgroups.

The subgroup lattice has 1083 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3498C211yesmaximal, characteristic, complemented
2C2×#3522C211yesmaximal, characteristic, complemented
3#59808C216yesmaximal, complemented
4#59420C213yesmaximal, complemented
5#59143C213yesmaximal, complemented
6#59041C213yesmaximal, complemented
7#44874C216yesmaximal, complemented
8#44871C216yesmaximal, complemented
9#39470C213yesmaximal, complemented
10#39438C216yesmaximal, complemented
11#38910C213yesmaximal, complemented
12#36576C211yesmaximal, characteristic, complemented
13#36457C211yesmaximal, characteristic, complemented
14#36456C211yesmaximal, characteristic, complemented
15#36430C212yesmaximal, complemented
16#36289C213yesmaximal, complemented
17#36121C213yesmaximal, complemented
18#36082C212yesmaximal, complemented
19#36076C212yesmaximal, complemented
20#34889C213yesmaximal, complemented
21#34258C212yesmaximal, complemented
22C4×#550C211yesmaximal, characteristic, complemented
23C4×#548C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2212yes—
25#3522—216no—
26#3498—216no—
27C2×#559C2213yescomplemented
28C2×Q82C2211yescharacteristic, complemented
29C2×#554C2213yescomplemented
30C2×#550C2212yes—
31C2×#550C2211yescharacteristic
32C2×#550C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#548C2212yescomplemented
35C2×#548C2212yescomplemented
36C2×#547C2216yescomplemented
37C2×#546C2216yescomplemented
38C2×D42C2213yes—
39C2×D42C2216yes—
40C2×D42C2213yes—
41C2×#542C2216yescomplemented
42C2×#535C2216yes—
43C2×#532C2213yes—
44C2×#532C2213yescomplemented
45C22×#127C2213yes—
46C2×#529C2213yescomplemented
47C2×#520C2212yescomplemented
48C2×C4×#41C2211yescharacteristic
49C2×C4×#41C2212yescomplemented
50C22×C4×Q8C2211yescharacteristic, complemented
51#2858C2213yescomplemented
52#2857C2213yescomplemented
53#2856C2213yescomplemented
54#2850C2216yescomplemented
55#2709C22112yescomplemented
56#2700C22112yescomplemented
57#2697C22112yescomplemented
58#2685C22112yescomplemented
59#2684C22112yescomplemented
60#2681C22112yescomplemented
61#2678C22112yescomplemented
62#2624C2216yescomplemented
63#2616C2216yescomplemented
64#2563C2213yescomplemented
65#2563C2213yescomplemented
66#2559C2216yescomplemented
67#2557C2216yescomplemented
68#2550C2213yescomplemented
69#2548C2213yescomplemented
70#2548C2213yescomplemented
71#2544C2213yescomplemented
72#2544C2216yescomplemented
73#2544C2216yescomplemented
74#2540C2213yescomplemented
75#2538C2213yescomplemented
76#2538C2213yescomplemented
77#2535C2216yescomplemented
78#2535C2213yescomplemented
79#2534C22112yescomplemented
80#2521C2216yescomplemented
81#2504C2216yescomplemented
82#2492C2211yescharacteristic, complemented
83#2491C2216yescomplemented
84#2491C2216yescomplemented
85#2490C2216yescomplemented
86#2490C2213yescomplemented
87#2486C2216yescomplemented
88#2472C22112yescomplemented
89#2472C22112yescomplemented
90#2464C2216yescomplemented
91#2452C2216yescomplemented
92#2445C2216yescomplemented
93#2445C2216yescomplemented
94#2445C2216yescomplemented
95#2439C2216yescomplemented
96#2435C2216yescomplemented
97#2435C2216yescomplemented
98#2435C2216yescomplemented
99#2435C2216yescomplemented
100#2435C2216yescomplemented
101#2431C2216yescomplemented
102#2428C2213yescomplemented
103#2428C2216yescomplemented
104#2427C2216yescomplemented
105#2427C2213yescomplemented
106#2426C2216yescomplemented
107#2420C2216yescomplemented
108#2420C2216yescomplemented
109#2420C2216yescomplemented
110#2416C2216yescomplemented
111#2415C2216yescomplemented
112#2414C2216yescomplemented
113#2408C2216yescomplemented
114#2408C2216yescomplemented
115#2408C2216yescomplemented
116#2408C2216yescomplemented
117#2405C22112yescomplemented
118#2404C22112yescomplemented
119#2395C2216yescomplemented
120#2388C2216yescomplemented
121#2367C2213yescomplemented
122#2366C2213yescomplemented
123#2363C2216yescomplemented
124#2362C2213yescomplemented
125#2361C2213yescomplemented
126#2354C2213yescomplemented
127#2352C2213yescomplemented
128#2351C2212yescomplemented
129#2351C2211yescharacteristic, complemented
130Q8×C4⋊C4C2211yescharacteristic, complemented
131#2341C2212yes—
132#2341C2211yescharacteristic
133#2341C2212yescomplemented
134#2341C2212yescomplemented
135#2341C2212yescomplemented
136#2341C2212yescomplemented
137Q8×C22⋊C4C2211yescharacteristic, complemented
138D4×C22⋊C4C2216yescomplemented
139D4×C22⋊C4C2216yescomplemented
140D4×C22⋊C4C2216yescomplemented
141D4×C22⋊C4C2216yescomplemented
142D4×C22⋊C4C2216yescomplemented
143D4×C22⋊C4C2216yescomplemented
144#2311C2216yescomplemented
145#2309C2216yescomplemented
146C4×#127C2213yescomplemented
147C4×#124C2213yescomplemented
148C4×#124C2213yescomplemented
149C4×C22⋊Q8C2213yescomplemented
150C4×C22⋊Q8C2213yescomplemented
151C4×#121C2216yescomplemented
152C4×#121C2216yescomplemented
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×#41C2316yes—
165C22×#41C2312yes—
166C22×#41C2311yescharacteristic
167C22×#41C2316yes—
168C23×Q8C2311yescharacteristic
169C23×D4C2316yes—
170C23×D4C2316yes—
171C23×D4C2316yes—
172C23×D4C2316yes—
173C23×D4C2316yes—
174#559—224no—
175Q82—28no—
176#554—224no—
177#550—216no—
178#550—28no—
179#550D4116yescomplemented
180#548—216no—
181#548—28no—
182#548—48no—
183#547—248no—
184#546—424no—
185D42—224no—
186D42—248no—
187D42—224no—
188#542—248no—
189#535—248no—
190#532—224no—
191#532—224no—
192C2×C4⋊Q8C2313yes—
193C2×C4⋊Q8C2311yescharacteristic
194C2×C4⋊Q8C2316yes—
195C2×#127—224no—
196C2×#127C2313yes—
197C2×#127C2313yes—
198C2×#127C2316yes—
199C2×#127C2316yes—
200C2×#127C2313yes—
201#529—224no—
202C2×#126C2316yes—
203C2×#125C2313yes—
204C2×#124C2313yes—
205C2×#124C2313yes—
206C2×#124C2316yes—
207C2×#124C2316yes—
208C2×#124C2316yes—
209C2×#124C2316yes—
210C2×#124C2316yes—
211C2×#124C2313yes—
212C2×#124C2316yes—
213C2×#123C23112yes—
214C2×#123C2316yes—
215C2×#123C23112yes—
216C2×C22⋊Q8C2316yes—
217C2×C22⋊Q8C2313yes—
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C23112yes—
220C2×C22⋊Q8C2316yes—
221C2×C22⋊Q8C2316yes—
222C2×C22⋊Q8C2313yes—
223C2×#121C2316yes—
224C2×#121C2313yes—
225C2×#121C2313yes—
226C2×#121C2316yes—
227C2×#121C2316yes—
228C2×#121C2313yes—
229C2×#121C2316yes—
230C2×#121C2313yes—
231C2×#121C2316yes—
232C2×#121C2316yes—
233C2×#121C2313yes—
234C2×#121C2316yes—
235C2×#121C2316yes—
236C2×#121C2316yes—
237C2×#120C23112yes—
238C2×#120C23112yes—
239C2×#120C23112yes—
240#520—216no—
241C4×#41—28no—
242C4×#41—48no—
243C2×C4×Q8—28no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2313yes—
251C2×C4×Q8C2313yes—
252C2×C4×Q8C2313yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4C2313yes—
255C2×C4×D4C2313yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2316yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2316yes—
264C2×C4×D4C2313yes—
265C2×C4×D4C2316yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2313yes—
269C2×C4×D4C2316yes—
270C2×C4×D4C2313yes—
271C2×C4×D4C2313yes—
272C2×#117C2316yes—
273C2×#117C2313yes—
274C2×#117C2316yes—
275C22×C4⋊C4C2316yes—
276C22×C4⋊C4C2313yes—
277C22×C22⋊C4C23112yes—
278C22×C22⋊C4C23112yes—
279C22×C42C2313yes—
280C22×C42C2313yes—
281C22×C42C2316yes—
282#400C2312yes—
283#399C2316yes—
284#398C2316yes—
285#397C23112yes—
286#397C2316yes—
287#397C2316yes—
288#397C2316yes—
289#397C23112yes—
290#396C23112yes—
291#396C23112yes—
292#395C2316yes—
293#394C23112yes—
294#394C23112yes—
295#394C23112yes—
296#394C23112yes—
297#394C23112yes—
298#394C2316yes—
299#394C2316yes—
300#394C2316yes—
301#394C2316yes—
302#394C2316yes—
303#394C23112yes—
304#394C23112yes—
305#394C23112yes—
306#394C23112yes—
307#393C23112yes—
308#393C23112yes—
309#393C2312yes—
310#392C2316yes—
311#392C2316yes—
312#392C2316yes—
313#392C23112yes—
314#391C2316yes—
315#391C2313yes—
316#391C2313yes—
317#391C2316yes—
318#391C2311yescharacteristic
319#391C2312yes—
320#391C2311yescharacteristic
321#390C2316yes—
322#390C2316yes—
323#390C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C2313yes—
327#390C2316yes—
328#390C23112yes—
329#390C2316yes—
330#390C2316yes—
331#390C2316yes—
332#390C2313yes—
333#390C2313yes—
334#390C2313yes—
335#390C2316yes—
336#390C2316yes—
337#390C2316yes—
338#390C2316yes—
339#390C2316yes—
340#390C2316yes—
341#390C2316yes—
342#390C2316yes—
343#390C2316yes—
344#389C2313yes—
345#389C2316yes—
346#389C2316yes—
347#389C2313yes—
348#389C2313yes—
349#389C2316yes—
350#389C2316yes—
351#389C2313yes—
352#388C2316yes—
353#388C23112yes—
354#388C2316yes—
355#388C23112yes—
356#388C2316yes—
357#388C2316yes—
358#388C2316yes—
359#388C2316yes—
360#388C2312yes—
361#388C2316yes—
362#387C2316yes—
363#387C2316yes—
364#386C23112yes—
365#386C23112yes—
366#386C2316yes—
367#386C2316yes—
368#386C2316yes—
369#386C2316yes—
370#386C23112yes—
371#386C23112yes—
372#386C23112yes—
373#386C23112yes—
374#386C2316yes—
375#386C23112yes—
376#386C2316yes—
377#386C2316yes—
378#386C2316yes—
379#385C2316yes—
380#385C2316yes—
381#384C2313yes—
382#382C2313yes—
383#382C2316yes—
384#382C2313yes—
385#381C23112yes—
386#380C2313yes—
387#380C2316yes—
388#380C2316yes—
389#380C2316yes—
390#380C2313yes—
391#380C2316yes—
392#380C2316yes—
393#380C2313yes—
394#380C2316yes—
395#380C2316yes—
396#380C2311yescharacteristic
397#379C23112yes—
398#379C23112yes—
399#379C23112yes—
400#379C23112yes—
401#379C23112yes—
402C4×C4⋊C4C2313yes—
403C4×C4⋊C4C2313yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2316yes—
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C4⋊C4C2311yescharacteristic
412C4×C22⋊C4C2313yes—
413C4×C22⋊C4C2313yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2313yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2313yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2313yes—
424C4×C22⋊C4C2311yescharacteristic
425C4×C22⋊C4C2316yes—
426C43C2313yes—
427C25C24112yes—
428H(5,𝔽2)—4128no—
429C2×#41—24no—
430C2×#41—28no—
431C2×#41—28no—
432C2×#41—28no—
433C2×#41—28no—
434C2×#41—24no—
435C2×#41—28no—
436C2×#41—224no—
437C2×#41—224no—
438C2×#41—224no—
439C2×#41—412no—
440C2×#41—412no—
441C2×#41—86no—
442C2×#41C2×D4116yes—
443C2×#41#4118yescomplemented
444C22×Q8—24no—
445C22×Q8—24no—
446C22×Q8—24no—
447C22×Q8C2411yescharacteristic
448C22×Q8C2413yes—
449C22×Q8C2412yes—
450C22×Q8C2416yes—
451C22×Q8C2411yescharacteristic
452C22×D4—224no—
453C22×D4—224no—
454C22×D4—224no—
455C22×D4—224no—
456C22×D4—224no—
457C22×D4—224no—
458C22×D4—224no—
459C22×D4—224no—
460C22×D4—412no—
461C22×D4—412no—
462C22×D4—412no—
463C22×D4—412no—
464C22×D4—412no—
465C22×D4—412no—
466C22×D4—86no—
467C22×D4C2413yes—
468C22×D4C2416yes—
469C22×D4C2413yes—
470C22×D4C2416yes—
471C22×D4C2416yes—
472C22×D4C2416yes—
473C22×D4C2416yes—
474C22×D4C2416yes—
475C22×D4C2413yes—
476C22×D4C2416yes—
477C22×D4C2413yes—
478C22×D4C2416yes—
479C22×D4C2416yes—
480C22×D4C24112yes—
481C22×D4C2416yes—
482C23×C4C2413yes—
483C23×C4C2411yescharacteristic
484C23×C4C2413yes—
485C23×C4C2416yes—
486C23×C4C2413yes—
487C23×C4C2413yes—
488C23×C4C2416yes—
489C23×C4C2413yes—
490C23×C4C24112yes—
491C23×C4C2416yes—
492C23×C4C2416yes—
493C4⋊Q8—24no—
494C4⋊Q8—224no—
495C4⋊Q8—212no—
496#127—212no—
497#127—224no—
498#127—224no—
499#127—212no—
500#127C2×D4124yes—
501#126—224no—
502#125—212no—
503#124—212no—
504#124—224no—
505#124—224no—
506#124—212no—
507#124—224no—
508#124—412no—
509#124—46no—
510#124—412no—
511#124—86no—
512#123—248no—
513#123—224no—
514#123—424no—
515C22⋊Q8—224no—
516C22⋊Q8—212no—
517C22⋊Q8—24no—
518C22⋊Q8—248no—
519C22⋊Q8—412no—
520C22⋊Q8—46no—
521C22⋊Q8—412no—
522#121—212no—
523#121—212no—
524#121—224no—
525#121—224no—
526#121—212no—
527#121—224no—
528#121—212no—
529#121—224no—
530#121—224no—
531#121—224no—
532#121—46no—
533#121—412no—
534#121—412no—
535#121C2×D4148yes—
536#120—248no—
537#120—248no—
538#120—424no—
539C4×Q8—24no—
540C4×Q8—24no—
541C4×Q8—28no—
542C4×Q8—24no—
543C4×Q8—24no—
544C4×Q8—28no—
545C4×Q8—212no—
546C4×Q8—212no—
547C4×Q8—212no—
548C4×Q8C2×D418yes—
549C4×D4—224no—
550C4×D4—224no—
551C4×D4—224no—
552C4×D4—224no—
553C4×D4—224no—
554C4×D4—212no—
555C4×D4—212no—
556C4×D4—212no—
557C4×D4—212no—
558C4×D4—212no—
559C4×D4—46no—
560C4×D4—46no—
561C4×D4—412no—
562C4×D4—412no—
563C4×D4—46no—
564C4×D4—412no—
565C4×D4—412no—
566C4×D4C2×D4124yes—
567#117—224no—
568#117—212no—
569#117—412no—
570C2×C4⋊C4—224no—
571C2×C4⋊C4—212no—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2413yes—
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2413yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C2413yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C22⋊C4—424no—
598C2×C22⋊C4—812no—
599C2×C22⋊C4C2413yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2411yescharacteristic
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C24112yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2413yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C24112yes—
617C2×C22⋊C4C24112yes—
618C2×C22⋊C4C24112yes—
619C2×C22⋊C4C24112yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C24112yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2413yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2413yes—
627C2×C22⋊C4C24112yes—
628C2×C22⋊C4C24112yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2411yescharacteristic
636C2×C42—212no—
637C2×C42—212no—
638C2×C42—412no—
639C2×C42C2413yes—
640C2×C42C2413yes—
641C2×C42C2416yes—
642C2×C42C2413yes—
643C2×C42C2413yes—
644C2×C42C2411yescharacteristic
645C2×C42C2413yes—
646C2×C42C2416yes—
647C2×C42C2413yes—
648C2×C42C2413yes—
649C2×C42C2413yes—
650C2×C42C2413yes—
651C2×C42C2411yescharacteristic
652C2×C42C2416yes—
653C2×C42C2413yes—
654C2×C42C2412yes—
655C2×C42C2413yes—
656#95C2412yes—
657#95C2411yescharacteristic
658#95C2411yescharacteristic
659#95C2412yes—
660#95C2412yes—
661#95C2412yes—
662#95C2412yes—
663#95C2413yes—
664#95C2413yes—
665#95C2416yes—
666#95C2413yes—
667#95C2413yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C2416yes—
674#95C2416yes—
675#95C2412yes—
676#95C2416yes—
677#95C2416yes—
678#95C24112yes—
679C24—224no—
680C24—224no—
681C24—412no—
682C24—412no—
683C24—412no—
684C24—412no—
685C24—412no—
686C24C2516yes—
687C24C2516yes—
688C24C2513yes—
689C24C2511yescharacteristic
690#41—264no—
691#41—232no—
692#41—496no—
693#41—432no—
694#41—848no—
695C2×Q8—22no—
696C2×Q8—26no—
697C2×Q8—24no—
698C2×Q8—212no—
699C2×Q8—26no—
700C2×Q8—24no—
701C2×Q8—26no—
702C2×Q8—22no—
703C2×Q8—22no—
704C2×Q8—42no—
705C2×Q8—46no—
706C2×Q8—46no—
707C2×Q8—416no—
708C2×Q8C22×D414yes—
709C2×Q8C2×#4114yes—
710C2×Q8H(5,𝔽2)14yes—
711C2×D4—212no—
712C2×D4—212no—
713C2×D4—212no—
714C2×D4—212no—
715C2×D4—26no—
716C2×D4—212no—
717C2×D4—212no—
718C2×D4—26no—
719C2×D4—212no—
720C2×D4—224no—
721C2×D4—212no—
722C2×D4—26no—
723C2×D4—26no—
724C2×D4—212no—
725C2×D4—212no—
726C2×D4—212no—
727C2×D4—212no—
728C2×D4—212no—
729C2×D4—212no—
730C2×D4—212no—
731C2×D4—26no—
732C2×D4—212no—
733C2×D4—212no—
734C2×D4—26no—
735C2×D4—26no—
736C2×D4—26no—
737C2×D4—26no—
738C2×D4—496no—
739C2×D4—496no—
740C2×D4—46no—
741C2×D4—43no—
742C2×D4—46no—
743C2×D4—46no—
744C2×D4—46no—
745C2×D4—46no—
746C2×D4—46no—
747C2×D4—46no—
748C2×D4—46no—
749C2×D4—46no—
750C2×D4—46no—
751C2×D4—46no—
752C2×D4—412no—
753C2×D4—412no—
754C2×D4—496no—
755C2×D4—848no—
756C2×D4—848no—
757C2×D4C22×D4112yes—
758C2×D4C22×D4124yes—
759C2×D4C22×D4124yes—
760C2×D4C2×#41112yes—
761C22×C4—26no—
762C22×C4—212no—
763C22×C4—212no—
764C22×C4—26no—
765C22×C4—26no—
766C22×C4—224no—
767C22×C4—22no—
768C22×C4—26no—
769C22×C4—26no—
770C22×C4—26no—
771C22×C4—26no—
772C22×C4—212no—
773C22×C4—26no—
774C22×C4—212no—
775C22×C4—26no—
776C22×C4—26no—
777C22×C4—212no—
778C22×C4—22no—
779C22×C4—26no—
780C22×C4—22no—
781C22×C4—26no—
782C22×C4—212no—
783C22×C4—43no—
784C22×C4—43no—
785C22×C4—46no—
786C22×C4—46no—
787C22×C4—412no—
788C22×C4—46no—
789C22×C4—412no—
790C22×C4—46no—
791C22×C4—46no—
792C22×C4C22×D4124yes—
793C22×C4C2×#41112yes—
794C22×C4C2513yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2511yescharacteristic
798C22×C4C2513yes—
799C22×C4C2513yes—
800C22×C4C2516yes—
801C22×C4C2513yes—
802C22×C4C2516yes—
803C22×C4C2511yescharacteristic
804C22×C4C2512yes—
805C22×C4C2513yes—
806C22×C4C2513yes—
807C22×C4C2512yes—
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2513yes—
812C22×C4C2511yescharacteristic
813C4⋊C4—26no—
814C4⋊C4—212no—
815C4⋊C4—212no—
816C4⋊C4—212no—
817C4⋊C4—24no—
818C4⋊C4—26no—
819C4⋊C4—24no—
820C4⋊C4—22no—
821C4⋊C4—26no—
822C4⋊C4—212no—
823C4⋊C4—212no—
824C4⋊C4—26no—
825C4⋊C4—26no—
826C4⋊C4—26no—
827C4⋊C4—212no—
828C4⋊C4—26no—
829C4⋊C4—212no—
830C4⋊C4—22no—
831C4⋊C4—26no—
832C4⋊C4—43no—
833C4⋊C4—46no—
834C4⋊C4—46no—
835C4⋊C4—46no—
836C4⋊C4C22×D4112yes—
837C4⋊C4C22×D414yes—
838C22⋊C4—212no—
839C22⋊C4—212no—
840C22⋊C4—212no—
841C22⋊C4—224no—
842C22⋊C4—212no—
843C22⋊C4—26no—
844C22⋊C4—212no—
845C22⋊C4—212no—
846C22⋊C4—24no—
847C22⋊C4—212no—
848C22⋊C4—212no—
849C22⋊C4—22no—
850C22⋊C4—26no—
851C22⋊C4—212no—
852C22⋊C4—412no—
853C22⋊C4—412no—
854C22⋊C4—46no—
855C22⋊C4—46no—
856C22⋊C4—46no—
857C22⋊C4—412no—
858C22⋊C4—412no—
859C22⋊C4—46no—
860C22⋊C4—46no—
861C22⋊C4—43no—
862C22⋊C4—43no—
863C22⋊C4—42no—
864C22⋊C4—412no—
865C22⋊C4—46no—
866C22⋊C4—412no—
867C22⋊C4—46no—
868C22⋊C4—412no—
869C22⋊C4—46no—
870C22⋊C4—46no—
871C22⋊C4—46no—
872C22⋊C4—46no—
873C22⋊C4C22×D4124yes—
874C22⋊C4H(5,𝔽2)14yescomplemented
875C42—22no—
876C42—26no—
877C42—26no—
878C42—26no—
879C42—26no—
880C42—26no—
881C42—212no—
882C42—26no—
883C42—26no—
884C42—212no—
885C42—26no—
886C42—22no—
887C42—26no—
888C42—42no—
889C42—46no—
890C42—43no—
891C42C22×D4112yes—
892C23—21no—
893C23—23no—
894C23—21no—
895C23—26no—
896C23—23no—
897C23—21no—
898C23—26no—
899C23—26no—
900C23—23no—
901C23—21no—
902C23—23no—
903C23—23no—
904C23—26no—
905C23—26no—
906C23—21no—
907C23—23no—
908C23—21no—
909C23—26no—
910C23—26no—
911C23—26no—
912C23—26no—
913C23—26no—
914C23—26no—
915C23—26no—
916C23—26no—
917C23—448no—
918C23—824no—
919C23—824no—
920C23—824no—
921C23—824no—
922C23—1612no—
923C23—1612no—
924C23C23×D4112yes—
925C23C22×#4116yes—
926C23C2×H(5,𝔽2)12yes—
927C23C2611yescharacteristic
928Q8—48no—
929Q8—412no—
930Q8—44no—
931Q8—812no—
932Q8#546116yescomplemented
933D4—224no—
934D4—248no—
935D4—224no—
936D4—424no—
937D4—424no—
938D4—424no—
939D4—424no—
940D4—412no—
941D4—424no—
942D4—424no—
943D4—424no—
944D4—412no—
945D4—812no—
946D4—812no—
947D4—824no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—23no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—23no—
957C2×C4—21no—
958C2×C4—248no—
959C2×C4—224no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—23no—
963C2×C4—23no—
964C2×C4—23no—
965C2×C4—26no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—23no—
969C2×C4—23no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—23no—
973C2×C4—26no—
974C2×C4—23no—
975C2×C4—23no—
976C2×C4—26no—
977C2×C4—26no—
978C2×C4—23no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—23no—
982C2×C4—23no—
983C2×C4—21no—
984C2×C4—22no—
985C2×C4—26no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—23no—
990C2×C4—23no—
991C2×C4—21no—
992C2×C4—23no—
993C2×C4—22no—
994C2×C4—23no—
995C2×C4—26no—
996C2×C4—412no—
997C2×C4—412no—
998C2×C4—424no—
999C2×C4—412no—
1000C2×C4—44no—
1001C2×C4—412no—
1002C2×C4—812no—
1003C2×C4—824no—
1004C2×C4—812no—
1005C2×C4C23×D416yes—
1006C2×C4C23×D414yes—
1007C2×C4C23×D416yes—
1008C2×C4C23×D412yes—
1009C2×C4C22×#4112yes—
1010C2×C4C22×#4116yes—
1011C2×C4C2×H(5,𝔽2)12yes—
1012C2×C4C2×H(5,𝔽2)12yes—
1013C2×C4C2×H(5,𝔽2)16yes—
1014C2×C4#58512yes—
1015C2×C4#58512yes—
1016C22—22no—
1017C22—212no—
1018C22—26no—
1019C22—22no—
1020C22—22no—
1021C22—26no—
1022C22—212no—
1023C22—26no—
1024C22—212no—
1025C22—43no—
1026C22—41no—
1027C22—46no—
1028C22—46no—
1029C22—43no—
1030C22—46no—
1031C22—41no—
1032C22—43no—
1033C22—46no—
1034C22—41no—
1035C22—43no—
1036C22—41no—
1037C22—46no—
1038C22—46no—
1039C22—46no—
1040C22—46no—
1041C22—46no—
1042C22—46no—
1043C22—46no—
1044C22—1648no—
1045C22C24×D411yescharacteristic
1046C22C23×#4111yescharacteristic
1047C22C22×H(5,𝔽2)11yescharacteristic
1048C22C22×H(5,𝔽2)11yescharacteristic
1049C22C2×#58511yescharacteristic
1050C22C2×#58511yescharacteristic
1051C22H(7,𝔽2)11yescharacteristic
1052C4—22no—
1053C4—26no—
1054C4—22no—
1055C4—24no—
1056C4—22no—
1057C4—43no—
1058C4—46no—
1059C4—41no—
1060C4—46no—
1061C4—43no—
1062C4—41no—
1063C4—43no—
1064C4—42no—
1065C4—43no—
1066C4—42no—
1067C4—42no—
1068C4—43no—
1069C4C2×#546112yes—
1070C4#350014yes—
1071C2—42no—
1072C2—412no—
1073C2—46no—
1074C2—86no—
1075C2C22×#54611yescharacteristic
1076C2#6280011yescharacteristic
1077C2C2×#350011yescharacteristic
1078C2#6292311yescharacteristic
1079C2D4×H(5,𝔽2)11yescharacteristic
1080C2#6301011yescharacteristic
1081C2#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×#3522C2semidirect
3. #59808C2semidirect
4. #59420C2semidirect
5. #59143C2semidirect
6. #59041C2semidirect
7. #44874C2semidirect
8. #44871C2semidirect
9. #39470C2semidirect
10. #39438C2semidirect
11. #38910C2semidirect
12. #36576C2semidirect
13. #36457C2semidirect
14. #36456C2semidirect
15. #36430C2semidirect
16. #36289C2semidirect
17. #36121C2semidirect
18. #36082C2semidirect
19. #36076C2semidirect
20. #34889C2semidirect
21. #34258C2semidirect
22. C4×#550C2semidirect
23. C4×#548C2semidirect
27. C2×#559C22semidirect
28. C2×Q82C22semidirect
29. C2×#554C22semidirect
34. C2×#548C22semidirect
35. C2×#548C22semidirect
36. C2×#547C22semidirect
37. C2×#546C22semidirect
41. C2×#542C22semidirect
44. C2×#532C22semidirect
46. C2×#529C22semidirect
47. C2×#520C22semidirect
49. C2×C4×#41C22semidirect
50. C22×C4×Q8C22semidirect
51. #2858C22semidirect
52. #2857C22semidirect
53. #2856C22semidirect
54. #2850C22semidirect
55. #2709C22semidirect
56. #2700C22semidirect
57. #2697C22semidirect
58. #2685C22semidirect
59. #2684C22semidirect
60. #2681C22semidirect
61. #2678C22semidirect
62. #2624C22semidirect
63. #2616C22semidirect
64. #2563C22semidirect
65. #2563C22semidirect
66. #2559C22semidirect
67. #2557C22semidirect
68. #2550C22semidirect
69. #2548C22semidirect
70. #2548C22semidirect
71. #2544C22semidirect
72. #2544C22semidirect
73. #2544C22semidirect
74. #2540C22semidirect
75. #2538C22semidirect
76. #2538C22semidirect
77. #2535C22semidirect
78. #2535C22semidirect
79. #2534C22semidirect
80. #2521C22semidirect
81. #2504C22semidirect
82. #2492C22semidirect
83. #2491C22semidirect
84. #2491C22semidirect
85. #2490C22semidirect
86. #2490C22semidirect
87. #2486C22semidirect
88. #2472C22semidirect
89. #2472C22semidirect
90. #2464C22semidirect
91. #2452C22semidirect
92. #2445C22semidirect
93. #2445C22semidirect
94. #2445C22semidirect
95. #2439C22semidirect
96. #2435C22semidirect
97. #2435C22semidirect
98. #2435C22semidirect
99. #2435C22semidirect
100. #2435C22semidirect
101. #2431C22semidirect
102. #2428C22semidirect
103. #2428C22semidirect
104. #2427C22semidirect
105. #2427C22semidirect
106. #2426C22semidirect
107. #2420C22semidirect
108. #2420C22semidirect
109. #2420C22semidirect
110. #2416C22semidirect
111. #2415C22semidirect
112. #2414C22semidirect
113. #2408C22semidirect
114. #2408C22semidirect
115. #2408C22semidirect
116. #2408C22semidirect
117. #2405C22semidirect
118. #2404C22semidirect
119. #2395C22semidirect
120. #2388C22semidirect
121. #2367C22semidirect
122. #2366C22semidirect
123. #2363C22semidirect
124. #2362C22semidirect
125. #2361C22semidirect
126. #2354C22semidirect
127. #2352C22semidirect
128. #2351C22semidirect
129. #2351C22semidirect
130. Q8×C4⋊C4C22semidirect
133. #2341C22semidirect
134. #2341C22semidirect
135. #2341C22semidirect
136. #2341C22semidirect
137. Q8×C22⋊C4C22semidirect
138. D4×C22⋊C4C22semidirect
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×#124C22semidirect
148. C4×#124C22semidirect
149. C4×C22⋊Q8C22semidirect
150. C4×C22⋊Q8C22semidirect
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
179. #550D4semidirect
443. C2×#41#41semidirect
874. C22⋊C4H(5,𝔽2)semidirect
932. 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×#35222
#598082
#594202
#591432
#590412
#448742
#448712
#394702
#394382
#389102
#365762
#364572
#364562
#364302
#362892
#361212
#360822
#360762
#348892
#342582
C4×#5502
C4×#5482