Finite Group Databasebeta

← #7655534

Subgroups — #7655534

Order 512.

8303 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#42987C213yesmaximal, complemented
4#42986C213yesmaximal, complemented
5#42911C213yesmaximal, complemented
6#42910C213yesmaximal, complemented
7#39953C216yesmaximal, complemented
8#39948C216yesmaximal, complemented
9#39881C216yesmaximal, complemented
10#39876C216yesmaximal, complemented
11#37550C213yesmaximal, complemented
12#36467C212yesmaximal, complemented
13#36465C212yesmaximal, complemented
14#36434C212yesmaximal, complemented
15#36430C212yesmaximal, complemented
16#36091C211yesmaximal, characteristic, complemented
17#36082C211yesmaximal, characteristic, complemented
18#35757C211yesmaximal, characteristic, complemented
19#35687C211yesmaximal, characteristic, complemented
20#35131C213yesmaximal, complemented
21#35129C213yesmaximal, complemented
22#34977C213yesmaximal, complemented
23#34125C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25C22×H(5,𝔽2)C2211yescharacteristic
26#3500—216no—
27#3480—216no—
28C2×#559C2213yescomplemented
29C2×#557C2211yescharacteristic, complemented
30C2×#556C2213yescomplemented
31C2×#553C2213yescomplemented
32C2×#553C2213yescomplemented
33C2×#550C2211yescharacteristic
34C2×#550C2212yes—
35C2×D4×Q8C2212yescomplemented
36C2×#548C2212yes—
37C2×#548C2212yes—
38C2×#548C2211yescharacteristic
39C2×#548C2212yes—
40C2×#548C2211yescharacteristic, complemented
41C2×#548C2212yescomplemented
42C2×#546C2216yes—
43C2×#546C2216yes—
44C2×#536C2213yes—
45C2×#535C2213yes—
46C2×#532C2213yes—
47C2×#532C2213yescomplemented
48C2×#529C2213yescomplemented
49C2×#529C2213yescomplemented
50C22×#124C2213yes—
51C2×C4×#41C2211yescharacteristic
52C2×C4×#41C2213yescomplemented
53C2×C4×#41C2211yescharacteristic, complemented
54C22×C4×Q8C2211yescharacteristic, complemented
55#2861C2216yescomplemented
56#2858C2216yescomplemented
57#2850C2216yescomplemented
58#2850C2216yescomplemented
59#2821C2216yescomplemented
60#2818C2216yescomplemented
61#2718C22112yescomplemented
62#2710C22112yescomplemented
63#2706C22112yescomplemented
64#2703C22112yescomplemented
65#2685C22112yescomplemented
66#2678C22112yescomplemented
67#2670C22112yescomplemented
68#2669C22112yescomplemented
69#2662C2216yescomplemented
70#2662C2216yescomplemented
71#2661C22112yescomplemented
72#2635C22112yescomplemented
73#2632C2216yescomplemented
74#2631C2216yescomplemented
75#2616C2213yes—
76#2616C2213yescomplemented
77#2615C2213yes—
78#2615C2213yescomplemented
79#2610C2213yescomplemented
80#2610C2216yescomplemented
81#2610C2213yescomplemented
82#2610C2211yescharacteristic, complemented
83#2610C2213yescomplemented
84#2592C2216yescomplemented
85#2567C2213yescomplemented
86#2563C2213yescomplemented
87#2562C2216yescomplemented
88#2548C2213yescomplemented
89#2545C2216yescomplemented
90#2544C2216yescomplemented
91#2542C2216yescomplemented
92#2541C2216yescomplemented
93#2541C2213yescomplemented
94#2540C2216yescomplemented
95#2540C2216yescomplemented
96#2540C2216yescomplemented
97#2540C2216yescomplemented
98#2536C2216yescomplemented
99#2535C2216yescomplemented
100#2500C2216yescomplemented
101#2492C2216yescomplemented
102#2491C2216yescomplemented
103#2490C2216yescomplemented
104#2489C2216yescomplemented
105#2482C2216yescomplemented
106#2436C2213yescomplemented
107#2435C2216yes—
108#2435C2213yes—
109#2434C2213yescomplemented
110#2433C2216yes—
111#2433C2213yes—
112#2432C2216yescomplemented
113#2431C2216yescomplemented
114#2431C2216yescomplemented
115#2429C2216yescomplemented
116#2428C2216yescomplemented
117#2427C2216yescomplemented
118#2426C2216yescomplemented
119#2417C2216yescomplemented
120#2416C2216yescomplemented
121#2415C2216yescomplemented
122#2414C2216yescomplemented
123#2414C2216yescomplemented
124#2414C2216yescomplemented
125#2411C22112yescomplemented
126#2409C2213yescomplemented
127#2409C2213yescomplemented
128#2408C2216yes—
129#2408C2216yes—
130#2408C2213yes—
131#2408C2213yes—
132#2407C2216yescomplemented
133#2407C2216yescomplemented
134#2404C2216yescomplemented
135#2388C2213yes—
136#2388C2213yes—
137#2388C2213yescomplemented
138#2388C2213yescomplemented
139#2357C2216yescomplemented
140#2351C2212yescomplemented
141#2347C2213yescomplemented
142#2347C2213yescomplemented
143#2341C2211yescharacteristic
144#2341C2211yescharacteristic
145#2341C2212yes—
146#2341C2212yes—
147Q8×C22⋊C4C2212yescomplemented
148Q8×C22⋊C4C2212yescomplemented
149#2321C2216yescomplemented
150#2321C2216yescomplemented
151#2321C22112yescomplemented
152C4×#127C2216yescomplemented
153C4×#124C2216yescomplemented
154C4×#121C2216yescomplemented
155C4×#121C2216yescomplemented
156#2293C2216yescomplemented
157#2283C2213yescomplemented
158C42×Q8C2212yescomplemented
159C4×#117C2213yescomplemented
160C2×2−1+4—28no—
161C2×2−1+4—48no—
162C2×H(5,𝔽2)—28no—
163C2×H(5,𝔽2)—48no—
164C22×#41C2312yes—
165C22×#41C2311yescharacteristic
166C22×#41C2311yescharacteristic
167C22×#41C2313yes—
168C22×#41C2313yes—
169C22×#41C2316yes—
170C22×#41C2313yes—
171C23×Q8C2312yes—
172C23×Q8C2311yescharacteristic
173C23×Q8C2313yes—
174C23×D4C2313yes—
175C23×D4C2316yes—
176#559—224no—
177#557—28no—
178#556—224no—
179#553—224no—
180#553—224no—
181#550—28no—
182#550—48no—
183D4×Q8—48no—
184#548—28no—
185#548—216no—
186#548—216no—
187#548—28no—
188#548—48no—
189#548—48no—
190#546—248no—
191#546—248no—
192#536—224no—
193#535—224no—
194#532—224no—
195#532—224no—
196C2×C4⋊Q8C2313yes—
197C2×C4⋊Q8C2313yes—
198C2×C4⋊Q8C2316yes—
199C2×#127C2313yes—
200C2×#127C2313yes—
201C2×#127C2316yes—
202C2×#127C2316yes—
203#529—224no—
204#529—224no—
205C2×#126C2316yes—
206C2×#126C2316yes—
207C2×#125C2313yes—
208C2×#125C2313yes—
209C2×#124—224no—
210C2×#124C2316yes—
211C2×#124C2316yes—
212C2×#124C2313yes—
213C2×#124C2313yes—
214C2×#124C2311yescharacteristic
215C2×#124C2316yes—
216C2×#124C2316yes—
217C2×#124C2313yes—
218C2×#124C2316yes—
219C2×#124C2316yes—
220C2×#124C2316yes—
221C2×#123C2316yes—
222C2×#123C2316yes—
223C2×#123C23112yes—
224C2×C22⋊Q8C2313yes—
225C2×C22⋊Q8C2316yes—
226C2×C22⋊Q8C2313yes—
227C2×C22⋊Q8C2316yes—
228C2×C22⋊Q8C2316yes—
229C2×C22⋊Q8C2316yes—
230C2×C22⋊Q8C2316yes—
231C2×C22⋊Q8C2316yes—
232C2×#121C2313yes—
233C2×#121C2316yes—
234C2×#121C2316yes—
235C2×#121C2313yes—
236C2×#121C2313yes—
237C2×#121C2316yes—
238C2×#121C2316yes—
239C2×#121C2313yes—
240C2×#121C2316yes—
241C2×#121C2316yes—
242C2×#121C2316yes—
243C2×#121C2316yes—
244C2×#121C2316yes—
245C2×#121C2316yes—
246C2×#121C2316yes—
247C2×#120C23112yes—
248C2×#120C2316yes—
249C2×#120C2316yes—
250C2×#120C23112yes—
251C4×#41—28no—
252C4×#41—224no—
253C4×#41D4116yescomplemented
254C2×C4×Q8—28no—
255C2×C4×Q8C2313yes—
256C2×C4×Q8C2313yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2313yes—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×D4C2313yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2313yes—
268C2×C4×D4C2316yes—
269C2×C4×D4C2313yes—
270C2×C4×D4C2313yes—
271C2×C4×D4C2313yes—
272C2×C4×D4C2313yes—
273C2×C4×D4C2313yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2316yes—
276C2×C4×D4C2316yes—
277C2×C4×D4C2316yes—
278C2×C4×D4C2316yes—
279C2×C4×D4C2316yes—
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×#117C2311yescharacteristic
283C2×#117C2313yes—
284C2×#117C2313yes—
285C2×#117C2313yes—
286C2×#117C2316yes—
287C2×#117C2313yes—
288C22×C4⋊C4C2313yes—
289C22×C22⋊C4C2316yes—
290C22×C22⋊C4C2316yes—
291C22×C42C2313yes—
292C22×C42C2313yes—
293C22×C42C2313yes—
294#400C23112yes—
295#399C23112yes—
296#399C23112yes—
297#398C23112yes—
298#397C23112yes—
299#397C23112yes—
300#396C23112yes—
301#396C23112yes—
302#395C2313yes—
303#395C2316yes—
304#395C2311yescharacteristic
305#395C2313yes—
306#395C2313yes—
307#394C23112yes—
308#394C2313yes—
309#394C2316yes—
310#394C23112yes—
311#394C2313yes—
312#394C2313yes—
313#394C2311yescharacteristic
314#394C23112yes—
315#394C23112yes—
316#394C2316yes—
317#394C2316yes—
318#394C2316yes—
319#394C2316yes—
320#394C23112yes—
321#394C23112yes—
322#393C2311yescharacteristic
323#393C2313yes—
324#393C2313yes—
325#393C2313yes—
326#393C2316yes—
327#393C23112yes—
328#392C2313yes—
329#392C2316yes—
330#392C23112yes—
331#392C23112yes—
332#392C2313yes—
333#392C2313yes—
334#392C2311yescharacteristic
335#392C23112yes—
336#392C23112yes—
337#392C23112yes—
338#392C2316yes—
339#392C2316yes—
340#392C2316yes—
341#392C2316yes—
342#391C2316yes—
343#391C2316yes—
344#391C2316yes—
345#391C2316yes—
346#391C2316yes—
347#390C2312yes—
348#390C2316yes—
349#390C2316yes—
350#390C2316yes—
351#390C2316yes—
352#390C2316yes—
353#390C23112yes—
354#390C23112yes—
355#390C23112yes—
356#390C2316yes—
357#390C2316yes—
358#390C2316yes—
359#390C2316yes—
360#390C2316yes—
361#390C2316yes—
362#390C2316yes—
363#390C2316yes—
364#390C2316yes—
365#389C2316yes—
366#389C2316yes—
367#389C2316yes—
368#389C2316yes—
369#388C2316yes—
370#388C23112yes—
371#388C2316yes—
372#388C2316yes—
373#388C23112yes—
374#388C23112yes—
375#388C23112yes—
376#388C23112yes—
377#388C23112yes—
378#388C2316yes—
379#388C23112yes—
380#388C23112yes—
381#388C2316yes—
382#388C2316yes—
383#388C2312yes—
384#388C2312yes—
385#386C2316yes—
386#386C23112yes—
387#386C23112yes—
388#386C23112yes—
389#386C2316yes—
390#386C2316yes—
391#386C23112yes—
392#386C2316yes—
393#386C2316yes—
394#386C2312yes—
395#385C2316yes—
396#385C23112yes—
397#385C2316yes—
398#384C2316yes—
399#383C2316yes—
400#382C2316yes—
401#382C2316yes—
402#381C2316yes—
403#380C2316yes—
404#380C2316yes—
405#380C2316yes—
406#380C2316yes—
407#380C2316yes—
408#380C2316yes—
409#380C2313yes—
410#380C2313yes—
411#379C2316yes—
412#379C23112yes—
413#379C2316yes—
414C4×C4⋊C4C2316yes—
415C4×C4⋊C4C2313yes—
416C4×C4⋊C4C2313yes—
417C4×C4⋊C4C2316yes—
418C4×C4⋊C4C2316yes—
419C4×C4⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2313yes—
425C4×C22⋊C4C2313yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428#376C2311yescharacteristic
429#376C2313yes—
430C43C2316yes—
431C25C2416yes—
4322−1+4—464no—
433H(5,𝔽2)—464no—
434C2×#41—24no—
435C2×#41—28no—
436C2×#41—28no—
437C2×#41—28no—
438C2×#41—28no—
439C2×#41—28no—
440C2×#41—224no—
441C2×#41—212no—
442C2×#41—212no—
443C2×#41—212no—
444C2×#41—412no—
445C2×#41—412no—
446C2×#41—46no—
447C2×#41—46no—
448C2×#41—412no—
449C2×#41—412no—
450C2×#41C2×D418yes—
451C22×Q8—24no—
452C22×Q8—28no—
453C22×Q8—28no—
454C22×Q8—28no—
455C22×Q8—28no—
456C22×Q8—212no—
457C22×Q8—412no—
458C22×Q8C2413yes—
459C22×Q8C2416yes—
460C22×Q8C2413yes—
461C22×Q8C2413yes—
462C22×Q8C2411yescharacteristic
463C22×Q8C2411yescharacteristic
464C22×D4—224no—
465C22×D4—212no—
466C22×D4—412no—
467C22×D4—412no—
468C22×D4—412no—
469C22×D4C2413yes—
470C22×D4C2416yes—
471C22×D4C2412yes—
472C22×D4C2413yes—
473C22×D4C2413yes—
474C22×D4C2413yes—
475C22×D4C2413yes—
476C22×D4C2416yes—
477C22×D4C2416yes—
478C22×D4C2416yes—
479C22×D4C2416yes—
480C22×D4C2416yes—
481C22×D4C2416yes—
482C22×D4C2416yes—
483C22×D4C2413yes—
484C22×D4C2411yescharacteristic
485C22×D4C2416yes—
486C22×D4C24112yes—
487C23×C4C2413yes—
488C23×C4C2413yes—
489C23×C4C2411yescharacteristic
490C23×C4C2416yes—
491C23×C4C2416yes—
492C23×C4C2413yes—
493C23×C4C2416yes—
494C23×C4C2413yes—
495C23×C4C2413yes—
496C23×C4C2413yes—
497C23×C4C2413yes—
498C23×C4C2413yes—
499C4⋊Q8—212no—
500C4⋊Q8—212no—
501C4⋊Q8—412no—
502#127—212no—
503#127—212no—
504#127—412no—
505#127—412no—
506#126—224no—
507#126—224no—
508#125—212no—
509#125—212no—
510#124—212no—
511#124—224no—
512#124—212no—
513#124—224no—
514#124—224no—
515#124—224no—
516#124—212no—
517#124—24no—
518#124—412no—
519#124—412no—
520#124—412no—
521#123—224no—
522#123—224no—
523#123—248no—
524C22⋊Q8—212no—
525C22⋊Q8—212no—
526C22⋊Q8—224no—
527C22⋊Q8—224no—
528C22⋊Q8—412no—
529C22⋊Q8—412no—
530C22⋊Q8—412no—
531C22⋊Q8—412no—
532#121—212no—
533#121—212no—
534#121—212no—
535#121—224no—
536#121—224no—
537#121—212no—
538#121—224no—
539#121—224no—
540#121—224no—
541#121—412no—
542#121—412no—
543#121—412no—
544#121—412no—
545#121—412no—
546#121—412no—
547#120—248no—
548#120—424no—
549#120—412no—
550#120—412no—
551C4×Q8—24no—
552C4×Q8—24no—
553C4×Q8—28no—
554C4×Q8—28no—
555C4×Q8—212no—
556C4×Q8—212no—
557C4×Q8—212no—
558C4×Q8—212no—
559C4×Q8C2×D418yes—
560C4×Q8C2×D418yes—
561C4×D4—212no—
562C4×D4—212no—
563C4×D4—212no—
564C4×D4—212no—
565C4×D4—224no—
566C4×D4—212no—
567C4×D4—212no—
568C4×D4—212no—
569C4×D4—212no—
570C4×D4—224no—
571C4×D4—224no—
572C4×D4—412no—
573C4×D4—412no—
574C4×D4—412no—
575C4×D4—412no—
576C4×D4C2×D4124yes—
577C4×D4C2×D4124yes—
578#117—212no—
579#117—212no—
580#117—24no—
581#117—212no—
582#117—412no—
583#117C2×D4124yes—
584C2×C4⋊C4—212no—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2413yes—
590C2×C4⋊C4C2413yes—
591C2×C4⋊C4C2413yes—
592C2×C4⋊C4C2413yes—
593C2×C4⋊C4C2413yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2416yes—
596C2×C4⋊C4C2416yes—
597C2×C4⋊C4C2416yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C2416yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2416yes—
603C2×C4⋊C4C2416yes—
604C2×C4⋊C4C2416yes—
605C2×C4⋊C4C24112yes—
606C2×C4⋊C4C2413yes—
607C2×C4⋊C4C2413yes—
608C2×C22⋊C4—224no—
609C2×C22⋊C4—224no—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C24112yes—
613C2×C22⋊C4C24112yes—
614C2×C22⋊C4C2411yescharacteristic
615C2×C22⋊C4C2411yescharacteristic
616C2×C22⋊C4C2413yes—
617C2×C22⋊C4C2413yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2413yes—
620C2×C22⋊C4C2413yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C2416yes—
640C2×C22⋊C4C2416yes—
641C2×C22⋊C4C24112yes—
642C2×C22⋊C4C24112yes—
643C2×C22⋊C4C24112yes—
644C2×C22⋊C4C24112yes—
645C2×C22⋊C4C2416yes—
646C2×C22⋊C4C2416yes—
647C2×C22⋊C4C2416yes—
648C2×C22⋊C4C2416yes—
649C2×C22⋊C4C2416yes—
650C2×C42—212no—
651C2×C42—212no—
652C2×C42C2×D4124yes—
653C2×C42C2411yescharacteristic
654C2×C42C2412yes—
655C2×C42C2413yes—
656C2×C42C2413yes—
657C2×C42C2413yes—
658C2×C42C2416yes—
659C2×C42C2416yes—
660C2×C42C2413yes—
661C2×C42C2413yes—
662C2×C42C2416yes—
663C2×C42C2416yes—
664C2×C42C2416yes—
665C2×C42C2411yescharacteristic
666C2×C42C2413yes—
667C2×C42C2413yes—
668C2×C42C2413yes—
669#95C2412yes—
670#95C2411yescharacteristic
671#95C2411yescharacteristic
672#95C2413yes—
673#95C2413yes—
674#95C2416yes—
675#95C2412yes—
676#95C2412yes—
677#95C2416yes—
678#95C2416yes—
679#95C2416yes—
680#95C2416yes—
681#95C24112yes—
682#95C2416yes—
683#95C2416yes—
684#95C24112yes—
685#95C24112yes—
686#95C24112yes—
687C24—212no—
688C24—412no—
689C24—412no—
690C24—46no—
691C24—46no—
692C24C2516yes—
693C24C2513yes—
694C24C2512yes—
695C24C2513yes—
696C24C2511yescharacteristic
697#41—232no—
698#41—448no—
699#41—448no—
700#41—448no—
701#41—496no—
702#41—416no—
703#41—432no—
704C2×Q8—26no—
705C2×Q8—26no—
706C2×Q8—212no—
707C2×Q8—26no—
708C2×Q8—22no—
709C2×Q8—212no—
710C2×Q8—212no—
711C2×Q8—212no—
712C2×Q8—26no—
713C2×Q8—46no—
714C2×Q8—43no—
715C2×Q8—42no—
716C2×Q8—448no—
717C2×Q8—416no—
718C2×Q8—432no—
719C2×Q8C22×D414yes—
720C2×Q8H(5,𝔽2)18yes—
721C2×D4—26no—
722C2×D4—26no—
723C2×D4—212no—
724C2×D4—212no—
725C2×D4—26no—
726C2×D4—24no—
727C2×D4—26no—
728C2×D4—212no—
729C2×D4—212no—
730C2×D4—26no—
731C2×D4—26no—
732C2×D4—212no—
733C2×D4—26no—
734C2×D4—22no—
735C2×D4—212no—
736C2×D4—212no—
737C2×D4—212no—
738C2×D4—212no—
739C2×D4—212no—
740C2×D4—212no—
741C2×D4—26no—
742C2×D4—24no—
743C2×D4—212no—
744C2×D4—42no—
745C2×D4—46no—
746C2×D4—46no—
747C2×D4—46no—
748C2×D4—43no—
749C2×D4—43no—
750C2×D4—43no—
751C2×D4—42no—
752C2×D4—46no—
753C2×D4—46no—
754C2×D4—448no—
755C2×D4—46no—
756C2×D4—46no—
757C2×D4—46no—
758C2×D4—412no—
759C2×D4—46no—
760C2×D4—46no—
761C2×D4—46no—
762C2×D4—46no—
763C2×D4—46no—
764C2×D4—46no—
765C2×D4—46no—
766C2×D4—46no—
767C2×D4—412no—
768C2×D4—412no—
769C2×D4—412no—
770C2×D4—496no—
771C2×D4C22×D4112yes—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—212no—
775C22×C4—22no—
776C22×C4—212no—
777C22×C4—26no—
778C22×C4—26no—
779C22×C4—26no—
780C22×C4—212no—
781C22×C4—212no—
782C22×C4—212no—
783C22×C4—212no—
784C22×C4—212no—
785C22×C4—212no—
786C22×C4—212no—
787C22×C4—212no—
788C22×C4—26no—
789C22×C4—26no—
790C22×C4—46no—
791C22×C4—412no—
792C22×C4—43no—
793C22×C4—43no—
794C22×C4—43no—
795C22×C4—43no—
796C22×C4—46no—
797C22×C4—46no—
798C22×C4C22×D4112yes—
799C22×C4C22×D4112yes—
800C22×C4C22×D4112yes—
801C22×C4C2516yes—
802C22×C4C2516yes—
803C22×C4C2511yescharacteristic
804C22×C4C2513yes—
805C22×C4C2513yes—
806C22×C4C2516yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2511yescharacteristic
810C22×C4C2513yes—
811C22×C4C2511yescharacteristic
812C22×C4C2511yescharacteristic
813C22×C4C2513yes—
814C22×C4C2513yes—
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2512yes—
818C22×C4C2513yes—
819C4⋊C4—26no—
820C4⋊C4—212no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—26no—
824C4⋊C4—26no—
825C4⋊C4—26no—
826C4⋊C4—26no—
827C4⋊C4—26no—
828C4⋊C4—212no—
829C4⋊C4—212no—
830C4⋊C4—212no—
831C4⋊C4—212no—
832C4⋊C4—212no—
833C4⋊C4—212no—
834C4⋊C4—46no—
835C4⋊C4—42no—
836C4⋊C4—46no—
837C4⋊C4—46no—
838C4⋊C4—46no—
839C4⋊C4—412no—
840C4⋊C4C22×D4112yes—
841C4⋊C4C22×D4112yes—
842C22⋊C4—26no—
843C22⋊C4—26no—
844C22⋊C4—212no—
845C22⋊C4—212no—
846C22⋊C4—212no—
847C22⋊C4—224no—
848C22⋊C4—224no—
849C22⋊C4—22no—
850C22⋊C4—22no—
851C22⋊C4—26no—
852C22⋊C4—212no—
853C22⋊C4—26no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—212no—
857C22⋊C4—212no—
858C22⋊C4—212no—
859C22⋊C4—212no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—46no—
863C22⋊C4—42no—
864C22⋊C4—42no—
865C22⋊C4—46no—
866C22⋊C4—46no—
867C22⋊C4—46no—
868C22⋊C4—46no—
869C22⋊C4—46no—
870C22⋊C4—46no—
871C22⋊C4—46no—
872C22⋊C4—412no—
873C22⋊C4—46no—
874C22⋊C4—412no—
875C22⋊C4—46no—
876C22⋊C4—46no—
877C22⋊C4—412no—
878C22⋊C4—412no—
879C22⋊C4—46no—
880C22⋊C4—46no—
881C22⋊C4C22×D4124yes—
882C42—22no—
883C42—26no—
884C42—26no—
885C42—26no—
886C42—26no—
887C42—26no—
888C42—212no—
889C42—212no—
890C42—24no—
891C42—46no—
892C42—46no—
893C42—46no—
894C42C22×D4112yes—
895C42C22×D414yes—
896C42C22×D4112yes—
897C42C22×D4112yes—
898C23—21no—
899C23—22no—
900C23—26no—
901C23—26no—
902C23—23no—
903C23—23no—
904C23—21no—
905C23—22no—
906C23—23no—
907C23—26no—
908C23—22no—
909C23—26no—
910C23—22no—
911C23—26no—
912C23—22no—
913C23—26no—
914C23—22no—
915C23—26no—
916C23—22no—
917C23—26no—
918C23—22no—
919C23—26no—
920C23—26no—
921C23—23no—
922C23—26no—
923C23—23no—
924C23—22no—
925C23—424no—
926C23—812no—
927C23—812no—
928C23—1612no—
929C23—1612no—
930C23C23×D416yes—
931C23#58512yes—
932C23C2611yescharacteristic
933Q8—412no—
934Q8—412no—
935Q8—44no—
936Q8—412no—
937Q8—424no—
938Q8#535116yes—
939D4—224no—
940D4—48no—
941D4—412no—
942D4—412no—
943D4—412no—
944D4—44no—
945D4—412no—
946D4—424no—
947D4—424no—
948D4—424no—
949D4—412no—
950D4—812no—
951D4—812no—
952D4—812no—
953D4—812no—
954D4—812no—
955D4—812no—
956D4—1612no—
957C2×C4—28no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—23no—
964C2×C4—23no—
965C2×C4—26no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—224no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—23no—
973C2×C4—23no—
974C2×C4—23no—
975C2×C4—26no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—26no—
979C2×C4—26no—
980C2×C4—22no—
981C2×C4—26no—
982C2×C4—22no—
983C2×C4—26no—
984C2×C4—22no—
985C2×C4—26no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—26no—
989C2×C4—26no—
990C2×C4—26no—
991C2×C4—26no—
992C2×C4—22no—
993C2×C4—26no—
994C2×C4—23no—
995C2×C4—23no—
996C2×C4—412no—
997C2×C4—412no—
998C2×C4—412no—
999C2×C4—424no—
1000C2×C4—424no—
1001C2×C4—412no—
1002C2×C4—424no—
1003C2×C4—412no—
1004C2×C4—86no—
1005C2×C4—86no—
1006C2×C4C23×D412yes—
1007C2×C4C23×D416yes—
1008C2×C4C23×D412yes—
1009C2×C4C23×D412yes—
1010C2×C4C23×D416yes—
1011C2×C4C23×D416yes—
1012C2×C4C2×H(5,𝔽2)112yes—
1013C2×C4#58514yes—
1014C2×C4#58512yes—
1015C22—24no—
1016C22—22no—
1017C22—26no—
1018C22—26no—
1019C22—26no—
1020C22—46no—
1021C22—42no—
1022C22—46no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—46no—
1028C22—46no—
1029C22—46no—
1030C22—46no—
1031C22—46no—
1032C22—42no—
1033C22—42no—
1034C22—46no—
1035C22—43no—
1036C22—42no—
1037C22—46no—
1038C22—43no—
1039C22—42no—
1040C22—46no—
1041C22—42no—
1042C22—46no—
1043C22—43no—
1044C22—1624no—
1045C22C24×D411yescharacteristic
1046C22C22×H(5,𝔽2)12yes—
1047C22C2×#58511yescharacteristic
1048C22C2×#58512yes—
1049C22C2×#58511yescharacteristic
1050C4—24no—
1051C4—22no—
1052C4—22no—
1053C4—26no—
1054C4—22no—
1055C4—26no—
1056C4—22no—
1057C4—46no—
1058C4—42no—
1059C4—46no—
1060C4—43no—
1061C4—41no—
1062C4—43no—
1063C4—41no—
1064C4—42no—
1065C4—46no—
1066C4—43no—
1067C4C2×#535112yes—
1068C2—42no—
1069C2—46no—
1070C2—82no—
1071C2—83no—
1072C2—86no—
1073C2C22×#53511yescharacteristic
1074C2#6281111yescharacteristic
1075C2#6281211yescharacteristic
1076C2#6302012yes—
1077C2#6303512yes—
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×#3500C2semidirect
2. C2×#3480C2semidirect
3. #42987C2semidirect
4. #42986C2semidirect
5. #42911C2semidirect
6. #42910C2semidirect
7. #39953C2semidirect
8. #39948C2semidirect
9. #39881C2semidirect
10. #39876C2semidirect
11. #37550C2semidirect
12. #36467C2semidirect
13. #36465C2semidirect
14. #36434C2semidirect
15. #36430C2semidirect
16. #36091C2semidirect
17. #36082C2semidirect
18. #35757C2semidirect
19. #35687C2semidirect
20. #35131C2semidirect
21. #35129C2semidirect
22. #34977C2semidirect
23. #34125C2semidirect
28. C2×#559C22semidirect
29. C2×#557C22semidirect
30. C2×#556C22semidirect
31. C2×#553C22semidirect
32. C2×#553C22semidirect
35. C2×D4×Q8C22semidirect
40. C2×#548C22semidirect
41. C2×#548C22semidirect
47. C2×#532C22semidirect
48. C2×#529C22semidirect
49. C2×#529C22semidirect
52. C2×C4×#41C22semidirect
53. C2×C4×#41C22semidirect
54. C22×C4×Q8C22semidirect
55. #2861C22semidirect
56. #2858C22semidirect
57. #2850C22semidirect
58. #2850C22semidirect
59. #2821C22semidirect
60. #2818C22semidirect
61. #2718C22semidirect
62. #2710C22semidirect
63. #2706C22semidirect
64. #2703C22semidirect
65. #2685C22semidirect
66. #2678C22semidirect
67. #2670C22semidirect
68. #2669C22semidirect
69. #2662C22semidirect
70. #2662C22semidirect
71. #2661C22semidirect
72. #2635C22semidirect
73. #2632C22semidirect
74. #2631C22semidirect
76. #2616C22semidirect
78. #2615C22semidirect
79. #2610C22semidirect
80. #2610C22semidirect
81. #2610C22semidirect
82. #2610C22semidirect
83. #2610C22semidirect
84. #2592C22semidirect
85. #2567C22semidirect
86. #2563C22semidirect
87. #2562C22semidirect
88. #2548C22semidirect
89. #2545C22semidirect
90. #2544C22semidirect
91. #2542C22semidirect
92. #2541C22semidirect
93. #2541C22semidirect
94. #2540C22semidirect
95. #2540C22semidirect
96. #2540C22semidirect
97. #2540C22semidirect
98. #2536C22semidirect
99. #2535C22semidirect
100. #2500C22semidirect
101. #2492C22semidirect
102. #2491C22semidirect
103. #2490C22semidirect
104. #2489C22semidirect
105. #2482C22semidirect
106. #2436C22semidirect
109. #2434C22semidirect
112. #2432C22semidirect
113. #2431C22semidirect
114. #2431C22semidirect
115. #2429C22semidirect
116. #2428C22semidirect
117. #2427C22semidirect
118. #2426C22semidirect
119. #2417C22semidirect
120. #2416C22semidirect
121. #2415C22semidirect
122. #2414C22semidirect
123. #2414C22semidirect
124. #2414C22semidirect
125. #2411C22semidirect
126. #2409C22semidirect
127. #2409C22semidirect
132. #2407C22semidirect
133. #2407C22semidirect
134. #2404C22semidirect
137. #2388C22semidirect
138. #2388C22semidirect
139. #2357C22semidirect
140. #2351C22semidirect
141. #2347C22semidirect
142. #2347C22semidirect
147. Q8×C22⋊C4C22semidirect
148. Q8×C22⋊C4C22semidirect
149. #2321C22semidirect
150. #2321C22semidirect
151. #2321C22semidirect
152. C4×#127C22semidirect
153. C4×#124C22semidirect
154. C4×#121C22semidirect
155. C4×#121C22semidirect
156. #2293C22semidirect
157. #2283C22semidirect
158. C42×Q8C22semidirect
159. C4×#117C22semidirect
253. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35002
C2×#34802
#429872
#429862
#429112
#429102
#399532
#399482
#398812
#398762
#375502
#364672
#364652
#364342
#364302
#360912
#360822
#357572
#356872
#351312
#351292
#349772
#341252