Finite Group Databasebeta

← #7655400

Subgroups — #7655400

Order 512.

8449 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3480C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#42683C213yesmaximal, complemented
4#42679C213yesmaximal, complemented
5#42484C213yesmaximal, complemented
6#42480C213yesmaximal, complemented
7#39881C216yesmaximal, complemented
8#39876C216yesmaximal, complemented
9#39863C216yesmaximal, complemented
10#39862C216yesmaximal, complemented
11#37544C213yesmaximal, complemented
12#36434C212yesmaximal, complemented
13#36430C212yesmaximal, complemented
14#36429C212yesmaximal, complemented
15#36428C212yesmaximal, complemented
16#36066C211yesmaximal, characteristic, complemented
17#36049C211yesmaximal, characteristic, complemented
18#35927C211yesmaximal, characteristic, complemented
19#35910C211yesmaximal, characteristic, complemented
20#35190C213yesmaximal, complemented
21#35102C213yesmaximal, complemented
22#34963C213yesmaximal, complemented
23#34197C211yesmaximal, characteristic, complemented
24C23×#41C2212yes—
25#3480—216no—
26C2×#559C2213yescomplemented
27C2×#557C2211yescharacteristic, complemented
28C2×#556C2213yescomplemented
29C2×#553C2213yescomplemented
30C2×#553C2213yescomplemented
31D4×#41—216no—
32C2×#550C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2212yescomplemented
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2212yescomplemented
37C2×#548C2211yescharacteristic
38C2×#548C2212yes—
39C2×#548C2211yescharacteristic, complemented
40C2×#548C2212yescomplemented
41C2×#548C2212yescomplemented
42C2×#547C2213yes—
43C2×#546C2216yes—
44C2×D42C2213yes—
45C2×#532C2213yes—
46C2×#532C2213yescomplemented
47C2×#529C2213yescomplemented
48C2×#529C2213yescomplemented
49C2×#525C2216yes—
50C2×C4×#41C2211yescharacteristic
51C2×C4×#41C2211yescharacteristic, complemented
52C2×C4×#41C2213yescomplemented
53C22×C4×Q8C2211yescharacteristic, complemented
54C22×C4×D4C2213yes—
55#2850C2216yescomplemented
56#2850C2216yescomplemented
57#2848C2216yescomplemented
58#2847C2216yescomplemented
59#2813C2216yescomplemented
60#2813C2216yescomplemented
61#2718C22112yescomplemented
62#2710C22112yescomplemented
63#2706C22112yescomplemented
64#2703C22112yescomplemented
65#2685C22112yescomplemented
66#2678C22112yescomplemented
67#2670C22112yescomplemented
68#2669C22112yescomplemented
69#2658C2213yescomplemented
70#2657C2213yescomplemented
71#2642C2213yescomplemented
72#2641C2213yescomplemented
73#2636C22112yescomplemented
74#2635C2216yescomplemented
75#2635C2216yescomplemented
76#2635C22112yescomplemented
77#2623C2216yescomplemented
78#2613C2216yes—
79#2603C22112yescomplemented
80#2598C2213yes—
81#2598C2211yescharacteristic
82#2598C2216yescomplemented
83#2598C2213yescomplemented
84#2598C2213yescomplemented
85#2580C2216yescomplemented
86#2568C2213yescomplemented
87#2562C2213yes—
88#2562C2213yescomplemented
89#2548C2213yescomplemented
90#2545C2216yescomplemented
91#2544C2216yescomplemented
92#2542C2213yescomplemented
93#2542C2216yescomplemented
94#2541C2213yescomplemented
95#2541C2216yescomplemented
96#2540C2213yes—
97#2540C2213yescomplemented
98#2540C2216yescomplemented
99#2540C2216yescomplemented
100#2536C2216yescomplemented
101#2535C2216yescomplemented
102#2535C2216yescomplemented
103#2500C2216yescomplemented
104#2492C2216yescomplemented
105#2491C2216yescomplemented
106#2490C2216yescomplemented
107#2489C2216yescomplemented
108#2487C2213yescomplemented
109#2487C2213yescomplemented
110#2482C2216yescomplemented
111#2435C2216yescomplemented
112#2433C2216yescomplemented
113#2432C2216yescomplemented
114#2432C2216yescomplemented
115#2431C2216yescomplemented
116#2431C2216yescomplemented
117#2431C2216yescomplemented
118#2429C2216yescomplemented
119#2428C2216yescomplemented
120#2427C2216yescomplemented
121#2426C2216yescomplemented
122#2417C2216yescomplemented
123#2416C2216yescomplemented
124#2415C2216yescomplemented
125#2414C2216yescomplemented
126#2408C2213yes—
127#2408C2213yes—
128#2408C2216yescomplemented
129#2408C2216yescomplemented
130#2407C2216yescomplemented
131#2407C2216yescomplemented
132#2407C2216yescomplemented
133#2407C2216yescomplemented
134#2404C2216yescomplemented
135#2398C2213yes—
136#2398C2213yescomplemented
137#2397C2213yes—
138#2397C2213yescomplemented
139#2357C2216yescomplemented
140#2351C2212yescomplemented
141#2346C2216yescomplemented
142#2341C2212yes—
143#2341C2212yescomplemented
144#2341C2212yescomplemented
145Q8×C22⋊C4C2212yescomplemented
146Q8×C22⋊C4C2212yescomplemented
147#2328C2216yescomplemented
148#2326C2216yescomplemented
149#2321C22112yescomplemented
150#2319C2213yescomplemented
151#2319C2213yescomplemented
152C4×#121C2216yescomplemented
153C4×#121C2216yescomplemented
154C4×#120C2216yescomplemented
155C4×#120C2216yescomplemented
156#2283C2213yescomplemented
157#2283C2213yescomplemented
158#2276C2211yescharacteristic, complemented
159#2276C2211yescharacteristic, complemented
160C22×#41—216no—
161C22×#41—48no—
162C22×#41—48no—
163C22×#41C2312yes—
164C22×#41C2311yescharacteristic
165C22×#41C2311yescharacteristic
166C22×#41C2316yes—
167C22×#41C2316yes—
168C22×#41C2313yes—
169C23×Q8C2312yes—
170C23×Q8C2311yescharacteristic
171C23×D4C2316yes—
172C23×D4C2313yes—
173C24×C4C2316yes—
174#559—224no—
175#557—28no—
176#556—224no—
177#553—224no—
178#553—224no—
179#550—28no—
180#550—28no—
181#550—48no—
182D4×Q8—28no—
183D4×Q8—48no—
184#548—28no—
185#548—216no—
186#548—28no—
187#548—48no—
188#548—48no—
189#547—224no—
190#546—248no—
191D42—224no—
192#532—224no—
193#532—224no—
194C2×C4⋊Q8C2313yes—
195C2×C4⋊Q8C2313yes—
196C2×C4⋊Q8C2316yes—
197C2×#127C2313yes—
198C2×#127C2313yes—
199C2×#127C2316yes—
200C2×#127C2316yes—
201#529—224no—
202#529—224no—
203C2×#126C2316yes—
204C2×#126C2316yes—
205C2×#125C2313yes—
206C2×#125C2313yes—
207C2×#124C2316yes—
208C2×#124C2313yes—
209C2×#124C2316yes—
210C2×#124C2313yes—
211C2×#124C2316yes—
212C2×#124C2316yes—
213C2×#124C2316yes—
214#525—248no—
215C2×#123C2316yes—
216C2×#123C23112yes—
217C2×#123C2316yes—
218C2×C22⋊Q8C2313yes—
219C2×C22⋊Q8C2316yes—
220C2×C22⋊Q8C2316yes—
221C2×C22⋊Q8C2313yes—
222C2×C22⋊Q8C2316yes—
223C2×C22⋊Q8C2316yes—
224C2×C22⋊Q8C2316yes—
225C2×C22⋊Q8C2316yes—
226C2×#121C2313yes—
227C2×#121C2316yes—
228C2×#121C2316yes—
229C2×#121C2313yes—
230C2×#121C2313yes—
231C2×#121C2316yes—
232C2×#121C2316yes—
233C2×#121C2316yes—
234C2×#121C2313yes—
235C2×#121C2316yes—
236C2×#121C2316yes—
237C2×#121C2316yes—
238C2×#121C2316yes—
239C2×#121C2316yes—
240C2×#121C2316yes—
241C2×#120C23112yes—
242C2×#120C23112yes—
243C2×#120C2316yes—
244C2×#120C2316yes—
245C4×#41—28no—
246C4×#41—224no—
247C4×#41D4116yescomplemented
248C2×C4×Q8—28no—
249C2×C4×Q8C2313yes—
250C2×C4×Q8C2313yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2313yes—
256C2×C4×Q8C2313yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×D4—224no—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2316yes—
264C2×C4×D4C2316yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2313yes—
268C2×C4×D4C2313yes—
269C2×C4×D4C2313yes—
270C2×C4×D4C2313yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2313yes—
273C2×C4×D4C2313yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2313yes—
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×#117C2313yes—
287C22×C4⋊C4C2313yes—
288C22×C4⋊C4C2313yes—
289C22×C22⋊C4C2316yes—
290C22×C42C2313yes—
291C22×C42C2313yes—
292C22×C42C2313yes—
293#400C2316yes—
294#400C2313yes—
295#400C2313yes—
296#400C2311yescharacteristic
297#400C2313yes—
298#400C23112yes—
299#399C2316yes—
300#399C2316yes—
301#399C2313yes—
302#399C2311yescharacteristic
303#399C2316yes—
304#399C2313yes—
305#399C2313yes—
306#399C23112yes—
307#398C23112yes—
308#397C23112yes—
309#397C2316yes—
310#397C2316yes—
311#396C23112yes—
312#396C23112yes—
313#394C2313yes—
314#394C2316yes—
315#394C2311yescharacteristic
316#394C2313yes—
317#394C2313yes—
318#394C23112yes—
319#394C23112yes—
320#394C23112yes—
321#394C23112yes—
322#394C23112yes—
323#394C23112yes—
324#394C23112yes—
325#394C23112yes—
326#393C2316yes—
327#393C2316yes—
328#392C2313yes—
329#392C2311yescharacteristic
330#392C2316yes—
331#392C2313yes—
332#392C2313yes—
333#392C23112yes—
334#392C23112yes—
335#392C23112yes—
336#392C23112yes—
337#392C23112yes—
338#392C23112yes—
339#392C2316yes—
340#392C2316yes—
341#391C2316yes—
342#391C2316yes—
343#391C2316yes—
344#391C2316yes—
345#391C2316yes—
346#390C2316yes—
347#390C2316yes—
348#390C23112yes—
349#390C23112yes—
350#390C2316yes—
351#390C2316yes—
352#390C2316yes—
353#390C2316yes—
354#390C2316yes—
355#390C2316yes—
356#390C2316yes—
357#390C2316yes—
358#390C2316yes—
359#389C2316yes—
360#389C2316yes—
361#389C2316yes—
362#389C2316yes—
363#388C23112yes—
364#388C23112yes—
365#388C23112yes—
366#388C23112yes—
367#388C2316yes—
368#388C23112yes—
369#388C23112yes—
370#388C23112yes—
371#388C2316yes—
372#388C2312yes—
373#388C2316yes—
374#386C2316yes—
375#386C23112yes—
376#386C23112yes—
377#386C2316yes—
378#386C23112yes—
379#386C23112yes—
380#386C23112yes—
381#386C2316yes—
382#386C2316yes—
383#386C2312yes—
384#386C2312yes—
385#386C2316yes—
386#386C2316yes—
387#386C2316yes—
388#386C2316yes—
389#385C23112yes—
390#385C2312yes—
391#385C2316yes—
392#385C2316yes—
393#385C2316yes—
394#385C23112yes—
395#385C2316yes—
396#385C2316yes—
397#384C2316yes—
398#383C2311yescharacteristic
399#383C2313yes—
400#382C2316yes—
401#382C2316yes—
402#382C2316yes—
403#381C2316yes—
404#381C2316yes—
405#380C2316yes—
406#380C2316yes—
407#380C2316yes—
408#380C2316yes—
409#380C2313yes—
410#380C2313yes—
411#380C2316yes—
412#380C2316yes—
413#380C2316yes—
414#379C23112yes—
415#379C2316yes—
416#379C2316yes—
417C4×C4⋊C4C2313yes—
418C4×C4⋊C4C2313yes—
419C4×C4⋊C4C2316yes—
420C4×C4⋊C4C2316yes—
421C4×C4⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428#376C2313yes—
429#376C2313yes—
430#376C2316yes—
431C25C2416yes—
432C2×#41—24no—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—28no—
436C2×#41—28no—
437C2×#41—28no—
438C2×#41—224no—
439C2×#41—212no—
440C2×#41—224no—
441C2×#41—46no—
442C2×#41—412no—
443C2×#41—412no—
444C2×#41—412no—
445C2×#41—412no—
446C2×#41—46no—
447C2×#41—4128no—
448C2×#41C2×D418yes—
449C22×Q8—24no—
450C22×Q8—28no—
451C22×Q8—28no—
452C22×Q8—28no—
453C22×Q8—28no—
454C22×Q8C2413yes—
455C22×Q8C2416yes—
456C22×Q8C2413yes—
457C22×Q8C2411yescharacteristic
458C22×D4—224no—
459C22×D4—212no—
460C22×D4—412no—
461C22×D4—412no—
462C22×D4—412no—
463C22×D4C2411yescharacteristic
464C22×D4C2413yes—
465C22×D4C2416yes—
466C22×D4C2412yes—
467C22×D4C2416yes—
468C22×D4C2413yes—
469C22×D4C2413yes—
470C22×D4C2413yes—
471C22×D4C2413yes—
472C22×D4C2413yes—
473C22×D4C2416yes—
474C22×D4C2416yes—
475C22×D4C2416yes—
476C22×D4C2416yes—
477C22×D4C24112yes—
478C22×D4C2416yes—
479C22×D4C24112yes—
480C23×C4—224no—
481C23×C4—412no—
482C23×C4—412no—
483C23×C4C2413yes—
484C23×C4C2413yes—
485C23×C4C2411yescharacteristic
486C23×C4C2416yes—
487C23×C4C2416yes—
488C23×C4C2413yes—
489C23×C4C2416yes—
490C23×C4C2413yes—
491C23×C4C2413yes—
492C23×C4C2413yes—
493C23×C4C2412yes—
494C23×C4C2416yes—
495C23×C4C2413yes—
496C23×C4C2413yes—
497C4⋊Q8—212no—
498C4⋊Q8—212no—
499C4⋊Q8—412no—
500#127—212no—
501#127—212no—
502#127—412no—
503#127—412no—
504#126—224no—
505#126—224no—
506#125—212no—
507#125—212no—
508#124—212no—
509#124—224no—
510#124—212no—
511#124—224no—
512#124—412no—
513#124—412no—
514#124—412no—
515#123—224no—
516#123—248no—
517#123—224no—
518C22⋊Q8—212no—
519C22⋊Q8—224no—
520C22⋊Q8—224no—
521C22⋊Q8—212no—
522C22⋊Q8—412no—
523C22⋊Q8—412no—
524C22⋊Q8—412no—
525C22⋊Q8—412no—
526#121—212no—
527#121—212no—
528#121—212no—
529#121—224no—
530#121—224no—
531#121—224no—
532#121—224no—
533#121—212no—
534#121—224no—
535#121—412no—
536#121—412no—
537#121—412no—
538#121—412no—
539#121—412no—
540#121—412no—
541#120—248no—
542#120—412no—
543#120—424no—
544#120—412no—
545C4×Q8—24no—
546C4×Q8—24no—
547C4×Q8—28no—
548C4×Q8—28no—
549C4×Q8—212no—
550C4×Q8—212no—
551C4×Q8—212no—
552C4×Q8—212no—
553C4×Q8C2×D418yes—
554C4×Q8C2×D418yes—
555C4×D4—212no—
556C4×D4—212no—
557C4×D4—212no—
558C4×D4—212no—
559C4×D4—224no—
560C4×D4—212no—
561C4×D4—24no—
562C4×D4—224no—
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—412no—
572C4×D4—412no—
573C4×D4—412no—
574C4×D4—412no—
575C4×D4C2×D4124yes—
576C4×D4C2×D4124yes—
577#117—212no—
578#117—212no—
579#117—24no—
580#117—212no—
581#117C2×D4124yes—
582C2×C4⋊C4—212no—
583C2×C4⋊C4—212no—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2413yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2413yes—
592C2×C4⋊C4C2413yes—
593C2×C4⋊C4C2413yes—
594C2×C4⋊C4C2413yes—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2416yes—
597C2×C4⋊C4C2416yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2416yes—
602C2×C4⋊C4C2416yes—
603C2×C4⋊C4C2416yes—
604C2×C4⋊C4C2416yes—
605C2×C4⋊C4C2416yes—
606C2×C4⋊C4C24112yes—
607C2×C4⋊C4C2413yes—
608C2×C4⋊C4C2413yes—
609C2×C22⋊C4—224no—
610C2×C22⋊C4C2412yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2411yescharacteristic
615C2×C22⋊C4C2411yescharacteristic
616C2×C22⋊C4C2413yes—
617C2×C22⋊C4C2413yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2413yes—
620C2×C22⋊C4C2413yes—
621C2×C22⋊C4C24112yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C24112yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C2416yes—
640C2×C22⋊C4C2416yes—
641C2×C22⋊C4C24112yes—
642C2×C22⋊C4C24112yes—
643C2×C22⋊C4C24112yes—
644C2×C22⋊C4C2416yes—
645C2×C22⋊C4C2416yes—
646C2×C22⋊C4C24112yes—
647C2×C22⋊C4C2416yes—
648C2×C42—212no—
649C2×C42—212no—
650C2×C42C2×D4124yes—
651C2×C42C2411yescharacteristic
652C2×C42C2413yes—
653C2×C42C2413yes—
654C2×C42C2413yes—
655C2×C42C2416yes—
656C2×C42C2416yes—
657C2×C42C2413yes—
658C2×C42C2413yes—
659C2×C42C2416yes—
660C2×C42C2416yes—
661C2×C42C2411yescharacteristic
662C2×C42C2413yes—
663C2×C42C2413yes—
664C2×C42C2413yes—
665#95C2411yescharacteristic
666#95C2411yescharacteristic
667#95C2416yes—
668#95C2413yes—
669#95C2413yes—
670#95C2416yes—
671#95C2416yes—
672#95C24112yes—
673#95C2412yes—
674#95C2412yes—
675#95C2412yes—
676#95C2416yes—
677#95C2416yes—
678#95C2416yes—
679#95C2416yes—
680#95C2416yes—
681#95C2416yes—
682#95C2416yes—
683#95C2412yes—
684#95C24112yes—
685#95C24112yes—
686C24—212no—
687C24—212no—
688C24—46no—
689C24—46no—
690C24—46no—
691C24—46no—
692C24—46no—
693C24C2516yes—
694C24C2513yes—
695C24C2513yes—
696C24C2512yes—
697C24C2511yescharacteristic
698#41—232no—
699#41—448no—
700#41—496no—
701#41—496no—
702#41—416no—
703#41—432no—
704C2×Q8—26no—
705C2×Q8—26no—
706C2×Q8—212no—
707C2×Q8—212no—
708C2×Q8—212no—
709C2×Q8—212no—
710C2×Q8—26no—
711C2×Q8—43no—
712C2×Q8—416no—
713C2×Q8—432no—
714C2×Q8C22×D414yes—
715C2×Q8H(5,𝔽2)18yes—
716C2×D4—24no—
717C2×D4—26no—
718C2×D4—26no—
719C2×D4—224no—
720C2×D4—24no—
721C2×D4—26no—
722C2×D4—24no—
723C2×D4—212no—
724C2×D4—26no—
725C2×D4—212no—
726C2×D4—212no—
727C2×D4—212no—
728C2×D4—22no—
729C2×D4—212no—
730C2×D4—26no—
731C2×D4—26no—
732C2×D4—26no—
733C2×D4—212no—
734C2×D4—212no—
735C2×D4—212no—
736C2×D4—212no—
737C2×D4—212no—
738C2×D4—212no—
739C2×D4—26no—
740C2×D4—42no—
741C2×D4—46no—
742C2×D4—46no—
743C2×D4—412no—
744C2×D4—412no—
745C2×D4—43no—
746C2×D4—43no—
747C2×D4—43no—
748C2×D4—46no—
749C2×D4—46no—
750C2×D4—46no—
751C2×D4—46no—
752C2×D4—412no—
753C2×D4—46no—
754C2×D4—46no—
755C2×D4—46no—
756C2×D4—46no—
757C2×D4—46no—
758C2×D4—412no—
759C2×D4—412no—
760C2×D4—412no—
761C2×D4—448no—
762C2×D4—496no—
763C2×D4C22×D4112yes—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—212no—
767C22×C4—22no—
768C22×C4—212no—
769C22×C4—26no—
770C22×C4—26no—
771C22×C4—26no—
772C22×C4—24no—
773C22×C4—212no—
774C22×C4—212no—
775C22×C4—212no—
776C22×C4—212no—
777C22×C4—212no—
778C22×C4—212no—
779C22×C4—212no—
780C22×C4—212no—
781C22×C4—212no—
782C22×C4—26no—
783C22×C4—26no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—46no—
787C22×C4—46no—
788C22×C4—46no—
789C22×C4—46no—
790C22×C4—46no—
791C22×C4—43no—
792C22×C4—43no—
793C22×C4—43no—
794C22×C4—43no—
795C22×C4—46no—
796C22×C4—46no—
797C22×C4—496no—
798C22×C4C22×D4112yes—
799C22×C4C22×D4112yes—
800C22×C4C22×D4112yes—
801C22×C4C2512yes—
802C22×C4C2516yes—
803C22×C4C2511yescharacteristic
804C22×C4C2512yes—
805C22×C4C2516yes—
806C22×C4C2513yes—
807C22×C4C2513yes—
808C22×C4C2512yes—
809C22×C4C2516yes—
810C22×C4C2511yescharacteristic
811C22×C4C2513yes—
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2513yes—
816C22×C4C2513yes—
817C22×C4C2511yescharacteristic
818C22×C4C2513yes—
819C4⋊C4—22no—
820C4⋊C4—26no—
821C4⋊C4—212no—
822C4⋊C4—26no—
823C4⋊C4—212no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—26no—
827C4⋊C4—26no—
828C4⋊C4—26no—
829C4⋊C4—26no—
830C4⋊C4—26no—
831C4⋊C4—212no—
832C4⋊C4—212no—
833C4⋊C4—212no—
834C4⋊C4—212no—
835C4⋊C4—42no—
836C4⋊C4—46no—
837C4⋊C4—46no—
838C4⋊C4—46no—
839C4⋊C4—46no—
840C4⋊C4—46no—
841C4⋊C4—412no—
842C4⋊C4C22×D4112yes—
843C4⋊C4C22×D4112yes—
844C22⋊C4—26no—
845C22⋊C4—26no—
846C22⋊C4—212no—
847C22⋊C4—212no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—212no—
851C22⋊C4—212no—
852C22⋊C4—212no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—26no—
856C22⋊C4—212no—
857C22⋊C4—26no—
858C22⋊C4—224no—
859C22⋊C4—212no—
860C22⋊C4—24no—
861C22⋊C4—212no—
862C22⋊C4—42no—
863C22⋊C4—42no—
864C22⋊C4—46no—
865C22⋊C4—46no—
866C22⋊C4—46no—
867C22⋊C4—46no—
868C22⋊C4—46no—
869C22⋊C4—46no—
870C22⋊C4—46no—
871C22⋊C4—46no—
872C22⋊C4—46no—
873C22⋊C4—412no—
874C22⋊C4—412no—
875C22⋊C4—46no—
876C22⋊C4—46no—
877C22⋊C4—46no—
878C22⋊C4—412no—
879C22⋊C4—412no—
880C22⋊C4—412no—
881C22⋊C4C22×D4124yes—
882C42—22no—
883C42—26no—
884C42—26no—
885C42—26no—
886C42—26no—
887C42—26no—
888C42—212no—
889C42—212no—
890C42—46no—
891C42—46no—
892C42C22×D4112yes—
893C42C22×D414yes—
894C42C22×D4112yes—
895C42C22×D4112yes—
896C23—22no—
897C23—21no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—26no—
902C23—22no—
903C23—22no—
904C23—23no—
905C23—23no—
906C23—26no—
907C23—21no—
908C23—22no—
909C23—22no—
910C23—23no—
911C23—26no—
912C23—26no—
913C23—26no—
914C23—26no—
915C23—26no—
916C23—26no—
917C23—26no—
918C23—26no—
919C23—23no—
920C23—26no—
921C23—23no—
922C23—424no—
923C23—424no—
924C23—812no—
925C23—812no—
926C23—812no—
927C23—812no—
928C23—812no—
929C23C23×D416yes—
930C23#58514yes—
931C23#58512yes—
932C23C2611yescharacteristic
933Q8—412no—
934Q8—412no—
935Q8—424no—
936Q8#535116yes—
937D4—28no—
938D4—224no—
939D4—424no—
940D4—412no—
941D4—412no—
942D4—412no—
943D4—48no—
944D4—412no—
945D4—448no—
946D4—424no—
947D4—412no—
948D4—812no—
949D4—812no—
950D4—812no—
951D4—812no—
952D4—812no—
953D4—1612no—
954C2×C4—28no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—23no—
958C2×C4—23no—
959C2×C4—26no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—224no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—23no—
968C2×C4—23no—
969C2×C4—23no—
970C2×C4—22no—
971C2×C4—26no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—26no—
975C2×C4—26no—
976C2×C4—22no—
977C2×C4—26no—
978C2×C4—22no—
979C2×C4—26no—
980C2×C4—22no—
981C2×C4—26no—
982C2×C4—26no—
983C2×C4—26no—
984C2×C4—22no—
985C2×C4—26no—
986C2×C4—22no—
987C2×C4—26no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—26no—
991C2×C4—23no—
992C2×C4—23no—
993C2×C4—22no—
994C2×C4—412no—
995C2×C4—412no—
996C2×C4—48no—
997C2×C4—424no—
998C2×C4—412no—
999C2×C4—424no—
1000C2×C4—424no—
1001C2×C4—424no—
1002C2×C4—412no—
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#58512yes—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—22no—
1018C22—26no—
1019C22—26no—
1020C22—24no—
1021C22—26no—
1022C22—42no—
1023C22—46no—
1024C22—42no—
1025C22—46no—
1026C22—42no—
1027C22—41no—
1028C22—42no—
1029C22—42no—
1030C22—41no—
1031C22—46no—
1032C22—46no—
1033C22—46no—
1034C22—46no—
1035C22—46no—
1036C22—46no—
1037C22—43no—
1038C22—43no—
1039C22—46no—
1040C22—46no—
1041C22—46no—
1042C22—43no—
1043C22—848no—
1044C22C24×D411yescharacteristic
1045C22C22×H(5,𝔽2)12yes—
1046C22C2×#58511yescharacteristic
1047C22C2×#58512yes—
1048C22C2×#58511yescharacteristic
1049C4—22no—
1050C4—22no—
1051C4—22no—
1052C4—26no—
1053C4—26no—
1054C4—22no—
1055C4—46no—
1056C4—42no—
1057C4—42no—
1058C4—46no—
1059C4—43no—
1060C4—41no—
1061C4—43no—
1062C4—41no—
1063C4—42no—
1064C4—46no—
1065C4—43no—
1066C4C2×#535112yes—
1067C2—42no—
1068C2—46no—
1069C2—44no—
1070C2—83no—
1071C2—86no—
1072C2C22×#53511yescharacteristic
1073C2#6281111yescharacteristic
1074C2#6281111yescharacteristic
1075C2#6301912yes—
1076C2#6302012yes—
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×#3480C2semidirect
2. C2×D4×#41C2semidirect
3. #42683C2semidirect
4. #42679C2semidirect
5. #42484C2semidirect
6. #42480C2semidirect
7. #39881C2semidirect
8. #39876C2semidirect
9. #39863C2semidirect
10. #39862C2semidirect
11. #37544C2semidirect
12. #36434C2semidirect
13. #36430C2semidirect
14. #36429C2semidirect
15. #36428C2semidirect
16. #36066C2semidirect
17. #36049C2semidirect
18. #35927C2semidirect
19. #35910C2semidirect
20. #35190C2semidirect
21. #35102C2semidirect
22. #34963C2semidirect
23. #34197C2semidirect
26. C2×#559C22semidirect
27. C2×#557C22semidirect
28. C2×#556C22semidirect
29. C2×#553C22semidirect
30. C2×#553C22semidirect
34. C2×#550C22semidirect
36. C2×D4×Q8C22semidirect
39. C2×#548C22semidirect
40. C2×#548C22semidirect
41. C2×#548C22semidirect
46. C2×#532C22semidirect
47. C2×#529C22semidirect
48. C2×#529C22semidirect
51. C2×C4×#41C22semidirect
52. C2×C4×#41C22semidirect
53. C22×C4×Q8C22semidirect
55. #2850C22semidirect
56. #2850C22semidirect
57. #2848C22semidirect
58. #2847C22semidirect
59. #2813C22semidirect
60. #2813C22semidirect
61. #2718C22semidirect
62. #2710C22semidirect
63. #2706C22semidirect
64. #2703C22semidirect
65. #2685C22semidirect
66. #2678C22semidirect
67. #2670C22semidirect
68. #2669C22semidirect
69. #2658C22semidirect
70. #2657C22semidirect
71. #2642C22semidirect
72. #2641C22semidirect
73. #2636C22semidirect
74. #2635C22semidirect
75. #2635C22semidirect
76. #2635C22semidirect
77. #2623C22semidirect
79. #2603C22semidirect
82. #2598C22semidirect
83. #2598C22semidirect
84. #2598C22semidirect
85. #2580C22semidirect
86. #2568C22semidirect
88. #2562C22semidirect
89. #2548C22semidirect
90. #2545C22semidirect
91. #2544C22semidirect
92. #2542C22semidirect
93. #2542C22semidirect
94. #2541C22semidirect
95. #2541C22semidirect
97. #2540C22semidirect
98. #2540C22semidirect
99. #2540C22semidirect
100. #2536C22semidirect
101. #2535C22semidirect
102. #2535C22semidirect
103. #2500C22semidirect
104. #2492C22semidirect
105. #2491C22semidirect
106. #2490C22semidirect
107. #2489C22semidirect
108. #2487C22semidirect
109. #2487C22semidirect
110. #2482C22semidirect
111. #2435C22semidirect
112. #2433C22semidirect
113. #2432C22semidirect
114. #2432C22semidirect
115. #2431C22semidirect
116. #2431C22semidirect
117. #2431C22semidirect
118. #2429C22semidirect
119. #2428C22semidirect
120. #2427C22semidirect
121. #2426C22semidirect
122. #2417C22semidirect
123. #2416C22semidirect
124. #2415C22semidirect
125. #2414C22semidirect
128. #2408C22semidirect
129. #2408C22semidirect
130. #2407C22semidirect
131. #2407C22semidirect
132. #2407C22semidirect
133. #2407C22semidirect
134. #2404C22semidirect
136. #2398C22semidirect
138. #2397C22semidirect
139. #2357C22semidirect
140. #2351C22semidirect
141. #2346C22semidirect
143. #2341C22semidirect
144. #2341C22semidirect
145. Q8×C22⋊C4C22semidirect
146. Q8×C22⋊C4C22semidirect
147. #2328C22semidirect
148. #2326C22semidirect
149. #2321C22semidirect
150. #2319C22semidirect
151. #2319C22semidirect
152. C4×#121C22semidirect
153. C4×#121C22semidirect
154. C4×#120C22semidirect
155. C4×#120C22semidirect
156. #2283C22semidirect
157. #2283C22semidirect
158. #2276C22semidirect
159. #2276C22semidirect
247. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34802
C2×D4×#412
#426832
#426792
#424842
#424802
#398812
#398762
#398632
#398622
#375442
#364342
#364302
#364292
#364282
#360662
#360492
#359272
#359102
#351902
#351022
#349632
#341972