Finite Group Databasebeta

← #7692372

Subgroups — #7692372

Order 512.

8724 conjugacy classes of subgroups.

The subgroup lattice has 1071 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#59412C213yesmaximal, complemented
4#59035C213yesmaximal, complemented
5#59033C213yesmaximal, complemented
6#59021C216yesmaximal, complemented
7#45010C216yesmaximal, complemented
8#45002C216yesmaximal, complemented
9#38951C213yesmaximal, complemented
10#38908C213yesmaximal, complemented
11#37670C216yesmaximal, complemented
12#36446C211yesmaximal, characteristic, complemented
13#36445C211yesmaximal, characteristic, complemented
14#36444C211yesmaximal, characteristic, complemented
15#36429C212yesmaximal, complemented
16#36153C213yesmaximal, complemented
17#36149C213yesmaximal, complemented
18#35996C212yesmaximal, complemented
19#35831C212yesmaximal, complemented
20#34700C213yesmaximal, complemented
21#34313C211yesmaximal, characteristic, complemented
22#34175C212yesmaximal, complemented
23C4×#550C211yesmaximal, characteristic, complemented
24C23×#41C2212yes—
25#3517—216no—
26C2×#557C2211yescharacteristic, complemented
27C2×#553C2216yescomplemented
28D4×#41—216no—
29C2×#550C2211yescharacteristic
30C2×#550C2211yescharacteristic
31C2×#550C2213yescomplemented
32C2×#550C2212yescomplemented
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2212yes—
35C2×#548C2212yescomplemented
36C2×#547C2213yes—
37C2×#547C2213yescomplemented
38C2×#546C2216yes—
39C2×#546C2216yes—
40C2×D42C2213yes—
41C2×#540C2216yescomplemented
42C2×#532C2213yes—
43C2×#532C2213yescomplemented
44C2×#529C2213yescomplemented
45C2×#525C2216yes—
46C2×#520C2212yescomplemented
47C2×#520C2212yescomplemented
48C2×C4×#41C2211yescharacteristic
49C2×C4×#41C2211yescharacteristic, complemented
50C22×C4×D4C2213yes—
51#2862C2213yescomplemented
52#2857C2213yescomplemented
53#2857C2213yescomplemented
54#2847C2216yescomplemented
55#2706C22112yescomplemented
56#2706C22112yescomplemented
57#2695C22112yescomplemented
58#2693C22112yescomplemented
59#2688C22112yescomplemented
60#2678C22112yescomplemented
61#2668C22112yescomplemented
62#2625C2216yescomplemented
63#2620C2216yescomplemented
64#2568C2213yescomplemented
65#2547C2213yes—
66#2547C2213yescomplemented
67#2544C2216yescomplemented
68#2542C2213yescomplemented
69#2538C2213yescomplemented
70#2537C2213yes—
71#2537C2216yescomplemented
72#2535C2216yescomplemented
73#2535C2216yescomplemented
74#2502C2216yescomplemented
75#2489C2216yescomplemented
76#2489C2216yescomplemented
77#2486C2216yescomplemented
78#2480C2216yescomplemented
79#2468C2216yescomplemented
80#2457C2216yescomplemented
81#2454C2211yescharacteristic
82#2454C2216yescomplemented
83#2447C2213yescomplemented
84#2447C2216yescomplemented
85#2447C2216yescomplemented
86#2444C22112yescomplemented
87#2442C2213yescomplemented
88#2441C2216yescomplemented
89#2435C2213yes—
90#2433C2216yescomplemented
91#2431C2216yescomplemented
92#2431C2216yescomplemented
93#2428C2216yescomplemented
94#2427C2213yes—
95#2427C2216yescomplemented
96#2427C2216yescomplemented
97#2427C2216yescomplemented
98#2425C22112yescomplemented
99#2424C22112yescomplemented
100#2422C2216yescomplemented
101#2422C2216yescomplemented
102#2420C2216yescomplemented
103#2420C2216yescomplemented
104#2420C2213yescomplemented
105#2418C2216yescomplemented
106#2418C22112yescomplemented
107#2417C2213yescomplemented
108#2417C2216yescomplemented
109#2417C2216yescomplemented
110#2416C2216yescomplemented
111#2415C2216yescomplemented
112#2412C22112yescomplemented
113#2408C2213yes—
114#2408C2216yescomplemented
115#2407C2216yescomplemented
116#2407C2216yescomplemented
117#2407C2216yescomplemented
118#2407C2216yescomplemented
119#2395C2216yescomplemented
120#2392C2216yescomplemented
121#2366C2213yescomplemented
122#2366C2213yescomplemented
123#2363C2213yescomplemented
124#2363C2213yescomplemented
125#2361C2216yescomplemented
126#2354C2213yescomplemented
127Q8×C4⋊C4C2211yescharacteristic, complemented
128Q8×C4⋊C4C2212yescomplemented
129Q8×C4⋊C4C2211yescharacteristic, complemented
130#2349C2216yescomplemented
131D4×C4⋊C4C2213yescomplemented
132#2341C2212yes—
133#2341C2211yescharacteristic
134#2341C2212yescomplemented
135#2341C2211yescharacteristic, complemented
136Q8×C22⋊C4C2212yescomplemented
137Q8×C22⋊C4C2212yescomplemented
138Q8×C22⋊C4C2212yescomplemented
139#2339C2216yescomplemented
140#2339C2216yescomplemented
141#2339C2216yescomplemented
142D4×C22⋊C4C2216yescomplemented
143D4×C22⋊C4C2216yescomplemented
144#2324C2216yescomplemented
145#2311C2216yescomplemented
146#2311C2216yescomplemented
147C4×#127C2213yescomplemented
148C4×#127C2213yescomplemented
149C4×#124C2213yes—
150C4×C22⋊Q8C2213yescomplemented
151C4×#121C2213yes—
152C4×#121C2213yescomplemented
153C4×#121C2213yescomplemented
154C4×#120C2216yescomplemented
155#2293C2213yescomplemented
156#2280C2216yescomplemented
157C2×#380C2216yescomplemented
158C42×Q8C2211yescharacteristic, complemented
159C42×D4C2213yescomplemented
160C22×#41—216no—
161C22×#41—216no—
162C22×#41—48no—
163C22×#41C2311yescharacteristic
164C22×#41C2316yes—
165C22×#41C2316yes—
166C22×#41C2312yes—
167C22×#41C2311yescharacteristic
168C22×#41C2316yes—
169C23×Q8C2312yes—
170C23×D4C2316yes—
171C23×D4C2313yes—
172C24×C4C2316yes—
173#557—28no—
174#553—248no—
175#550—216no—
176#550—28no—
177#550—224no—
178#550D4116yescomplemented
179D4×Q8—28no—
180#548—216no—
181#548—48no—
182#547—224no—
183#547—224no—
184#546—248no—
185#546—424no—
186D42—224no—
187#540—248no—
188#532—224no—
189#532—224no—
190C2×C4⋊Q8C2313yes—
191C2×C4⋊Q8C2313yes—
192C2×#127C2313yes—
193C2×#127C2316yes—
194C2×#127C2313yes—
195#529—224no—
196C2×#126C2316yes—
197C2×#125C2311yescharacteristic
198C2×#125C2316yes—
199C2×#124C2313yes—
200C2×#124C2316yes—
201C2×#124C2313yes—
202C2×#124C2316yes—
203#525—248no—
204C2×#123C23112yes—
205C2×#123C23112yes—
206C2×#123C2316yes—
207C2×#123C23112yes—
208C2×C22⋊Q8C2316yes—
209C2×C22⋊Q8C2316yes—
210C2×C22⋊Q8C2313yes—
211C2×C22⋊Q8C2316yes—
212C2×C22⋊Q8C2316yes—
213C2×C22⋊Q8C2313yes—
214C2×#121C2313yes—
215C2×#121C2316yes—
216C2×#121C2313yes—
217C2×#121C2316yes—
218C2×#121C2316yes—
219C2×#121C2313yes—
220C2×#121C2313yes—
221C2×#121C2316yes—
222C2×#121C2316yes—
223C2×#121C2316yes—
224C2×#121C23112yes—
225C2×#121C2316yes—
226C2×#121C23112yes—
227C2×#121C2316yes—
228C2×#120C23112yes—
229C2×#120C23112yes—
230C2×#120C2316yes—
231#520—216no—
232#520—48no—
233C4×#41—28no—
234C4×#41—28no—
235C2×C4×Q8C2313yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—224no—
244C2×C4×D4C2313yes—
245C2×C4×D4C2313yes—
246C2×C4×D4C2316yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2316yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C2313yes—
253C2×C4×D4C2313yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2316yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2316yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2316yes—
264C2×C4×D4C2316yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2313yes—
268C2×#117C2316yes—
269C2×#117C2313yes—
270C2×#117C2313yes—
271C2×#117C2316yes—
272C22×C4⋊C4C2316yes—
273C22×C4⋊C4C2313yes—
274C22×C4⋊C4C2316yes—
275C22×C22⋊C4C2316yes—
276C22×C22⋊C4C23112yes—
277C22×C42C2313yes—
278C22×C42C2313yes—
279#400C23112yes—
280#400C2316yes—
281#399C2312yes—
282#399C23112yes—
283#398C23112yes—
284#398C2316yes—
285#398C2316yes—
286#397C23112yes—
287#397C23112yes—
288#397C2316yes—
289#397C2316yes—
290#397C2316yes—
291#397C2316yes—
292#397C23112yes—
293#397C23112yes—
294#396C2316yes—
295#396C23112yes—
296#396C2312yes—
297#396C23112yes—
298#394C23112yes—
299#394C23112yes—
300#394C2316yes—
301#394C2316yes—
302#394C2316yes—
303#394C2316yes—
304#394C2316yes—
305#394C23112yes—
306#394C23112yes—
307#392C2316yes—
308#392C23112yes—
309#392C23112yes—
310#392C23112yes—
311#391C2316yes—
312#391C2316yes—
313#391C2316yes—
314#391C2316yes—
315#391C2316yes—
316#391C2316yes—
317#391C2313yes—
318#391C2316yes—
319#391C2313yes—
320#390C2313yes—
321#390C2313yes—
322#390C2316yes—
323#390C2316yes—
324#390C2313yes—
325#390C2316yes—
326#390C2316yes—
327#390C2313yes—
328#390C2316yes—
329#390C2316yes—
330#390C2316yes—
331#390C2313yes—
332#390C2313yes—
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#389C2316yes—
336#389C2313yes—
337#389C2316yes—
338#389C2316yes—
339#389C2316yes—
340#389C2313yes—
341#389C2313yes—
342#389C2313yes—
343#389C2316yes—
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#388C2316yes—
347#388C2316yes—
348#388C2316yes—
349#388C2316yes—
350#388C2316yes—
351#388C2316yes—
352#388C2316yes—
353#387C2316yes—
354#386C23112yes—
355#386C23112yes—
356#386C23112yes—
357#386C23112yes—
358#386C23112yes—
359#386C2316yes—
360#386C23112yes—
361#386C23112yes—
362#386C23112yes—
363#386C2316yes—
364#386C2316yes—
365#386C2316yes—
366#386C2316yes—
367#386C23112yes—
368#386C2316yes—
369#385C23112yes—
370#385C2316yes—
371#385C23112yes—
372#385C2316yes—
373#385C23112yes—
374#385C2316yes—
375#385C2312yes—
376#384C2313yes—
377#384C2313yes—
378#384C2316yes—
379#382C2313yes—
380#382C2316yes—
381#382C2316yes—
382#381C2316yes—
383#381C2316yes—
384#381C23112yes—
385#380C23112yes—
386#380C2316yes—
387#380C2316yes—
388#380C2316yes—
389#380C2316yes—
390#380C2316yes—
391#380C2316yes—
392#380C2316yes—
393#380C2313yes—
394#380C2316yes—
395#380C2313yes—
396#380C2316yes—
397#380C2316yes—
398#380C23112yes—
399#380C2313yes—
400#380C2313yes—
401#380C2316yes—
402#380C2312yes—
403#379C2316yes—
404#379C2316yes—
405#379C2316yes—
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C4⋊C4C2316yes—
412C4×C4⋊C4C2313yes—
413C4×C4⋊C4C2311yescharacteristic
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2313yes—
417C4×C22⋊C4C2313yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2313yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2313yes—
424C4×C22⋊C4C2313yes—
425C2×#95C23112yes—
426C43C2313yes—
427C25C2416yes—
428C2×#41—24no—
429C2×#41—24no—
430C2×#41—28no—
431C2×#41—24no—
432C2×#41—28no—
433C2×#41—24no—
434C2×#41—24no—
435C2×#41—224no—
436C2×#41—224no—
437C2×#41—224no—
438C2×#41—224no—
439C2×#41—224no—
440C2×#41—412no—
441C2×#41—412no—
442C2×#41—412no—
443C2×#41—412no—
444C2×#41—4128no—
445C2×#41C2×D4116yes—
446C2×#41#4118yescomplemented
447C22×Q8—28no—
448C22×Q8—28no—
449C22×Q8—28no—
450C22×Q8C2413yes—
451C22×Q8C2416yes—
452C22×Q8C2411yescharacteristic
453C22×D4—212no—
454C22×D4—224no—
455C22×D4—224no—
456C22×D4—212no—
457C22×D4—46no—
458C22×D4—412no—
459C22×D4C2413yes—
460C22×D4C2413yes—
461C22×D4C2416yes—
462C22×D4C24112yes—
463C22×D4C2416yes—
464C22×D4C2413yes—
465C22×D4C2413yes—
466C22×D4C2411yescharacteristic
467C22×D4C2416yes—
468C22×D4C2416yes—
469C22×D4C2416yes—
470C22×D4C24112yes—
471C22×D4C2416yes—
472C23×C4—224no—
473C23×C4—224no—
474C23×C4—412no—
475C23×C4C2413yes—
476C23×C4C2413yes—
477C23×C4C2413yes—
478C23×C4C2416yes—
479C23×C4C2416yes—
480C23×C4C2412yes—
481C23×C4C2416yes—
482C23×C4C2416yes—
483C23×C4C2413yes—
484C23×C4C2413yes—
485C23×C4C24112yes—
486C23×C4C2413yes—
487C23×C4C24112yes—
488C4⋊Q8—212no—
489C4⋊Q8—212no—
490#127—224no—
491#127—212no—
492#127C2×D4124yes—
493#126—224no—
494#125—24no—
495#125—224no—
496#124—212no—
497#124—224no—
498#124—212no—
499#124—412no—
500#123—248no—
501#123—224no—
502#123—248no—
503#123—424no—
504C22⋊Q8—224no—
505C22⋊Q8—224no—
506C22⋊Q8—212no—
507C22⋊Q8—46no—
508C22⋊Q8—412no—
509C22⋊Q8—412no—
510#121—224no—
511#121—212no—
512#121—224no—
513#121—224no—
514#121—224no—
515#121—224no—
516#121—248no—
517#121—212no—
518#121—212no—
519#121—224no—
520#121—212no—
521#121—424no—
522#121—412no—
523#121C2×D4148yes—
524#120—248no—
525#120—412no—
526#120—424no—
527C4×Q8—24no—
528C4×Q8—24no—
529C4×Q8—28no—
530C4×Q8—24no—
531C4×Q8—24no—
532C4×Q8—28no—
533C4×Q8—212no—
534C4×Q8C2×D418yes—
535C4×D4—212no—
536C4×D4—224no—
537C4×D4—224no—
538C4×D4—224no—
539C4×D4—224no—
540C4×D4—224no—
541C4×D4—224no—
542C4×D4—212no—
543C4×D4—24no—
544C4×D4—212no—
545C4×D4—212no—
546C4×D4—224no—
547C4×D4—212no—
548C4×D4—212no—
549C4×D4—212no—
550C4×D4—412no—
551C4×D4—46no—
552C4×D4—412no—
553C4×D4—412no—
554C4×D4—412no—
555C4×D4—46no—
556C4×D4—412no—
557C4×D4—412no—
558C4×D4C2×D4124yes—
559#117—224no—
560#117—212no—
561#117—212no—
562#117—412no—
563C2×C4⋊C4—224no—
564C2×C4⋊C4—212no—
565C2×C4⋊C4—412no—
566C2×C4⋊C4C2413yes—
567C2×C4⋊C4C2416yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2413yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C24112yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2413yes—
596C2×C22⋊C4—224no—
597C2×C22⋊C4—424no—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C24112yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2413yes—
612C2×C22⋊C4C2413yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C24112yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C24112yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2413yes—
624C2×C22⋊C4C2413yes—
625C2×C22⋊C4C2413yes—
626C2×C22⋊C4C2413yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C24112yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2416yes—
634C2×C42—212no—
635C2×C42—212no—
636C2×C42C2413yes—
637C2×C42C2413yes—
638C2×C42C2413yes—
639C2×C42C2413yes—
640C2×C42C2416yes—
641C2×C42C2416yes—
642C2×C42C2413yes—
643C2×C42C2411yescharacteristic
644C2×C42C2413yes—
645C2×C42C2411yescharacteristic
646C2×C42C2413yes—
647C2×C42C2413yes—
648C2×C42C2411yescharacteristic
649C2×C42C2413yes—
650C2×C42C2413yes—
651#95C2413yes—
652#95C2416yes—
653#95C24112yes—
654#95C24112yes—
655#95C2411yescharacteristic
656#95C2411yescharacteristic
657#95C2412yes—
658#95C2412yes—
659#95C2413yes—
660#95C2413yes—
661#95C2413yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C24112yes—
674C24—212no—
675C24—212no—
676C24—212no—
677C24—46no—
678C24—46no—
679C24—46no—
680C24—46no—
681C24C2513yes—
682C24C2516yes—
683C24C2513yes—
684C24C2512yes—
685#41—232no—
686#41—264no—
687#41—496no—
688#41—496no—
689#41—416no—
690#41—848no—
691C2×Q8—26no—
692C2×Q8—212no—
693C2×Q8—212no—
694C2×Q8—26no—
695C2×Q8—212no—
696C2×Q8—26no—
697C2×Q8—432no—
698C2×Q8C22×D414yes—
699C2×Q8C2×#4114yes—
700C2×Q8H(5,𝔽2)14yes—
701C2×D4—212no—
702C2×D4—224no—
703C2×D4—26no—
704C2×D4—224no—
705C2×D4—212no—
706C2×D4—212no—
707C2×D4—224no—
708C2×D4—212no—
709C2×D4—212no—
710C2×D4—22no—
711C2×D4—26no—
712C2×D4—26no—
713C2×D4—212no—
714C2×D4—26no—
715C2×D4—26no—
716C2×D4—212no—
717C2×D4—26no—
718C2×D4—26no—
719C2×D4—22no—
720C2×D4—26no—
721C2×D4—26no—
722C2×D4—43no—
723C2×D4—46no—
724C2×D4—46no—
725C2×D4—412no—
726C2×D4—46no—
727C2×D4—46no—
728C2×D4—46no—
729C2×D4—412no—
730C2×D4—46no—
731C2×D4—46no—
732C2×D4—46no—
733C2×D4—46no—
734C2×D4—412no—
735C2×D4—448no—
736C2×D4—496no—
737C2×D4C22×D4124yes—
738C2×D4C22×D4112yes—
739C2×D4C22×D4124yes—
740C2×D4C2×#41112yes—
741C2×D4H(5,𝔽2)14yes—
742C22×C4—26no—
743C22×C4—212no—
744C22×C4—212no—
745C22×C4—26no—
746C22×C4—212no—
747C22×C4—212no—
748C22×C4—224no—
749C22×C4—26no—
750C22×C4—26no—
751C22×C4—26no—
752C22×C4—212no—
753C22×C4—24no—
754C22×C4—212no—
755C22×C4—26no—
756C22×C4—24no—
757C22×C4—212no—
758C22×C4—212no—
759C22×C4—26no—
760C22×C4—26no—
761C22×C4—26no—
762C22×C4—212no—
763C22×C4—26no—
764C22×C4—26no—
765C22×C4—26no—
766C22×C4—26no—
767C22×C4—42no—
768C22×C4—46no—
769C22×C4—46no—
770C22×C4—496no—
771C22×C4—412no—
772C22×C4—43no—
773C22×C4—43no—
774C22×C4—43no—
775C22×C4—43no—
776C22×C4—412no—
777C22×C4—412no—
778C22×C4—412no—
779C22×C4—412no—
780C22×C4C22×D4124yes—
781C22×C4C2×#41112yes—
782C22×C4C2513yes—
783C22×C4C2516yes—
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C22×C4C2513yes—
787C22×C4C2512yes—
788C22×C4C2511yescharacteristic
789C22×C4C2512yes—
790C22×C4C2513yes—
791C22×C4C2516yes—
792C22×C4C2516yes—
793C22×C4C2511yescharacteristic
794C22×C4C2513yes—
795C22×C4C2513yes—
796C22×C4C2512yes—
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C22×C4C2513yes—
800C22×C4C2511yescharacteristic
801C4⋊C4—26no—
802C4⋊C4—212no—
803C4⋊C4—26no—
804C4⋊C4—212no—
805C4⋊C4—212no—
806C4⋊C4—24no—
807C4⋊C4—26no—
808C4⋊C4—24no—
809C4⋊C4—212no—
810C4⋊C4—212no—
811C4⋊C4—22no—
812C4⋊C4—212no—
813C4⋊C4—22no—
814C4⋊C4—26no—
815C4⋊C4—26no—
816C4⋊C4—212no—
817C4⋊C4—26no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—46no—
821C4⋊C4—42no—
822C4⋊C4—42no—
823C4⋊C4—43no—
824C4⋊C4—46no—
825C4⋊C4—46no—
826C4⋊C4—46no—
827C4⋊C4—412no—
828C4⋊C4—46no—
829C4⋊C4C22×D414yes—
830C4⋊C4C22×D4112yes—
831C22⋊C4—212no—
832C22⋊C4—212no—
833C22⋊C4—212no—
834C22⋊C4—212no—
835C22⋊C4—224no—
836C22⋊C4—26no—
837C22⋊C4—212no—
838C22⋊C4—212no—
839C22⋊C4—212no—
840C22⋊C4—24no—
841C22⋊C4—212no—
842C22⋊C4—212no—
843C22⋊C4—212no—
844C22⋊C4—212no—
845C22⋊C4—26no—
846C22⋊C4—212no—
847C22⋊C4—24no—
848C22⋊C4—46no—
849C22⋊C4—412no—
850C22⋊C4—42no—
851C22⋊C4—46no—
852C22⋊C4—42no—
853C22⋊C4—46no—
854C22⋊C4—46no—
855C22⋊C4—43no—
856C22⋊C4—43no—
857C22⋊C4—43no—
858C22⋊C4—43no—
859C22⋊C4—42no—
860C22⋊C4—412no—
861C22⋊C4—46no—
862C22⋊C4—46no—
863C22⋊C4—46no—
864C22⋊C4—412no—
865C22⋊C4—46no—
866C22⋊C4C22×D4124yes—
867C42—22no—
868C42—22no—
869C42—26no—
870C42—26no—
871C42—26no—
872C42—26no—
873C42—212no—
874C42—26no—
875C42—26no—
876C42—212no—
877C42—26no—
878C42—22no—
879C42—26no—
880C42—43no—
881C42C22×D4112yes—
882C23—22no—
883C23—23no—
884C23—22no—
885C23—26no—
886C23—23no—
887C23—26no—
888C23—26no—
889C23—22no—
890C23—23no—
891C23—26no—
892C23—22no—
893C23—23no—
894C23—23no—
895C23—26no—
896C23—22no—
897C23—22no—
898C23—26no—
899C23—23no—
900C23—23no—
901C23—23no—
902C23—23no—
903C23—23no—
904C23—23no—
905C23—23no—
906C23—23no—
907C23—424no—
908C23—424no—
909C23—424no—
910C23—812no—
911C23—812no—
912C23—812no—
913C23—812no—
914C23C23×D4112yes—
915C23C22×#4116yes—
916C23C2×H(5,𝔽2)14yes—
917C23C2611yescharacteristic
918Q8—424no—
919Q8—412no—
920Q8#546116yescomplemented
921D4—224no—
922D4—248no—
923D4—28no—
924D4—224no—
925D4—424no—
926D4—412no—
927D4—424no—
928D4—448no—
929D4—412no—
930D4—812no—
931D4—812no—
932D4—812no—
933D4—824no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—23no—
941C2×C4—23no—
942C2×C4—224no—
943C2×C4—248no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—23no—
949C2×C4—23no—
950C2×C4—26no—
951C2×C4—26no—
952C2×C4—23no—
953C2×C4—21no—
954C2×C4—26no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—23no—
958C2×C4—23no—
959C2×C4—26no—
960C2×C4—23no—
961C2×C4—23no—
962C2×C4—26no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—21no—
966C2×C4—23no—
967C2×C4—21no—
968C2×C4—23no—
969C2×C4—22no—
970C2×C4—26no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—23no—
975C2×C4—23no—
976C2×C4—26no—
977C2×C4—21no—
978C2×C4—23no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—48no—
984C2×C4—424no—
985C2×C4—424no—
986C2×C4—424no—
987C2×C4—412no—
988C2×C4—412no—
989C2×C4—412no—
990C2×C4—86no—
991C2×C4—86no—
992C2×C4—824no—
993C2×C4—1612no—
994C2×C4C23×D416yes—
995C2×C4C23×D414yes—
996C2×C4C23×D416yes—
997C2×C4C23×D412yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4116yes—
1000C2×C4C2×H(5,𝔽2)16yes—
1001C2×C4C2×H(5,𝔽2)12yes—
1002C2×C4#58512yes—
1003C2×C4#58512yes—
1004C22—26no—
1005C22—24no—
1006C22—212no—
1007C22—24no—
1008C22—212no—
1009C22—24no—
1010C22—26no—
1011C22—26no—
1012C22—212no—
1013C22—46no—
1014C22—43no—
1015C22—42no—
1016C22—46no—
1017C22—43no—
1018C22—43no—
1019C22—46no—
1020C22—42no—
1021C22—46no—
1022C22—43no—
1023C22—42no—
1024C22—42no—
1025C22—43no—
1026C22—43no—
1027C22—43no—
1028C22—43no—
1029C22—43no—
1030C22—43no—
1031C22—43no—
1032C22—848no—
1033C22C24×D411yescharacteristic
1034C22C23×#4111yescharacteristic
1035C22C22×H(5,𝔽2)11yescharacteristic
1036C22C22×H(5,𝔽2)11yescharacteristic
1037C22C2×#58511yescharacteristic
1038C22C2×#58511yescharacteristic
1039C222−1+611yescharacteristic
1040C4—26no—
1041C4—22no—
1042C4—22no—
1043C4—24no—
1044C4—43no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—43no—
1049C4—46no—
1050C4—43no—
1051C4—43no—
1052C4—46no—
1053C4—42no—
1054C4—41no—
1055C4—41no—
1056C4—46no—
1057C4C2×#546112yes—
1058C4#348814yes—
1059C2—412no—
1060C2—46no—
1061C2—44no—
1062C2—83no—
1063C2C22×#54611yescharacteristic
1064C2C2×#348811yescharacteristic
1065C2#6281611yescharacteristic
1066C2#6292211yescharacteristic
1067C2#6298511yescharacteristic
1068C2#6298811yescharacteristic
1069C2#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×#3517C2semidirect
2. C2×D4×#41C2semidirect
3. #59412C2semidirect
4. #59035C2semidirect
5. #59033C2semidirect
6. #59021C2semidirect
7. #45010C2semidirect
8. #45002C2semidirect
9. #38951C2semidirect
10. #38908C2semidirect
11. #37670C2semidirect
12. #36446C2semidirect
13. #36445C2semidirect
14. #36444C2semidirect
15. #36429C2semidirect
16. #36153C2semidirect
17. #36149C2semidirect
18. #35996C2semidirect
19. #35831C2semidirect
20. #34700C2semidirect
21. #34313C2semidirect
22. #34175C2semidirect
23. C4×#550C2semidirect
26. C2×#557C22semidirect
27. C2×#553C22semidirect
31. C2×#550C22semidirect
32. C2×#550C22semidirect
35. C2×#548C22semidirect
37. C2×#547C22semidirect
41. C2×#540C22semidirect
43. C2×#532C22semidirect
44. C2×#529C22semidirect
46. C2×#520C22semidirect
47. C2×#520C22semidirect
49. C2×C4×#41C22semidirect
51. #2862C22semidirect
52. #2857C22semidirect
53. #2857C22semidirect
54. #2847C22semidirect
55. #2706C22semidirect
56. #2706C22semidirect
57. #2695C22semidirect
58. #2693C22semidirect
59. #2688C22semidirect
60. #2678C22semidirect
61. #2668C22semidirect
62. #2625C22semidirect
63. #2620C22semidirect
64. #2568C22semidirect
66. #2547C22semidirect
67. #2544C22semidirect
68. #2542C22semidirect
69. #2538C22semidirect
71. #2537C22semidirect
72. #2535C22semidirect
73. #2535C22semidirect
74. #2502C22semidirect
75. #2489C22semidirect
76. #2489C22semidirect
77. #2486C22semidirect
78. #2480C22semidirect
79. #2468C22semidirect
80. #2457C22semidirect
82. #2454C22semidirect
83. #2447C22semidirect
84. #2447C22semidirect
85. #2447C22semidirect
86. #2444C22semidirect
87. #2442C22semidirect
88. #2441C22semidirect
90. #2433C22semidirect
91. #2431C22semidirect
92. #2431C22semidirect
93. #2428C22semidirect
95. #2427C22semidirect
96. #2427C22semidirect
97. #2427C22semidirect
98. #2425C22semidirect
99. #2424C22semidirect
100. #2422C22semidirect
101. #2422C22semidirect
102. #2420C22semidirect
103. #2420C22semidirect
104. #2420C22semidirect
105. #2418C22semidirect
106. #2418C22semidirect
107. #2417C22semidirect
108. #2417C22semidirect
109. #2417C22semidirect
110. #2416C22semidirect
111. #2415C22semidirect
112. #2412C22semidirect
114. #2408C22semidirect
115. #2407C22semidirect
116. #2407C22semidirect
117. #2407C22semidirect
118. #2407C22semidirect
119. #2395C22semidirect
120. #2392C22semidirect
121. #2366C22semidirect
122. #2366C22semidirect
123. #2363C22semidirect
124. #2363C22semidirect
125. #2361C22semidirect
126. #2354C22semidirect
127. Q8×C4⋊C4C22semidirect
128. Q8×C4⋊C4C22semidirect
129. Q8×C4⋊C4C22semidirect
130. #2349C22semidirect
131. D4×C4⋊C4C22semidirect
134. #2341C22semidirect
135. #2341C22semidirect
136. Q8×C22⋊C4C22semidirect
137. Q8×C22⋊C4C22semidirect
138. Q8×C22⋊C4C22semidirect
139. #2339C22semidirect
140. #2339C22semidirect
141. #2339C22semidirect
142. D4×C22⋊C4C22semidirect
143. D4×C22⋊C4C22semidirect
144. #2324C22semidirect
145. #2311C22semidirect
146. #2311C22semidirect
147. C4×#127C22semidirect
148. C4×#127C22semidirect
150. C4×C22⋊Q8C22semidirect
152. C4×#121C22semidirect
153. C4×#121C22semidirect
154. C4×#120C22semidirect
155. #2293C22semidirect
156. #2280C22semidirect
157. C2×#380C22semidirect
158. C42×Q8C22semidirect
159. C42×D4C22semidirect
178. #550D4semidirect
446. C2×#41#41semidirect
920. Q8#546semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×D4×#412
#594122
#590352
#590332
#590212
#450102
#450022
#389512
#389082
#376702
#364462
#364452
#364442
#364292
#361532
#361492
#359962
#358312
#347002
#343132
#341752
C4×#5502