Finite Group Databasebeta

← #7643903

Subgroups — #7643903

Order 512.

6976 conjugacy classes of subgroups.

The subgroup lattice has 1089 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C212yesmaximal, complemented
2#42173C214yesmaximal, complemented
3#42172C214yesmaximal, complemented
4#42169C214yesmaximal, complemented
5#42168C214yesmaximal, complemented
6#41990C214yesmaximal, complemented
7#41989C214yesmaximal, complemented
8#41986C214yesmaximal, complemented
9#41985C214yesmaximal, complemented
10#37447C212yesmaximal, complemented
11#37446C212yesmaximal, complemented
12#37442C212yesmaximal, complemented
13#37439C212yesmaximal, complemented
14#37130C214yesmaximal, complemented
15#37129C214yesmaximal, complemented
16#35365C218yesmaximal, complemented
17#35119C211yesmaximal, characteristic, complemented
18#35119C211yesmaximal, characteristic, complemented
19#34594C212yesmaximal, complemented
20C2×#2319C211yesmaximal, characteristic, complemented
21#3505—232no—
22C2×#553C2212yes—
23C2×#553C2214yes—
24C2×#553C2212yescomplemented
25C2×#553C2214yescomplemented
26C2×#552C2212yes—
27C2×#552C2212yescomplemented
28C2×#551C2214yes—
29C2×#551C2214yescomplemented
30C2×#548C2212yes—
31C2×#548C2212yescomplemented
32C2×#546C2212yes—
33C2×#546C2212yescomplemented
34C2×#539C2214yescomplemented
35C2×#538C2214yes—
36C2×#534C2214yes—
37C2×#529C2212yescomplemented
38C2×#529C2212yescomplemented
39C2×#525C2212yes—
40C2×#525C2212yes—
41C22×C22⋊Q8C2212yescomplemented
42C22×#121C2212yescomplemented
43C2×#518C2214yescomplemented
44C22×C4×D4C2211yescharacteristic
45#2854C2214yescomplemented
46#2854C2214yescomplemented
47#2817C2214yescomplemented
48#2816C2214yescomplemented
49#2816C2214yescomplemented
50#2815C2214yescomplemented
51#2814C2214yescomplemented
52#2814C2214yescomplemented
53#2813C2214yescomplemented
54#2813C2214yescomplemented
55#2727C2214yescomplemented
56#2726C2214yescomplemented
57#2725C2218yescomplemented
58#2724C2214yes—
59#2707C2218yescomplemented
60#2705C2218yescomplemented
61#2704C2218yescomplemented
62#2702C2218yescomplemented
63#2701C2218yescomplemented
64#2701C2218yescomplemented
65#2699C2218yescomplemented
66#2697C2218yes—
67#2683C2214yescomplemented
68#2682C2214yescomplemented
69#2682C2214yescomplemented
70#2682C2214yescomplemented
71#2681C2218yescomplemented
72#2679C2214yes—
73#2678C2218yescomplemented
74#2678C2218yescomplemented
75#2664C2214yescomplemented
76#2664C2214yescomplemented
77#2662C2214yescomplemented
78#2662C2214yescomplemented
79#2659C2212yescomplemented
80#2659C2211yescharacteristic, complemented
81#2659C2211yescharacteristic, complemented
82#2656C2212yes—
83#2656C2211yescharacteristic
84#2656C2211yescharacteristic
85#2639C2212yescomplemented
86#2639C2212yescomplemented
87#2639C2212yescomplemented
88#2639C2212yescomplemented
89#2638C2214yescomplemented
90#2638C2214yescomplemented
91#2635C2214yescomplemented
92#2635C2214yescomplemented
93#2627C2214yescomplemented
94#2626C2214yescomplemented
95#2625C2214yescomplemented
96#2624C2214yescomplemented
97#2623C2214yescomplemented
98#2623C2214yescomplemented
99#2618C2214yescomplemented
100#2618C2218yescomplemented
101#2617C2214yescomplemented
102#2616C2214yescomplemented
103#2615C2214yescomplemented
104#2614C2214yescomplemented
105#2613C2214yescomplemented
106#2611C2214yescomplemented
107#2611C2214yescomplemented
108#2610C2214yescomplemented
109#2610C2214yescomplemented
110#2604C2214yescomplemented
111#2604C2214yescomplemented
112#2603C2214yescomplemented
113#2603C2214yescomplemented
114#2564C2218yescomplemented
115#2543C2218yescomplemented
116#2487C2214yescomplemented
117#2486C2214yescomplemented
118#2484C2214yescomplemented
119#2482C2214yescomplemented
120#2480C2218yescomplemented
121#2478C2218yescomplemented
122#2476C2218yescomplemented
123#2474C2218yescomplemented
124#2472C2218yescomplemented
125#2470C2218yescomplemented
126#2468C2218yescomplemented
127#2466C2218yescomplemented
128#2464C2218yescomplemented
129#2461C2218yescomplemented
130#2459C2218yescomplemented
131#2457C2218yescomplemented
132#2456C2218yescomplemented
133#2455C2218yescomplemented
134#2424C2218yescomplemented
135#2418C2218yescomplemented
136#2417C2218yescomplemented
137#2416C2218yescomplemented
138#2412C2218yescomplemented
139#2412C2218yescomplemented
140#2410C2218yescomplemented
141#2410C2218yescomplemented
142#2409C2214yescomplemented
143#2408C2214yescomplemented
144#2406C2214yescomplemented
145#2404C2214yescomplemented
146#2396C2214yescomplemented
147#2396C2214yescomplemented
148#2392C2214yescomplemented
149#2392C2214yescomplemented
150#2325C2214yescomplemented
151#2325C2214yescomplemented
152#2319C2214yes—
153#2319C2214yescomplemented
154#2319C2214yescomplemented
155#2319C2214yescomplemented
156C4×#121C2218yescomplemented
157C2×#390C2212yes—
158C2×#389C2212yescomplemented
159C2×#388C2214yescomplemented
160C2×#381C2212yescomplemented
161C2×#380C2212yescomplemented
162C2×C4×C4⋊C4C2211yescharacteristic, complemented
163C2×#376C2211yescharacteristic, complemented
164C22×#41C2312yes—
165C22×#41C2312yes—
166C23×Q8C2312yes—
167C23×D4C2314yes—
168C23×D4C2312yes—
169C23×D4C2311yescharacteristic
170C24×C4C2312yes—
171#553—216no—
172#553—232no—
173#553—216no—
174#553—232no—
175#552—216no—
176#552—216no—
177#551—232no—
178#551—232no—
179#548—216no—
180#548—216no—
181#546—216no—
182#546—216no—
183#539—232no—
184#538—232no—
185#534—232no—
186#529—216no—
187#529—216no—
188C2×#126C2314yes—
189C2×#126C2314yes—
190C2×#126C2314yes—
191C2×#126C2314yes—
192C2×#126C2314yes—
193C2×#126C2314yes—
194C2×#125C2312yes—
195C2×#125C2312yes—
196C2×#125C2314yes—
197C2×#125C2314yes—
198C2×#124C2312yes—
199C2×#124C2312yes—
200C2×#124C2314yes—
201C2×#124C2314yes—
202#525—216no—
203#525—216no—
204C2×#123C2314yes—
205C2×#123C2314yes—
206C2×#123C2314yes—
207C2×#123C2314yes—
208C2×#123C2314yes—
209C2×#123C2314yes—
210C2×#123C2314yes—
211C2×#123C2314yes—
212C2×#123C2314yes—
213C2×#123C2314yes—
214C2×#123C2318yes—
215C2×#123C2318yes—
216C2×C22⋊Q8—216no—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2318yes—
228C2×#121—216no—
229C2×#121C2312yes—
230C2×#121C2314yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2318yes—
246C2×#121C2318yes—
247C2×#120C2314yes—
248C2×#120C2314yes—
249C2×#120C2314yes—
250C2×#120C2314yes—
251C2×#120C2318yes—
252C2×#120C2318yes—
253#518—232no—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×D4D4116yescomplemented
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×#117C2314yes—
275C2×#117C2314yes—
276C2×#117C2312yes—
277C2×#117C2312yes—
278C2×#117C2314yes—
279C2×#117C2314yes—
280C22×C4⋊C4C2314yes—
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2314yes—
285C22×C4⋊C4C2311yescharacteristic
286C22×C22⋊C4C2314yes—
287C22×C22⋊C4C2314yes—
288C22×C22⋊C4C2314yes—
289C22×C22⋊C4C2314yes—
290C22×C22⋊C4C2314yes—
291C22×C22⋊C4C2314yes—
292C22×C22⋊C4C2312yes—
293C22×C42C2312yes—
294C22×C42C2312yes—
295C22×C42C2311yescharacteristic
296#400C2318yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#399C2318yes—
302#399C2314yes—
303#399C2314yes—
304#399C2314yes—
305#399C2314yes—
306#398C2314yes—
307#398C2318yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2318yes—
312#398C2318yes—
313#398C2318yes—
314#398C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2318yes—
321#397C2318yes—
322#397C2318yes—
323#397C2314yes—
324#396C2318yes—
325#396C2318yes—
326#396C2318yes—
327#396C2318yes—
328#396C2318yes—
329#396C2318yes—
330#396C2318yes—
331#396C2318yes—
332#395C2318yes—
333#395C2314yes—
334#395C2314yes—
335#395C2314yes—
336#395C2314yes—
337#394C2314yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2314yes—
344#394C2314yes—
345#394C2314yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#393C2318yes—
355#393C2314yes—
356#393C2314yes—
357#393C2314yes—
358#393C2314yes—
359#392C2314yes—
360#392C2314yes—
361#392C2314yes—
362#392C2318yes—
363#392C2318yes—
364#392C2318yes—
365#392C2318yes—
366#392C2318yes—
367#392C2314yes—
368#391C2318yes—
369#390C2314yes—
370#390C2318yes—
371#390C2314yes—
372#390C2314yes—
373#390C2314yes—
374#390C2314yes—
375#390C2314yes—
376#390C2318yes—
377#390C2318yes—
378#389C2318yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2318yes—
386#389C2318yes—
387#389C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#381C2314yes—
427#381C2314yes—
428#381C2314yes—
429#381C2314yes—
430#381C2318yes—
431#381C2318yes—
432#380C2314yes—
433#380C2318yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2318yes—
440#380C2318yes—
441#379C2318yes—
442#379C2318yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2318yes—
446C4×C22⋊C4C2318yes—
447C4×C22⋊C4C2318yes—
448#376C2314yes—
449#376C2314yes—
450C2×#95C2314yes—
451C2×#95C2312yes—
452C2×#95C2311yescharacteristic
453C2×#95C2311yescharacteristic
454C2×#95C2312yes—
455C25C2412yes—
456C25C2414yes—
457C2×#41—28no—
458C2×#41—28no—
459C2×#41—84no—
460C2×#41—84no—
461C22×Q8—28no—
462C22×Q8—84no—
463C22×Q8C2412yes—
464C22×Q8C2412yes—
465C22×Q8C2414yes—
466C22×D4—216no—
467C22×D4—28no—
468C22×D4—44no—
469C22×D4—416no—
470C22×D4—84no—
471C22×D4C2×D418yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2414yes—
475C22×D4C2414yes—
476C22×D4C2414yes—
477C22×D4C2414yes—
478C22×D4C2412yes—
479C22×D4C2412yes—
480C22×D4C2414yes—
481C22×D4C2414yes—
482C22×D4C2414yes—
483C22×D4C2418yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2411yescharacteristic
487C22×D4C2412yes—
488C22×D4C2411yescharacteristic
489C23×C4—84no—
490C23×C4C2×D4116yes—
491C23×C4C2411yescharacteristic
492C23×C4C2412yes—
493C23×C4C2414yes—
494C23×C4C2412yes—
495C23×C4C2414yes—
496C23×C4C2414yes—
497C23×C4C2414yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2414yes—
501C23×C4C2414yes—
502C23×C4C2412yes—
503C23×C4C2411yescharacteristic
504C23×C4C2412yes—
505C23×C4C2412yes—
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2411yescharacteristic
509#126—216no—
510#126—216no—
511#126—216no—
512#126—216no—
513#126—216no—
514#126—216no—
515#125—216no—
516#125—216no—
517#125—28no—
518#125—28no—
519#124—216no—
520#124—216no—
521#124—28no—
522#124—28no—
523#123—216no—
524#123—216no—
525#123—216no—
526#123—216no—
527#123—216no—
528#123—216no—
529#123—216no—
530#123—216no—
531#123—216no—
532#123—216no—
533#123—88no—
534#123—88no—
535C22⋊Q8—28no—
536C22⋊Q8—28no—
537C22⋊Q8—216no—
538C22⋊Q8—28no—
539C22⋊Q8—28no—
540C22⋊Q8—216no—
541C22⋊Q8—28no—
542C22⋊Q8—28no—
543C22⋊Q8—216no—
544C22⋊Q8—216no—
545C22⋊Q8—88no—
546#121—216no—
547#121—216no—
548#121—216no—
549#121—216no—
550#121—28no—
551#121—28no—
552#121—216no—
553#121—28no—
554#121—28no—
555#121—216no—
556#121—28no—
557#121—28no—
558#121—216no—
559#121—216no—
560#121—48no—
561#121—48no—
562#121—416no—
563#121—88no—
564#120—216no—
565#120—216no—
566#120—216no—
567#120—216no—
568#120—88no—
569#120—88no—
570C4×Q8—28no—
571C4×Q8—28no—
572C4×D4—216no—
573C4×D4—216no—
574C4×D4—216no—
575C4×D4—216no—
576C4×D4—216no—
577C4×D4—216no—
578C4×D4—216no—
579C4×D4—216no—
580C4×D4—216no—
581C4×D4—216no—
582C4×D4—28no—
583C4×D4—28no—
584C4×D4—88no—
585C4×D4C2×D4116yes—
586C4×D4C2×D4116yes—
587C4×D4C2×D4116yes—
588C4×D4C2×D4116yes—
589#117—28no—
590#117—28no—
591#117—216no—
592#117—216no—
593#117—216no—
594#117—216no—
595C2×C4⋊C4—28no—
596C2×C4⋊C4—28no—
597C2×C4⋊C4—216no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4—84no—
600C2×C4⋊C4C2×D418yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C22⋊C4—216no—
636C2×C22⋊C4—216no—
637C2×C22⋊C4—216no—
638C2×C22⋊C4—216no—
639C2×C22⋊C4—84no—
640C2×C22⋊C4—84no—
641C2×C22⋊C4C2×D4116yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C42—44no—
683C2×C42—82no—
684C2×C42C2×D418yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2418yes—
690C2×C42C2414yes—
691C2×C42C2414yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713C24—28no—
714C24—28no—
715C24—42no—
716C24—44no—
717C24—42no—
718C24—48no—
719C24—44no—
720C24—48no—
721C24—44no—
722C24C22×D418yes—
723C24C2514yes—
724C24C2514yes—
725C24C2512yes—
726C24C2512yes—
727C24C2511yescharacteristic
728#41—816no—
729#41—816no—
730C2×Q8—24no—
731C2×Q8—24no—
732C2×Q8—28no—
733C2×Q8—44no—
734C2×Q8—44no—
735C2×Q8—48no—
736C2×Q8—816no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—28no—
741C2×D4—216no—
742C2×D4—216no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—24no—
748C2×D4—24no—
749C2×D4—28no—
750C2×D4—416no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—48no—
759C2×D4—44no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—44no—
765C2×D4—48no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—464no—
775C2×D4—816no—
776C2×D4C22×D414yes—
777C2×D4C22×D418yes—
778C2×D4C22×D414yes—
779C22×C4—24no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—41no—
791C22×C4—44no—
792C22×C4—42no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—41no—
798C22×C4—48no—
799C22×C4—44no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—44no—
803C22×C4—42no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—44no—
809C22×C4—48no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—42no—
813C22×C4—44no—
814C22×C4—816no—
815C22×C4C22×D414yes—
816C22×C4C22×D414yes—
817C22×C4C22×D414yes—
818C22×C4C22×D418yes—
819C22×C4C22×D418yes—
820C22×C4C22×D418yes—
821C22×C4C22×D418yes—
822C22×C4C22×D418yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2518yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4C22×D414yes—
870C4⋊C4C22×D418yes—
871C4⋊C4C22×D414yes—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4C22×D418yes—
909C22⋊C4C22×D418yes—
910C22⋊C4C22×D418yes—
911C22⋊C4C22×D418yes—
912C42—28no—
913C42—28no—
914C42—28no—
915C42—28no—
916C42—44no—
917C42—44no—
918C42—48no—
919C42C22×D418yes—
920C42C22×D418yes—
921C23—22no—
922C23—21no—
923C23—21no—
924C23—24no—
925C23—24no—
926C23—22no—
927C23—22no—
928C23—24no—
929C23—24no—
930C23—22no—
931C23—22no—
932C23—216no—
933C23—24no—
934C23—24no—
935C23—28no—
936C23—28no—
937C23—24no—
938C23—28no—
939C23—28no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—48no—
944C23—48no—
945C23—416no—
946C23—88no—
947C23—88no—
948C23—88no—
949C23—88no—
950C23—168no—
951C23—168no—
952C23C23×D414yes—
953C23C23×D414yes—
954C23C23×D412yes—
955C23#58514yes—
956C23C2611yescharacteristic
957Q8—48no—
958Q8—48no—
959Q8—88no—
960D4—44no—
961D4—48no—
962D4—44no—
963D4—48no—
964D4—48no—
965D4—416no—
966D4—416no—
967D4—416no—
968D4—416no—
969D4—88no—
970D4—88no—
971D4—88no—
972D4—88no—
973D4—88no—
974D4—816no—
975D4—164no—
976D4—164no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—28no—
996C2×C4—28no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—28no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—28no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—44no—
1009C2×C4—48no—
1010C2×C4—48no—
1011C2×C4—48no—
1012C2×C4—48no—
1013C2×C4—48no—
1014C2×C4—44no—
1015C2×C4—416no—
1016C2×C4—88no—
1017C2×C4—88no—
1018C2×C4—88no—
1019C2×C4—88no—
1020C2×C4—88no—
1021C2×C4—88no—
1022C2×C4—84no—
1023C2×C4—84no—
1024C2×C4—88no—
1025C2×C4C23×D414yes—
1026C2×C4C23×D414yes—
1027C2×C4C23×D414yes—
1028C2×C4C23×D412yes—
1029C2×C4C23×D412yes—
1030C2×C4C23×D414yes—
1031C22—22no—
1032C22—22no—
1033C22—24no—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—24no—
1041C22—44no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—44no—
1046C22—44no—
1047C22—44no—
1048C22—44no—
1049C22—48no—
1050C22—48no—
1051C22—48no—
1052C22—48no—
1053C22—44no—
1054C22—44no—
1055C22—816no—
1056C22—1616no—
1057C22#344914yes—
1058C22C24×D411yescharacteristic
1059C22C2×#58512yes—
1060C22H(7,𝔽2)12yes—
1061C22H(7,𝔽2)11yescharacteristic
1062C222−1+611yescharacteristic
1063C4—24no—
1064C4—24no—
1065C4—24no—
1066C4—24no—
1067C4—22no—
1068C4—22no—
1069C4—44no—
1070C4—44no—
1071C4—44no—
1072C4—44no—
1073C4—48no—
1074C4—44no—
1075C4—44no—
1076C4—44no—
1077C4—44no—
1078C2—24no—
1079C2—44no—
1080C2—44no—
1081C2—84no—
1082C2—84no—
1083C2C2×#344911yescharacteristic
1084C2#6284211yescharacteristic
1085C2#6285311yescharacteristic
1086C2#6287012yes—
1087C2#6287212yes—
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×#3505C2semidirect
2. #42173C2semidirect
3. #42172C2semidirect
4. #42169C2semidirect
5. #42168C2semidirect
6. #41990C2semidirect
7. #41989C2semidirect
8. #41986C2semidirect
9. #41985C2semidirect
10. #37447C2semidirect
11. #37446C2semidirect
12. #37442C2semidirect
13. #37439C2semidirect
14. #37130C2semidirect
15. #37129C2semidirect
16. #35365C2semidirect
17. #35119C2semidirect
18. #35119C2semidirect
19. #34594C2semidirect
20. C2×#2319C2semidirect
24. C2×#553C22semidirect
25. C2×#553C22semidirect
27. C2×#552C22semidirect
29. C2×#551C22semidirect
31. C2×#548C22semidirect
33. C2×#546C22semidirect
34. C2×#539C22semidirect
37. C2×#529C22semidirect
38. C2×#529C22semidirect
41. C22×C22⋊Q8C22semidirect
42. C22×#121C22semidirect
43. C2×#518C22semidirect
45. #2854C22semidirect
46. #2854C22semidirect
47. #2817C22semidirect
48. #2816C22semidirect
49. #2816C22semidirect
50. #2815C22semidirect
51. #2814C22semidirect
52. #2814C22semidirect
53. #2813C22semidirect
54. #2813C22semidirect
55. #2727C22semidirect
56. #2726C22semidirect
57. #2725C22semidirect
59. #2707C22semidirect
60. #2705C22semidirect
61. #2704C22semidirect
62. #2702C22semidirect
63. #2701C22semidirect
64. #2701C22semidirect
65. #2699C22semidirect
67. #2683C22semidirect
68. #2682C22semidirect
69. #2682C22semidirect
70. #2682C22semidirect
71. #2681C22semidirect
73. #2678C22semidirect
74. #2678C22semidirect
75. #2664C22semidirect
76. #2664C22semidirect
77. #2662C22semidirect
78. #2662C22semidirect
79. #2659C22semidirect
80. #2659C22semidirect
81. #2659C22semidirect
85. #2639C22semidirect
86. #2639C22semidirect
87. #2639C22semidirect
88. #2639C22semidirect
89. #2638C22semidirect
90. #2638C22semidirect
91. #2635C22semidirect
92. #2635C22semidirect
93. #2627C22semidirect
94. #2626C22semidirect
95. #2625C22semidirect
96. #2624C22semidirect
97. #2623C22semidirect
98. #2623C22semidirect
99. #2618C22semidirect
100. #2618C22semidirect
101. #2617C22semidirect
102. #2616C22semidirect
103. #2615C22semidirect
104. #2614C22semidirect
105. #2613C22semidirect
106. #2611C22semidirect
107. #2611C22semidirect
108. #2610C22semidirect
109. #2610C22semidirect
110. #2604C22semidirect
111. #2604C22semidirect
112. #2603C22semidirect
113. #2603C22semidirect
114. #2564C22semidirect
115. #2543C22semidirect
116. #2487C22semidirect
117. #2486C22semidirect
118. #2484C22semidirect
119. #2482C22semidirect
120. #2480C22semidirect
121. #2478C22semidirect
122. #2476C22semidirect
123. #2474C22semidirect
124. #2472C22semidirect
125. #2470C22semidirect
126. #2468C22semidirect
127. #2466C22semidirect
128. #2464C22semidirect
129. #2461C22semidirect
130. #2459C22semidirect
131. #2457C22semidirect
132. #2456C22semidirect
133. #2455C22semidirect
134. #2424C22semidirect
135. #2418C22semidirect
136. #2417C22semidirect
137. #2416C22semidirect
138. #2412C22semidirect
139. #2412C22semidirect
140. #2410C22semidirect
141. #2410C22semidirect
142. #2409C22semidirect
143. #2408C22semidirect
144. #2406C22semidirect
145. #2404C22semidirect
146. #2396C22semidirect
147. #2396C22semidirect
148. #2392C22semidirect
149. #2392C22semidirect
150. #2325C22semidirect
151. #2325C22semidirect
153. #2319C22semidirect
154. #2319C22semidirect
155. #2319C22semidirect
156. C4×#121C22semidirect
158. C2×#389C22semidirect
159. C2×#388C22semidirect
160. C2×#381C22semidirect
161. C2×#380C22semidirect
162. C2×C4×C4⋊C4C22semidirect
163. C2×#376C22semidirect
256. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
#421732
#421722
#421692
#421682
#419902
#419892
#419862
#419852
#374472
#374462
#374422
#374392
#371302
#371292
#353652
#351192
#345942
C2×#23192