Finite Group Databasebeta

← #7654819

Subgroups — #7654819

Order 512.

5906 conjugacy classes of subgroups.

The subgroup lattice has 1069 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42401C214yesmaximal, complemented
2#42035C214yesmaximal, complemented
3#42011C214yesmaximal, complemented
4#39262C214yesmaximal, complemented
5#39256C214yesmaximal, complemented
6#37954C214yesmaximal, complemented
7#37852C214yesmaximal, complemented
8#37764C214yesmaximal, complemented
9#37662C214yesmaximal, complemented
10#37636C211yesmaximal, characteristic, complemented
11#37626C211yesmaximal, characteristic, complemented
12#37623C211yesmaximal, characteristic, complemented
13#36168C214yesmaximal, complemented
14#36123C214yesmaximal, complemented
15#35729C214yesmaximal, complemented
16#35237C212yesmaximal, complemented
17#35207C212yesmaximal, complemented
18#35171C212yesmaximal, complemented
19#34943C211yesmaximal, characteristic, complemented
20#34925C211yesmaximal, characteristic, complemented
21C2×#2537C211yesmaximal, characteristic, complemented
22#34207C211yesmaximal, characteristic, complemented
23#34126C212yesmaximal, complemented
24C2×#546C2214yes—
25C2×#540C2214yescomplemented
26C2×#532C2211yescharacteristic
27C2×#532C2214yescomplemented
28C22×#121C2214yes—
29C2×#520C2212yes—
30C22×C4×D4C2212yes—
31#2856C2214yescomplemented
32#2854C2214yescomplemented
33#2854C2214yescomplemented
34#2851C2214yescomplemented
35#2847C2214yes—
36#2847C2214yes—
37#2843C2214yescomplemented
38#2832C2214yescomplemented
39#2828C2214yescomplemented
40#2778C2218yescomplemented
41#2756C2218yescomplemented
42#2746C2218yescomplemented
43#2741C2218yescomplemented
44#2737C2218yescomplemented
45#2717C2218yescomplemented
46#2708C2218yescomplemented
47#2703C2218yescomplemented
48#2699C2218yescomplemented
49#2688C2218yescomplemented
50#2686C2218yescomplemented
51#2671C2218yescomplemented
52#2661C2218yescomplemented
53#2660C2214yescomplemented
54#2653C2218yescomplemented
55#2647C2214yescomplemented
56#2635C2214yescomplemented
57#2632C2214yescomplemented
58#2631C2218yescomplemented
59#2628C2214yescomplemented
60#2627C2214yes—
61#2624C2214yescomplemented
62#2624C2214yescomplemented
63#2619C2214yescomplemented
64#2610C2214yescomplemented
65#2598C2214yescomplemented
66#2591C2214yescomplemented
67#2578C2218yescomplemented
68#2572C2214yescomplemented
69#2571C2211yescharacteristic, complemented
70#2564C2214yes—
71#2563C2212yescomplemented
72#2563C2212yescomplemented
73#2555C2218yescomplemented
74#2555C2214yescomplemented
75#2552C2212yescomplemented
76#2551C2211yescharacteristic, complemented
77#2543C2218yescomplemented
78#2541C2212yescomplemented
79#2541C2212yescomplemented
80#2537C2211yescharacteristic
81#2537C2214yes—
82#2537C2214yes—
83#2537C2214yes—
84#2537C2212yes—
85#2537C2211yescharacteristic
86#2535C2214yescomplemented
87#2535C2214yescomplemented
88#2531C2218yescomplemented
89#2510C2218yes—
90#2510C2218yescomplemented
91#2504C2214yes—
92#2495C2214yescomplemented
93#2495C2214yescomplemented
94#2494C2214yescomplemented
95#2494C2214yescomplemented
96#2491C2214yescomplemented
97#2491C2214yescomplemented
98#2490C2214yescomplemented
99#2490C2214yescomplemented
100#2476C2218yescomplemented
101#2472C2218yes—
102#2464C2218yescomplemented
103#2464C2218yescomplemented
104#2458C2218yescomplemented
105#2443C2218yescomplemented
106#2442C2214yes—
107#2440C2214yes—
108#2433C2214yes—
109#2430C2218yescomplemented
110#2428C2214yescomplemented
111#2428C2214yescomplemented
112#2428C2214yescomplemented
113#2428C2214yescomplemented
114#2422C2214yescomplemented
115#2422C2214yescomplemented
116#2420C2214yescomplemented
117#2420C2214yescomplemented
118#2419C2218yescomplemented
119#2418C2218yes—
120#2412C2218yes—
121#2410C2218yes—
122#2408C2214yes—
123#2406C2214yescomplemented
124#2404C2218yes—
125#2398C2214yescomplemented
126#2388C2214yescomplemented
127C2×#394C2214yes—
128#2361C2214yes—
129#2361C2214yes—
130#2358C2218yes—
131#2357C2212yescomplemented
132#2357C2212yescomplemented
133#2354C2214yescomplemented
134#2353C2214yes—
135#2353C2214yescomplemented
136#2353C2214yescomplemented
137#2349C2212yescomplemented
138#2349C2212yescomplemented
139D4×C4⋊C4C2214yescomplemented
140#2345C2212yes—
141#2345C2212yes—
142#2342C2214yes—
143#2342C2214yes—
144D4×C22⋊C4C2212yes—
145D4×C22⋊C4C2212yes—
146#2328C2214yescomplemented
147#2328C2214yescomplemented
148#2326C2212yescomplemented
149#2326C2212yescomplemented
150#2324C2214yescomplemented
151#2324C2214yescomplemented
152#2314C2214yescomplemented
153#2311C2212yes—
154C4×C4⋊Q8C2211yescharacteristic, complemented
155C4×C4⋊Q8C2211yescharacteristic, complemented
156C4×#127C2211yescharacteristic, complemented
157C4×#127C2211yescharacteristic, complemented
158C4×#121C2214yescomplemented
159C4×#121C2214yescomplemented
160#2293C2212yescomplemented
161#2293C2212yescomplemented
162#2290C2214yescomplemented
163#2290C2214yescomplemented
164C2×#384C2211yescharacteristic
165#2283C2212yes—
166#2283C2214yescomplemented
167#2280C2214yes—
168C2×#380C2214yes—
169C42×D4C2212yescomplemented
170C42×D4C2212yescomplemented
171C4×#117C2211yescharacteristic
172C2×C4×C22⋊C4C2214yes—
173C22×#41C2312yes—
174C22×#41C2314yes—
175C23×D4C2312yes—
176C23×D4C2314yes—
177C24×C4C2314yes—
178#546—416no—
179#540—416no—
180#532—28no—
181#532—416no—
182C2×C4⋊Q8C2311yescharacteristic
183C2×C4⋊Q8C2314yes—
184C2×#127C2311yescharacteristic
185C2×#127C2314yes—
186C2×#127C2314yes—
187C2×#125C2314yes—
188C2×#124C2312yes—
189C2×#124C2314yes—
190C2×#124C2318yes—
191C2×#123C2318yes—
192C2×#123C2318yes—
193C2×#123C2318yes—
194C2×C22⋊Q8C2314yes—
195C2×#121—416no—
196C2×#121C2314yes—
197C2×#121C2314yes—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2318yes—
206C2×#121C2318yes—
207C2×#121C2314yes—
208C2×#121C2318yes—
209C2×#121C2318yes—
210C2×#121C2318yes—
211C2×#121C2318yes—
212C2×#120C2318yes—
213C2×#120C2318yes—
214#520—48no—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×D4—216no—
218C2×C4×D4C2312yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2318yes—
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2314yes—
240C2×#117C2314yes—
241C2×#117C2314yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2314yes—
245C22×C4⋊C4C2314yes—
246C22×C22⋊C4C2314yes—
247C22×C22⋊C4C2314yes—
248C22×C22⋊C4C2314yes—
249C22×C22⋊C4C2318yes—
250C22×C42C2314yes—
251C22×C42C2314yes—
252C22×C42C2311yescharacteristic
253#401C2318yes—
254#400C2314yes—
255#400C2314yes—
256#400C2318yes—
257#400C2318yes—
258#400C2314yes—
259#399C2314yes—
260#399C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#395C2314yes—
274#395C2314yes—
275#395C2318yes—
276#395C2314yes—
277#394C2314yes—
278#394C2314yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2314yes—
284#394C2314yes—
285#394C2314yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2314yes—
292#394C2318yes—
293#393C2318yes—
294#393C2318yes—
295#393C2314yes—
296#393C2318yes—
297#392C2318yes—
298#392C2318yes—
299#392C2314yes—
300#392C2314yes—
301#392C2318yes—
302#392C2318yes—
303#392C2318yes—
304#392C2318yes—
305#391C2312yes—
306#391C2312yes—
307#390C2312yes—
308#390C2312yes—
309#390C2314yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2314yes—
314#390C2318yes—
315#390C2318yes—
316#390C2314yes—
317#390C2312yes—
318#390C2312yes—
319#390C2312yes—
320#390C2312yes—
321#390C2318yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2312yes—
328#389C2312yes—
329#389C2312yes—
330#389C2312yes—
331#389C2314yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2314yes—
336#388C2314yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2314yes—
343#388C2314yes—
344#388C2314yes—
345#388C2314yes—
346#388C2314yes—
347#388C2314yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2314yes—
354#387C2318yes—
355#387C2314yes—
356#387C2314yes—
357#387C2314yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2314yes—
374#386C2314yes—
375#386C2314yes—
376#386C2314yes—
377#386C2318yes—
378#386C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2314yes—
385#385C2314yes—
386#385C2314yes—
387#385C2314yes—
388#385C2318yes—
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2314yes—
392#384C2312yes—
393#384C2314yes—
394#383C2318yes—
395#383C2314yes—
396#383C2314yes—
397#382C2314yes—
398#382C2314yes—
399#382C2314yes—
400#382C2312yes—
401#382C2312yes—
402#381C2318yes—
403#381C2314yes—
404#381C2314yes—
405#381C2314yes—
406#381C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2318yes—
413#380C2314yes—
414#380C2318yes—
415#380C2312yes—
416#380C2312yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2318yes—
424#380C2314yes—
425#379C2314yes—
426#379C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2312yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2312yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454#376C2311yescharacteristic
455#376C2311yescharacteristic
456#376C2314yes—
457#376C2314yes—
458C2×#95C2314yes—
459C2×#95C2314yes—
460C2×#95C2314yes—
461C43C2311yescharacteristic
462C43C2311yescharacteristic
463C25C2414yes—
464C2×#41—28no—
465C2×#41—48no—
466C2×#41—44no—
467C2×#41—44no—
468C2×#41—416no—
469C22×Q8C2412yes—
470C22×Q8C2414yes—
471C22×D4—28no—
472C22×D4—28no—
473C22×D4—44no—
474C22×D4—48no—
475C22×D4—416no—
476C22×D4C2414yes—
477C22×D4C2414yes—
478C22×D4C2412yes—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C22×D4C2412yes—
482C22×D4C2412yes—
483C22×D4C2418yes—
484C22×D4C2418yes—
485C22×D4C2418yes—
486C22×D4C2418yes—
487C22×D4C2418yes—
488C22×D4C2414yes—
489C23×C4—216no—
490C23×C4—48no—
491C23×C4—48no—
492C23×C4C2414yes—
493C23×C4C2414yes—
494C23×C4C2414yes—
495C23×C4C2411yescharacteristic
496C23×C4C2412yes—
497C23×C4C2414yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2414yes—
501C23×C4C2414yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C23×C4C2414yes—
505C23×C4C2414yes—
506C23×C4C2414yes—
507C4⋊Q8—24no—
508C4⋊Q8—48no—
509#127—216no—
510#127—24no—
511#127—48no—
512#125—48no—
513#124—28no—
514#124—48no—
515#124—416no—
516#123—416no—
517#123—416no—
518#123—416no—
519C22⋊Q8—48no—
520#121—216no—
521#121—216no—
522#121—216no—
523#121—48no—
524#121—416no—
525#121—416no—
526#121—416no—
527#121—416no—
528#121—416no—
529#121—48no—
530#121—48no—
531#121—48no—
532#121—48no—
533#121—48no—
534#121—48no—
535#121—416no—
536#120—416no—
537#120—416no—
538C4×Q8—44no—
539C4×Q8—44no—
540C4×D4—28no—
541C4×D4—28no—
542C4×D4—216no—
543C4×D4—216no—
544C4×D4—28no—
545C4×D4—28no—
546C4×D4—216no—
547C4×D4—28no—
548C4×D4—28no—
549C4×D4—216no—
550C4×D4—44no—
551C4×D4—44no—
552C4×D4—44no—
553C4×D4—48no—
554C4×D4—48no—
555C4×D4—44no—
556C4×D4—48no—
557C4×D4—48no—
558C4×D4—416no—
559#117—24no—
560#117—48no—
561#117—48no—
562#117—48no—
563#117—42no—
564C2×C4⋊C4—28no—
565C2×C4⋊C4—48no—
566C2×C4⋊C4—48no—
567C2×C4⋊C4—44no—
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C22⋊C4—216no—
597C2×C22⋊C4—216no—
598C2×C22⋊C4—48no—
599C2×C22⋊C4—416no—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2411yescharacteristic
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2411yescharacteristic
638C2×C42—48no—
639C2×C42—48no—
640C2×C42#4118yescomplemented
641C2×C42C2412yes—
642C2×C42C2412yes—
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2414yes—
646C2×C42C2414yes—
647C2×C42C2414yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2414yes—
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2414yes—
657C2×C42C2412yes—
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#95C2412yes—
661#95C2412yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2418yes—
671#95C2412yes—
672#95C2412yes—
673#95C2414yes—
674#95C2418yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2418yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693C24—28no—
694C24—28no—
695C24—28no—
696C24—28no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24C2514yes—
701C24C2514yes—
702C24C2514yes—
703C24C2511yescharacteristic
704#41—432no—
705#41—832no—
706C2×Q8—24no—
707C2×Q8—42no—
708C2×Q8—42no—
709C2×Q8—44no—
710C2×Q8—48no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—216no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—216no—
717C2×D4—216no—
718C2×D4—216no—
719C2×D4—24no—
720C2×D4—28no—
721C2×D4—24no—
722C2×D4—28no—
723C2×D4—24no—
724C2×D4—28no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—28no—
728C2×D4—24no—
729C2×D4—432no—
730C2×D4—42no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—42no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—44no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—832no—
749C2×D4H(5,𝔽2)18yes—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—48no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—48no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—48no—
790C22×C4—832no—
791C22×C4C2×#4114yes—
792C22×C4C2×#4118yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2514yes—
806C22×C4C2512yes—
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2512yes—
812C4⋊C4—28no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—28no—
816C4⋊C4—22no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—22no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—44no—
826C4⋊C4—42no—
827C4⋊C4—42no—
828C4⋊C4—44no—
829C4⋊C4—48no—
830C4⋊C4—42no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C22⋊C4—28no—
841C22⋊C4—216no—
842C22⋊C4—216no—
843C22⋊C4—22no—
844C22⋊C4—28no—
845C22⋊C4—28no—
846C22⋊C4—24no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4—28no—
851C22⋊C4—28no—
852C22⋊C4—216no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4H(5,𝔽2)14yes—
878C42—24no—
879C42—28no—
880C42—22no—
881C42—22no—
882C42—24no—
883C42—28no—
884C42—24no—
885C42—28no—
886C42—24no—
887C42—44no—
888C42—44no—
889C42—44no—
890C42—44no—
891C42—41no—
892C42—41no—
893C42—44no—
894C42C2×#4118yes—
895C42C2×#4114yes—
896C42C2×#4114yes—
897C23—22no—
898C23—22no—
899C23—24no—
900C23—24no—
901C23—24no—
902C23—24no—
903C23—24no—
904C23—24no—
905C23—24no—
906C23—24no—
907C23—24no—
908C23—24no—
909C23—28no—
910C23—24no—
911C23—24no—
912C23—24no—
913C23—24no—
914C23—28no—
915C23—24no—
916C23—24no—
917C23—416no—
918C23—416no—
919C23—416no—
920C23—416no—
921C23—88no—
922C23—88no—
923C23—88no—
924C23C22×#4112yes—
925C23C2×H(5,𝔽2)18yes—
926C23C2×H(5,𝔽2)12yes—
927C23#58512yes—
928C23C2611yescharacteristic
929Q8—48no—
930Q8—88no—
931D4—216no—
932D4—416no—
933D4—48no—
934D4—416no—
935D4—416no—
936D4—416no—
937D4—48no—
938D4—816no—
939D4—816no—
940D4—816no—
941D4—88no—
942D4—168no—
943D4—168no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—28no—
953C2×C4—216no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—28no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—416no—
990C2×C4—416no—
991C2×C4—416no—
992C2×C4—416no—
993C2×C4—88no—
994C2×C4—88no—
995C2×C4—88no—
996C2×C4—88no—
997C2×C4—88no—
998C2×C4—88no—
999C2×C4—88no—
1000C2×C4—88no—
1001C2×C4—164no—
1002C2×C4C22×#4112yes—
1003C2×C4C22×#4112yes—
1004C2×C4C22×#4114yes—
1005C2×C4C22×#4114yes—
1006C2×C4C2×H(5,𝔽2)12yes—
1007C2×C4C2×H(5,𝔽2)12yes—
1008C2×C4C2×H(5,𝔽2)14yes—
1009C2×C4#58514yes—
1010C22—22no—
1011C22—24no—
1012C22—22no—
1013C22—24no—
1014C22—28no—
1015C22—28no—
1016C22—28no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—48no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—48no—
1031C22—44no—
1032C22—44no—
1033C22—832no—
1034C22#346014yes—
1035C22C23×#4111yescharacteristic
1036C22C22×H(5,𝔽2)12yes—
1037C22C22×H(5,𝔽2)11yescharacteristic
1038C22C2×#58511yescharacteristic
1039C22C2×#58512yes—
1040C4—22no—
1041C4—22no—
1042C4—24no—
1043C4—22no—
1044C4—22no—
1045C4—44no—
1046C4—44no—
1047C4—44no—
1048C4—41no—
1049C4—42no—
1050C4—42no—
1051C4—44no—
1052C4—44no—
1053C4—41no—
1054C4—44no—
1055C4—44no—
1056C4—44no—
1057C4—44no—
1058C4#349418yes—
1059C2—24no—
1060C2—48no—
1061C2—84no—
1062C2—84no—
1063C2C2×#346011yescharacteristic
1064C2C2×#349412yes—
1065C2#6301111yescharacteristic
1066C2#6301812yes—
1067C2#6302411yescharacteristic
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. #42401C2semidirect
2. #42035C2semidirect
3. #42011C2semidirect
4. #39262C2semidirect
5. #39256C2semidirect
6. #37954C2semidirect
7. #37852C2semidirect
8. #37764C2semidirect
9. #37662C2semidirect
10. #37636C2semidirect
11. #37626C2semidirect
12. #37623C2semidirect
13. #36168C2semidirect
14. #36123C2semidirect
15. #35729C2semidirect
16. #35237C2semidirect
17. #35207C2semidirect
18. #35171C2semidirect
19. #34943C2semidirect
20. #34925C2semidirect
21. C2×#2537C2semidirect
22. #34207C2semidirect
23. #34126C2semidirect
25. C2×#540C22semidirect
27. C2×#532C22semidirect
31. #2856C22semidirect
32. #2854C22semidirect
33. #2854C22semidirect
34. #2851C22semidirect
37. #2843C22semidirect
38. #2832C22semidirect
39. #2828C22semidirect
40. #2778C22semidirect
41. #2756C22semidirect
42. #2746C22semidirect
43. #2741C22semidirect
44. #2737C22semidirect
45. #2717C22semidirect
46. #2708C22semidirect
47. #2703C22semidirect
48. #2699C22semidirect
49. #2688C22semidirect
50. #2686C22semidirect
51. #2671C22semidirect
52. #2661C22semidirect
53. #2660C22semidirect
54. #2653C22semidirect
55. #2647C22semidirect
56. #2635C22semidirect
57. #2632C22semidirect
58. #2631C22semidirect
59. #2628C22semidirect
61. #2624C22semidirect
62. #2624C22semidirect
63. #2619C22semidirect
64. #2610C22semidirect
65. #2598C22semidirect
66. #2591C22semidirect
67. #2578C22semidirect
68. #2572C22semidirect
69. #2571C22semidirect
71. #2563C22semidirect
72. #2563C22semidirect
73. #2555C22semidirect
74. #2555C22semidirect
75. #2552C22semidirect
76. #2551C22semidirect
77. #2543C22semidirect
78. #2541C22semidirect
79. #2541C22semidirect
86. #2535C22semidirect
87. #2535C22semidirect
88. #2531C22semidirect
90. #2510C22semidirect
92. #2495C22semidirect
93. #2495C22semidirect
94. #2494C22semidirect
95. #2494C22semidirect
96. #2491C22semidirect
97. #2491C22semidirect
98. #2490C22semidirect
99. #2490C22semidirect
100. #2476C22semidirect
102. #2464C22semidirect
103. #2464C22semidirect
104. #2458C22semidirect
105. #2443C22semidirect
109. #2430C22semidirect
110. #2428C22semidirect
111. #2428C22semidirect
112. #2428C22semidirect
113. #2428C22semidirect
114. #2422C22semidirect
115. #2422C22semidirect
116. #2420C22semidirect
117. #2420C22semidirect
118. #2419C22semidirect
123. #2406C22semidirect
125. #2398C22semidirect
126. #2388C22semidirect
131. #2357C22semidirect
132. #2357C22semidirect
133. #2354C22semidirect
135. #2353C22semidirect
136. #2353C22semidirect
137. #2349C22semidirect
138. #2349C22semidirect
139. D4×C4⋊C4C22semidirect
146. #2328C22semidirect
147. #2328C22semidirect
148. #2326C22semidirect
149. #2326C22semidirect
150. #2324C22semidirect
151. #2324C22semidirect
152. #2314C22semidirect
154. C4×C4⋊Q8C22semidirect
155. C4×C4⋊Q8C22semidirect
156. C4×#127C22semidirect
157. C4×#127C22semidirect
158. C4×#121C22semidirect
159. C4×#121C22semidirect
160. #2293C22semidirect
161. #2293C22semidirect
162. #2290C22semidirect
163. #2290C22semidirect
166. #2283C22semidirect
169. C42×D4C22semidirect
170. C42×D4C22semidirect
640. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#424012
#420352
#420112
#392622
#392562
#379542
#378522
#377642
#376622
#376362
#376262
#376232
#361682
#361232
#357292
#352372
#352072
#351712
#349432
#349252
C2×#25372
#342072
#341262