Finite Group Databasebeta

← #7688610

Subgroups — #7688610

Order 512.

5776 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59713C214yesmaximal, complemented
2#59465C211yesmaximal, characteristic, complemented
3#59303C211yesmaximal, characteristic, complemented
4#59233C211yesmaximal, characteristic, complemented
5#59135C214yesmaximal, complemented
6#59115C214yesmaximal, complemented
7#44377C214yesmaximal, complemented
8#43882C214yesmaximal, complemented
9#43575C214yesmaximal, complemented
10#40127C214yesmaximal, complemented
11#40121C214yesmaximal, complemented
12#39742C214yesmaximal, complemented
13#36596C212yesmaximal, complemented
14#36407C212yesmaximal, complemented
15#36273C212yesmaximal, complemented
16#36182C211yesmaximal, characteristic, complemented
17#36122C214yesmaximal, complemented
18#35929C214yesmaximal, complemented
19#34978C211yesmaximal, characteristic, complemented
20#34925C211yesmaximal, characteristic, complemented
21C2×#2551C211yesmaximal, characteristic, complemented
22#34323C214yesmaximal, complemented
23C4×#553C212yesmaximal, complemented
24C2×#555C2214yes—
25C2×#553C2214yes—
26C2×#553C2212yes—
27C2×#553C2212yes—
28C2×#548C2214yes—
29C2×#532C2214yes—
30C22×C4⋊Q8C2214yes—
31#2859C2211yescharacteristic
32#2858C2214yes—
33#2857C2214yes—
34#2856C2214yes—
35#2856C2211yescharacteristic
36#2856C2211yescharacteristic
37#2795C2214yes—
38#2785C2214yes—
39#2784C2214yes—
40#2775C2218yes—
41#2737C2218yes—
42#2731C2218yes—
43#2731C2218yes—
44#2727C2218yes—
45#2705C2218yes—
46#2705C2218yes—
47#2686C2218yes—
48#2682C2218yes—
49#2663C2214yes—
50#2662C2214yes—
51#2656C2214yes—
52#2612C2214yes—
53#2610C2218yes—
54#2610C2214yes—
55#2604C2214yes—
56#2591C2214yes—
57#2574C2218yes—
58#2571C2211yescharacteristic
59#2566C2212yes—
60#2564C2214yes—
61#2563C2214yes—
62#2563C2214yes—
63#2556C2218yes—
64#2555C2214yes—
65#2555C2218yes—
66#2554C2218yes—
67#2552C2212yes—
68#2551C2212yes—
69#2551C2214yes—
70#2551C2211yescharacteristic
71#2551C2214yes—
72#2551C2211yescharacteristic
73#2551C2214yes—
74#2545C2218yes—
75#2543C2218yes—
76#2541C2212yes—
77#2537C2211yescharacteristic
78#2521C2218yes—
79#2512C2214yes—
80#2512C2214yes—
81#2504C2212yes—
82#2500C2212yes—
83#2500C2214yes—
84#2497C2214yes—
85#2491C2214yes—
86#2491C2214yes—
87#2491C2218yes—
88#2491C2214yes—
89#2491C2218yes—
90#2491C2214yes—
91#2490C2214yes—
92#2474C2218yes—
93#2461C2218yes—
94#2454C2214yes—
95#2454C2214yes—
96#2452C2214yes—
97#2452C2214yes—
98#2452C2218yes—
99#2445C2214yes—
100#2441C2214yes—
101#2441C2214yes—
102#2439C2214yes—
103#2439C2218yes—
104#2439C2214yes—
105#2436C2218yes—
106#2436C2214yes—
107#2432C2218yes—
108#2430C2214yes—
109#2428C2214yes—
110#2428C2214yes—
111#2422C2214yes—
112#2416C2218yes—
113#2416C2214yes—
114#2416C2214yes—
115#2416C2214yes—
116#2416C2218yes—
117#2414C2214yes—
118#2414C2214yes—
119#2396C2214yes—
120#2388C2214yes—
121C2×#395C2214yes—
122#2374C2214yes—
123#2373C2218yes—
124#2373C2214yes—
125#2370C2214yes—
126#2370C2212yes—
127#2369C2214yes—
128#2366C2212yes—
129#2364C2214yes—
130#2363C2214yes—
131#2363C2214yes—
132#2363C2212yes—
133#2361C2214yes—
134#2361C2218yes—
135#2361C2212yes—
136#2359C2218yes—
137#2357C2212yes—
138#2354C2212yes—
139#2354C2212yes—
140#2353C2214yes—
141#2352C2218yes—
142#2352C2214yes—
143#2352C2212yes—
144#2349C2214yes—
145#2347C2212yes—
146#2346C2214yes—
147#2345C2212yes—
148#2335C2218yes—
149#2334C2218yes—
150#2325C2218yes—
151C4×C4⋊Q8C2214yes—
152C4×#127C2211yescharacteristic
153C4×#125C2214yes—
154C4×#125C2212yes—
155C4×#126C2214yes—
156C4×#123C2214yes—
157C4×#121C2214yes—
158C4×#121C2214yes—
159C4×#121C2214yes—
160C4×#121C2212yes—
161C4×#121C2212yes—
162#2296C2214yes—
163#2293C2214yes—
164C2×#389C2214yes—
165#2285C2211yescharacteristic
166C2×#384C2211yescharacteristic
167#2275C2214yes—
168C42×D4C2214yes—
169C42×D4C2212yes—
170C42×D4C2211yescharacteristic
171C4×#117C2212yes—
172C2×C4×C4⋊C4C2212yes—
173C22×#41C2314yes—
174C23×Q8C2314yes—
175#555—416no—
176#553—232no—
177#553—216no—
178#553—48no—
179#548—416no—
180#532—416no—
181C2×C4⋊Q8—416no—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2314yes—
186C2×C4⋊Q8C2318yes—
187C2×C4⋊Q8C2318yes—
188C2×#127C2311yescharacteristic
189C2×#127C2314yes—
190C2×#126C2314yes—
191C2×#126C2318yes—
192C2×#126C2314yes—
193C2×#125C2312yes—
194C2×#125C2314yes—
195C2×#125C2312yes—
196C2×#124C2318yes—
197C2×#124C2318yes—
198C2×#124C2314yes—
199C2×#124C2318yes—
200C2×#124C2318yes—
201C2×#123C2318yes—
202C2×#123C2314yes—
203C2×#123C2314yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2318yes—
206C2×#121C2318yes—
207C2×#121C2312yes—
208C2×#121C2314yes—
209C2×#121C2312yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2318yes—
216C2×#121C2312yes—
217C2×#121C2312yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2318yes—
221C2×#121C2318yes—
222C2×C4×Q8C2314yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2318yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2312yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2318yes—
239C2×#117C2314yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2314yes—
243C2×#117C2318yes—
244C2×#117C2312yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2318yes—
248C22×C4⋊C4C2314yes—
249C22×C4⋊C4C2312yes—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2314yes—
253C22×C42C2314yes—
254#400C2314yes—
255#400C2314yes—
256#399C2314yes—
257#399C2314yes—
258#399C2318yes—
259#398C2318yes—
260#397C2318yes—
261#397C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#395C2314yes—
270#395C2318yes—
271#395C2314yes—
272#395C2314yes—
273#395C2314yes—
274#395C2318yes—
275#394C2314yes—
276#394C2314yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#393C2314yes—
286#393C2314yes—
287#393C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2314yes—
291#393C2318yes—
292#393C2314yes—
293#392C2318yes—
294#392C2314yes—
295#392C2314yes—
296#392C2318yes—
297#391C2318yes—
298#391C2318yes—
299#391C2318yes—
300#390C2314yes—
301#390C2312yes—
302#390C2314yes—
303#390C2318yes—
304#390C2312yes—
305#390C2312yes—
306#390C2318yes—
307#390C2314yes—
308#390C2314yes—
309#390C2314yes—
310#390C2318yes—
311#390C2314yes—
312#390C2318yes—
313#390C2312yes—
314#390C2314yes—
315#390C2318yes—
316#390C2312yes—
317#390C2314yes—
318#390C2314yes—
319#389C2312yes—
320#389C2312yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2318yes—
325#389C2314yes—
326#389C2318yes—
327#389C2318yes—
328#389C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2312yes—
332#389C2314yes—
333#389C2318yes—
334#389C2318yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#388C2314yes—
339#388C2314yes—
340#388C2314yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2314yes—
352#388C2314yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2314yes—
357#388C2314yes—
358#388C2314yes—
359#388C2314yes—
360#387C2314yes—
361#387C2314yes—
362#387C2314yes—
363#387C2314yes—
364#387C2314yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2314yes—
370#387C2318yes—
371#387C2314yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2314yes—
378#386C2318yes—
379#386C2314yes—
380#386C2314yes—
381#386C2314yes—
382#386C2314yes—
383#386C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2314yes—
390#384C2311yescharacteristic
391#384C2314yes—
392#384C2312yes—
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#384C2314yes—
396#383C2314yes—
397#382C2312yes—
398#382C2314yes—
399#382C2318yes—
400#382C2312yes—
401#382C2312yes—
402#381C2314yes—
403#380C2312yes—
404#380C2318yes—
405#380C2318yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2318yes—
410#380C2314yes—
411#380C2312yes—
412#380C2314yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2318yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2318yes—
429C4×C4⋊C4C2312yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2312yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2318yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2312yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2312yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2318yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2314yes—
456#376C2314yes—
457#376C2314yes—
458C2×#95C2314yes—
459C2×#95C2314yes—
460C2×#95C2314yes—
461C43C2314yes—
462C43C2311yescharacteristic
463C2×#41—48no—
464C2×#41—416no—
465C22×Q8—48no—
466C22×Q8—416no—
467C22×Q8C2414yes—
468C22×Q8C2418yes—
469C22×Q8C2414yes—
470C22×D4C2414yes—
471C22×D4C2414yes—
472C22×D4C2411yescharacteristic
473C22×D4C2412yes—
474C22×D4C2414yes—
475C22×D4C2414yes—
476C22×D4C2418yes—
477C22×D4C2412yes—
478C22×D4C2418yes—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C23×C4C2414yes—
482C23×C4C2412yes—
483C23×C4C2414yes—
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2414yes—
487C23×C4C2412yes—
488C23×C4C2414yes—
489C23×C4C2418yes—
490C23×C4C2414yes—
491C23×C4C2414yes—
492C23×C4C2414yes—
493C4⋊Q8—216no—
494C4⋊Q8—216no—
495C4⋊Q8—48no—
496C4⋊Q8—48no—
497C4⋊Q8—416no—
498C4⋊Q8—416no—
499#127—24no—
500#127—48no—
501#126—216no—
502#126—232no—
503#126—48no—
504#125—28no—
505#125—216no—
506#125—44no—
507#124—48no—
508#124—416no—
509#124—416no—
510#124—416no—
511#124—416no—
512#123—232no—
513#123—216no—
514#123—48no—
515C22⋊Q8—48no—
516C22⋊Q8—416no—
517#121—232no—
518#121—216no—
519#121—28no—
520#121—216no—
521#121—28no—
522#121—216no—
523#121—216no—
524#121—44no—
525#121—416no—
526#121—416no—
527#121—48no—
528#121—48no—
529#121—416no—
530#121—48no—
531#121—48no—
532#121—44no—
533C4×Q8—48no—
534C4×D4—216no—
535C4×D4—232no—
536C4×D4—216no—
537C4×D4—28no—
538C4×D4—216no—
539C4×D4—28no—
540C4×D4—28no—
541C4×D4—216no—
542C4×D4—216no—
543C4×D4—24no—
544C4×D4—28no—
545C4×D4—48no—
546C4×D4—48no—
547C4×D4—44no—
548C4×D4—48no—
549C4×D4—416no—
550#117—216no—
551#117—28no—
552#117—28no—
553#117—44no—
554#117—416no—
555#117—48no—
556C2×C4⋊C4—28no—
557C2×C4⋊C4—48no—
558C2×C4⋊C4—416no—
559C2×C4⋊C4—44no—
560C2×C4⋊C4#41116yescomplemented
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2411yescharacteristic
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2412yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2411yescharacteristic
630C2×C42—24no—
631C2×C42—24no—
632C2×C42—48no—
633C2×C42—48no—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2414yes—
637C2×C42C2418yes—
638C2×C42C2411yescharacteristic
639C2×C42C2412yes—
640C2×C42C2414yes—
641C2×C42C2412yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2414yes—
645C2×C42C2412yes—
646C2×C42C2411yescharacteristic
647C2×C42C2412yes—
648C2×C42C2411yescharacteristic
649C2×C42C2418yes—
650C2×C42C2414yes—
651C2×C42C2414yes—
652C2×C42C2414yes—
653C2×C42C2414yes—
654C2×C42C2411yescharacteristic
655C2×C42C2414yes—
656C2×C42C2411yescharacteristic
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2418yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2412yes—
672#95C2412yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2412yes—
678#95C2414yes—
679#95C2418yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688C24C2511yescharacteristic
689C24C2514yes—
690C24C2514yes—
691C24C2511yescharacteristic
692#41—832no—
693C2×Q8—216no—
694C2×Q8—216no—
695C2×Q8—44no—
696C2×Q8—48no—
697C2×Q8—44no—
698C2×Q8—48no—
699C2×Q8—48no—
700C2×Q8—832no—
701C2×D4—28no—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—24no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—22no—
708C2×D4—24no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—216no—
712C2×D4—24no—
713C2×D4—28no—
714C2×D4—216no—
715C2×D4—24no—
716C2×D4—28no—
717C2×D4—24no—
718C2×D4—44no—
719C2×D4—42no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—42no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—48no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—22no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—24no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—24no—
740C22×C4—22no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—24no—
746C22×C4—28no—
747C22×C4—216no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—41no—
754C22×C4—44no—
755C22×C4—41no—
756C22×C4—44no—
757C22×C4—48no—
758C22×C4—48no—
759C22×C4—48no—
760C22×C4—44no—
761C22×C4—48no—
762C22×C4C2×#4118yes—
763C22×C4C2×#41116yes—
764C22×C4C2511yescharacteristic
765C22×C4C2512yes—
766C22×C4C2514yes—
767C22×C4C2512yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2511yescharacteristic
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2512yes—
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C22×C4C2514yes—
781C22×C4C2511yescharacteristic
782C22×C4C2512yes—
783C4⋊C4—28no—
784C4⋊C4—24no—
785C4⋊C4—28no—
786C4⋊C4—216no—
787C4⋊C4—24no—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—216no—
791C4⋊C4—28no—
792C4⋊C4—24no—
793C4⋊C4—216no—
794C4⋊C4—28no—
795C4⋊C4—216no—
796C4⋊C4—28no—
797C4⋊C4—24no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—22no—
801C4⋊C4—24no—
802C4⋊C4—42no—
803C4⋊C4—42no—
804C4⋊C4—44no—
805C4⋊C4—48no—
806C4⋊C4—48no—
807C4⋊C4—48no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—42no—
811C4⋊C4—48no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4C2×#4118yes—
815C4⋊C4C2×#4118yes—
816C4⋊C4C2×#41116yes—
817C4⋊C4H(5,𝔽2)18yes—
818C22⋊C4—24no—
819C22⋊C4—28no—
820C22⋊C4—216no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—216no—
824C22⋊C4—216no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—24no—
828C22⋊C4—216no—
829C22⋊C4—28no—
830C22⋊C4—28no—
831C22⋊C4—216no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—22no—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—48no—
846C22⋊C4—44no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—44no—
851C22⋊C4H(5,𝔽2)14yes—
852C42—216no—
853C42—28no—
854C42—28no—
855C42—24no—
856C42—24no—
857C42—28no—
858C42—28no—
859C42—28no—
860C42—28no—
861C42—22no—
862C42—28no—
863C42—22no—
864C42—24no—
865C42—24no—
866C42—22no—
867C42—44no—
868C42—44no—
869C42—44no—
870C42—44no—
871C42—44no—
872C42—41no—
873C42—48no—
874C422−1+414yes—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—28no—
879C23—24no—
880C23—22no—
881C23—24no—
882C23—22no—
883C23—24no—
884C23—24no—
885C23—21no—
886C23—28no—
887C23—24no—
888C23—24no—
889C23—24no—
890C23—21no—
891C23—24no—
892C23—24no—
893C23—24no—
894C23—21no—
895C23C22×#4114yes—
896C23C2×H(5,𝔽2)12yes—
897C23C2611yescharacteristic
898Q8—416no—
899Q8—816no—
900Q8—88no—
901D4—416no—
902D4—416no—
903D4—44no—
904D4—48no—
905D4—416no—
906D4—88no—
907D4—816no—
908D4—84no—
909D4—816no—
910D4—88no—
911D4—164no—
912C2×C4—24no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—21no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—24no—
923C2×C4—21no—
924C2×C4—24no—
925C2×C4—216no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—28no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—21no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—21no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—28no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—416no—
956C2×C4—44no—
957C2×C4—416no—
958C2×C4—44no—
959C2×C4—416no—
960C2×C4—416no—
961C2×C4—48no—
962C2×C4—816no—
963C2×C4—88no—
964C2×C4—88no—
965C2×C4—88no—
966C2×C4C22×#4118yes—
967C2×C4C22×#4118yes—
968C2×C4C22×#4114yes—
969C2×C4C22×#4114yes—
970C2×C4C2×H(5,𝔽2)12yes—
971C2×C4C2×H(5,𝔽2)18yes—
972C2×C4C2×H(5,𝔽2)12yes—
973C2×C4C2×H(5,𝔽2)14yes—
974C2×C4C2×2−1+412yes—
975C2×C4C2×2−1+414yes—
976C22—24no—
977C22—22no—
978C22—24no—
979C22—22no—
980C22—48no—
981C22—44no—
982C22—42no—
983C22—44no—
984C22—44no—
985C22—44no—
986C22—41no—
987C22—42no—
988C22—44no—
989C22—48no—
990C22—44no—
991C22—41no—
992C22—44no—
993C22—44no—
994C22—44no—
995C22—44no—
996C22—41no—
997C22#348314yes—
998C22C23×#4112yes—
999C22C22×H(5,𝔽2)12yes—
1000C22C22×H(5,𝔽2)11yescharacteristic
1001C22C22×2−1+411yescharacteristic
1002C222−1+611yescharacteristic
1003C4—28no—
1004C4—28no—
1005C4—22no—
1006C4—28no—
1007C4—24no—
1008C4—22no—
1009C4—22no—
1010C4—42no—
1011C4—44no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4—42no—
1016C4—44no—
1017C4—41no—
1018C4—44no—
1019C4—44no—
1020C4—41no—
1021C4#351118yes—
1022C2—24no—
1023C2—84no—
1024C2—84no—
1025C2—81no—
1026C2C2×#348311yescharacteristic
1027C2C2×#351112yes—
1028C2#6291511yescharacteristic
1029C2#6298412yes—
1030C2#6301111yescharacteristic
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. #59713C2semidirect
2. #59465C2semidirect
3. #59303C2semidirect
4. #59233C2semidirect
5. #59135C2semidirect
6. #59115C2semidirect
7. #44377C2semidirect
8. #43882C2semidirect
9. #43575C2semidirect
10. #40127C2semidirect
11. #40121C2semidirect
12. #39742C2semidirect
13. #36596C2semidirect
14. #36407C2semidirect
15. #36273C2semidirect
16. #36182C2semidirect
17. #36122C2semidirect
18. #35929C2semidirect
19. #34978C2semidirect
20. #34925C2semidirect
21. C2×#2551C2semidirect
22. #34323C2semidirect
23. C4×#553C2semidirect
560. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
#597132
#594652
#593032
#592332
#591352
#591152
#443772
#438822
#435752
#401272
#401212
#397422
#365962
#364072
#362732
#361822
#361222
#359292
#349782
#349252
C2×#25512
#343232
C4×#5532