Finite Group Databasebeta

← #7672499

Subgroups — #7672499

Order 512.

5378 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59222C214yesmaximal, complemented
2#59221C214yesmaximal, complemented
3#59216C214yesmaximal, complemented
4#59215C214yesmaximal, complemented
5#39141C214yesmaximal, complemented
6#39140C214yesmaximal, complemented
7#37947C214yesmaximal, complemented
8#37946C214yesmaximal, complemented
9#36624C211yesmaximal, characteristic, complemented
10#36530C214yesmaximal, complemented
11#36522C214yesmaximal, complemented
12#36202C214yesmaximal, complemented
13#36172C214yesmaximal, complemented
14#35518C212yesmaximal, complemented
15#35516C212yesmaximal, complemented
16#35339C211yesmaximal, characteristic, complemented
17#35328C211yesmaximal, characteristic, complemented
18#35160C212yesmaximal, complemented
19#34274C212yesmaximal, complemented
20#34208C211yesmaximal, characteristic, complemented
21#34184C211yesmaximal, characteristic, complemented
22C4×#525C211yesmaximal, characteristic, complemented
23C2×#2283C211yesmaximal, characteristic, complemented
24C2×#537C2212yes—
25C2×#532C2211yescharacteristic
26C2×#525C2211yescharacteristic
27C2×#525C2212yes—
28C2×#520C2212yes—
29C2×#520C2212yes—
30C2×C4×#41C2211yescharacteristic
31C23×C42C2211yescharacteristic
32#2864C2212yescomplemented
33#2864C2212yescomplemented
34#2857C2212yes—
35#2856C2212yes—
36#2854C2212yes—
37#2854C2212yes—
38#2852C2218yes—
39#2850C2212yes—
40#2850C2212yes—
41#2850C2214yescomplemented
42#2847C2212yes—
43#2847C2212yes—
44#2776C2218yescomplemented
45#2770C2218yescomplemented
46#2757C2218yescomplemented
47#2749C2218yescomplemented
48#2746C2218yes—
49#2739C2218yes—
50#2701C2218yes—
51#2688C2218yes—
52#2647C2214yescomplemented
53#2643C2218yes—
54#2621C2212yescomplemented
55#2619C2212yescomplemented
56#2606C2218yescomplemented
57#2603C2218yescomplemented
58#2578C2218yes—
59#2578C2218yescomplemented
60#2576C2218yes—
61#2570C2214yescomplemented
62#2570C2214yescomplemented
63#2569C2214yes—
64#2569C2214yes—
65#2559C2218yes—
66#2543C2214yes—
67#2543C2214yes—
68#2538C2214yes—
69#2537C2214yes—
70#2536C2214yes—
71#2536C2212yescomplemented
72#2536C2212yescomplemented
73#2535C2214yes—
74#2535C2212yescomplemented
75#2535C2212yescomplemented
76#2531C2218yescomplemented
77#2530C2218yescomplemented
78#2529C2218yescomplemented
79#2526C2218yescomplemented
80#2525C2218yescomplemented
81#2522C2218yes—
82#2518C2218yes—
83#2516C2218yes—
84#2515C2218yescomplemented
85#2514C2214yescomplemented
86#2513C2214yescomplemented
87#2512C2214yescomplemented
88#2511C2214yescomplemented
89#2510C2218yescomplemented
90#2497C2214yescomplemented
91#2496C2214yescomplemented
92#2495C2214yescomplemented
93#2494C2214yescomplemented
94#2487C2214yes—
95#2486C2214yes—
96#2485C2214yes—
97#2485C2214yes—
98#2467C2218yes—
99#2464C2218yes—
100#2457C2218yes—
101#2444C2218yes—
102#2425C2218yes—
103#2424C2218yes—
104#2423C2214yes—
105#2422C2214yes—
106#2421C2214yes—
107#2420C2214yes—
108#2419C2218yes—
109#2418C2218yes—
110#2417C2214yes—
111#2416C2214yes—
112#2415C2214yes—
113#2414C2214yes—
114#2374C2218yes—
115#2373C2218yescomplemented
116#2364C2218yes—
117#2364C2214yes—
118#2364C2214yes—
119#2363C2214yescomplemented
120#2363C2214yescomplemented
121#2362C2214yescomplemented
122#2362C2214yescomplemented
123#2361C2214yescomplemented
124#2361C2214yescomplemented
125#2360C2214yescomplemented
126#2360C2214yescomplemented
127#2353C2218yescomplemented
128#2352C2214yescomplemented
129#2352C2214yescomplemented
130#2351C2212yescomplemented
131#2351C2212yescomplemented
132#2349C2214yes—
133#2349C2214yes—
134#2349C2212yescomplemented
135#2349C2212yescomplemented
136#2328C2212yescomplemented
137#2327C2212yescomplemented
138#2325C2218yes—
139#2317C2212yes—
140#2317C2212yes—
141#2317C2214yescomplemented
142#2316C2212yes—
143#2311C2212yes—
144#2311C2212yes—
145C4×#124C2214yescomplemented
146C4×C22⋊Q8C2212yes—
147C4×C22⋊Q8C2212yes—
148C4×#123C2212yes—
149C4×#123C2212yes—
150C4×#121C2214yes—
151C4×#121C2214yes—
152C4×#121C2212yes—
153C4×#121C2212yes—
154C4×#121C2218yes—
155C4×#120C2212yes—
156C4×#120C2212yes—
157#2297C2212yes—
158#2297C2211yescharacteristic
159#2296C2211yescharacteristic
160#2290C2214yes—
161#2285C2211yescharacteristic
162#2285C2212yescomplemented
163#2283C2214yes—
164#2283C2214yes—
165#2283C2214yes—
166#2283C2214yes—
167C2×#383C2212yes—
168C2×#382C2211yescharacteristic
169C2×#382C2211yescharacteristic
170C2×#382C2212yescomplemented
171#2280C2211yescharacteristic
172C2×#381C2212yes—
173C2×#380C2212yes—
174C42×D4C2214yes—
175C4×#117C2211yescharacteristic
176C2×C4×C4⋊C4C2212yes—
177C2×C4×C22⋊C4C2212yes—
178C2×#376C2212yes—
179C22×#41C2312yes—
180C22×#41C2311yescharacteristic
181C24×C4C2311yescharacteristic
182C24×C4C2311yescharacteristic
183C24×C4C2311yescharacteristic
184#537—216no—
185#532—28no—
186C2×C4⋊Q8C2311yescharacteristic
187C2×#127C2311yescharacteristic
188C2×#126C2318yes—
189C2×#124C2312yes—
190#525—28no—
191#525—48no—
192C2×#123C2312yes—
193C2×#123C2314yes—
194C2×#123C2318yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2312yes—
200C2×#121C2318yes—
201C2×#121C2312yes—
202C2×#121C2312yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2312yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2312yes—
209C2×#121C2312yes—
210C2×#121C2318yes—
211C2×#120C2312yes—
212C2×#120C2314yes—
213#520—48no—
214#520—48no—
215C4×#41—28no—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2314yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2318yes—
228C2×C4×D4C2318yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2312yes—
240C2×#117C2312yes—
241C2×#117C2314yes—
242C2×#117C2314yes—
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2314yes—
246C22×C4⋊C4C2314yes—
247C22×C22⋊C4C2314yes—
248C22×C42—28no—
249C22×C42C2312yes—
250C22×C42C2312yes—
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2312yes—
254C22×C42C2311yescharacteristic
255C22×C42C2312yes—
256C22×C42C2312yes—
257C22×C42C2314yes—
258C22×C42C2311yescharacteristic
259#401C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#399C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2314yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#397C2318yes—
274#397C2314yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2314yes—
280#397C2318yes—
281#397C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2314yes—
289#394C2314yes—
290#394C2318yes—
291#394C2318yes—
292#392C2314yes—
293#392C2314yes—
294#392C2318yes—
295#391C2314yes—
296#391C2314yes—
297#391C2312yes—
298#391C2312yes—
299#391C2312yes—
300#390C2314yes—
301#390C2314yes—
302#390C2312yes—
303#390C2312yes—
304#390C2314yes—
305#390C2314yes—
306#390C2318yes—
307#390C2312yes—
308#390C2318yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2318yes—
319#389C2314yes—
320#389C2314yes—
321#389C2318yes—
322#389C2318yes—
323#389C2312yes—
324#389C2312yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2314yes—
330#388C2318yes—
331#388C2318yes—
332#388C2314yes—
333#388C2314yes—
334#388C2314yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2314yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2314yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2314yes—
359#387C2318yes—
360#387C2314yes—
361#386C2318yes—
362#386C2318yes—
363#386C2314yes—
364#386C2318yes—
365#386C2314yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2312yes—
370#386C2314yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2314yes—
375#386C2314yes—
376#386C2314yes—
377#386C2314yes—
378#386C2318yes—
379#386C2318yes—
380#386C2314yes—
381#386C2312yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2312yes—
390#385C2312yes—
391#385C2314yes—
392#385C2314yes—
393#384C2314yes—
394#384C2314yes—
395#384C2312yes—
396#383C2318yes—
397#383C2318yes—
398#383C2318yes—
399#382C2314yes—
400#382C2312yes—
401#382C2312yes—
402#382C2314yes—
403#382C2312yes—
404#382C2314yes—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2312yes—
408#382C2314yes—
409#382C2312yes—
410#382C2312yes—
411#382C2312yes—
412#382C2312yes—
413#381C2318yes—
414#381C2318yes—
415#381C2312yes—
416#381C2318yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2318yes—
422#380C2312yes—
423#380C2312yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2318yes—
429#380C2314yes—
430#380C2314yes—
431#380C2312yes—
432#380C2312yes—
433#380C2314yes—
434#380C2314yes—
435#379C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2318yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C22⋊C4C2312yes—
451C4×C22⋊C4C2312yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2318yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2314yes—
466#376C2312yes—
467#376C2318yes—
468#376C2318yes—
469C2×#95C2312yes—
470C2×#95C2312yes—
471C2×#95C2314yes—
472C2×#95C2312yes—
473C2×#95C2312yes—
474C2×#95C2314yes—
475C2×#95C2314yes—
476C2×#95C2314yes—
477C43C2312yes—
478C25C2411yescharacteristic
479C2×#41—24no—
480C2×#41—28no—
481C2×#41—28no—
482C2×#41—24no—
483C2×#41—28no—
484C2×#41#4118yes—
485C22×Q8C2412yes—
486C22×Q8C2411yescharacteristic
487C22×D4C2414yes—
488C22×D4C2412yes—
489C22×D4C2414yes—
490C22×D4C2412yes—
491C22×D4C2411yescharacteristic
492C22×D4C2414yes—
493C22×D4C2414yes—
494C22×D4C2418yes—
495C22×D4C2412yes—
496C22×D4C2412yes—
497C23×C4—24no—
498C23×C4—24no—
499C23×C4—24no—
500C23×C4—24no—
501C23×C4—24no—
502C23×C4—44no—
503C23×C4—44no—
504C23×C4C2414yes—
505C23×C4C2412yes—
506C23×C4C2412yes—
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C23×C4C2412yes—
510C23×C4C2412yes—
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2412yes—
514C23×C4C2414yes—
515C23×C4C2414yes—
516C23×C4C2412yes—
517C23×C4C2412yes—
518C23×C4C2411yescharacteristic
519C23×C4C2418yes—
520C23×C4C2418yes—
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C4⋊Q8—24no—
525#127—24no—
526#126—416no—
527#124—28no—
528#123—28no—
529#123—416no—
530#123—48no—
531C22⋊Q8—28no—
532C22⋊Q8—216no—
533C22⋊Q8—216no—
534C22⋊Q8—44no—
535C22⋊Q8—44no—
536#121—28no—
537#121—216no—
538#121—232no—
539#121—28no—
540#121—28no—
541#121—216no—
542#121—48no—
543#121—416no—
544#121—44no—
545#121—44no—
546#121—48no—
547#120—28no—
548#120—48no—
549C4×Q8—24no—
550C4×Q8—24no—
551C4×Q8—48no—
552C4×Q8—48no—
553C4×D4—28no—
554C4×D4—28no—
555C4×D4—216no—
556C4×D4—24no—
557C4×D4—24no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—416no—
561C4×D4—48no—
562C4×D4—48no—
563C4×D4—48no—
564C4×D4—48no—
565C4×D4—48no—
566C4×D4—48no—
567C4×D4—416no—
568C4×D4—416no—
569#117—24no—
570#117—24no—
571#117—24no—
572#117—28no—
573#117—28no—
574#117—48no—
575#117—48no—
576C2×C4⋊C4—28no—
577C2×C4⋊C4—28no—
578C2×C4⋊C4—48no—
579C2×C4⋊C4—48no—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C22⋊C4—48no—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C42—24no—
644C2×C42—24no—
645C2×C42—24no—
646C2×C42—28no—
647C2×C42—28no—
648C2×C42—28no—
649C2×C42—28no—
650C2×C42—28no—
651C2×C42—48no—
652C2×C42#4118yes—
653C2×C42C2412yes—
654C2×C42C2414yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2418yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2418yes—
667C2×C42C2418yes—
668C2×C42C2414yes—
669C2×C42C2414yes—
670C2×C42C2418yes—
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675#95C2414yes—
676#95C2414yes—
677#95C2412yes—
678#95C2412yes—
679#95C2418yes—
680#95C2418yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704#95C2418yes—
705#95C2414yes—
706#95C2418yes—
707#95C2412yes—
708#95C2412yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713C24—22no—
714C24—24no—
715C24—22no—
716C24—22no—
717C24—42no—
718C24C2514yes—
719C24C2512yes—
720C24C2512yes—
721C24C2511yescharacteristic
722#41—232no—
723#41—432no—
724C2×Q8—22no—
725C2×Q8—24no—
726C2×Q8—24no—
727C2×Q8—22no—
728C2×Q8—24no—
729C2×Q8C2×#4114yes—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—216no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—22no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—22no—
746C2×D4—24no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—48no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4C2×#4118yes—
757C2×D4C2×#4114yes—
758C22×C4—22no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—28no—
778C22×C4—24no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—48no—
801C22×C4—48no—
802C22×C4—48no—
803C22×C4—48no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—416no—
807C22×C4—416no—
808C22×C4—416no—
809C22×C4C2×#4118yes—
810C22×C4C2×#4114yes—
811C22×C4C2×#4114yes—
812C22×C4C2×#4114yes—
813C22×C4C2×#4114yes—
814C22×C4H(5,𝔽2)14yes—
815C22×C4C2512yes—
816C22×C4C2518yes—
817C22×C4C2512yes—
818C22×C4C2518yes—
819C22×C4C2514yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—216no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—28no—
867C22⋊C4—216no—
868C22⋊C4—24no—
869C22⋊C4—28no—
870C22⋊C4—216no—
871C22⋊C4—28no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—216no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—48no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—24no—
900C42—24no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—28no—
907C42—24no—
908C42—216no—
909C42—48no—
910C42—48no—
911C42—48no—
912C42—44no—
913C42—44no—
914C42C2×#4114yes—
915C42C2×#4114yes—
916C42C2×#4114yes—
917C42C2×#4114yes—
918C23—22no—
919C23—22no—
920C23—28no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—24no—
927C23—22no—
928C23—22no—
929C23—24no—
930C23—22no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—48no—
939C23—48no—
940C23—44no—
941C23—44no—
942C23C22×#4114yes—
943C23C22×#4112yes—
944C23C22×#4112yes—
945C23C2×H(5,𝔽2)12yes—
946C23#58514yes—
947C23C2611yescharacteristic
948Q8—28no—
949Q8—48no—
950D4—216no—
951D4—28no—
952D4—416no—
953D4—416no—
954D4—48no—
955D4—84no—
956D4—84no—
957D4—816no—
958D4—88no—
959D4—88no—
960C2×C4—28no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—216no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—28no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—28no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—28no—
986C2×C4—28no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—48no—
1004C2×C4—48no—
1005C2×C4—48no—
1006C2×C4—48no—
1007C2×C4—44no—
1008C2×C4—44no—
1009C2×C4—48no—
1010C2×C4—48no—
1011C2×C4—416no—
1012C2×C4—84no—
1013C2×C4—84no—
1014C2×C4—88no—
1015C2×C4—88no—
1016C2×C4—168no—
1017C2×C4—168no—
1018C2×C4#553116yes—
1019C2×C4C22×#4112yes—
1020C2×C4C22×#4112yes—
1021C2×C4C22×#4112yes—
1022C2×C4C22×#4112yes—
1023C2×C4C22×#4114yes—
1024C2×C4C22×#4112yes—
1025C2×C4C22×#4112yes—
1026C2×C4C22×#4112yes—
1027C2×C4C22×#4112yes—
1028C2×C4C2×H(5,𝔽2)12yes—
1029C2×C4C2×H(5,𝔽2)12yes—
1030C2×C4#58514yes—
1031C22—24no—
1032C22—22no—
1033C22—22no—
1034C22—24no—
1035C22—24no—
1036C22—28no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—416no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—44no—
1046C22—42no—
1047C22—42no—
1048C22—44no—
1049C22—44no—
1050C22—44no—
1051C22—44no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22C2×#55314yes—
1056C22C23×#4111yescharacteristic
1057C22C23×#4111yescharacteristic
1058C22C22×H(5,𝔽2)11yescharacteristic
1059C22C2×#58512yes—
1060C22C2×#58512yes—
1061C4—24no—
1062C4—22no—
1063C4—22no—
1064C4—22no—
1065C4—22no—
1066C4—24no—
1067C4—48no—
1068C4—44no—
1069C4—42no—
1070C4—42no—
1071C4—42no—
1072C4—48no—
1073C4—44no—
1074C4—44no—
1075C4—44no—
1076C4—42no—
1077C4—44no—
1078C4C2×#55314yes—
1079C4C2×#55314yes—
1080C2—24no—
1081C2—44no—
1082C2—44no—
1083C2—84no—
1084C2C22×#55311yescharacteristic
1085C2#6281012yes—
1086C2#6281411yescharacteristic
1087C2#6281411yescharacteristic
1088C2#6283012yes—
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. #59222C2semidirect
2. #59221C2semidirect
3. #59216C2semidirect
4. #59215C2semidirect
5. #39141C2semidirect
6. #39140C2semidirect
7. #37947C2semidirect
8. #37946C2semidirect
9. #36624C2semidirect
10. #36530C2semidirect
11. #36522C2semidirect
12. #36202C2semidirect
13. #36172C2semidirect
14. #35518C2semidirect
15. #35516C2semidirect
16. #35339C2semidirect
17. #35328C2semidirect
18. #35160C2semidirect
19. #34274C2semidirect
20. #34208C2semidirect
21. #34184C2semidirect
22. C4×#525C2semidirect
23. C2×#2283C2semidirect
32. #2864C22semidirect
33. #2864C22semidirect
41. #2850C22semidirect
44. #2776C22semidirect
45. #2770C22semidirect
46. #2757C22semidirect
47. #2749C22semidirect
52. #2647C22semidirect
54. #2621C22semidirect
55. #2619C22semidirect
56. #2606C22semidirect
57. #2603C22semidirect
59. #2578C22semidirect
61. #2570C22semidirect
62. #2570C22semidirect
71. #2536C22semidirect
72. #2536C22semidirect
74. #2535C22semidirect
75. #2535C22semidirect
76. #2531C22semidirect
77. #2530C22semidirect
78. #2529C22semidirect
79. #2526C22semidirect
80. #2525C22semidirect
84. #2515C22semidirect
85. #2514C22semidirect
86. #2513C22semidirect
87. #2512C22semidirect
88. #2511C22semidirect
89. #2510C22semidirect
90. #2497C22semidirect
91. #2496C22semidirect
92. #2495C22semidirect
93. #2494C22semidirect
115. #2373C22semidirect
119. #2363C22semidirect
120. #2363C22semidirect
121. #2362C22semidirect
122. #2362C22semidirect
123. #2361C22semidirect
124. #2361C22semidirect
125. #2360C22semidirect
126. #2360C22semidirect
127. #2353C22semidirect
128. #2352C22semidirect
129. #2352C22semidirect
130. #2351C22semidirect
131. #2351C22semidirect
134. #2349C22semidirect
135. #2349C22semidirect
136. #2328C22semidirect
137. #2327C22semidirect
141. #2317C22semidirect
145. C4×#124C22semidirect
162. #2285C22semidirect
170. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
#592222
#592212
#592162
#592152
#391412
#391402
#379472
#379462
#366242
#365302
#365222
#362022
#361722
#355182
#355162
#353392
#353282
#351602
#342742
#342082
#341842
C4×#5252
C2×#22832