Finite Group Databasebeta

← #7679263

Subgroups — #7679263

Order 512.

5042 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59684C214yesmaximal, complemented
2#59682C214yesmaximal, complemented
3#59221C214yesmaximal, complemented
4#59216C214yesmaximal, complemented
5#45349C212yesmaximal, complemented
6#45344C212yesmaximal, complemented
7#45312C212yesmaximal, complemented
8#45310C214yesmaximal, complemented
9#45299C212yesmaximal, complemented
10#45297C214yesmaximal, complemented
11#39814C218yesmaximal, complemented
12#39729C214yesmaximal, complemented
13#36604C214yesmaximal, complemented
14#35545C212yesmaximal, complemented
15#35517C212yesmaximal, complemented
16#35178C212yesmaximal, complemented
17#35178C211yesmaximal, characteristic, complemented
18#34948C211yesmaximal, characteristic, complemented
19#34937C211yesmaximal, characteristic
20#34266C212yesmaximal, complemented
21#34208C211yesmaximal, characteristic, complemented
22#34189C211yesmaximal, characteristic, complemented
23C2×#2351C211yesmaximal, characteristic, complemented
24C4×#536C211yesmaximal, characteristic, complemented
25C2×#536C2211yescharacteristic
26C2×#536C2212yes—
27C2×#532C2211yescharacteristic
28C2×#532C2212yes—
29C2×#520C2212yes—
30C2×C4×#41C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×Q8C2212yes—
33#2854C2214yes—
34#2854C2218yes—
35#2801C2218yes—
36#2800C2218yes—
37#2776C2218yes—
38#2772C2218yes—
39#2772C2218yes—
40#2766C2218yes—
41#2761C2218yes—
42#2757C2218yes—
43#2753C2218yes—
44#2739C2218yes—
45#2725C2218yes—
46#2701C2218yes—
47#2618C2218yes—
48#2618C2214yes—
49#2608C2218yes—
50#2606C2218yes—
51#2597C2218yes—
52#2596C2218yes—
53#2587C2218yes—
54#2585C2218yes—
55#2576C2218yes—
56#2571C2212yes—
57#2570C2212yes—
58#2570C2212yes—
59#2569C2212yes—
60#2569C2212yes—
61#2559C2218yes—
62#2558C2218yes—
63#2554C2218yes—
64#2552C2212yes—
65#2548C2214yes—
66#2548C2212yes—
67#2548C2211yescharacteristic
68#2547C2211yescharacteristic
69#2546C2211yescharacteristic
70#2546C2214yes—
71#2546C2212yes—
72#2545C2212yes—
73#2545C2214yes—
74#2545C2214yes—
75#2545C2214yes—
76#2544C2212yes—
77#2543C2212yes—
78#2543C2212yes—
79#2541C2211yescharacteristic
80#2538C2214yes—
81#2538C2214yes—
82#2538C2214yes—
83#2536C2212yes—
84#2536C2214yes—
85#2536C2212yes—
86#2536C2214yes—
87#2529C2218yes—
88#2526C2218yes—
89#2525C2218yes—
90#2522C2218yes—
91#2518C2218yes—
92#2518C2218yes—
93#2516C2218yes—
94#2515C2218yes—
95#2514C2214yes—
96#2513C2214yes—
97#2512C2214yes—
98#2511C2214yes—
99#2510C2218yes—
100#2497C2214yes—
101#2496C2214yes—
102#2495C2214yes—
103#2494C2214yes—
104#2487C2214yes—
105#2486C2214yes—
106#2485C2214yes—
107#2485C2214yes—
108#2481C2218yes—
109#2448C2214yes—
110#2447C2214yes—
111#2446C2214yes—
112#2445C2214yes—
113#2444C2218yes—
114#2443C2218yes—
115#2442C2214yes—
116#2416C2214yes—
117#2402C2212yes—
118#2402C2212yes—
119#2392C2212yes—
120#2392C2212yes—
121#2374C2218yes—
122#2373C2218yes—
123#2367C2214yes—
124#2367C2214yes—
125#2365C2214yes—
126#2365C2214yes—
127#2364C2214yes—
128#2364C2214yes—
129#2362C2214yes—
130#2362C2214yes—
131#2360C2214yes—
132#2360C2214yes—
133#2357C2212yes—
134#2357C2212yes—
135#2356C2212yes—
136#2356C2212yes—
137#2353C2214yes—
138#2353C2214yes—
139#2352C2214yes—
140#2352C2214yes—
141#2351C2212yes—
142#2351C2214yes—
143#2351C2212yes—
144#2351C2214yes—
145#2351C2212yes—
146#2351C2212yes—
147#2328C2212yes—
148#2327C2212yes—
149#2327C2212yes—
150#2326C2212yes—
151#2323C2214yes—
152#2322C2214yes—
153#2322C2218yes—
154#2317C2211yescharacteristic
155#2314C2214yes—
156#2311C2211yescharacteristic
157#2311C2212yes—
158#2311C2212yes—
159#2311C2212yes—
160#2310C2211yescharacteristic
161C4×C4⋊Q8C2212yes—
162C4×#125C2214yes—
163C4×#124C2214yes—
164C4×#124C2212yes—
165C4×C22⋊Q8C2214yes—
166C4×#123C2214yes—
167C4×#123C2218yes—
168C4×#121C2214yes—
169#2297C2212yes—
170#2296C2212yes—
171C2×#389C2214yes—
172C2×#389C2212yes—
173#2285C2211yescharacteristic
174#2285C2212yes—
175#2283C2212yes—
176#2283C2212yes—
177C2×#382C2212yes—
178C2×#382C2211yescharacteristic
179#2274C2212yes—
180C4×#117C2211yescharacteristic
181C2×C4×C4⋊C4C2211yescharacteristic
182C2×C4×C4⋊C4C2212yes—
183C22×#41C2311yescharacteristic
184C22×#41C2312yes—
185C23×Q8C2311yescharacteristic
186#536—28no—
187#536—216no—
188#532—28no—
189#532—48no—
190C2×C4⋊Q8C2312yes—
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2314yes—
193C2×C4⋊Q8C2312yes—
194C2×#127C2311yescharacteristic
195C2×#127C2312yes—
196C2×#126C2318yes—
197C2×#125C2314yes—
198C2×#124C2312yes—
199C2×#124C2314yes—
200C2×#124C2312yes—
201C2×#124C2312yes—
202C2×#124C2312yes—
203C2×#123C2314yes—
204C2×#123C2318yes—
205C2×#123C2318yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×#121C2312yes—
210C2×#121C2312yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214#520—48no—
215C4×#41—28no—
216C2×C4×Q8—28no—
217C2×C4×Q8—48no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2318yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2312yes—
244C2×#117C2314yes—
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2314yes—
249C22×C4⋊C4C2314yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2314yes—
252C22×C42C2312yes—
253C22×C42C2312yes—
254C22×C42C2312yes—
255C22×C42C2314yes—
256C22×C42C2311yescharacteristic
257#401C2318yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#399C2318yes—
267#398C2314yes—
268#398C2314yes—
269#398C2314yes—
270#398C2314yes—
271#398C2312yes—
272#398C2318yes—
273#398C2318yes—
274#398C2314yes—
275#398C2318yes—
276#398C2314yes—
277#398C2312yes—
278#397C2318yes—
279#397C2312yes—
280#397C2318yes—
281#397C2318yes—
282#397C2312yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#396C2318yes—
287#396C2314yes—
288#396C2318yes—
289#396C2314yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#394C2318yes—
296#394C2312yes—
297#394C2314yes—
298#394C2318yes—
299#394C2314yes—
300#394C2314yes—
301#394C2314yes—
302#394C2312yes—
303#394C2318yes—
304#394C2318yes—
305#392C2312yes—
306#392C2312yes—
307#391C2312yes—
308#391C2312yes—
309#391C2314yes—
310#391C2312yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2312yes—
315#391C2312yes—
316#390C2312yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2318yes—
321#390C2318yes—
322#390C2318yes—
323#390C2312yes—
324#390C2312yes—
325#390C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2318yes—
329#389C2312yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2314yes—
334#389C2318yes—
335#389C2318yes—
336#389C2318yes—
337#389C2318yes—
338#389C2318yes—
339#389C2318yes—
340#389C2314yes—
341#389C2318yes—
342#389C2318yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2314yes—
369#388C2318yes—
370#388C2314yes—
371#387C2314yes—
372#387C2314yes—
373#387C2314yes—
374#387C2314yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#386C2314yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2314yes—
395#386C2318yes—
396#386C2314yes—
397#386C2318yes—
398#386C2318yes—
399#386C2314yes—
400#386C2314yes—
401#385C2314yes—
402#385C2314yes—
403#385C2314yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#384C2312yes—
409#384C2312yes—
410#384C2312yes—
411#384C2312yes—
412#383C2318yes—
413#383C2314yes—
414#383C2314yes—
415#382C2314yes—
416#382C2312yes—
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2312yes—
420#382C2312yes—
421#382C2312yes—
422#382C2318yes—
423#382C2312yes—
424#382C2312yes—
425#382C2312yes—
426#382C2314yes—
427#382C2314yes—
428#381C2314yes—
429#381C2314yes—
430#381C2318yes—
431#381C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2312yes—
440#380C2314yes—
441#380C2314yes—
442#380C2312yes—
443#380C2314yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2318yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2318yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2318yes—
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2318yes—
475C4×C22⋊C4C2318yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480#376C2312yes—
481#376C2314yes—
482#376C2314yes—
483C2×#95C2311yescharacteristic
484C2×#95C2311yescharacteristic
485C2×#95C2312yes—
486C2×#95C2312yes—
487C2×#95C2314yes—
488C43C2312yes—
489C2×#41—24no—
490C2×#41—28no—
491C2×#41—24no—
492C2×#41—28no—
493C2×#41—28no—
494C2×#41—24no—
495C22×Q8—24no—
496C22×Q8—24no—
497C22×Q8#4118yes—
498C22×Q8C2411yescharacteristic
499C22×Q8C2412yes—
500C22×Q8C2412yes—
501C22×Q8C2412yes—
502C22×D4C2412yes—
503C22×D4C2414yes—
504C22×D4C2411yescharacteristic
505C22×D4C2412yes—
506C22×D4C2412yes—
507C22×D4C2414yes—
508C22×D4C2412yes—
509C22×D4C2414yes—
510C23×C4C2414yes—
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2414yes—
516C23×C4C2412yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2418yes—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C4⋊Q8—28no—
524C4⋊Q8—216no—
525C4⋊Q8—24no—
526C4⋊Q8—44no—
527#127—24no—
528#127—44no—
529#126—416no—
530#125—48no—
531#124—28no—
532#124—216no—
533#124—28no—
534#124—44no—
535#124—44no—
536#123—216no—
537#123—232no—
538#123—416no—
539C22⋊Q8—216no—
540C22⋊Q8—216no—
541C22⋊Q8—216no—
542#121—28no—
543#121—28no—
544#121—48no—
545#121—48no—
546#121—48no—
547C4×Q8—28no—
548C4×Q8—28no—
549C4×Q8—28no—
550C4×Q8—28no—
551C4×Q8—24no—
552C4×Q8—24no—
553C4×Q8—48no—
554C4×Q8—48no—
555C4×Q8—48no—
556C4×Q8—48no—
557C4×Q8—48no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—24no—
561C4×D4—24no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4—48no—
565C4×D4—48no—
566C4×D4—48no—
567C4×D4—416no—
568#117—24no—
569#117—24no—
570#117—28no—
571#117—24no—
572#117—28no—
573#117—48no—
574C2×C4⋊C4—28no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—28no—
577C2×C4⋊C4—44no—
578C2×C4⋊C4—48no—
579C2×C4⋊C4—48no—
580C2×C4⋊C4—48no—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2414yes—
649C2×C42—28no—
650C2×C42—28no—
651C2×C42—28no—
652C2×C42—48no—
653C2×C42#4118yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2414yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2418yes—
667C2×C42C2418yes—
668C2×C42C2418yes—
669C2×C42C2414yes—
670C2×C42C2418yes—
671C2×C42C2414yes—
672C2×C42C2418yes—
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2412yes—
681#95C2411yescharacteristic
682#95C2411yescharacteristic
683#95C2412yes—
684#95C2414yes—
685#95C2411yescharacteristic
686#95C2411yescharacteristic
687#95C2418yes—
688#95C2418yes—
689#95C2412yes—
690#95C2412yes—
691#95C2414yes—
692#95C2414yes—
693#95C2418yes—
694#95C2418yes—
695#95C2412yes—
696#95C2412yes—
697#95C2418yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2414yes—
705#95C2418yes—
706#95C2418yes—
707#95C2414yes—
708#95C2418yes—
709#95C2414yes—
710#95C2418yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2418yes—
719C24C2512yes—
720C24C2514yes—
721C24C2511yescharacteristic
722#41—416no—
723#41—432no—
724C2×Q8—232no—
725C2×Q8—24no—
726C2×Q8—24no—
727C2×Q8—22no—
728C2×Q8—24no—
729C2×Q8—22no—
730C2×Q8—24no—
731C2×Q8—24no—
732C2×Q8—24no—
733C2×Q8—24no—
734C2×Q8—22no—
735C2×Q8C2×#4118yes—
736C2×Q8C2×#4118yes—
737C2×D4—24no—
738C2×D4—28no—
739C2×D4—24no—
740C2×D4—28no—
741C2×D4—28no—
742C2×D4—24no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—24no—
748C2×D4—24no—
749C2×D4—24no—
750C2×D4—22no—
751C2×D4—28no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—28no—
765C22×C4—24no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—42no—
775C22×C4—44no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—44no—
779C22×C4—42no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—42no—
784C22×C4—48no—
785C22×C4—48no—
786C22×C4—48no—
787C22×C4C2×#4118yes—
788C22×C4C2×#4114yes—
789C22×C4C2×#4114yes—
790C22×C4C2×#4114yes—
791C22×C4C2×#4114yes—
792C22×C4H(5,𝔽2)14yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2514yes—
797C22×C4C2518yes—
798C22×C4C2514yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2512yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2514yes—
811C22×C4C2512yes—
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—216no—
828C4⋊C4—216no—
829C4⋊C4—216no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—216no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—28no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—24no—
861C22⋊C4—28no—
862C22⋊C4—28no—
863C22⋊C4—216no—
864C22⋊C4—216no—
865C22⋊C4—216no—
866C22⋊C4—28no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—28no—
886C42—28no—
887C42—24no—
888C42—28no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—48no—
895C42—48no—
896C42—44no—
897C42—48no—
898C42—48no—
899C42—44no—
900C42—48no—
901C42C2×#4114yes—
902C42C2×#4114yes—
903C42C2×#4114yes—
904C42C2×#4114yes—
905C23—22no—
906C23—22no—
907C23—24no—
908C23—22no—
909C23—22no—
910C23—24no—
911C23—24no—
912C23—22no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23C22×#4112yes—
920C23C22×#4112yes—
921C23C2×H(5,𝔽2)12yes—
922C23C2611yescharacteristic
923Q8—216no—
924Q8—216no—
925Q8—44no—
926Q8—48no—
927D4—48no—
928D4—416no—
929D4—44no—
930D4—48no—
931D4—84no—
932D4—84no—
933D4—88no—
934D4—88no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—216no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—28no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—28no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—44no—
981C2×C4—44no—
982C2×C4—48no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—416no—
986C2×C4—84no—
987C2×C4—84no—
988C2×C4—84no—
989C2×C4—88no—
990C2×C4—168no—
991C2×C4#553116yes—
992C2×C4C22×#4112yes—
993C2×C4C22×#4112yes—
994C2×C4C22×#4112yes—
995C2×C4C22×#4112yes—
996C2×C4C22×#4118yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4C2×H(5,𝔽2)12yes—
1002C2×C4C2×H(5,𝔽2)12yes—
1003C2×C4#58514yes—
1004C22—24no—
1005C22—22no—
1006C22—22no—
1007C22—24no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—42no—
1012C22—44no—
1013C22—42no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—42no—
1019C22—44no—
1020C22C2×#55314yes—
1021C22C23×#4111yescharacteristic
1022C22C23×#4111yescharacteristic
1023C22C22×H(5,𝔽2)11yescharacteristic
1024C22C2×#58512yes—
1025C222−1+612yes—
1026C4—22no—
1027C4—22no—
1028C4—22no—
1029C4—22no—
1030C4—24no—
1031C4—28no—
1032C4—44no—
1033C4—44no—
1034C4—44no—
1035C4—44no—
1036C4—42no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—48no—
1041C4—42no—
1042C4—44no—
1043C4—42no—
1044C4—44no—
1045C4C2×#55314yes—
1046C4C2×#55314yes—
1047C2—24no—
1048C2—82no—
1049C2—84no—
1050C2C22×#55311yescharacteristic
1051C2#6281511yescharacteristic
1052C2#6286011yescharacteristic
1053C2#6295412yes—
1054C2#6300712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34937C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59684C2semidirect
2. #59682C2semidirect
3. #59221C2semidirect
4. #59216C2semidirect
5. #45349C2semidirect
6. #45344C2semidirect
7. #45312C2semidirect
8. #45310C2semidirect
9. #45299C2semidirect
10. #45297C2semidirect
11. #39814C2semidirect
12. #39729C2semidirect
13. #36604C2semidirect
14. #35545C2semidirect
15. #35517C2semidirect
16. #35178C2semidirect
17. #35178C2semidirect
18. #34948C2semidirect
20. #34266C2semidirect
21. #34208C2semidirect
22. #34189C2semidirect
23. C2×#2351C2semidirect
24. C4×#536C2semidirect

Maximal subgroups

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

subgroupindex
#596842
#596822
#592212
#592162
#453492
#453442
#453122
#453102
#452992
#452972
#398142
#397292
#366042
#355452
#355172
#351782
#349482
#349372
#342662
#342082
#341892
C2×#23512
C4×#5362