Finite Group Databasebeta

← #7679245

Subgroups — #7679245

Order 512.

4908 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59449C214yesmaximal, complemented
2#59446C214yesmaximal, complemented
3#59332C214yesmaximal, complemented
4#59331C214yesmaximal, complemented
5#45350C212yesmaximal, complemented
6#45318C212yesmaximal, complemented
7#45211C212yesmaximal, complemented
8#45147C214yesmaximal, complemented
9#45056C212yesmaximal, complemented
10#44958C214yesmaximal, complemented
11#38924C214yesmaximal, complemented
12#38271C218yesmaximal, complemented
13#36338C214yesmaximal, complemented
14#35558C212yesmaximal, complemented
15#35531C212yesmaximal
16#35181C212yesmaximal, complemented
17#35172C211yesmaximal, characteristic, complemented
18#34948C211yesmaximal, characteristic, complemented
19#34947C211yesmaximal, characteristic, complemented
20#34252C212yesmaximal, complemented
21#34215C211yesmaximal, characteristic, complemented
22#34184C211yesmaximal, characteristic, complemented
23C2×#2357C211yesmaximal, characteristic, complemented
24C4×#535C211yesmaximal, characteristic
25C2×#535C2211yescharacteristic
26C2×#533C2211yescharacteristic
27C2×#520C2212yes—
28C2×C4×#41C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30#2851C2218yes—
31#2848C2214yes—
32#2777C2218yescomplemented
33#2773C2218yescomplemented
34#2772C2218yescomplemented
35#2761C2218yescomplemented
36#2754C2218yescomplemented
37#2743C2218yescomplemented
38#2741C2218yescomplemented
39#2738C2218yescomplemented
40#2707C2218yescomplemented
41#2702C2218yescomplemented
42#2698C2218yescomplemented
43#2687C2218yescomplemented
44#2646C2218yes—
45#2626C2214yes—
46#2601C2218yescomplemented
47#2580C2212yes—
48#2580C2212yes—
49#2575C2218yescomplemented
50#2571C2214yescomplemented
51#2571C2214yescomplemented
52#2571C2212yescomplemented
53#2570C2214yescomplemented
54#2570C2214yescomplemented
55#2570C2214yescomplemented
56#2570C2214yescomplemented
57#2570C2212yescomplemented
58#2570C2212yescomplemented
59#2569C2212yes—
60#2569C2212yes—
61#2568C2211yescharacteristic, complemented
62#2567C2211yescharacteristic, complemented
63#2566C2214yes—
64#2566C2212yescomplemented
65#2565C2212yescomplemented
66#2564C2212yes—
67#2564C2212yes—
68#2563C2212yes—
69#2563C2211yescharacteristic, complemented
70#2558C2218yescomplemented
71#2556C2218yescomplemented
72#2553C2218yescomplemented
73#2552C2214yescomplemented
74#2552C2212yescomplemented
75#2552C2214yescomplemented
76#2542C2212yes—
77#2542C2211yescharacteristic, complemented
78#2538C2214yes—
79#2532C2218yescomplemented
80#2530C2218yescomplemented
81#2529C2218yescomplemented
82#2519C2218yescomplemented
83#2519C2218yescomplemented
84#2517C2218yescomplemented
85#2515C2218yescomplemented
86#2513C2214yes—
87#2513C2214yes—
88#2513C2214yes—
89#2513C2214yes—
90#2512C2214yes—
91#2512C2214yes—
92#2512C2214yes—
93#2512C2214yes—
94#2504C2214yes—
95#2501C2214yes—
96#2500C2214yes—
97#2500C2214yes—
98#2498C2218yescomplemented
99#2488C2218yescomplemented
100#2480C2218yes—
101#2480C2218yes—
102#2477C2218yescomplemented
103#2468C2218yescomplemented
104#2460C2218yescomplemented
105#2448C2214yes—
106#2448C2214yes—
107#2445C2214yes—
108#2445C2214yes—
109#2442C2214yes—
110#2419C2218yescomplemented
111#2418C2218yes—
112#2418C2218yes—
113#2417C2214yes—
114#2402C2212yescomplemented
115#2402C2212yescomplemented
116#2396C2212yescomplemented
117#2396C2212yescomplemented
118#2373C2218yescomplemented
119#2368C2214yes—
120#2368C2214yes—
121#2359C2218yescomplemented
122#2357C2212yes—
123#2357C2212yes—
124#2357C2214yes—
125#2357C2212yes—
126#2357C2212yes—
127#2357C2214yes—
128#2357C2214yescomplemented
129#2356C2214yescomplemented
130#2355C2214yescomplemented
131#2355C2214yescomplemented
132#2355C2214yescomplemented
133#2354C2214yescomplemented
134#2351C2212yescomplemented
135#2351C2212yescomplemented
136#2349C2214yes—
137#2349C2214yes—
138#2349C2212yescomplemented
139#2349C2212yescomplemented
140#2347C2214yescomplemented
141#2346C2214yescomplemented
142#2345C2214yescomplemented
143#2344C2214yescomplemented
144#2331C2212yescomplemented
145#2331C2212yescomplemented
146#2328C2212yes—
147#2326C2212yes—
148#2324C2214yes—
149#2321C2214yes—
150#2318C2218yes—
151#2317C2211yescharacteristic
152#2317C2212yes—
153#2317C2212yes—
154#2317C2212yes—
155#2317C2214yescomplemented
156#2311C2211yescharacteristic
157#2309C2211yescharacteristic
158#2309C2212yes—
159C4×#127C2212yes—
160C4×#125C2214yescomplemented
161C4×#125C2214yescomplemented
162C4×#124C2212yes—
163C4×C22⋊Q8C2214yescomplemented
164C4×#121C2214yes—
165C4×#120C2214yes—
166#2297C2212yes—
167#2296C2212yes—
168C2×#390C2212yes—
169#2290C2218yes—
170C2×#388C2214yes—
171#2285C2211yescharacteristic
172#2285C2212yes—
173#2285C2212yes—
174#2285C2212yescomplemented
175C2×#382C2211yescharacteristic
176C2×#382C2212yescomplemented
177C2×#381C2212yes—
178#2274C2212yes—
179C4×#117C2211yescharacteristic
180C2×C4×C4⋊C4C2212yes—
181C2×C4×C4⋊C4C2211yescharacteristic
182C2×C4×C22⋊C4C2212yes—
183C22×#41C2311yescharacteristic
184C23×D4C2311yescharacteristic
185C24×C4C2312yes—
186#535—28no—
187#533—28no—
188C2×C4⋊Q8C2311yescharacteristic
189C2×C4⋊Q8C2311yescharacteristic
190C2×#127C2312yes—
191C2×#126C2318yes—
192C2×#126C2318yes—
193C2×#125C2312yes—
194C2×#125C2314yes—
195C2×#125C2318yes—
196C2×#124C2312yes—
197C2×#123C2318yes—
198C2×#123C2318yes—
199C2×C22⋊Q8C2312yes—
200C2×C22⋊Q8C2312yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2318yes—
203C2×#121C2314yes—
204C2×#120C2314yes—
205#520—216no—
206C4×#41—28no—
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2311yescharacteristic
209C2×C4×Q8C2312yes—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2312yes—
212C2×C4×D4—28no—
213C2×C4×D4C2311yescharacteristic
214C2×C4×D4C2312yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2312yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2318yes—
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2312yes—
227C2×#117C2312yes—
228C2×#117C2311yescharacteristic
229C2×#117C2312yes—
230C2×#117C2314yes—
231C2×#117C2318yes—
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2314yes—
235C22×C4⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2314yes—
238C22×C22⋊C4C2314yes—
239C22×C42C2312yes—
240C22×C42C2312yes—
241C22×C42C2314yes—
242C22×C42C2311yescharacteristic
243#400C2312yes—
244#400C2312yes—
245#400C2314yes—
246#400C2314yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2314yes—
252#400C2314yes—
253#399C2312yes—
254#399C2312yes—
255#399C2318yes—
256#399C2314yes—
257#399C2314yes—
258#399C2318yes—
259#398C2314yes—
260#398C2314yes—
261#398C2314yes—
262#398C2314yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2314yes—
268#398C2314yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2314yes—
280#396C2314yes—
281#396C2318yes—
282#396C2318yes—
283#395C2312yes—
284#395C2312yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#393C2314yes—
290#393C2314yes—
291#393C2312yes—
292#393C2312yes—
293#391C2312yes—
294#391C2312yes—
295#391C2312yes—
296#391C2314yes—
297#391C2318yes—
298#391C2318yes—
299#390C2312yes—
300#390C2312yes—
301#390C2318yes—
302#390C2314yes—
303#390C2312yes—
304#390C2314yes—
305#390C2314yes—
306#390C2314yes—
307#390C2314yes—
308#390C2312yes—
309#390C2312yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2312yes—
323#389C2312yes—
324#389C2314yes—
325#389C2314yes—
326#389C2312yes—
327#389C2312yes—
328#389C2318yes—
329#389C2318yes—
330#389C2318yes—
331#389C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#387C2314yes—
353#387C2314yes—
354#387C2314yes—
355#387C2314yes—
356#387C2318yes—
357#387C2318yes—
358#387C2314yes—
359#387C2314yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#386C2314yes—
371#386C2314yes—
372#386C2314yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#385C2314yes—
378#385C2314yes—
379#385C2318yes—
380#385C2318yes—
381#385C2314yes—
382#385C2314yes—
383#385C2318yes—
384#385C2314yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#384C2312yes—
391#384C2312yes—
392#384C2314yes—
393#384C2312yes—
394#384C2312yes—
395#384C2314yes—
396#384C2314yes—
397#384C2312yes—
398#384C2312yes—
399#383C2318yes—
400#382C2312yes—
401#382C2314yes—
402#382C2314yes—
403#382C2312yes—
404#382C2312yes—
405#382C2312yes—
406#382C2312yes—
407#382C2312yes—
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2314yes—
411#382C2314yes—
412#382C2318yes—
413#382C2312yes—
414#382C2318yes—
415#382C2314yes—
416#382C2312yes—
417#382C2314yes—
418#382C2312yes—
419#381C2318yes—
420#381C2318yes—
421#381C2314yes—
422#381C2314yes—
423#380C2318yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2312yes—
429#380C2314yes—
430#380C2314yes—
431#380C2318yes—
432#380C2312yes—
433#380C2314yes—
434#380C2314yes—
435#379C2314yes—
436#379C2318yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2318yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2318yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2318yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2311yescharacteristic
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2318yes—
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476#376C2312yes—
477#376C2318yes—
478C2×#95C2311yescharacteristic
479C2×#95C2311yescharacteristic
480C2×#95C2314yes—
481C2×#95C2312yes—
482C2×#95C2312yes—
483C2×#95C2314yes—
484C2×#95C2314yes—
485C43C2312yes—
486C25C2412yes—
487C2×#41—24no—
488C2×#41—24no—
489C2×#41#4118yes—
490C22×Q8C2411yescharacteristic
491C22×Q8C2412yes—
492C22×Q8C2412yes—
493C22×D4—24no—
494C22×D4—24no—
495C22×D4—24no—
496C22×D4C2412yes—
497C22×D4C2412yes—
498C22×D4C2412yes—
499C22×D4C2411yescharacteristic
500C22×D4C2418yes—
501C23×C4—28no—
502C23×C4—84no—
503C23×C4C2412yes—
504C23×C4C2412yes—
505C23×C4C2414yes—
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2418yes—
509C23×C4C2412yes—
510C23×C4C2414yes—
511C23×C4C2414yes—
512C23×C4C2412yes—
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C4⋊Q8—24no—
517C4⋊Q8—24no—
518#127—28no—
519#126—416no—
520#126—88no—
521#125—28no—
522#125—48no—
523#125—88no—
524#124—28no—
525#123—416no—
526#123—88no—
527C22⋊Q8—28no—
528C22⋊Q8—28no—
529C22⋊Q8—48no—
530C22⋊Q8—88no—
531#121—216no—
532#120—216no—
533C4×Q8—216no—
534C4×Q8—24no—
535C4×Q8—24no—
536C4×Q8—28no—
537C4×Q8—28no—
538C4×D4—232no—
539C4×D4—216no—
540C4×D4—28no—
541C4×D4—28no—
542C4×D4—28no—
543C4×D4—28no—
544C4×D4—28no—
545C4×D4—28no—
546C4×D4—24no—
547C4×D4—24no—
548C4×D4—88no—
549#117—24no—
550#117—216no—
551#117—28no—
552#117—28no—
553#117—24no—
554#117—24no—
555#117—28no—
556#117—88no—
557C2×C4⋊C4—24no—
558C2×C4⋊C4—216no—
559C2×C4⋊C4—28no—
560C2×C4⋊C4—44no—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C22⋊C4—28no—
606C2×C22⋊C4—48no—
607C2×C22⋊C4—84no—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2412yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
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×C42—28no—
635C2×C42—28no—
636C2×C42—84no—
637C2×C42#4118yes—
638C2×C42C2412yes—
639C2×C42C2418yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2418yes—
651C2×C42C2418yes—
652C2×C42C2414yes—
653C2×C42C2414yes—
654C2×C42C2418yes—
655C2×C42C2418yes—
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#95C2414yes—
661#95C2412yes—
662#95C2414yes—
663#95C2412yes—
664#95C2412yes—
665#95C2411yescharacteristic
666#95C2411yescharacteristic
667#95C2414yes—
668#95C2418yes—
669#95C2412yes—
670#95C2411yescharacteristic
671#95C2411yescharacteristic
672#95C2418yes—
673#95C2414yes—
674#95C2418yes—
675#95C2418yes—
676#95C2414yes—
677#95C2414yes—
678#95C2418yes—
679#95C2414yes—
680#95C2414yes—
681#95C2418yes—
682#95C2414yes—
683#95C2418yes—
684#95C2418yes—
685#95C2414yes—
686#95C2418yes—
687#95C2418yes—
688#95C2414yes—
689#95C2414yes—
690#95C2412yes—
691#95C2412yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704C24—24no—
705C24—24no—
706C24—24no—
707C24—44no—
708C24—44no—
709C24C2514yes—
710C24C2512yes—
711C24C2511yescharacteristic
712#41—232no—
713C2×Q8—22no—
714C2×Q8—24no—
715C2×Q8—24no—
716C2×Q8—22no—
717C2×Q8—44no—
718C2×Q8—44no—
719C2×Q8C2×#4114yes—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—216no—
723C2×D4—22no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—22no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—416no—
734C2×D4C2×#4118yes—
735C2×D4C2×#4114yes—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—216no—
741C22×C4—28no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—42no—
749C22×C4—44no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—48no—
757C22×C4—44no—
758C22×C4—48no—
759C22×C4—44no—
760C22×C4—48no—
761C22×C4—48no—
762C22×C4—816no—
763C22×C4C2×#4118yes—
764C22×C4C2×#4114yes—
765C22×C4C2×#4114yes—
766C22×C4C2×#4114yes—
767C22×C4C2×#4114yes—
768C22×C42−1+414yes—
769C22×C4C2512yes—
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2514yes—
773C22×C4C2518yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2512yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2514yes—
781C22×C4C2512yes—
782C22×C4C2511yescharacteristic
783C22×C4C2512yes—
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C22×C4C2511yescharacteristic
787C22×C4C2512yes—
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C4⋊C4—28no—
791C4⋊C4—24no—
792C4⋊C4—24no—
793C4⋊C4—24no—
794C4⋊C4—216no—
795C4⋊C4—28no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—44no—
817C4⋊C4—48no—
818C4⋊C4—48no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—44no—
824C4⋊C4—48no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C22⋊C4—216no—
835C22⋊C4—28no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—28no—
839C22⋊C4—24no—
840C22⋊C4—28no—
841C22⋊C4—28no—
842C22⋊C4—24no—
843C22⋊C4—24no—
844C22⋊C4—216no—
845C22⋊C4—216no—
846C22⋊C4—28no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—44no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—44no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—44no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C42—24no—
861C42—24no—
862C42—24no—
863C42—216no—
864C42—28no—
865C42—28no—
866C42—24no—
867C42—24no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—24no—
872C42—48no—
873C42—48no—
874C42—48no—
875C42—44no—
876C42—44no—
877C42—48no—
878C42C2×#4114yes—
879C42C2×#4114yes—
880C42C2×#4114yes—
881C42C2×#4114yes—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—24no—
887C23—24no—
888C23—24no—
889C23—24no—
890C23—24no—
891C23—28no—
892C23—28no—
893C23—48no—
894C23—48no—
895C23—48no—
896C23—88no—
897C23—88no—
898C23C22×#4114yes—
899C23C22×#4112yes—
900C23C22×#4112yes—
901C23C2×2−1+412yes—
902C23C2611yescharacteristic
903Q8—28no—
904Q8—84no—
905Q8—84no—
906D4—216no—
907D4—28no—
908D4—48no—
909D4—48no—
910D4—816no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—216no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—28no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—28no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—28no—
947C2×C4—24no—
948C2×C4—28no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—44no—
957C2×C4—44no—
958C2×C4—48no—
959C2×C4—48no—
960C2×C4—84no—
961C2×C4—84no—
962C2×C4—88no—
963C2×C4—88no—
964C2×C4—88no—
965C2×C4—816no—
966C2×C4—84no—
967C2×C4#552116yes—
968C2×C4C22×#4114yes—
969C2×C4C22×#4112yes—
970C2×C4C22×#4112yes—
971C2×C4C22×#4112yes—
972C2×C4C22×#4112yes—
973C2×C4C22×#4112yes—
974C2×C4C22×#4112yes—
975C2×C4C22×#4112yes—
976C2×C4C22×#4112yes—
977C2×C4C2×2−1+412yes—
978C2×C4C2×2−1+412yes—
979C2×C4#58514yes—
980C22—24no—
981C22—22no—
982C22—22no—
983C22—24no—
984C22—28no—
985C22—24no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—48no—
990C22—44no—
991C22—44no—
992C22—48no—
993C22—44no—
994C22—816no—
995C22C2×#55214yes—
996C22C23×#4111yescharacteristic
997C22C23×#4111yescharacteristic
998C22C22×2−1+411yescharacteristic
999C22C2×#58512yes—
1000C22H(7,𝔽2)12yes—
1001C4—22no—
1002C4—22no—
1003C4—22no—
1004C4—22no—
1005C4—24no—
1006C4—24no—
1007C4—44no—
1008C4—48no—
1009C4—44no—
1010C4—44no—
1011C4—42no—
1012C4—44no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—44no—
1017C4—42no—
1018C4—42no—
1019C4—42no—
1020C4C2×#55214yes—
1021C4C2×#55214yes—
1022C2—24no—
1023C2—44no—
1024C2—84no—
1025C2C22×#55211yescharacteristic
1026C2#6281511yescharacteristic
1027C2#6285511yescharacteristic
1028C2#6295812yes—
1029C2#6301012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59449C2semidirect
2. #59446C2semidirect
3. #59332C2semidirect
4. #59331C2semidirect
5. #45350C2semidirect
6. #45318C2semidirect
7. #45211C2semidirect
8. #45147C2semidirect
9. #45056C2semidirect
10. #44958C2semidirect
11. #38924C2semidirect
12. #38271C2semidirect
13. #36338C2semidirect
14. #35558C2semidirect
16. #35181C2semidirect
17. #35172C2semidirect
18. #34948C2semidirect
19. #34947C2semidirect
20. #34252C2semidirect
21. #34215C2semidirect
22. #34184C2semidirect
23. C2×#2357C2semidirect
32. #2777C22semidirect
33. #2773C22semidirect
34. #2772C22semidirect
35. #2761C22semidirect
36. #2754C22semidirect
37. #2743C22semidirect
38. #2741C22semidirect
39. #2738C22semidirect
40. #2707C22semidirect
41. #2702C22semidirect
42. #2698C22semidirect
43. #2687C22semidirect
46. #2601C22semidirect
49. #2575C22semidirect
50. #2571C22semidirect
51. #2571C22semidirect
52. #2571C22semidirect
53. #2570C22semidirect
54. #2570C22semidirect
55. #2570C22semidirect
56. #2570C22semidirect
57. #2570C22semidirect
58. #2570C22semidirect
61. #2568C22semidirect
62. #2567C22semidirect
64. #2566C22semidirect
65. #2565C22semidirect
69. #2563C22semidirect
70. #2558C22semidirect
71. #2556C22semidirect
72. #2553C22semidirect
73. #2552C22semidirect
74. #2552C22semidirect
75. #2552C22semidirect
77. #2542C22semidirect
79. #2532C22semidirect
80. #2530C22semidirect
81. #2529C22semidirect
82. #2519C22semidirect
83. #2519C22semidirect
84. #2517C22semidirect
85. #2515C22semidirect
98. #2498C22semidirect
99. #2488C22semidirect
102. #2477C22semidirect
103. #2468C22semidirect
104. #2460C22semidirect
110. #2419C22semidirect
114. #2402C22semidirect
115. #2402C22semidirect
116. #2396C22semidirect
117. #2396C22semidirect
118. #2373C22semidirect
121. #2359C22semidirect
128. #2357C22semidirect
129. #2356C22semidirect
130. #2355C22semidirect
131. #2355C22semidirect
132. #2355C22semidirect
133. #2354C22semidirect
134. #2351C22semidirect
135. #2351C22semidirect
138. #2349C22semidirect
139. #2349C22semidirect
140. #2347C22semidirect
141. #2346C22semidirect
142. #2345C22semidirect
143. #2344C22semidirect
144. #2331C22semidirect
145. #2331C22semidirect
155. #2317C22semidirect
160. C4×#125C22semidirect
161. C4×#125C22semidirect
163. C4×C22⋊Q8C22semidirect
174. #2285C22semidirect
176. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
#594492
#594462
#593322
#593312
#453502
#453182
#452112
#451472
#450562
#449582
#389242
#382712
#363382
#355582
#355312
#351812
#351722
#349482
#349472
#342522
#342152
#341842
C2×#23572
C4×#5352