Finite Group Databasebeta

← #7989685

Subgroups — #7989685

Order 512.

5778 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59424C214yesmaximal, complemented
3#59143C211yesmaximal, characteristic, complemented
4#59070C211yesmaximal, characteristic, complemented
5#49703C214yesmaximal, complemented
6#48265C214yesmaximal, complemented
7#45728C214yesmaximal, complemented
8#44991C214yesmaximal, complemented
9#44883C214yesmaximal, complemented
10#42556C214yesmaximal, complemented
11#42551C214yesmaximal, complemented
12#39351C212yesmaximal, complemented
13#38985C212yesmaximal, complemented
14#38110C214yesmaximal, complemented
15#38021C214yesmaximal, complemented
16#36564C212yesmaximal, complemented
17#36121C211yesmaximal, characteristic
18D4×C22⋊Q8C214yesmaximal, complemented
19#35225C214yesmaximal, complemented
20#34772C212yesmaximal, complemented
21#34498C211yesmaximal, characteristic, complemented
22#34368C211yesmaximal, characteristic, complemented
23C2×#2366C211yesmaximal, characteristic, complemented
24C2×#559C2211yescharacteristic
25C2×D4×Q8C2214yescomplemented
26C2×#546C2212yes—
27C2×#542C2214yescomplemented
28C2×#532C2211yescharacteristic
29C22×#127C2211yescharacteristic
30C22×C22⋊Q8C2214yes—
31C22×C4×D4C2214yes—
32#2858C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2214yes—
35#2856C2211yescharacteristic
36#2849C2214yes—
37#2848C2218yes—
38#2827C2218yescomplemented
39#2796C2218yescomplemented
40#2786C2218yescomplemented
41#2751C2218yescomplemented
42#2740C2218yescomplemented
43#2730C2218yescomplemented
44#2728C2218yescomplemented
45#2723C2218yescomplemented
46#2717C2214yescomplemented
47#2715C2218yescomplemented
48#2709C2214yes—
49#2705C2218yescomplemented
50#2702C2218yescomplemented
51#2700C2218yescomplemented
52#2695C2218yescomplemented
53#2687C2218yescomplemented
54#2683C2214yescomplemented
55#2681C2218yescomplemented
56#2672C2218yescomplemented
57#2644C2214yescomplemented
58#2638C2218yescomplemented
59#2630C2218yescomplemented
60#2624C2214yescomplemented
61#2623C2214yescomplemented
62#2618C2214yescomplemented
63#2601C2218yescomplemented
64#2592C2214yescomplemented
65#2586C2218yescomplemented
66#2567C2212yescomplemented
67#2560C2218yescomplemented
68#2551C2212yescomplemented
69#2549C2218yes—
70#2548C2212yes—
71#2544C2214yes—
72#2544C2212yes—
73#2542C2214yescomplemented
74#2538C2214yescomplemented
75#2538C2214yescomplemented
76#2522C2214yescomplemented
77#2520C2214yescomplemented
78#2512C2214yescomplemented
79#2512C2214yescomplemented
80#2512C2214yescomplemented
81#2511C2212yescomplemented
82#2507C2214yescomplemented
83#2507C2214yescomplemented
84#2507C2212yescomplemented
85#2505C2214yes—
86#2502C2212yes—
87#2497C2212yescomplemented
88#2492C2212yescomplemented
89#2491C2214yescomplemented
90#2487C2212yes—
91#2480C2218yes—
92#2480C2218yes—
93#2472C2218yes—
94#2468C2218yescomplemented
95#2461C2218yescomplemented
96#2452C2214yescomplemented
97#2452C2214yescomplemented
98#2452C2214yescomplemented
99#2452C2214yescomplemented
100#2451C2214yescomplemented
101#2450C2214yes—
102#2449C2218yescomplemented
103#2449C2218yescomplemented
104#2448C2214yescomplemented
105#2447C2214yescomplemented
106#2447C2214yescomplemented
107#2445C2214yes—
108#2445C2214yes—
109#2440C2214yes—
110#2440C2212yes—
111#2437C2218yes—
112#2437C2218yes—
113#2436C2214yescomplemented
114#2435C2214yes—
115#2435C2212yes—
116#2431C2212yes—
117#2428C2214yes—
118#2427C2214yescomplemented
119#2422C2214yescomplemented
120#2422C2214yescomplemented
121#2417C2212yes—
122#2417C2218yescomplemented
123#2413C2214yescomplemented
124#2412C2214yes—
125#2409C2218yescomplemented
126#2409C2214yescomplemented
127#2408C2214yes—
128#2406C2214yescomplemented
129#2405C2214yes—
130#2402C2214yescomplemented
131#2396C2214yescomplemented
132#2379C2214yescomplemented
133#2376C2214yescomplemented
134#2369C2212yescomplemented
135#2369C2214yescomplemented
136#2367C2214yescomplemented
137#2366C2211yescharacteristic
138#2366C2214yes—
139#2366C2214yes—
140#2366C2211yescharacteristic
141#2366C2212yes—
142#2366C2214yes—
143#2366C2211yescharacteristic
144#2354C2214yescomplemented
145Q8×C4⋊C4C2212yescomplemented
146D4×C4⋊C4C2214yescomplemented
147D4×C4⋊C4C2214yescomplemented
148D4×C4⋊C4C2214yescomplemented
149#2345C2214yes—
150#2342C2214yes—
151D4×C22⋊C4C2214yes—
152D4×C22⋊C4C2214yes—
153#2326C2214yescomplemented
154#2324C2214yescomplemented
155#2324C2214yescomplemented
156#2322C2214yescomplemented
157#2319C2214yescomplemented
158#2319C2214yescomplemented
159#2311C2214yescomplemented
160C4×C4⋊Q8C2212yescomplemented
161C4×#127C2211yescharacteristic
162C4×C22⋊Q8C2212yes—
163C4×C22⋊Q8C2214yes—
164C4×C22⋊Q8C2214yes—
165C4×C22⋊Q8C2212yescomplemented
166#2295C2212yescomplemented
167C2×#390C2214yes—
168#2290C2214yes—
169C2×#386C2214yes—
170#2285C2212yescomplemented
171C42×D4C2211yescharacteristic
172C2×C4×C4⋊C4C2212yes—
173C22×#41C2312yes—
174C23×Q8C2314yes—
175C23×D4C2314yes—
176C23×D4C2312yes—
177C24×C4C2314yes—
178#559—28no—
179D4×Q8—416no—
180#546—48no—
181#542—416no—
182#532—28no—
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2311yescharacteristic
185C2×C4⋊Q8C2314yes—
186C2×C4⋊Q8C2314yes—
187C2×#127—28no—
188C2×#127C2311yescharacteristic
189C2×#127C2314yes—
190C2×#127C2312yes—
191C2×#127C2311yescharacteristic
192C2×#126C2318yes—
193C2×#126C2318yes—
194C2×#124C2314yes—
195C2×#124C2312yes—
196C2×#124C2314yes—
197C2×#124C2312yes—
198C2×#124C2318yes—
199C2×#124C2312yes—
200C2×#123C2314yes—
201C2×#123C2318yes—
202C2×#123C2314yes—
203C2×#123C2314yes—
204C2×#123C2314yes—
205C2×C22⋊Q8—416no—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2312yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C2318yes—
211C2×C22⋊Q8C2318yes—
212C2×C22⋊Q8C2318yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2318yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2312yes—
220C2×#121C2314yes—
221C2×#120C2314yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×D4—416no—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2318yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2314yes—
239C2×#117C2314yes—
240C2×#117C2314yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2314yes—
244C22×C4⋊C4C2314yes—
245C22×C4⋊C4C2314yes—
246C22×C22⋊C4C2314yes—
247C22×C22⋊C4C2314yes—
248C22×C22⋊C4C2318yes—
249C22×C22⋊C4C2314yes—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#399C2318yes—
259#399C2318yes—
260#399C2314yes—
261#398C2314yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2314yes—
266#398C2314yes—
267#398C2314yes—
268#398C2314yes—
269#398C2314yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#396C2318yes—
279#396C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2314yes—
283#396C2318yes—
284#396C2314yes—
285#396C2318yes—
286#395C2318yes—
287#395C2318yes—
288#395C2318yes—
289#395C2314yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#393C2318yes—
300#393C2318yes—
301#393C2314yes—
302#393C2318yes—
303#392C2318yes—
304#391C2314yes—
305#391C2314yes—
306#391C2318yes—
307#391C2314yes—
308#391C2312yes—
309#391C2312yes—
310#391C2318yes—
311#391C2312yes—
312#391C2318yes—
313#391C2312yes—
314#391C2312yes—
315#390C2318yes—
316#390C2314yes—
317#390C2312yes—
318#390C2318yes—
319#390C2314yes—
320#390C2314yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2312yes—
329#390C2314yes—
330#390C2314yes—
331#390C2318yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2312yes—
338#389C2314yes—
339#389C2318yes—
340#389C2314yes—
341#389C2314yes—
342#389C2318yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2312yes—
347#389C2312yes—
348#389C2318yes—
349#389C2314yes—
350#389C2312yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2314yes—
362#388C2314yes—
363#387C2318yes—
364#387C2314yes—
365#387C2314yes—
366#387C2318yes—
367#387C2318yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
371#387C2314yes—
372#387C2314yes—
373#387C2314yes—
374#386C2318yes—
375#386C2314yes—
376#386C2314yes—
377#386C2314yes—
378#386C2314yes—
379#386C2314yes—
380#386C2314yes—
381#386C2314yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2314yes—
386#386C2314yes—
387#386C2318yes—
388#386C2318yes—
389#386C2314yes—
390#386C2314yes—
391#385C2318yes—
392#385C2318yes—
393#385C2314yes—
394#385C2318yes—
395#385C2318yes—
396#385C2314yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2314yes—
401#385C2314yes—
402#385C2318yes—
403#385C2318yes—
404#385C2314yes—
405#385C2314yes—
406#385C2314yes—
407#385C2314yes—
408#385C2314yes—
409#384C2311yescharacteristic
410#384C2312yes—
411#384C2314yes—
412#384C2314yes—
413#384C2312yes—
414#384C2312yes—
415#382C2314yes—
416#381C2314yes—
417#381C2318yes—
418#381C2314yes—
419#380C2314yes—
420#380C2318yes—
421#380C2318yes—
422#380C2318yes—
423#380C2312yes—
424#380C2312yes—
425#380C2314yes—
426#380C2318yes—
427#380C2312yes—
428#380C2314yes—
429#380C2314yes—
430#380C2318yes—
431#380C2312yes—
432#379C2318yes—
433#379C2318yes—
434#379C2314yes—
435C4×C4⋊C4C2318yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2312yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376C2314yes—
462C2×#95C2314yes—
463C43C2311yescharacteristic
464C25C2414yes—
465C2×#41—28no—
466C2×#41—44no—
467C2×#41—82no—
468C22×Q8—48no—
469C22×Q8—416no—
470C22×Q8C2412yes—
471C22×Q8C2414yes—
472C22×Q8C2418yes—
473C22×Q8C2412yes—
474C22×D4—216no—
475C22×D4—28no—
476C22×D4—216no—
477C22×D4—48no—
478C22×D4—44no—
479C22×D4—82no—
480C22×D4C2411yescharacteristic
481C22×D4C2414yes—
482C22×D4C2418yes—
483C22×D4C2414yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2412yes—
487C22×D4C2414yes—
488C22×D4C2412yes—
489C23×C4—416no—
490C23×C4—48no—
491C23×C4C2412yes—
492C23×C4C2414yes—
493C23×C4C2414yes—
494C23×C4C2414yes—
495C23×C4C2411yescharacteristic
496C23×C4C2411yescharacteristic
497C23×C4C2412yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2414yes—
501C23×C4C2418yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C4⋊Q8—216no—
505C4⋊Q8—28no—
506C4⋊Q8—24no—
507C4⋊Q8—48no—
508#127—28no—
509#127—216no—
510#127—24no—
511#127#4118yes—
512#126—416no—
513#126—88no—
514#124—28no—
515#124—216no—
516#124—44no—
517#124—48no—
518#124—416no—
519#124—82no—
520#123—216no—
521#123—416no—
522#123—48no—
523#123—84no—
524#123—84no—
525C22⋊Q8—28no—
526C22⋊Q8—28no—
527C22⋊Q8—216no—
528C22⋊Q8—416no—
529C22⋊Q8—44no—
530C22⋊Q8—416no—
531C22⋊Q8—416no—
532C22⋊Q8—416no—
533C22⋊Q8—416no—
534C22⋊Q8—416no—
535C22⋊Q8—416no—
536#121—216no—
537#121—44no—
538#121—48no—
539#121—48no—
540#120—48no—
541C4×Q8—28no—
542C4×Q8—48no—
543C4×Q8—48no—
544C4×D4—216no—
545C4×D4—216no—
546C4×D4—28no—
547C4×D4—216no—
548C4×D4—216no—
549C4×D4—24no—
550C4×D4—48no—
551C4×D4—48no—
552C4×D4—48no—
553C4×D4—48no—
554C4×D4—44no—
555C4×D4—416no—
556C4×D4—416no—
557#117—48no—
558#117—84no—
559C2×C4⋊C4—28no—
560C2×C4⋊C4—28no—
561C2×C4⋊C4—48no—
562C2×C4⋊C4—48no—
563C2×C4⋊C4—48no—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C22⋊C4—216no—
603C2×C22⋊C4—416no—
604C2×C22⋊C4—48no—
605C2×C22⋊C4—84no—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2411yescharacteristic
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2411yescharacteristic
640C2×C42—24no—
641C2×C42—24no—
642C2×C42—48no—
643C2×C42C2414yes—
644C2×C42C2414yes—
645C2×C42C2411yescharacteristic
646C2×C42C2412yes—
647C2×C42C2414yes—
648C2×C42C2412yes—
649C2×C42C2414yes—
650C2×C42C2412yes—
651C2×C42C2411yescharacteristic
652C2×C42C2412yes—
653C2×C42C2411yescharacteristic
654C2×C42C2418yes—
655C2×C42C2414yes—
656C2×C42C2414yes—
657C2×C42C2418yes—
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2412yes—
670#95C2412yes—
671#95C2412yes—
672#95C2414yes—
673#95C2418yes—
674#95C2418yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2418yes—
679#95C2418yes—
680#95C2414yes—
681#95C2418yes—
682#95C2418yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2418yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693C24—28no—
694C24—28no—
695C24—216no—
696C24—48no—
697C24—44no—
698C24C2514yes—
699C24C2511yescharacteristic
700C24C2514yes—
701C24C2511yescharacteristic
702#41—816no—
703C2×Q8—24no—
704C2×Q8—24no—
705C2×Q8—24no—
706C2×Q8—28no—
707C2×Q8—28no—
708C2×Q8—216no—
709C2×Q8—24no—
710C2×Q8—44no—
711C2×Q8—48no—
712C2×Q8—42no—
713C2×Q8—48no—
714C2×Q8—42no—
715C2×Q8—832no—
716C2×D4—216no—
717C2×D4—22no—
718C2×D4—24no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—24no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—216no—
727C2×D4—28no—
728C2×D4—464no—
729C2×D4—48no—
730C2×D4—42no—
731C2×D4—42no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—42no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—48no—
740C2×D4—816no—
741C2×D4C2×#41116yes—
742C2×D4C2×#4118yes—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—28no—
746C22×C4—22no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—24no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—28no—
754C22×C4—28no—
755C22×C4—24no—
756C22×C4—216no—
757C22×C4—22no—
758C22×C4—24no—
759C22×C4—28no—
760C22×C4—216no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—48no—
776C22×C4—44no—
777C22×C4—832no—
778C22×C42−1+418yes—
779C22×C4C2511yescharacteristic
780C22×C4C2511yescharacteristic
781C22×C4C2514yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2512yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2514yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C4⋊C4—24no—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—28no—
802C4⋊C4—24no—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—22no—
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—216no—
812C4⋊C4—28no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—48no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—42no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—48no—
829C4⋊C4—44no—
830C4⋊C4—48no—
831C4⋊C4—44no—
832C4⋊C4—48no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4H(5,𝔽2)18yes—
836C22⋊C4—216no—
837C22⋊C4—216no—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4—24no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—216no—
846C22⋊C4—216no—
847C22⋊C4—22no—
848C22⋊C4—28no—
849C22⋊C4—24no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—48no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—44no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—44no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4H(5,𝔽2)14yes—
870C42—24no—
871C42—22no—
872C42—22no—
873C42—24no—
874C42—28no—
875C42—28no—
876C42—28no—
877C42—28no—
878C42—22no—
879C42—24no—
880C42—24no—
881C42—44no—
882C42—44no—
883C42—48no—
884C42—48no—
885C42—41no—
886C42C2×#4114yes—
887C23—21no—
888C23—22no—
889C23—21no—
890C23—28no—
891C23—24no—
892C23—28no—
893C23—24no—
894C23—21no—
895C23—24no—
896C23—22no—
897C23—24no—
898C23—28no—
899C23—21no—
900C23—22no—
901C23—28no—
902C23—24no—
903C23—21no—
904C23—432no—
905C23—416no—
906C23—416no—
907C23—88no—
908C23—816no—
909C23C22×#4118yes—
910C23C2×H(5,𝔽2)12yes—
911C23C2×2−1+414yes—
912C23C2611yescharacteristic
913Q8—416no—
914Q8—48no—
915Q8—816no—
916Q8—84no—
917D4—232no—
918D4—48no—
919D4—432no—
920D4—44no—
921D4—416no—
922D4—84no—
923D4—88no—
924D4—88no—
925D4—164no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—216no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—21no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—21no—
973C2×C4—416no—
974C2×C4—44no—
975C2×C4—416no—
976C2×C4—44no—
977C2×C4—416no—
978C2×C4—48no—
979C2×C4—816no—
980C2×C4—88no—
981C2×C4—88no—
982C2×C4—88no—
983C2×C4—88no—
984C2×C4—88no—
985C2×C4C22×#4112yes—
986C2×C4C22×#4114yes—
987C2×C4C2×H(5,𝔽2)12yes—
988C2×C4C2×H(5,𝔽2)18yes—
989C2×C4C2×H(5,𝔽2)12yes—
990C2×C4C2×H(5,𝔽2)14yes—
991C2×C4C2×2−1+414yes—
992C2×C4C2×2−1+414yes—
993C22—22no—
994C22—22no—
995C22—24no—
996C22—24no—
997C22—28no—
998C22—216no—
999C22—44no—
1000C22—44no—
1001C22—48no—
1002C22—41no—
1003C22—44no—
1004C22—44no—
1005C22—41no—
1006C22—41no—
1007C22—44no—
1008C22—42no—
1009C22—48no—
1010C22—42no—
1011C22—48no—
1012C22—832no—
1013C22#355014yes—
1014C22C23×#4111yescharacteristic
1015C22C22×H(5,𝔽2)11yescharacteristic
1016C22C22×H(5,𝔽2)12yes—
1017C22C22×2−1+412yes—
1018C22H(7,𝔽2)11yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—28no—
1022C4—22no—
1023C4—24no—
1024C4—41no—
1025C4—44no—
1026C4—44no—
1027C4—44no—
1028C4—44no—
1029C4—44no—
1030C4—41no—
1031C4—42no—
1032C4—44no—
1033C4—44no—
1034C4—42no—
1035C4—44no—
1036C4—44no—
1037C4#352018yes—
1038C2—24no—
1039C2—48no—
1040C2—81no—
1041C2—84no—
1042C2C2×#355011yescharacteristic
1043C2C2×#352012yes—
1044C2#6291712yes—
1045C2#6298311yescharacteristic
1046C2#6301111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59817C2semidirect
2. #59424C2semidirect
3. #59143C2semidirect
4. #59070C2semidirect
5. #49703C2semidirect
6. #48265C2semidirect
7. #45728C2semidirect
8. #44991C2semidirect
9. #44883C2semidirect
10. #42556C2semidirect
11. #42551C2semidirect
12. #39351C2semidirect
13. #38985C2semidirect
14. #38110C2semidirect
15. #38021C2semidirect
16. #36564C2semidirect
18. D4×C22⋊Q8C2semidirect
19. #35225C2semidirect
20. #34772C2semidirect
21. #34498C2semidirect
22. #34368C2semidirect
23. C2×#2366C2semidirect
25. C2×D4×Q8C22semidirect
27. C2×#542C22semidirect
38. #2827C22semidirect
39. #2796C22semidirect
40. #2786C22semidirect
41. #2751C22semidirect
42. #2740C22semidirect
43. #2730C22semidirect
44. #2728C22semidirect
45. #2723C22semidirect
46. #2717C22semidirect
47. #2715C22semidirect
49. #2705C22semidirect
50. #2702C22semidirect
51. #2700C22semidirect
52. #2695C22semidirect
53. #2687C22semidirect
54. #2683C22semidirect
55. #2681C22semidirect
56. #2672C22semidirect
57. #2644C22semidirect
58. #2638C22semidirect
59. #2630C22semidirect
60. #2624C22semidirect
61. #2623C22semidirect
62. #2618C22semidirect
63. #2601C22semidirect
64. #2592C22semidirect
65. #2586C22semidirect
66. #2567C22semidirect
67. #2560C22semidirect
68. #2551C22semidirect
73. #2542C22semidirect
74. #2538C22semidirect
75. #2538C22semidirect
76. #2522C22semidirect
77. #2520C22semidirect
78. #2512C22semidirect
79. #2512C22semidirect
80. #2512C22semidirect
81. #2511C22semidirect
82. #2507C22semidirect
83. #2507C22semidirect
84. #2507C22semidirect
87. #2497C22semidirect
88. #2492C22semidirect
89. #2491C22semidirect
94. #2468C22semidirect
95. #2461C22semidirect
96. #2452C22semidirect
97. #2452C22semidirect
98. #2452C22semidirect
99. #2452C22semidirect
100. #2451C22semidirect
102. #2449C22semidirect
103. #2449C22semidirect
104. #2448C22semidirect
105. #2447C22semidirect
106. #2447C22semidirect
113. #2436C22semidirect
118. #2427C22semidirect
119. #2422C22semidirect
120. #2422C22semidirect
122. #2417C22semidirect
123. #2413C22semidirect
125. #2409C22semidirect
126. #2409C22semidirect
128. #2406C22semidirect
130. #2402C22semidirect
131. #2396C22semidirect
132. #2379C22semidirect
133. #2376C22semidirect
134. #2369C22semidirect
135. #2369C22semidirect
136. #2367C22semidirect
144. #2354C22semidirect
145. Q8×C4⋊C4C22semidirect
146. D4×C4⋊C4C22semidirect
147. D4×C4⋊C4C22semidirect
148. D4×C4⋊C4C22semidirect
153. #2326C22semidirect
154. #2324C22semidirect
155. #2324C22semidirect
156. #2322C22semidirect
157. #2319C22semidirect
158. #2319C22semidirect
159. #2311C22semidirect
160. C4×C4⋊Q8C22semidirect
165. C4×C22⋊Q8C22semidirect
166. #2295C22semidirect
170. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#598172
#594242
#591432
#590702
#497032
#482652
#457282
#449912
#448832
#425562
#425512
#393512
#389852
#381102
#380212
#365642
#361212
D4×C22⋊Q82
#352252
#347722
#344982
#343682
C2×#23662