Finite Group Databasebeta

← #7989581

Subgroups — #7989581

Order 512.

5817 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59816C211yesmaximal, characteristic
2#59420C211yesmaximal, characteristic, complemented
3#59420C211yesmaximal, characteristic, complemented
4#59398C214yesmaximal, complemented
5#49771C214yesmaximal, complemented
6#48235C214yesmaximal, complemented
7#45694C214yesmaximal, complemented
8#45006C214yesmaximal, complemented
9#44874C214yesmaximal, complemented
10#42601C214yesmaximal, complemented
11#42535C214yesmaximal, complemented
12#39377C212yesmaximal, complemented
13#39116C214yesmaximal, complemented
14#39042C214yesmaximal, complemented
15#38975C212yesmaximal, complemented
16#36559C211yesmaximal, characteristic, complemented
17#36464C212yesmaximal, complemented
18D4×#123C214yesmaximal, complemented
19#35225C214yesmaximal, complemented
20#34918C212yesmaximal, complemented
21#34498C211yesmaximal, characteristic, complemented
22#34493C211yesmaximal, characteristic, complemented
23C4×D42C211yesmaximal, characteristic, complemented
24C2×#559C2211yescharacteristic
25C2×#554C2212yescomplemented
26C2×D42C2211yescharacteristic
27C2×D42C2211yescharacteristic
28C2×D42C2214yes—
29C2×#542C2214yescomplemented
30C22×#123C2214yescomplemented
31C22×C4×D4C2214yescomplemented
32#2868C2211yescharacteristic, complemented
33#2859C2211yescharacteristic, complemented
34#2859C2211yescharacteristic, complemented
35#2854C2214yescomplemented
36#2849C2218yescomplemented
37#2848C2214yescomplemented
38#2827C2218yescomplemented
39#2770C2218yescomplemented
40#2761C2218yescomplemented
41#2749C2218yescomplemented
42#2743C2218yescomplemented
43#2741C2218yescomplemented
44#2737C2218yescomplemented
45#2735C2218yescomplemented
46#2718C2218yescomplemented
47#2707C2218yescomplemented
48#2697C2214yescomplemented
49#2697C2214yescomplemented
50#2697C2218yescomplemented
51#2696C2218yescomplemented
52#2685C2218yescomplemented
53#2684C2218yescomplemented
54#2681C2218yescomplemented
55#2679C2214yes—
56#2674C2218yescomplemented
57#2644C2214yescomplemented
58#2638C2218yescomplemented
59#2630C2218yescomplemented
60#2628C2214yescomplemented
61#2627C2214yescomplemented
62#2626C2214yescomplemented
63#2597C2218yescomplemented
64#2597C2214yescomplemented
65#2595C2214yescomplemented
66#2592C2212yescomplemented
67#2580C2212yescomplemented
68#2578C2218yescomplemented
69#2570C2212yescomplemented
70#2566C2212yescomplemented
71#2566C2212yescomplemented
72#2563C2212yescomplemented
73#2561C2214yescomplemented
74#2561C2214yescomplemented
75#2559C2218yescomplemented
76#2558C2218yescomplemented
77#2544C2212yes—
78#2538C2212yescomplemented
79#2538C2212yescomplemented
80#2538C2214yescomplemented
81#2537C2214yes—
82#2537C2212yes—
83#2534C2214yescomplemented
84#2534C2214yescomplemented
85#2518C2218yescomplemented
86#2516C2214yescomplemented
87#2513C2212yescomplemented
88#2511C2212yescomplemented
89#2507C2214yescomplemented
90#2501C2214yescomplemented
91#2497C2214yescomplemented
92#2496C2214yescomplemented
93#2495C2214yescomplemented
94#2491C2214yescomplemented
95#2486C2214yescomplemented
96#2485C2214yescomplemented
97#2480C2218yescomplemented
98#2472C2218yescomplemented
99#2468C2218yescomplemented
100#2461C2218yescomplemented
101#2458C2214yescomplemented
102#2452C2214yescomplemented
103#2452C2214yescomplemented
104#2447C2212yescomplemented
105#2445C2214yes—
106#2445C2212yes—
107#2443C2218yescomplemented
108#2443C2218yescomplemented
109#2440C2214yescomplemented
110#2435C2214yescomplemented
111#2435C2214yescomplemented
112#2435C2214yescomplemented
113#2427C2214yescomplemented
114#2427C2214yescomplemented
115#2426C2214yescomplemented
116#2423C2214yescomplemented
117#2422C2214yescomplemented
118#2422C2214yescomplemented
119#2420C2214yescomplemented
120#2420C2214yescomplemented
121#2418C2218yescomplemented
122#2418C2218yescomplemented
123#2417C2214yescomplemented
124#2415C2214yescomplemented
125#2412C2218yescomplemented
126#2408C2214yes—
127#2408C2214yes—
128#2408C2214yes—
129#2405C2218yescomplemented
130#2398C2214yescomplemented
131#2395C2214yescomplemented
132#2376C2214yescomplemented
133#2375C2214yescomplemented
134#2367C2214yescomplemented
135#2366C2211yescharacteristic
136#2363C2214yescomplemented
137#2363C2214yescomplemented
138#2361C2214yescomplemented
139#2358C2214yescomplemented
140#2354C2212yescomplemented
141Q8×C4⋊C4C2212yescomplemented
142D4×C4⋊C4C2214yescomplemented
143D4×C4⋊C4C2212yescomplemented
144D4×C4⋊C4C2214yescomplemented
145#2347C2214yescomplemented
146#2345C2214yescomplemented
147D4×C22⋊C4C2214yescomplemented
148D4×C22⋊C4C2214yescomplemented
149D4×C22⋊C4C2214yescomplemented
150D4×C22⋊C4C2214yescomplemented
151#2326C2214yescomplemented
152#2324C2214yescomplemented
153#2322C2214yescomplemented
154#2321C2214yescomplemented
155#2319C2214yescomplemented
156#2319C2214yescomplemented
157#2309C2214yescomplemented
158C4×#127C2211yescharacteristic
159C4×#127C2211yescharacteristic
160C4×#127C2212yes—
161C4×#127C2211yescharacteristic
162C4×#124C2212yescomplemented
163C4×#124C2212yescomplemented
164C4×C22⋊Q8C2214yescomplemented
165C4×#123C2214yescomplemented
166C4×#121C2214yescomplemented
167C4×#120C2214yescomplemented
168#2295C2212yescomplemented
169#2293C2212yescomplemented
170#2290C2214yescomplemented
171C42×Q8C2211yescharacteristic, complemented
172C42×D4C2212yescomplemented
173C23×D4C2314yes—
174C23×D4C2314yes—
175C23×D4C2314yes—
176C24×C4C2314yes—
177#559—28no—
178#554—48no—
179D42—28no—
180D42—28no—
181D42—416no—
182#542—416no—
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2314yes—
185C2×#127C2312yes—
186C2×#127C2311yescharacteristic
187C2×#126C2318yes—
188C2×#125C2312yes—
189C2×#125C2312yes—
190C2×#124C2314yes—
191C2×#124C2312yes—
192C2×#124C2312yes—
193C2×#124C2318yes—
194C2×#123—416no—
195C2×#123C2314yes—
196C2×#123C2314yes—
197C2×#123C2318yes—
198C2×#123C2318yes—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2318yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2314yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2318yes—
212C2×#120C2314yes—
213C2×#120C2314yes—
214C2×#120C2318yes—
215C2×#120C2318yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2314yes—
220C2×C4×D4—416no—
221C2×C4×D4C2312yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2318yes—
237C2×C4×D4C2318yes—
238C2×#117C2314yes—
239C2×#117C2314yes—
240C22×C4⋊C4C2314yes—
241C22×C4⋊C4C2314yes—
242C22×C4⋊C4C2314yes—
243C22×C22⋊C4C2314yes—
244C22×C22⋊C4C2314yes—
245C22×C22⋊C4C2314yes—
246C22×C22⋊C4C2318yes—
247C22×C42C2314yes—
248#400C2314yes—
249#400C2318yes—
250#400C2314yes—
251#400C2318yes—
252#400C2314yes—
253#399C2318yes—
254#399C2314yes—
255#399C2318yes—
256#398C2314yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2314yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2314yes—
267#397C2314yes—
268#397C2314yes—
269#397C2318yes—
270#397C2314yes—
271#397C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2318yes—
278#395C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2314yes—
283#394C2314yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2314yes—
289#394C2314yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#393C2314yes—
295#393C2318yes—
296#393C2318yes—
297#393C2314yes—
298#392C2318yes—
299#391C2312yes—
300#391C2312yes—
301#391C2312yes—
302#391C2312yes—
303#390C2312yes—
304#390C2312yes—
305#390C2314yes—
306#390C2312yes—
307#390C2312yes—
308#390C2314yes—
309#390C2312yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2312yes—
314#390C2314yes—
315#390C2318yes—
316#390C2314yes—
317#390C2318yes—
318#390C2314yes—
319#390C2312yes—
320#390C2312yes—
321#390C2312yes—
322#390C2314yes—
323#390C2318yes—
324#389C2312yes—
325#389C2312yes—
326#389C2312yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2318yes—
331#389C2312yes—
332#389C2314yes—
333#389C2318yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#388C2314yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2314yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2314yes—
350#388C2314yes—
351#388C2314yes—
352#388C2314yes—
353#388C2314yes—
354#388C2314yes—
355#388C2318yes—
356#388C2314yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2314yes—
361#387C2314yes—
362#387C2314yes—
363#387C2314yes—
364#387C2318yes—
365#387C2318yes—
366#387C2314yes—
367#387C2314yes—
368#387C2314yes—
369#387C2318yes—
370#386C2318yes—
371#386C2314yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2314yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2314yes—
382#386C2314yes—
383#386C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2314yes—
387#385C2318yes—
388#385C2314yes—
389#385C2314yes—
390#385C2318yes—
391#385C2314yes—
392#385C2314yes—
393#385C2314yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#384C2312yes—
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2312yes—
402#384C2314yes—
403#384C2314yes—
404#383C2318yes—
405#382C2312yes—
406#382C2312yes—
407#382C2312yes—
408#382C2312yes—
409#381C2314yes—
410#381C2314yes—
411#381C2314yes—
412#381C2318yes—
413#381C2314yes—
414#380C2318yes—
415#380C2318yes—
416#380C2318yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#379C2314yes—
427#379C2314yes—
428#379C2314yes—
429#379C2314yes—
430#379C2318yes—
431#379C2314yes—
432#379C2318yes—
433#379C2318yes—
434#379C2314yes—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2318yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2312yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2318yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2314yes—
460#376C2314yes—
461C43C2311yescharacteristic
462C43C2311yescharacteristic
463C43C2311yescharacteristic
464C25C2414yes—
465C25C2414yes—
466C22×Q8C2412yes—
467C22×Q8C2411yescharacteristic
468C22×Q8C2414yes—
469C22×D4—216no—
470C22×D4—216no—
471C22×D4—216no—
472C22×D4—48no—
473C22×D4—48no—
474C22×D4—48no—
475C22×D4—48no—
476C22×D4—416no—
477C22×D4C2412yes—
478C22×D4C2418yes—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C22×D4C2412yes—
482C22×D4C2414yes—
483C22×D4C2418yes—
484C22×D4C2418yes—
485C22×D4C2412yes—
486C23×C4—48no—
487C23×C4—416no—
488C23×C4C2414yes—
489C23×C4C2414yes—
490C23×C4C2414yes—
491C23×C4C2414yes—
492C23×C4C2414yes—
493C23×C4C2414yes—
494C23×C4C2418yes—
495C23×C4C2414yes—
496C23×C4C2414yes—
497C23×C4C2414yes—
498C4⋊Q8—48no—
499C4⋊Q8—44no—
500#127—28no—
501#127#4118yes—
502#126—416no—
503#125—44no—
504#125—44no—
505#124—216no—
506#124—28no—
507#124—44no—
508#124—416no—
509#123—216no—
510#123—216no—
511#123—416no—
512#123—416no—
513#123—416no—
514#123—416no—
515C22⋊Q8—416no—
516C22⋊Q8—48no—
517C22⋊Q8—48no—
518C22⋊Q8—48no—
519C22⋊Q8—48no—
520C22⋊Q8—48no—
521#121—216no—
522#121—216no—
523#121—216no—
524#121—416no—
525#121—48no—
526#120—216no—
527#120—216no—
528#120—416no—
529#120—416no—
530C4×Q8—24no—
531C4×Q8—28no—
532C4×Q8—44no—
533C4×Q8—48no—
534C4×D4—216no—
535C4×D4—28no—
536C4×D4—216no—
537C4×D4—28no—
538C4×D4—28no—
539C4×D4—48no—
540C4×D4—48no—
541C4×D4—48no—
542C4×D4—44no—
543C4×D4—48no—
544C4×D4—48no—
545C4×D4—48no—
546C4×D4—44no—
547C4×D4—44no—
548C4×D4—44no—
549C4×D4—416no—
550C4×D4—416no—
551#117—48no—
552#117—48no—
553C2×C4⋊C4—216no—
554C2×C4⋊C4—48no—
555C2×C4⋊C4—48no—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2411yescharacteristic
591C2×C22⋊C4—48no—
592C2×C22⋊C4—48no—
593C2×C22⋊C4—48no—
594C2×C22⋊C4—416no—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
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⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C42—48no—
637C2×C42C2412yes—
638C2×C42C2414yes—
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2414yes—
648C2×C42C2418yes—
649C2×C42C2414yes—
650C2×C42C2414yes—
651C2×C42C2418yes—
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2418yes—
669#95C2418yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2412yes—
677#95C2412yes—
678#95C2412yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2414yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686C24—28no—
687C24—216no—
688C24—28no—
689C24—44no—
690C24—48no—
691C24—44no—
692C24—44no—
693C24—48no—
694C24—48no—
695C24—44no—
696C24C2514yes—
697C24C2514yes—
698C24C2514yes—
699C2×Q8—24no—
700C2×Q8—22no—
701C2×Q8—24no—
702C2×Q8—24no—
703C2×Q8—42no—
704C2×Q8—44no—
705C2×Q8—48no—
706C2×D4—216no—
707C2×D4—216no—
708C2×D4—28no—
709C2×D4—216no—
710C2×D4—28no—
711C2×D4—216no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—28no—
715C2×D4—24no—
716C2×D4—28no—
717C2×D4—24no—
718C2×D4—28no—
719C2×D4—24no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—48no—
723C2×D4—42no—
724C2×D4—44no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—44no—
730C2×D4—464no—
731C2×D4—832no—
732C2×D4—832no—
733C2×D4C2×#41116yes—
734C2×D4C2×#4118yes—
735C2×D4H(5,𝔽2)18yes—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—216no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—48no—
753C22×C4—44no—
754C22×C4—48no—
755C22×C4—48no—
756C22×C4—48no—
757C22×C4—48no—
758C22×C4—44no—
759C22×C4—48no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—832no—
763C22×C4C2512yes—
764C22×C4C2512yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2512yes—
770C22×C4C2514yes—
771C22×C4C2511yescharacteristic
772C22×C4C2511yescharacteristic
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2511yescharacteristic
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C22×C4C2512yes—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—24no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—22no—
795C4⋊C4—22no—
796C4⋊C4—24no—
797C4⋊C4—28no—
798C4⋊C4—48no—
799C4⋊C4—48no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—42no—
806C4⋊C4—42no—
807C4⋊C4—42no—
808C4⋊C4—42no—
809C4⋊C4—42no—
810C4⋊C4—42no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—48no—
816C4⋊C4—48no—
817C4⋊C4H(5,𝔽2)14yes—
818C22⋊C4—216no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—216no—
824C22⋊C4—216no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—28no—
831C22⋊C4—28no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—48no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—48no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—48no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C42—28no—
860C42—24no—
861C42—28no—
862C42—24no—
863C42—24no—
864C42—22no—
865C42—22no—
866C42—22no—
867C42—24no—
868C42—24no—
869C42—24no—
870C42—44no—
871C42—44no—
872C42—41no—
873C42—41no—
874C42—41no—
875C42—48no—
876C42—48no—
877C42C2×#4114yes—
878C23—24no—
879C23—24no—
880C23—24no—
881C23—28no—
882C23—24no—
883C23—24no—
884C23—24no—
885C23—28no—
886C23—24no—
887C23—24no—
888C23—24no—
889C23—24no—
890C23—24no—
891C23—24no—
892C23—24no—
893C23—24no—
894C23—24no—
895C23—416no—
896C23—432no—
897C23—88no—
898C23—816no—
899C23—816no—
900C23—88no—
901C23—88no—
902C23—88no—
903C23—88no—
904C23—168no—
905C23C22×#4118yes—
906C23C2×H(5,𝔽2)18yes—
907C23C2611yescharacteristic
908Q8—44no—
909Q8—48no—
910Q8—164no—
911D4—216no—
912D4—232no—
913D4—48no—
914D4—416no—
915D4—432no—
916D4—48no—
917D4—88no—
918D4—816no—
919D4—816no—
920C2×C4—21no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—28no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—416no—
965C2×C4—416no—
966C2×C4—416no—
967C2×C4—88no—
968C2×C4—88no—
969C2×C4—88no—
970C2×C4—88no—
971C2×C4—816no—
972C2×C4—88no—
973C2×C4—88no—
974C2×C4C22×#4112yes—
975C2×C4C22×#4114yes—
976C2×C4C2×H(5,𝔽2)12yes—
977C2×C4C2×H(5,𝔽2)12yes—
978C2×C4C2×H(5,𝔽2)12yes—
979C2×C4C2×H(5,𝔽2)14yes—
980C2×C4#58514yes—
981C22—28no—
982C22—28no—
983C22—28no—
984C22—216no—
985C22—28no—
986C22—44no—
987C22—44no—
988C22—44no—
989C22—44no—
990C22—44no—
991C22—44no—
992C22—48no—
993C22—44no—
994C22—44no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—44no—
1000C22—832no—
1001C22—1616no—
1002C22C23×#4111yescharacteristic
1003C22C22×H(5,𝔽2)11yescharacteristic
1004C22C22×H(5,𝔽2)12yes—
1005C22C2×#58512yes—
1006C222−1+611yescharacteristic
1007C4—22no—
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—44no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4—41no—
1016C4—44no—
1017C4—41no—
1018C4—41no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—42no—
1023C4—44no—
1024C4—42no—
1025C4—42no—
1026C4#351318yes—
1027C2—48no—
1028C2—48no—
1029C2—84no—
1030C2#6275911yescharacteristic
1031C2C2×#351312yes—
1032C2#6292112yes—
1033C2#6298411yescharacteristic
1034C2#6301111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59816C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59420C2semidirect
3. #59420C2semidirect
4. #59398C2semidirect
5. #49771C2semidirect
6. #48235C2semidirect
7. #45694C2semidirect
8. #45006C2semidirect
9. #44874C2semidirect
10. #42601C2semidirect
11. #42535C2semidirect
12. #39377C2semidirect
13. #39116C2semidirect
14. #39042C2semidirect
15. #38975C2semidirect
16. #36559C2semidirect
17. #36464C2semidirect
18. D4×#123C2semidirect
19. #35225C2semidirect
20. #34918C2semidirect
21. #34498C2semidirect
22. #34493C2semidirect
23. C4×D42C2semidirect
25. C2×#554C22semidirect
29. C2×#542C22semidirect
30. C22×#123C22semidirect
31. C22×C4×D4C22semidirect
32. #2868C22semidirect
33. #2859C22semidirect
34. #2859C22semidirect
35. #2854C22semidirect
36. #2849C22semidirect
37. #2848C22semidirect
38. #2827C22semidirect
39. #2770C22semidirect
40. #2761C22semidirect
41. #2749C22semidirect
42. #2743C22semidirect
43. #2741C22semidirect
44. #2737C22semidirect
45. #2735C22semidirect
46. #2718C22semidirect
47. #2707C22semidirect
48. #2697C22semidirect
49. #2697C22semidirect
50. #2697C22semidirect
51. #2696C22semidirect
52. #2685C22semidirect
53. #2684C22semidirect
54. #2681C22semidirect
56. #2674C22semidirect
57. #2644C22semidirect
58. #2638C22semidirect
59. #2630C22semidirect
60. #2628C22semidirect
61. #2627C22semidirect
62. #2626C22semidirect
63. #2597C22semidirect
64. #2597C22semidirect
65. #2595C22semidirect
66. #2592C22semidirect
67. #2580C22semidirect
68. #2578C22semidirect
69. #2570C22semidirect
70. #2566C22semidirect
71. #2566C22semidirect
72. #2563C22semidirect
73. #2561C22semidirect
74. #2561C22semidirect
75. #2559C22semidirect
76. #2558C22semidirect
78. #2538C22semidirect
79. #2538C22semidirect
80. #2538C22semidirect
83. #2534C22semidirect
84. #2534C22semidirect
85. #2518C22semidirect
86. #2516C22semidirect
87. #2513C22semidirect
88. #2511C22semidirect
89. #2507C22semidirect
90. #2501C22semidirect
91. #2497C22semidirect
92. #2496C22semidirect
93. #2495C22semidirect
94. #2491C22semidirect
95. #2486C22semidirect
96. #2485C22semidirect
97. #2480C22semidirect
98. #2472C22semidirect
99. #2468C22semidirect
100. #2461C22semidirect
101. #2458C22semidirect
102. #2452C22semidirect
103. #2452C22semidirect
104. #2447C22semidirect
107. #2443C22semidirect
108. #2443C22semidirect
109. #2440C22semidirect
110. #2435C22semidirect
111. #2435C22semidirect
112. #2435C22semidirect
113. #2427C22semidirect
114. #2427C22semidirect
115. #2426C22semidirect
116. #2423C22semidirect
117. #2422C22semidirect
118. #2422C22semidirect
119. #2420C22semidirect
120. #2420C22semidirect
121. #2418C22semidirect
122. #2418C22semidirect
123. #2417C22semidirect
124. #2415C22semidirect
125. #2412C22semidirect
129. #2405C22semidirect
130. #2398C22semidirect
131. #2395C22semidirect
132. #2376C22semidirect
133. #2375C22semidirect
134. #2367C22semidirect
136. #2363C22semidirect
137. #2363C22semidirect
138. #2361C22semidirect
139. #2358C22semidirect
140. #2354C22semidirect
141. Q8×C4⋊C4C22semidirect
142. D4×C4⋊C4C22semidirect
143. D4×C4⋊C4C22semidirect
144. D4×C4⋊C4C22semidirect
145. #2347C22semidirect
146. #2345C22semidirect
147. D4×C22⋊C4C22semidirect
148. D4×C22⋊C4C22semidirect
149. D4×C22⋊C4C22semidirect
150. D4×C22⋊C4C22semidirect
151. #2326C22semidirect
152. #2324C22semidirect
153. #2322C22semidirect
154. #2321C22semidirect
155. #2319C22semidirect
156. #2319C22semidirect
157. #2309C22semidirect
162. C4×#124C22semidirect
163. C4×#124C22semidirect
164. C4×C22⋊Q8C22semidirect
165. C4×#123C22semidirect
166. C4×#121C22semidirect
167. C4×#120C22semidirect
168. #2295C22semidirect
169. #2293C22semidirect
170. #2290C22semidirect
171. C42×Q8C22semidirect
172. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#598162
#594202
#593982
#497712
#482352
#456942
#450062
#448742
#426012
#425352
#393772
#391162
#390422
#389752
#365592
#364642
D4×#1232
#352252
#349182
#344982
#344932
C4×D422