Finite Group Databasebeta

← #7688617

Subgroups — #7688617

Order 512.

5937 conjugacy classes of subgroups.

The subgroup lattice has 991 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59643C214yesmaximal, complemented
2#59420C211yesmaximal, characteristic, complemented
3#59410C212yesmaximal, complemented
4#59099C214yesmaximal, complemented
5#59094C214yesmaximal, complemented
6#44378C214yesmaximal, complemented
7#43584C218yesmaximal, complemented
8#40103C214yesmaximal, complemented
9#39953C214yesmaximal, complemented
10#39785C214yesmaximal, complemented
11#36609C211yesmaximal, characteristic, complemented
12#36597C212yesmaximal, complemented
13#36406C212yesmaximal, complemented
14#36260C212yesmaximal, complemented
15#36150C214yesmaximal, complemented
16#35932C214yesmaximal, complemented
17#34929C212yesmaximal, complemented
18#34925C211yesmaximal, characteristic, complemented
19#34320C214yesmaximal, complemented
20C4×#559C212yesmaximal, complemented
21C2×#559C2212yes—
22C2×#559C2211yescharacteristic
23C2×#556C2212yescomplemented
24C2×#547C2212yes—
25C2×#546C2214yes—
26C2×#546C2214yes—
27C2×D42C2211yescharacteristic
28C2×#533C2214yescomplemented
29C2×#532C2214yescomplemented
30#2862C2211yescharacteristic, complemented
31#2858C2212yes—
32#2858C2214yescomplemented
33#2857C2214yescomplemented
34#2856C2214yes—
35#2773C2218yescomplemented
36#2752C2214yescomplemented
37#2740C2218yescomplemented
38#2711C2218yescomplemented
39#2710C2218yescomplemented
40#2707C2218yescomplemented
41#2706C2218yescomplemented
42#2705C2218yescomplemented
43#2697C2214yes—
44#2688C2218yescomplemented
45#2678C2218yescomplemented
46#2670C2214yescomplemented
47#2667C2214yescomplemented
48#2661C2218yescomplemented
49#2607C2214yescomplemented
50#2592C2214yescomplemented
51#2580C2212yescomplemented
52#2557C2218yescomplemented
53#2556C2218yescomplemented
54#2555C2214yescomplemented
55#2554C2218yescomplemented
56#2554C2218yescomplemented
57#2554C2218yescomplemented
58#2553C2218yescomplemented
59#2553C2218yescomplemented
60#2551C2211yescharacteristic, complemented
61#2546C2212yescomplemented
62#2545C2214yescomplemented
63#2544C2214yescomplemented
64#2542C2212yes—
65#2541C2212yes—
66#2540C2214yes—
67#2540C2214yes—
68#2540C2214yescomplemented
69#2539C2218yes—
70#2539C2218yes—
71#2538C2212yes—
72#2537C2211yescharacteristic, complemented
73#2534C2214yes—
74#2516C2218yescomplemented
75#2513C2214yescomplemented
76#2506C2214yescomplemented
77#2501C2214yes—
78#2499C2214yescomplemented
79#2492C2214yescomplemented
80#2491C2214yescomplemented
81#2490C2218yescomplemented
82#2472C2218yescomplemented
83#2458C2218yescomplemented
84#2457C2218yescomplemented
85#2454C2218yescomplemented
86#2452C2214yes—
87#2448C2214yescomplemented
88#2448C2218yescomplemented
89#2447C2214yescomplemented
90#2437C2214yescomplemented
91#2435C2214yes—
92#2433C2214yes—
93#2432C2214yes—
94#2431C2214yes—
95#2429C2214yescomplemented
96#2428C2214yescomplemented
97#2427C2214yes—
98#2427C2214yescomplemented
99#2427C2214yescomplemented
100#2426C2214yescomplemented
101#2426C2214yescomplemented
102#2426C2218yescomplemented
103#2426C2214yescomplemented
104#2423C2214yescomplemented
105#2420C2214yes—
106#2417C2214yescomplemented
107#2414C2218yescomplemented
108#2414C2214yescomplemented
109#2411C2218yescomplemented
110#2407C2218yescomplemented
111#2404C2214yescomplemented
112#2396C2218yescomplemented
113#2388C2214yescomplemented
114#2374C2218yescomplemented
115#2374C2214yescomplemented
116#2374C2214yescomplemented
117#2367C2212yes—
118#2367C2214yescomplemented
119#2367C2212yescomplemented
120#2367C2214yescomplemented
121#2366C2212yes—
122#2363C2218yescomplemented
123#2363C2214yescomplemented
124#2363C2214yescomplemented
125#2360C2214yescomplemented
126#2360C2214yescomplemented
127#2358C2218yescomplemented
128#2357C2212yes—
129#2357C2212yescomplemented
130#2357C2214yescomplemented
131#2357C2212yescomplemented
132#2355C2212yescomplemented
133#2355C2212yescomplemented
134#2352C2214yescomplemented
135#2342C2218yescomplemented
136#2341C2214yes—
137#2341C2214yescomplemented
138D4×C22⋊C4C2214yes—
139#2335C2218yescomplemented
140#2333C2218yescomplemented
141#2321C2218yescomplemented
142C4×C4⋊Q8C2212yescomplemented
143C4×C4⋊Q8C2214yescomplemented
144C4×#127C2211yescharacteristic
145C4×#127C2212yes—
146C4×#124C2212yes—
147C4×#124C2214yescomplemented
148C4×#124C2214yescomplemented
149C4×#124C2212yescomplemented
150C4×C22⋊Q8C2214yescomplemented
151C4×#123C2214yescomplemented
152C4×#123C2214yescomplemented
153C4×#121C2214yescomplemented
154#2297C2214yes—
155#2293C2214yes—
156C2×#390C2214yes—
157#2273C2214yescomplemented
158C42×Q8C2211yescharacteristic, complemented
159C42×Q8C2212yescomplemented
160C42×D4C2212yes—
161C42×D4C2214yescomplemented
162C42×D4C2212yescomplemented
163C22×#41C2314yes—
164C22×#41C2314yes—
165C23×D4C2314yes—
166#559—216no—
167#559—44no—
168#556—48no—
169#547—48no—
170#546—232no—
171#546—416no—
172D42—44no—
173#533—416no—
174#532—416no—
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2314yes—
178C2×#127C2311yescharacteristic
179C2×#127C2312yes—
180C2×#127C2314yes—
181C2×#126C2318yes—
182C2×#125C2318yes—
183C2×#124C2314yes—
184C2×#124C2312yes—
185C2×#124C2312yes—
186C2×#124C2314yes—
187C2×#124C2314yes—
188C2×#124C2314yes—
189C2×#124C2314yes—
190C2×#124C2318yes—
191C2×#123C2318yes—
192C2×#123C2314yes—
193C2×#123C2314yes—
194C2×#123C2318yes—
195C2×#123C2318yes—
196C2×#123C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2318yes—
202C2×C22⋊Q8C2314yes—
203C2×#121C2318yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2318yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2318yes—
210C2×#121C2314yes—
211C2×#120C2318yes—
212C2×#120C2318yes—
213C2×#120C2314yes—
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2318yes—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2314yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2312yes—
236C2×#117C2318yes—
237C2×#117C2314yes—
238C22×C4⋊C4C2314yes—
239C22×C22⋊C4C2318yes—
240C22×C22⋊C4C2314yes—
241C22×C22⋊C4C2318yes—
242C22×C42C2314yes—
243C22×C42C2314yes—
244#400C2318yes—
245#399C2314yes—
246#399C2318yes—
247#399C2318yes—
248#399C2318yes—
249#399C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#395C2314yes—
264#394C2318yes—
265#394C2314yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#393C2314yes—
274#393C2314yes—
275#393C2318yes—
276#392C2314yes—
277#392C2318yes—
278#392C2318yes—
279#392C2318yes—
280#392C2318yes—
281#392C2318yes—
282#391C2314yes—
283#391C2318yes—
284#391C2314yes—
285#391C2312yes—
286#391C2314yes—
287#391C2314yes—
288#391C2312yes—
289#391C2314yes—
290#390C2314yes—
291#390C2312yes—
292#390C2312yes—
293#390C2314yes—
294#390C2314yes—
295#390C2312yes—
296#390C2318yes—
297#390C2318yes—
298#390C2314yes—
299#390C2318yes—
300#390C2318yes—
301#390C2314yes—
302#390C2312yes—
303#390C2314yes—
304#390C2318yes—
305#390C2318yes—
306#390C2318yes—
307#390C2314yes—
308#390C2318yes—
309#390C2314yes—
310#390C2318yes—
311#390C2318yes—
312#390C2312yes—
313#390C2314yes—
314#390C2318yes—
315#390C2314yes—
316#390C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2318yes—
321#389C2314yes—
322#389C2318yes—
323#389C2318yes—
324#389C2314yes—
325#389C2314yes—
326#388C2314yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2314yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2314yes—
338#388C2314yes—
339#388C2314yes—
340#388C2314yes—
341#388C2314yes—
342#388C2314yes—
343#388C2318yes—
344#388C2318yes—
345#388C2314yes—
346#388C2314yes—
347#388C2314yes—
348#388C2314yes—
349#388C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2314yes—
355#387C2314yes—
356#387C2314yes—
357#387C2314yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2314yes—
367#386C2314yes—
368#386C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2314yes—
374#385C2314yes—
375#384C2311yescharacteristic
376#384C2312yes—
377#384C2314yes—
378#382C2312yes—
379#382C2312yes—
380#382C2312yes—
381#382C2312yes—
382#382C2314yes—
383#381C2314yes—
384#381C2314yes—
385#381C2314yes—
386#381C2314yes—
387#380C2318yes—
388#380C2314yes—
389#380C2314yes—
390#380C2318yes—
391#380C2314yes—
392#380C2318yes—
393#379C2318yes—
394#379C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2312yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C43C2312yes—
438C43C2311yescharacteristic
439C43C2314yes—
440C25C2414yes—
441C2×#41—216no—
442C2×#41—48no—
443C2×#41—416no—
444C2×#41—48no—
445C2×#41—48no—
446C22×Q8C2412yes—
447C22×Q8C2414yes—
448C22×Q8C2411yescharacteristic
449C22×Q8C2414yes—
450C22×D4—216no—
451C22×D4—48no—
452C22×D4—48no—
453C22×D4C2412yes—
454C22×D4C2414yes—
455C22×D4C2414yes—
456C22×D4C2412yes—
457C22×D4C2414yes—
458C22×D4C2412yes—
459C22×D4C2418yes—
460C22×D4C2418yes—
461C22×D4C2418yes—
462C22×D4C2418yes—
463C22×D4C2414yes—
464C23×C4C2414yes—
465C23×C4C2414yes—
466C23×C4C2414yes—
467C23×C4C2418yes—
468C23×C4C2414yes—
469C23×C4C2414yes—
470C23×C4C2414yes—
471C23×C4C2414yes—
472C23×C4C2414yes—
473C4⋊Q8—216no—
474C4⋊Q8—28no—
475C4⋊Q8—48no—
476#127—28no—
477#127—24no—
478#127—48no—
479#126—416no—
480#125—416no—
481#124—28no—
482#124—216no—
483#124—216no—
484#124—28no—
485#124—48no—
486#124—48no—
487#124—48no—
488#124—416no—
489#123—216no—
490#123—232no—
491#123—216no—
492#123—416no—
493#123—416no—
494#123—48no—
495C22⋊Q8—216no—
496C22⋊Q8—216no—
497C22⋊Q8—416no—
498C22⋊Q8—48no—
499C22⋊Q8—48no—
500C22⋊Q8—48no—
501#121—232no—
502#121—216no—
503#121—216no—
504#121—416no—
505#121—48no—
506#121—48no—
507#121—416no—
508#121—48no—
509#120—232no—
510#120—48no—
511#120—416no—
512C4×Q8—28no—
513C4×Q8—28no—
514C4×Q8—28no—
515C4×Q8—28no—
516C4×Q8—42no—
517C4×Q8—48no—
518C4×Q8—416no—
519C4×Q8—48no—
520C4×D4—216no—
521C4×D4—28no—
522C4×D4—28no—
523C4×D4—28no—
524C4×D4—216no—
525C4×D4—28no—
526C4×D4—28no—
527C4×D4—48no—
528C4×D4—48no—
529C4×D4—44no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—416no—
533C4×D4#41116yescomplemented
534#117—416no—
535#117—48no—
536C2×C4⋊C4—48no—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C22⋊C4—232no—
566C2×C22⋊C4—48no—
567C2×C22⋊C4—416no—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C42—48no—
606C2×C42—48no—
607C2×C42C2414yes—
608C2×C42C2412yes—
609C2×C42C2412yes—
610C2×C42C2411yescharacteristic
611C2×C42C2414yes—
612C2×C42C2412yes—
613C2×C42C2414yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2414yes—
617C2×C42C2418yes—
618C2×C42C2418yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2412yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2414yes—
626C2×C42C2411yescharacteristic
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2411yescharacteristic
630#95C2411yescharacteristic
631#95C2414yes—
632#95C2412yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2418yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2418yes—
649#95C2414yes—
650#95C2414yes—
651#95C2411yescharacteristic
652#95C2414yes—
653#95C2412yes—
654#95C2414yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2414yes—
659C24—216no—
660C24—44no—
661C24—48no—
662C24—44no—
663C24—44no—
664C24C2514yes—
665C24C2514yes—
666C24C2514yes—
667#41—832no—
668#41—832no—
669C2×Q8—24no—
670C2×Q8—24no—
671C2×Q8—28no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×Q8—28no—
675C2×Q8—216no—
676C2×Q8—28no—
677C2×Q8—41no—
678C2×Q8—44no—
679C2×D4—28no—
680C2×D4—216no—
681C2×D4—216no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—24no—
685C2×D4—28no—
686C2×D4—216no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—24no—
694C2×D4—216no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—42no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—44no—
710C2×D4—832no—
711C2×D4C2×#4118yes—
712C22×C4—216no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—28no—
716C22×C4—28no—
717C22×C4—28no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—28no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4C2×#41116yes—
738C22×C4C2512yes—
739C22×C4C2514yes—
740C22×C4C2511yescharacteristic
741C22×C4C2512yes—
742C22×C4C2514yes—
743C22×C4C2518yes—
744C22×C4C2514yes—
745C22×C4C2514yes—
746C22×C4C2512yes—
747C22×C4C2514yes—
748C22×C4C2512yes—
749C22×C4C2514yes—
750C22×C4C2512yes—
751C22×C4C2514yes—
752C22×C4C2511yescharacteristic
753C22×C4C2511yescharacteristic
754C22×C4C2512yes—
755C4⋊C4—24no—
756C4⋊C4—28no—
757C4⋊C4—28no—
758C4⋊C4—24no—
759C4⋊C4—24no—
760C4⋊C4—216no—
761C4⋊C4—24no—
762C4⋊C4—28no—
763C4⋊C4—24no—
764C4⋊C4—216no—
765C4⋊C4—24no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—28no—
769C4⋊C4—216no—
770C4⋊C4—28no—
771C4⋊C4—24no—
772C4⋊C4—48no—
773C4⋊C4—48no—
774C4⋊C4—42no—
775C4⋊C4—44no—
776C4⋊C4—41no—
777C4⋊C4—48no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4C2×#4118yes—
782C4⋊C4H(5,𝔽2)18yes—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—28no—
786C22⋊C4—216no—
787C22⋊C4—216no—
788C22⋊C4—216no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—216no—
793C22⋊C4—28no—
794C22⋊C4—216no—
795C22⋊C4—216no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—48no—
807C22⋊C4—48no—
808C22⋊C4—44no—
809C22⋊C4—44no—
810C22⋊C4—44no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—44no—
815C22⋊C4—48no—
816C22⋊C4—48no—
817C22⋊C4—48no—
818C22⋊C4—44no—
819C22⋊C4C2×#41116yes—
820C42—28no—
821C42—24no—
822C42—24no—
823C42—24no—
824C42—24no—
825C42—28no—
826C42—28no—
827C42—24no—
828C42—28no—
829C42—22no—
830C42—44no—
831C42—44no—
832C42—44no—
833C42—44no—
834C42—42no—
835C42—44no—
836C42—41no—
837C42—48no—
838C42—48no—
839C42—44no—
840C42—42no—
841C42C2×#4118yes—
842C42H(5,𝔽2)14yes—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—28no—
851C23—24no—
852C23—24no—
853C23—28no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—416no—
862C23—816no—
863C23—816no—
864C23—164no—
865C23—164no—
866C23C22×#4118yes—
867C23C2611yescharacteristic
868Q8—44no—
869Q8—416no—
870Q8—48no—
871Q8—416no—
872D4—216no—
873D4—416no—
874D4—48no—
875D4—416no—
876D4—816no—
877D4—84no—
878D4—816no—
879D4—88no—
880D4—816no—
881D4—816no—
882D4—88no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—22no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—24no—
899C2×C4—28no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—28no—
912C2×C4—28no—
913C2×C4—28no—
914C2×C4—24no—
915C2×C4—21no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—24no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—416no—
923C2×C4—416no—
924C2×C4—416no—
925C2×C4—416no—
926C2×C4—88no—
927C2×C4—88no—
928C2×C4—88no—
929C2×C4—816no—
930C2×C4—164no—
931C2×C4C22×#4118yes—
932C2×C4C22×#4114yes—
933C2×C4C22×#4114yes—
934C2×C4C22×#4114yes—
935C2×C4C2×H(5,𝔽2)18yes—
936C2×C4C2×H(5,𝔽2)12yes—
937C2×C4C2×H(5,𝔽2)14yes—
938C2×C4C2×H(5,𝔽2)14yes—
939C2×C4#58512yes—
940C22—28no—
941C22—28no—
942C22—28no—
943C22—44no—
944C22—44no—
945C22—44no—
946C22—44no—
947C22—44no—
948C22—44no—
949C22—48no—
950C22—44no—
951C22—44no—
952C22—44no—
953C22—48no—
954C22—44no—
955C22—44no—
956C22—44no—
957C22—44no—
958C22—44no—
959C22—1616no—
960C22C23×#4112yes—
961C22C22×H(5,𝔽2)12yes—
962C22C22×H(5,𝔽2)11yescharacteristic
963C22C2×#58511yescharacteristic
964C222−1+611yescharacteristic
965C4—24no—
966C4—28no—
967C4—22no—
968C4—28no—
969C4—22no—
970C4—24no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—44no—
975C4—44no—
976C4—44no—
977C4—48no—
978C4—44no—
979C4—44no—
980C4—41no—
981C4#350818yes—
982C2—48no—
983C2—84no—
984C2—84no—
985C2#41211yescharacteristic
986C2C2×#350812yes—
987C2#6293111yescharacteristic
988C2#6298412yes—
989C2#6301211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59643C2semidirect
2. #59420C2semidirect
3. #59410C2semidirect
4. #59099C2semidirect
5. #59094C2semidirect
6. #44378C2semidirect
7. #43584C2semidirect
8. #40103C2semidirect
9. #39953C2semidirect
10. #39785C2semidirect
11. #36609C2semidirect
12. #36597C2semidirect
13. #36406C2semidirect
14. #36260C2semidirect
15. #36150C2semidirect
16. #35932C2semidirect
17. #34929C2semidirect
18. #34925C2semidirect
19. #34320C2semidirect
20. C4×#559C2semidirect
23. C2×#556C22semidirect
28. C2×#533C22semidirect
29. C2×#532C22semidirect
30. #2862C22semidirect
32. #2858C22semidirect
33. #2857C22semidirect
35. #2773C22semidirect
36. #2752C22semidirect
37. #2740C22semidirect
38. #2711C22semidirect
39. #2710C22semidirect
40. #2707C22semidirect
41. #2706C22semidirect
42. #2705C22semidirect
44. #2688C22semidirect
45. #2678C22semidirect
46. #2670C22semidirect
47. #2667C22semidirect
48. #2661C22semidirect
49. #2607C22semidirect
50. #2592C22semidirect
51. #2580C22semidirect
52. #2557C22semidirect
53. #2556C22semidirect
54. #2555C22semidirect
55. #2554C22semidirect
56. #2554C22semidirect
57. #2554C22semidirect
58. #2553C22semidirect
59. #2553C22semidirect
60. #2551C22semidirect
61. #2546C22semidirect
62. #2545C22semidirect
63. #2544C22semidirect
68. #2540C22semidirect
72. #2537C22semidirect
74. #2516C22semidirect
75. #2513C22semidirect
76. #2506C22semidirect
78. #2499C22semidirect
79. #2492C22semidirect
80. #2491C22semidirect
81. #2490C22semidirect
82. #2472C22semidirect
83. #2458C22semidirect
84. #2457C22semidirect
85. #2454C22semidirect
87. #2448C22semidirect
88. #2448C22semidirect
89. #2447C22semidirect
90. #2437C22semidirect
95. #2429C22semidirect
96. #2428C22semidirect
98. #2427C22semidirect
99. #2427C22semidirect
100. #2426C22semidirect
101. #2426C22semidirect
102. #2426C22semidirect
103. #2426C22semidirect
104. #2423C22semidirect
106. #2417C22semidirect
107. #2414C22semidirect
108. #2414C22semidirect
109. #2411C22semidirect
110. #2407C22semidirect
111. #2404C22semidirect
112. #2396C22semidirect
113. #2388C22semidirect
114. #2374C22semidirect
115. #2374C22semidirect
116. #2374C22semidirect
118. #2367C22semidirect
119. #2367C22semidirect
120. #2367C22semidirect
122. #2363C22semidirect
123. #2363C22semidirect
124. #2363C22semidirect
125. #2360C22semidirect
126. #2360C22semidirect
127. #2358C22semidirect
129. #2357C22semidirect
130. #2357C22semidirect
131. #2357C22semidirect
132. #2355C22semidirect
133. #2355C22semidirect
134. #2352C22semidirect
135. #2342C22semidirect
137. #2341C22semidirect
139. #2335C22semidirect
140. #2333C22semidirect
141. #2321C22semidirect
142. C4×C4⋊Q8C22semidirect
143. C4×C4⋊Q8C22semidirect
147. C4×#124C22semidirect
148. C4×#124C22semidirect
149. C4×#124C22semidirect
150. C4×C22⋊Q8C22semidirect
151. C4×#123C22semidirect
152. C4×#123C22semidirect
153. C4×#121C22semidirect
157. #2273C22semidirect
158. C42×Q8C22semidirect
159. C42×Q8C22semidirect
161. C42×D4C22semidirect
162. C42×D4C22semidirect
533. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#596432
#594202
#594102
#590992
#590942
#443782
#435842
#401032
#399532
#397852
#366092
#365972
#364062
#362602
#361502
#359322
#349292
#349252
#343202
C4×#5592