Finite Group Databasebeta

← #7631023

Subgroups — #7631023

Order 512.

5754 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36640C211yesmaximal, characteristic, complemented
2#36631C211yesmaximal, characteristic, complemented
3#36621C214yesmaximal, complemented
4#36537C214yesmaximal, complemented
5#36477C212yesmaximal, complemented
6#36468C212yesmaximal, complemented
7#36440C214yesmaximal, complemented
8#36331C218yesmaximal, complemented
9#36254C214yesmaximal, complemented
10#36196C212yesmaximal, complemented
11#36174C212yesmaximal, complemented
12#36136C212yesmaximal, complemented
13#36114C212yesmaximal, complemented
14#35236C212yesmaximal, complemented
15#35218C214yesmaximal, complemented
16#35086C212yesmaximal, complemented
17#35081C212yesmaximal, complemented
18#35049C218yesmaximal, complemented
19#34319C214yesmaximal, complemented
20#34243C212yesmaximal, complemented
21C2×C42×D4C211yesmaximal, characteristic, complemented
22C2×#553C2214yes—
23C2×#529C2212yes—
24C2×#529C2214yescomplemented
25C22×C4×D4C2212yes—
26C22×C4×D4C2211yescharacteristic
27C23×C42C2212yes—
28#2864C2214yescomplemented
29#2861C2212yescomplemented
30#2860C2214yescomplemented
31#2859C2211yescharacteristic, complemented
32#2859C2211yescharacteristic, complemented
33#2859C2211yescharacteristic, complemented
34#2859C2212yescomplemented
35#2858C2211yescharacteristic, complemented
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2855C2214yescomplemented
39#2854C2214yes—
40#2854C2214yescomplemented
41#2853C2218yescomplemented
42#2852C2218yes—
43#2852C2218yescomplemented
44#2851C2212yes—
45#2851C2212yes—
46#2851C2214yes—
47#2851C2214yescomplemented
48#2850C2212yes—
49#2850C2214yescomplemented
50#2849C2218yes—
51#2848C2214yes—
52#2847C2214yes—
53#2652C2218yescomplemented
54#2648C2218yescomplemented
55#2636C2218yes—
56#2608C2218yescomplemented
57#2602C2218yes—
58#2602C2218yescomplemented
59#2600C2218yes—
60#2597C2218yescomplemented
61#2596C2218yescomplemented
62#2595C2218yescomplemented
63#2587C2218yescomplemented
64#2575C2218yescomplemented
65#2573C2218yescomplemented
66#2570C2214yescomplemented
67#2566C2214yes—
68#2562C2214yes—
69#2562C2214yescomplemented
70#2559C2218yescomplemented
71#2554C2218yescomplemented
72#2540C2214yes—
73#2538C2212yes—
74#2538C2212yes—
75#2537C2212yes—
76#2537C2212yes—
77#2535C2214yes—
78#2533C2218yescomplemented
79#2526C2218yescomplemented
80#2518C2218yescomplemented
81#2505C2218yes—
82#2497C2214yescomplemented
83#2496C2214yescomplemented
84#2496C2214yescomplemented
85#2495C2214yescomplemented
86#2490C2214yescomplemented
87#2489C2214yescomplemented
88#2487C2214yes—
89#2480C2218yes—
90#2479C2218yescomplemented
91#2470C2218yescomplemented
92#2466C2218yes—
93#2466C2218yescomplemented
94#2456C2218yes—
95#2444C2218yes—
96#2429C2214yescomplemented
97#2428C2214yescomplemented
98#2424C2218yes—
99#2422C2214yes—
100#2421C2214yescomplemented
101#2420C2214yes—
102#2420C2214yescomplemented
103#2411C2218yes—
104#2408C2214yes—
105#2374C2218yescomplemented
106#2373C2218yescomplemented
107#2370C2214yescomplemented
108#2370C2214yescomplemented
109#2367C2214yescomplemented
110#2363C2214yes—
111#2363C2218yescomplemented
112#2361C2214yes—
113#2359C2218yes—
114#2357C2214yes—
115#2357C2218yescomplemented
116#2355C2212yescomplemented
117#2354C2212yescomplemented
118#2352C2214yes—
119#2352C2214yescomplemented
120Q8×C4⋊C4C2212yescomplemented
121D4×C4⋊C4C2214yes—
122D4×C4⋊C4C2212yescomplemented
123#2346C2214yescomplemented
124#2344C2214yescomplemented
125#2334C2218yescomplemented
126#2334C2218yescomplemented
127#2333C2218yescomplemented
128#2324C2214yes—
129#2324C2214yes—
130#2314C2214yescomplemented
131C4×C4⋊Q8C2211yescharacteristic, complemented
132C4×#127C2211yescharacteristic, complemented
133C4×#125C2214yescomplemented
134C4×#125C2212yescomplemented
135C4×#125C2212yescomplemented
136C4×#124C2212yescomplemented
137C4×C22⋊Q8C2214yes—
138C4×C22⋊Q8C2214yescomplemented
139C4×#123C2218yescomplemented
140C4×#121C2214yes—
141C4×#121C2214yes—
142C4×#121C2214yescomplemented
143C4×#120C2218yes—
144#2296C2214yes—
145#2293C2214yescomplemented
146#2290C2218yes—
147#2290C2218yescomplemented
148#2285C2212yes—
149#2283C2214yescomplemented
150#2274C2214yescomplemented
151C42×D4C2212yes—
152C42×D4C2212yes—
153C42×D4C2212yes—
154C42×D4C2212yes—
155C42×D4C2212yes—
156C42×D4C2212yes—
157C42×D4C2214yes—
158C2×C4×C4⋊C4C2212yes—
159C2×C4×C4⋊C4C2211yescharacteristic
160C2×C4×C22⋊C4C2212yes—
161C2×C4×C22⋊C4C2214yes—
162C2×C43C2211yescharacteristic
163C23×D4C2311yescharacteristic
164C24×C4C2312yes—
165C24×C4C2314yes—
166#553—232no—
167C2×C4⋊Q8C2311yescharacteristic
168C2×#127C2311yescharacteristic
169#529—216no—
170#529—416no—
171C2×#126C2314yes—
172C2×#126C2318yes—
173C2×#126C2318yes—
174C2×#125C2314yes—
175C2×#125C2312yes—
176C2×#125C2312yes—
177C2×#125C2312yes—
178C2×#124C2312yes—
179C2×#124C2312yes—
180C2×#123C2318yes—
181C2×#123C2314yes—
182C2×#123C2318yes—
183C2×C22⋊Q8C2312yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2314yes—
186C2×#121C2314yes—
187C2×#121C2314yes—
188C2×#121C2318yes—
189C2×#121C2312yes—
190C2×#121C2314yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#120C2318yes—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2314yes—
196C2×C4×D4—216no—
197C2×C4×D4—28no—
198C2×C4×D4C2314yes—
199C2×C4×D4C2312yes—
200C2×C4×D4C2312yes—
201C2×C4×D4C2312yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2318yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2318yes—
214C2×C4×D4C2312yes—
215C2×#117C2314yes—
216C2×#117C2314yes—
217C2×#117C2318yes—
218C2×#117C2314yes—
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2314yes—
224C22×C42—48no—
225C22×C42C2311yescharacteristic
226C22×C42C2314yes—
227C22×C42C2312yes—
228C22×C42C2311yescharacteristic
229C22×C42C2314yes—
230C22×C42C2314yes—
231C22×C42C2312yes—
232C22×C42C2314yes—
233C22×C42C2312yes—
234C22×C42C2314yes—
235C22×C42C2311yescharacteristic
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#399C2318yes—
242#398C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#396C2318yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#392C2318yes—
259#392C2318yes—
260#391C2312yes—
261#391C2314yes—
262#391C2312yes—
263#390C2312yes—
264#390C2314yes—
265#390C2314yes—
266#390C2314yes—
267#390C2318yes—
268#390C2318yes—
269#390C2314yes—
270#390C2318yes—
271#390C2314yes—
272#390C2314yes—
273#390C2312yes—
274#390C2314yes—
275#389C2314yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#389C2318yes—
285#389C2314yes—
286#389C2318yes—
287#389C2318yes—
288#389C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#388C2318yes—
295#388C2318yes—
296#388C2318yes—
297#388C2318yes—
298#388C2318yes—
299#388C2318yes—
300#388C2314yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2314yes—
309#388C2314yes—
310#388C2318yes—
311#388C2318yes—
312#388C2314yes—
313#388C2314yes—
314#388C2318yes—
315#388C2314yes—
316#388C2314yes—
317#388C2314yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#386C2318yes—
335#386C2318yes—
336#386C2318yes—
337#386C2318yes—
338#386C2318yes—
339#386C2314yes—
340#386C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2314yes—
344#386C2318yes—
345#386C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#384C2311yescharacteristic
359#384C2311yescharacteristic
360#384C2314yes—
361#384C2312yes—
362#384C2312yes—
363#383C2318yes—
364#382C2314yes—
365#382C2312yes—
366#382C2312yes—
367#382C2314yes—
368#382C2318yes—
369#382C2314yes—
370#382C2312yes—
371#381C2318yes—
372#381C2318yes—
373#381C2318yes—
374#380C2314yes—
375#380C2314yes—
376#380C2314yes—
377#380C2314yes—
378#380C2314yes—
379#380C2314yes—
380#380C2314yes—
381#380C2314yes—
382#380C2314yes—
383#380C2314yes—
384#380C2314yes—
385#379C2318yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2318yes—
389C4×C4⋊C4C2318yes—
390C4×C4⋊C4C2312yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2311yescharacteristic
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2318yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2318yes—
397C4×C4⋊C4C2312yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2311yescharacteristic
409C4×C22⋊C4C2314yes—
410C4×C22⋊C4C2318yes—
411C4×C22⋊C4C2314yes—
412C4×C22⋊C4C2314yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2314yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429#376C2318yes—
430C2×#95C2312yes—
431C2×#95C2314yes—
432C43C2311yescharacteristic
433C43C2311yescharacteristic
434C43C2312yes—
435C43C2311yescharacteristic
436C43C2311yescharacteristic
437C43C2312yes—
438C25C2412yes—
439C22×Q8C2412yes—
440C22×D4—28no—
441C22×D4—24no—
442C22×D4C2412yes—
443C22×D4C2414yes—
444C22×D4C2412yes—
445C22×D4C2412yes—
446C22×D4C2418yes—
447C22×D4C2418yes—
448C22×D4C2414yes—
449C23×C4—216no—
450C23×C4—28no—
451C23×C4—44no—
452C23×C4—48no—
453C23×C4—44no—
454C23×C4—48no—
455C23×C4C2414yes—
456C23×C4C2414yes—
457C23×C4C2412yes—
458C23×C4C2412yes—
459C23×C4C2414yes—
460C23×C4C2414yes—
461C23×C4C2414yes—
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2411yescharacteristic
465C23×C4C2412yes—
466C23×C4C2418yes—
467C23×C4C2414yes—
468C23×C4C2414yes—
469C23×C4C2414yes—
470C4⋊Q8—42no—
471#127—42no—
472#126—232no—
473#126—216no—
474#126—416no—
475#125—28no—
476#125—216no—
477#125—28no—
478#125—44no—
479#124—28no—
480#124—28no—
481#123—216no—
482#123—232no—
483#123—416no—
484C22⋊Q8—28no—
485C22⋊Q8—48no—
486C22⋊Q8—48no—
487#121—216no—
488#121—216no—
489#121—28no—
490#121—232no—
491#121—48no—
492#121—48no—
493#121—48no—
494#120—416no—
495C4×Q8—28no—
496C4×Q8—48no—
497C4×D4—28no—
498C4×D4—216no—
499C4×D4—216no—
500C4×D4—232no—
501C4×D4—28no—
502C4×D4—216no—
503C4×D4—28no—
504C4×D4—28no—
505C4×D4—28no—
506C4×D4—28no—
507C4×D4—28no—
508C4×D4—28no—
509C4×D4—216no—
510C4×D4—48no—
511C4×D4—416no—
512C4×D4—416no—
513C4×D4#41116yes—
514#117—216no—
515#117—216no—
516#117—416no—
517#117—48no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—28no—
520C2×C4⋊C4—216no—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2412yes—
550C2×C22⋊C4—28no—
551C2×C22⋊C4—216no—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2414yes—
581C2×C42—28no—
582C2×C42—216no—
583C2×C42—24no—
584C2×C42—48no—
585C2×C42—48no—
586C2×C42—48no—
587C2×C42—48no—
588C2×C42—44no—
589C2×C42—42no—
590C2×C42—44no—
591C2×C42#4118yes—
592C2×C42C2414yes—
593C2×C42C2414yes—
594C2×C42C2418yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2412yes—
598C2×C42C2414yes—
599C2×C42C2411yescharacteristic
600C2×C42C2414yes—
601C2×C42C2411yescharacteristic
602C2×C42C2412yes—
603C2×C42C2411yescharacteristic
604C2×C42C2418yes—
605C2×C42C2418yes—
606C2×C42C2418yes—
607C2×C42C2412yes—
608C2×C42C2412yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2414yes—
614C2×C42C2414yes—
615C2×C42C2412yes—
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2412yes—
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622#95C2412yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2412yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2414yes—
634#95C2418yes—
635#95C2414yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2414yes—
641#95C2418yes—
642#95C2414yes—
643#95C2418yes—
644#95C2414yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651C24—28no—
652C24—24no—
653C24—28no—
654C24—42no—
655C24—42no—
656C24C2514yes—
657C24C2514yes—
658C24C2511yescharacteristic
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—24no—
662C2×D4—232no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—216no—
668C2×D4—216no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—44no—
680C2×D4—48no—
681C2×D4—44no—
682C2×D4C2×#4118yes—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—24no—
691C22×C4—28no—
692C22×C4—24no—
693C22×C4—28no—
694C22×C4—24no—
695C22×C4—28no—
696C22×C4—28no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—216no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—42no—
720C22×C4—48no—
721C22×C4—48no—
722C22×C4—464no—
723C22×C4—432no—
724C22×C4C2×#4114yes—
725C22×C4C2×#4114yes—
726C22×C4C2×#4114yes—
727C22×C4C2×#41116yes—
728C22×C4C2512yes—
729C22×C4C2514yes—
730C22×C4C2514yes—
731C22×C4C2518yes—
732C22×C4C2514yes—
733C22×C4C2514yes—
734C22×C4C2518yes—
735C22×C4C2514yes—
736C22×C4C2514yes—
737C22×C4C2512yes—
738C22×C4C2511yescharacteristic
739C22×C4C2511yescharacteristic
740C22×C4C2512yes—
741C22×C4C2511yescharacteristic
742C22×C4C2511yescharacteristic
743C22×C4C2512yes—
744C22×C4C2511yescharacteristic
745C22×C4C2511yescharacteristic
746C4⋊C4—28no—
747C4⋊C4—24no—
748C4⋊C4—24no—
749C4⋊C4—24no—
750C4⋊C4—28no—
751C4⋊C4—216no—
752C4⋊C4—28no—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—24no—
756C4⋊C4—216no—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—24no—
760C4⋊C4—28no—
761C4⋊C4—216no—
762C4⋊C4—216no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—48no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—44no—
771C4⋊C4—48no—
772C4⋊C4—48no—
773C4⋊C4—44no—
774C4⋊C4C2×#4118yes—
775C22⋊C4—28no—
776C22⋊C4—216no—
777C22⋊C4—28no—
778C22⋊C4—216no—
779C22⋊C4—216no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—216no—
785C22⋊C4—28no—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4C2×#41116yes—
804C42—24no—
805C42—24no—
806C42—24no—
807C42—28no—
808C42—216no—
809C42—24no—
810C42—22no—
811C42—28no—
812C42—28no—
813C42—28no—
814C42—22no—
815C42—22no—
816C42—42no—
817C42—44no—
818C42—42no—
819C42—44no—
820C42—42no—
821C42—42no—
822C42—42no—
823C42—42no—
824C42—42no—
825C42—48no—
826C42—48no—
827C42—48no—
828C42C2×#4118yes—
829C42C2×#4114yes—
830C42C2×#4114yes—
831C42C2×#4114yes—
832C42C2×#4114yes—
833C42H(5,𝔽2)14yes—
834C23—22no—
835C23—21no—
836C23—21no—
837C23—216no—
838C23—24no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—416no—
852C23—416no—
853C23—48no—
854C23—48no—
855C23C22×#4118yes—
856C23C22×#4112yes—
857C23#58514yes—
858C23C2611yescharacteristic
859Q8—48no—
860D4—216no—
861D4—216no—
862D4—416no—
863D4—48no—
864D4—88no—
865D4—816no—
866D4—816no—
867C2×C4—216no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—24no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—24no—
881C2×C4—28no—
882C2×C4—28no—
883C2×C4—28no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—28no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—28no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—28no—
898C2×C4—22no—
899C2×C4—28no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—28no—
903C2×C4—24no—
904C2×C4—28no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—416no—
909C2×C4—416no—
910C2×C4—48no—
911C2×C4—416no—
912C2×C4—416no—
913C2×C4—416no—
914C2×C4—416no—
915C2×C4—48no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—816no—
919C2×C4C22×#4118yes—
920C2×C4C22×#4114yes—
921C2×C4C22×#4114yes—
922C2×C4C22×#4112yes—
923C2×C4C22×#4112yes—
924C2×C4C22×#4112yes—
925C2×C4C22×#4112yes—
926C2×C4C22×#4112yes—
927C2×C4C22×#4114yes—
928C2×C4C22×#4112yes—
929C2×C4C2×H(5,𝔽2)14yes—
930C2×C4C2×H(5,𝔽2)12yes—
931C2×C4#58512yes—
932C22—22no—
933C22—24no—
934C22—24no—
935C22—22no—
936C22—28no—
937C22—28no—
938C22—28no—
939C22—432no—
940C22—44no—
941C22—44no—
942C22—44no—
943C22—44no—
944C22—44no—
945C22—44no—
946C22—44no—
947C22—44no—
948C22—44no—
949C22—44no—
950C22—44no—
951C22#351214yes—
952C22C23×#4111yescharacteristic
953C22C23×#4112yes—
954C22C22×H(5,𝔽2)11yescharacteristic
955C22C2×#58511yescharacteristic
956C22C2×#58512yes—
957C4—22no—
958C4—24no—
959C4—24no—
960C4—28no—
961C4—22no—
962C4—22no—
963C4—24no—
964C4—22no—
965C4—44no—
966C4—44no—
967C4—44no—
968C4—48no—
969C4—44no—
970C4—42no—
971C4—48no—
972C4—44no—
973C4#344414yes—
974C4#350614yes—
975C2—24no—
976C2—48no—
977C2—84no—
978C2C2×#344411yescharacteristic
979C2C2×#350611yescharacteristic
980C2#6277312yes—
981C2C2×#351211yescharacteristic
982C2#6281612yes—
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. #36640C2semidirect
2. #36631C2semidirect
3. #36621C2semidirect
4. #36537C2semidirect
5. #36477C2semidirect
6. #36468C2semidirect
7. #36440C2semidirect
8. #36331C2semidirect
9. #36254C2semidirect
10. #36196C2semidirect
11. #36174C2semidirect
12. #36136C2semidirect
13. #36114C2semidirect
14. #35236C2semidirect
15. #35218C2semidirect
16. #35086C2semidirect
17. #35081C2semidirect
18. #35049C2semidirect
19. #34319C2semidirect
20. #34243C2semidirect
21. C2×C42×D4C2semidirect
24. C2×#529C22semidirect
28. #2864C22semidirect
29. #2861C22semidirect
30. #2860C22semidirect
31. #2859C22semidirect
32. #2859C22semidirect
33. #2859C22semidirect
34. #2859C22semidirect
35. #2858C22semidirect
38. #2855C22semidirect
40. #2854C22semidirect
41. #2853C22semidirect
43. #2852C22semidirect
47. #2851C22semidirect
49. #2850C22semidirect
53. #2652C22semidirect
54. #2648C22semidirect
56. #2608C22semidirect
58. #2602C22semidirect
60. #2597C22semidirect
61. #2596C22semidirect
62. #2595C22semidirect
63. #2587C22semidirect
64. #2575C22semidirect
65. #2573C22semidirect
66. #2570C22semidirect
69. #2562C22semidirect
70. #2559C22semidirect
71. #2554C22semidirect
78. #2533C22semidirect
79. #2526C22semidirect
80. #2518C22semidirect
82. #2497C22semidirect
83. #2496C22semidirect
84. #2496C22semidirect
85. #2495C22semidirect
86. #2490C22semidirect
87. #2489C22semidirect
90. #2479C22semidirect
91. #2470C22semidirect
93. #2466C22semidirect
96. #2429C22semidirect
97. #2428C22semidirect
100. #2421C22semidirect
102. #2420C22semidirect
105. #2374C22semidirect
106. #2373C22semidirect
107. #2370C22semidirect
108. #2370C22semidirect
109. #2367C22semidirect
111. #2363C22semidirect
115. #2357C22semidirect
116. #2355C22semidirect
117. #2354C22semidirect
119. #2352C22semidirect
120. Q8×C4⋊C4C22semidirect
122. D4×C4⋊C4C22semidirect
123. #2346C22semidirect
124. #2344C22semidirect
125. #2334C22semidirect
126. #2334C22semidirect
127. #2333C22semidirect
130. #2314C22semidirect
131. C4×C4⋊Q8C22semidirect
132. C4×#127C22semidirect
133. C4×#125C22semidirect
134. C4×#125C22semidirect
135. C4×#125C22semidirect
136. C4×#124C22semidirect
138. C4×C22⋊Q8C22semidirect
139. C4×#123C22semidirect
142. C4×#121C22semidirect
145. #2293C22semidirect
147. #2290C22semidirect
149. #2283C22semidirect
150. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#366402
#366312
#366212
#365372
#364772
#364682
#364402
#363312
#362542
#361962
#361742
#361362
#361142
#352362
#352182
#350862
#350812
#350492
#343192
#342432
C2×C42×D42