Finite Group Databasebeta

← #7655929

Subgroups — #7655929

Order 512.

5142 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42661C214yesmaximal, complemented
2#42460C214yesmaximal, complemented
3#41686C218yesmaximal, complemented
4#41012C218yesmaximal, complemented
5#39632C212yesmaximal, complemented
6#39423C214yesmaximal, complemented
7#39375C212yesmaximal, complemented
8#37941C214yesmaximal, complemented
9#37546C212yesmaximal, complemented
10#37461C214yesmaximal, complemented
11#36579C212yesmaximal, complemented
12#36160C212yesmaximal, complemented
13#36028C214yesmaximal, complemented
14#35745C214yesmaximal, complemented
15#35167C211yesmaximal, characteristic, complemented
16#35003C212yesmaximal, complemented
17#34594C211yesmaximal, characteristic, complemented
18#34578C212yesmaximal, complemented
19#34243C212yesmaximal, complemented
20C2×#2367C211yesmaximal, characteristic, complemented
21C2×#556C2212yescomplemented
22C2×#555C2212yes—
23C2×#544C2212yes—
24C2×#538C2214yes—
25C2×#529C2212yes—
26C22×#124C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29#2857C2212yes—
30#2857C2212yes—
31#2850C2214yes—
32#2847C2214yes—
33#2837C2218yescomplemented
34#2832C2218yescomplemented
35#2820C2214yes—
36#2819C2214yes—
37#2806C2214yescomplemented
38#2804C2214yescomplemented
39#2788C2218yescomplemented
40#2780C2218yescomplemented
41#2779C2218yescomplemented
42#2739C2218yescomplemented
43#2731C2218yescomplemented
44#2727C2214yes—
45#2716C2218yescomplemented
46#2711C2218yescomplemented
47#2710C2218yes—
48#2707C2218yescomplemented
49#2701C2218yescomplemented
50#2682C2214yes—
51#2667C2218yescomplemented
52#2665C2218yescomplemented
53#2664C2214yescomplemented
54#2662C2218yes—
55#2662C2214yescomplemented
56#2662C2218yescomplemented
57#2659C2211yescharacteristic
58#2659C2212yes—
59#2659C2212yes—
60#2656C2211yescharacteristic
61#2654C2218yescomplemented
62#2650C2218yescomplemented
63#2646C2214yes—
64#2639C2212yes—
65#2630C2218yescomplemented
66#2626C2214yes—
67#2626C2214yes—
68#2620C2214yes—
69#2620C2214yes—
70#2618C2212yes—
71#2618C2212yes—
72#2617C2214yes—
73#2601C2218yescomplemented
74#2592C2214yes—
75#2592C2214yescomplemented
76#2581C2214yescomplemented
77#2568C2212yescomplemented
78#2563C2212yes—
79#2559C2218yescomplemented
80#2558C2218yescomplemented
81#2555C2218yescomplemented
82#2553C2218yescomplemented
83#2552C2214yescomplemented
84#2551C2214yescomplemented
85#2550C2218yescomplemented
86#2545C2218yescomplemented
87#2540C2214yes—
88#2538C2212yescomplemented
89#2537C2212yes—
90#2522C2218yescomplemented
91#2521C2218yescomplemented
92#2521C2218yescomplemented
93#2519C2218yescomplemented
94#2512C2214yes—
95#2511C2214yescomplemented
96#2502C2214yescomplemented
97#2501C2214yes—
98#2492C2214yescomplemented
99#2491C2214yes—
100#2491C2218yescomplemented
101#2485C2214yes—
102#2481C2218yes—
103#2472C2218yes—
104#2470C2218yescomplemented
105#2469C2218yescomplemented
106#2464C2218yescomplemented
107#2459C2218yes—
108#2458C2218yescomplemented
109#2450C2218yes—
110#2421C2214yescomplemented
111#2420C2214yes—
112#2418C2218yes—
113#2417C2214yescomplemented
114#2416C2214yes—
115#2414C2214yes—
116#2411C2218yes—
117#2409C2214yes—
118#2408C2214yes—
119#2396C2218yescomplemented
120#2396C2218yescomplemented
121#2396C2214yescomplemented
122#2392C2214yescomplemented
123#2370C2214yescomplemented
124#2367C2218yes—
125#2367C2214yes—
126#2367C2214yes—
127#2367C2214yescomplemented
128#2363C2214yes—
129#2362C2214yescomplemented
130#2359C2218yes—
131#2355C2212yescomplemented
132#2355C2212yescomplemented
133#2354C2212yes—
134#2354C2212yescomplemented
135#2352C2214yes—
136Q8×C4⋊C4C2212yescomplemented
137D4×C4⋊C4C2214yes—
138D4×C4⋊C4C2212yescomplemented
139#2334C2218yescomplemented
140#2325C2214yes—
141#2316C2212yes—
142#2314C2214yescomplemented
143C4×C22⋊Q8C2214yes—
144C4×C22⋊Q8C2214yes—
145C4×#121C2212yes—
146C4×#121C2212yes—
147C4×#121C2214yes—
148C2×#391C2211yescharacteristic
149C2×#390C2211yescharacteristic
150C2×#388C2212yes—
151C2×#388C2212yes—
152C2×#385C2212yes—
153#2285C2212yes—
154#2280C2214yes—
155#2274C2214yescomplemented
156C2×C4×C4⋊C4C2211yescharacteristic
157C2×C4×C4⋊C4C2211yescharacteristic
158C2×C4×C22⋊C4C2212yes—
159C23×Q8C2311yescharacteristic
160C23×D4C2311yescharacteristic
161C24×C4C2312yes—
162#556—48no—
163#555—48no—
164#544—48no—
165#538—416no—
166C2×C4⋊Q8C2312yes—
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2318yes—
169#529—216no—
170C2×#126C2314yes—
171C2×#126C2318yes—
172C2×#126C2318yes—
173C2×#125C2312yes—
174C2×#125C2318yes—
175C2×#124—28no—
176C2×#124C2312yes—
177C2×#124C2314yes—
178C2×#124C2314yes—
179C2×#124C2314yes—
180C2×#124C2318yes—
181C2×#124C2318yes—
182C2×#123C2314yes—
183C2×#123C2318yes—
184C2×#123C2318yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2312yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2314yes—
190C2×#121C2312yes—
191C2×#121C2312yes—
192C2×#121C2312yes—
193C2×#121C2314yes—
194C2×#121C2314yes—
195C2×#121C2314yes—
196C2×#121C2318yes—
197C2×#121C2314yes—
198C2×#120C2318yes—
199C2×C4×Q8—44no—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2314yes—
206C2×C4×D4—44no—
207C2×C4×D4C2314yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2312yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2318yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2314yes—
216C2×#117C2314yes—
217C2×#117C2314yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C2×#117C2314yes—
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2314yes—
226C22×C4⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C42C2312yes—
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2314yes—
241#400C2318yes—
242#400C2318yes—
243#399C2318yes—
244#399C2318yes—
245#399C2318yes—
246#399C2314yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2314yes—
251#398C2314yes—
252#398C2318yes—
253#398C2314yes—
254#398C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2314yes—
259#397C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2314yes—
265#396C2314yes—
266#396C2314yes—
267#396C2314yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#395C2318yes—
273#395C2318yes—
274#395C2314yes—
275#395C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2314yes—
286#394C2314yes—
287#394C2314yes—
288#393C2318yes—
289#393C2318yes—
290#393C2318yes—
291#393C2314yes—
292#393C2318yes—
293#393C2318yes—
294#392C2318yes—
295#392C2318yes—
296#392C2314yes—
297#391C2314yes—
298#391C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2318yes—
307#390C2314yes—
308#390C2314yes—
309#390C2312yes—
310#390C2314yes—
311#390C2318yes—
312#390C2314yes—
313#390C2318yes—
314#390C2314yes—
315#390C2314yes—
316#390C2318yes—
317#390C2312yes—
318#389C2318yes—
319#389C2318yes—
320#389C2312yes—
321#389C2314yes—
322#389C2314yes—
323#389C2318yes—
324#389C2318yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2312yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2314yes—
350#388C2314yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2314yes—
366#386C2314yes—
367#386C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#384C2314yes—
377#384C2312yes—
378#384C2312yes—
379#384C2312yes—
380#384C2312yes—
381#382C2314yes—
382#382C2314yes—
383#382C2314yes—
384#381C2318yes—
385#380C2314yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2312yes—
395#380C2312yes—
396#380C2318yes—
397#380C2314yes—
398#379C2318yes—
399C4×C4⋊C4C2312yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2318yes—
424C2×#95C2312yes—
425C2×#95C2312yes—
426C2×#95C2311yescharacteristic
427C2×#95C2311yescharacteristic
428C2×#95C2312yes—
429C25C2412yes—
430C22×Q8—24no—
431C22×Q8—42no—
432C22×Q8—42no—
433C22×Q8C2412yes—
434C22×Q8C2412yes—
435C22×Q8C2412yes—
436C22×Q8C2414yes—
437C22×Q8C2414yes—
438C22×D4—24no—
439C22×D4—42no—
440C22×D4—42no—
441C22×D4C2414yes—
442C22×D4C2412yes—
443C22×D4C2412yes—
444C22×D4C2412yes—
445C22×D4C2412yes—
446C22×D4C2412yes—
447C22×D4C2418yes—
448C22×D4C2418yes—
449C23×C4—28no—
450C23×C4—44no—
451C23×C4—82no—
452C23×C4C2414yes—
453C23×C4C2412yes—
454C23×C4C2414yes—
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2412yes—
459C23×C4C2411yescharacteristic
460C23×C4C2412yes—
461C23×C4C2414yes—
462C23×C4C2418yes—
463C23×C4C2411yescharacteristic
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C4⋊Q8—44no—
467C4⋊Q8—44no—
468C4⋊Q8—416no—
469#126—216no—
470#126—416no—
471#126—416no—
472#125—28no—
473#125—416no—
474#124—216no—
475#124—216no—
476#124—28no—
477#124—416no—
478#124—48no—
479#124—416no—
480#123—216no—
481#123—416no—
482#123—88no—
483C22⋊Q8—28no—
484C22⋊Q8—216no—
485C22⋊Q8—48no—
486C22⋊Q8—48no—
487C22⋊Q8—48no—
488#121—28no—
489#121—28no—
490#121—28no—
491#121—48no—
492#121—416no—
493#121—48no—
494#121—48no—
495#121—84no—
496#120—416no—
497C4×Q8—28no—
498C4×Q8—28no—
499C4×Q8—48no—
500C4×Q8—48no—
501C4×Q8—44no—
502C4×Q8—84no—
503C4×D4—216no—
504C4×D4—28no—
505C4×D4—28no—
506C4×D4—44no—
507C4×D4—44no—
508C4×D4—44no—
509C4×D4—48no—
510C4×D4—416no—
511C4×D4—84no—
512#117—216no—
513#117—216no—
514#117—48no—
515#117—48no—
516#117—84no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—24no—
520C2×C4⋊C4—42no—
521C2×C4⋊C4—48no—
522C2×C4⋊C4—44no—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2411yescharacteristic
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2411yescharacteristic
563C2×C22⋊C4—28no—
564C2×C22⋊C4—28no—
565C2×C22⋊C4—28no—
566C2×C22⋊C4—44no—
567C2×C22⋊C4—82no—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C42—42no—
598C2×C42—42no—
599C2×C42—44no—
600C2×C42—82no—
601C2×C42#4118yes—
602C2×C42C2418yes—
603C2×C42C2414yes—
604C2×C42C2412yes—
605C2×C42C2412yes—
606C2×C42C2414yes—
607C2×C42C2418yes—
608C2×C42C2418yes—
609C2×C42C2412yes—
610C2×C42C2418yes—
611C2×C42C2414yes—
612C2×C42C2414yes—
613C2×C42C2412yes—
614C2×C42C2414yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617#95C2414yes—
618#95C2414yes—
619#95C2418yes—
620#95C2414yes—
621#95C2414yes—
622#95C2418yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2414yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2414yes—
639#95C2414yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643C24—24no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24C2514yes—
651C24C2514yes—
652C24C2511yescharacteristic
653C2×Q8—24no—
654C2×Q8—24no—
655C2×Q8—24no—
656C2×Q8—24no—
657C2×Q8—28no—
658C2×Q8—24no—
659C2×Q8—42no—
660C2×Q8—42no—
661C2×Q8—42no—
662C2×Q8—42no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—44no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×Q8—416no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—416no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—28no—
704C22×C4—24no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—28no—
709C22×C4—28no—
710C22×C4—41no—
711C22×C4—42no—
712C22×C4—41no—
713C22×C4—41no—
714C22×C4—42no—
715C22×C4—44no—
716C22×C4—41no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—42no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—42no—
723C22×C4—41no—
724C22×C4—42no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—41no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—816no—
732C22×C4C2×#4114yes—
733C22×C4C2×#4114yes—
734C22×C4C2×#4114yes—
735C22×C4H(5,𝔽2)14yes—
736C22×C42−1+414yes—
737C22×C4C2512yes—
738C22×C4C2514yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2518yes—
743C22×C4C2512yes—
744C22×C4C2512yes—
745C22×C4C2514yes—
746C22×C4C2518yes—
747C22×C4C2512yes—
748C22×C4C2511yescharacteristic
749C22×C4C2512yes—
750C22×C4C2512yes—
751C22×C4C2512yes—
752C22×C4C2512yes—
753C22×C4C2511yescharacteristic
754C4⋊C4—28no—
755C4⋊C4—28no—
756C4⋊C4—24no—
757C4⋊C4—28no—
758C4⋊C4—24no—
759C4⋊C4—28no—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—28no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—24no—
766C4⋊C4—216no—
767C4⋊C4—28no—
768C4⋊C4—28no—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—28no—
772C4⋊C4—42no—
773C4⋊C4—48no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—42no—
777C4⋊C4—42no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—42no—
782C4⋊C4—44no—
783C4⋊C4—42no—
784C4⋊C4—48no—
785C4⋊C4—44no—
786C4⋊C4—48no—
787C4⋊C4—48no—
788C4⋊C4—48no—
789C4⋊C4—44no—
790C4⋊C4—48no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4H(5,𝔽2)14yes—
794C22⋊C4—28no—
795C22⋊C4—216no—
796C22⋊C4—216no—
797C22⋊C4—216no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—216no—
803C22⋊C4—28no—
804C22⋊C4—216no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—44no—
808C22⋊C4—48no—
809C22⋊C4—44no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—44no—
815C22⋊C4—44no—
816C22⋊C4—48no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—48no—
821C22⋊C4—48no—
822C22⋊C4—44no—
823C42—28no—
824C42—24no—
825C42—24no—
826C42—28no—
827C42—216no—
828C42—42no—
829C42—42no—
830C42—44no—
831C42—44no—
832C42—44no—
833C42—48no—
834C42—48no—
835C42—48no—
836C42C2×#4118yes—
837C42C2×#4118yes—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—48no—
857C23—48no—
858C23—48no—
859C23—84no—
860C23—84no—
861C23—84no—
862C23—84no—
863C23C22×#4112yes—
864C23C2×H(5,𝔽2)12yes—
865C23C2×2−1+412yes—
866C23C2611yescharacteristic
867Q8—48no—
868Q8—48no—
869Q8—48no—
870Q8—88no—
871Q8—164no—
872D4—48no—
873D4—48no—
874D4—416no—
875D4—48no—
876D4—84no—
877D4—84no—
878D4—168no—
879D4—168no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—28no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—28no—
906C2×C4—22no—
907C2×C4—28no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—28no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—28no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—22no—
923C2×C4—28no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—416no—
928C2×C4—48no—
929C2×C4—48no—
930C2×C4—416no—
931C2×C4—88no—
932C2×C4—82no—
933C2×C4—82no—
934C2×C4—84no—
935C2×C4—168no—
936C2×C4C22×#4114yes—
937C2×C4C22×#4114yes—
938C2×C4C22×#4112yes—
939C2×C4C22×#4112yes—
940C2×C4C2×H(5,𝔽2)14yes—
941C2×C4C2×H(5,𝔽2)14yes—
942C2×C4C2×H(5,𝔽2)12yes—
943C2×C4C2×2−1+414yes—
944C2×C4#58512yes—
945C22—22no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—44no—
952C22—44no—
953C22—44no—
954C22—44no—
955C22—44no—
956C22—44no—
957C22—44no—
958C22—44no—
959C22—44no—
960C22—44no—
961C22—44no—
962C22—44no—
963C22—44no—
964C22—44no—
965C22—816no—
966C22#351114yes—
967C22C23×#4111yescharacteristic
968C22C22×H(5,𝔽2)11yescharacteristic
969C22C22×H(5,𝔽2)11yescharacteristic
970C22C22×2−1+411yescharacteristic
971C22C2×#58511yescharacteristic
972C22H(7,𝔽2)11yescharacteristic
973C222−1+611yescharacteristic
974C4—24no—
975C4—24no—
976C4—24no—
977C4—24no—
978C4—24no—
979C4—22no—
980C4—44no—
981C4—44no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—48no—
986C4—44no—
987C4—44no—
988C4—44no—
989C4—48no—
990C4#346014yes—
991C2—24no—
992C2—84no—
993C2—84no—
994C2C2×#346011yescharacteristic
995C2C2×#351111yescharacteristic
996C2#6284511yescharacteristic
997C2#6289411yescharacteristic
998C2#6289511yescharacteristic
999C2#6295911yescharacteristic
1000C2#6296111yescharacteristic
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. #42661C2semidirect
2. #42460C2semidirect
3. #41686C2semidirect
4. #41012C2semidirect
5. #39632C2semidirect
6. #39423C2semidirect
7. #39375C2semidirect
8. #37941C2semidirect
9. #37546C2semidirect
10. #37461C2semidirect
11. #36579C2semidirect
12. #36160C2semidirect
13. #36028C2semidirect
14. #35745C2semidirect
15. #35167C2semidirect
16. #35003C2semidirect
17. #34594C2semidirect
18. #34578C2semidirect
19. #34243C2semidirect
20. C2×#2367C2semidirect
21. C2×#556C22semidirect
33. #2837C22semidirect
34. #2832C22semidirect
37. #2806C22semidirect
38. #2804C22semidirect
39. #2788C22semidirect
40. #2780C22semidirect
41. #2779C22semidirect
42. #2739C22semidirect
43. #2731C22semidirect
45. #2716C22semidirect
46. #2711C22semidirect
48. #2707C22semidirect
49. #2701C22semidirect
51. #2667C22semidirect
52. #2665C22semidirect
53. #2664C22semidirect
55. #2662C22semidirect
56. #2662C22semidirect
61. #2654C22semidirect
62. #2650C22semidirect
65. #2630C22semidirect
73. #2601C22semidirect
75. #2592C22semidirect
76. #2581C22semidirect
77. #2568C22semidirect
79. #2559C22semidirect
80. #2558C22semidirect
81. #2555C22semidirect
82. #2553C22semidirect
83. #2552C22semidirect
84. #2551C22semidirect
85. #2550C22semidirect
86. #2545C22semidirect
88. #2538C22semidirect
90. #2522C22semidirect
91. #2521C22semidirect
92. #2521C22semidirect
93. #2519C22semidirect
95. #2511C22semidirect
96. #2502C22semidirect
98. #2492C22semidirect
100. #2491C22semidirect
104. #2470C22semidirect
105. #2469C22semidirect
106. #2464C22semidirect
108. #2458C22semidirect
110. #2421C22semidirect
113. #2417C22semidirect
119. #2396C22semidirect
120. #2396C22semidirect
121. #2396C22semidirect
122. #2392C22semidirect
123. #2370C22semidirect
127. #2367C22semidirect
129. #2362C22semidirect
131. #2355C22semidirect
132. #2355C22semidirect
134. #2354C22semidirect
136. Q8×C4⋊C4C22semidirect
138. D4×C4⋊C4C22semidirect
139. #2334C22semidirect
142. #2314C22semidirect
155. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#426612
#424602
#416862
#410122
#396322
#394232
#393752
#379412
#375462
#374612
#365792
#361602
#360282
#357452
#351672
#350032
#345942
#345782
#342432
C2×#23672