Finite Group Databasebeta

← #8425256

Subgroups — #8425256

Order 512.

5433 conjugacy classes of subgroups.

The subgroup lattice has 1015 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59420C211yesmaximal, characteristic, complemented
2#59244C212yesmaximal, complemented
3#59049C214yesmaximal, complemented
4#58814C218yesmaximal, complemented
5#53055C214yesmaximal, complemented
6#52977C214yesmaximal, complemented
7#52405C214yesmaximal, complemented
8#42987C214yesmaximal, complemented
9#42604C214yesmaximal, complemented
10#40657C214yesmaximal, complemented
11#39342C212yesmaximal, complemented
12#39137C212yesmaximal, complemented
13#39030C214yesmaximal, complemented
14#37782C214yesmaximal, complemented
15#37621C212yesmaximal, complemented
16#37516C214yesmaximal, complemented
17#36464C212yesmaximal, complemented
18#36211C211yesmaximal, characteristic, complemented
19#34925C211yesmaximal, characteristic, complemented
20#34889C212yesmaximal, complemented
21C2×#559C2211yescharacteristic
22C2×#556C2214yescomplemented
23C2×D42C2211yescharacteristic
24C2×#535C2214yes—
25C2×#532C2212yes—
26C2×#532C2214yescomplemented
27C2×#529C2212yescomplemented
28#2859C2211yescharacteristic, complemented
29#2856C2212yes—
30#2854C2214yes—
31#2829C2218yescomplemented
32#2828C2218yescomplemented
33#2826C2218yescomplemented
34#2824C2218yescomplemented
35#2818C2218yescomplemented
36#2815C2214yescomplemented
37#2813C2218yescomplemented
38#2812C2214yescomplemented
39#2779C2218yescomplemented
40#2764C2214yescomplemented
41#2737C2218yescomplemented
42#2715C2218yescomplemented
43#2714C2218yescomplemented
44#2714C2218yescomplemented
45#2712C2218yescomplemented
46#2705C2218yescomplemented
47#2703C2218yescomplemented
48#2697C2214yes—
49#2697C2218yescomplemented
50#2685C2218yescomplemented
51#2685C2218yescomplemented
52#2682C2218yescomplemented
53#2678C2218yescomplemented
54#2673C2218yescomplemented
55#2670C2218yes—
56#2670C2218yescomplemented
57#2670C2214yescomplemented
58#2669C2218yes—
59#2665C2214yescomplemented
60#2662C2218yescomplemented
61#2662C2218yescomplemented
62#2650C2218yescomplemented
63#2648C2218yescomplemented
64#2632C2218yescomplemented
65#2628C2214yescomplemented
66#2620C2214yescomplemented
67#2619C2214yes—
68#2616C2214yescomplemented
69#2615C2214yes—
70#2615C2214yescomplemented
71#2562C2214yescomplemented
72#2559C2214yescomplemented
73#2558C2218yescomplemented
74#2557C2214yescomplemented
75#2555C2214yescomplemented
76#2551C2211yescharacteristic, complemented
77#2550C2212yescomplemented
78#2548C2218yescomplemented
79#2548C2214yescomplemented
80#2544C2212yes—
81#2541C2214yes—
82#2541C2212yes—
83#2540C2212yes—
84#2540C2214yescomplemented
85#2540C2214yescomplemented
86#2538C2212yes—
87#2538C2212yescomplemented
88#2537C2212yes—
89#2537C2214yescomplemented
90#2537C2211yescharacteristic, complemented
91#2535C2212yescomplemented
92#2535C2212yescomplemented
93#2534C2214yes—
94#2521C2214yescomplemented
95#2518C2218yescomplemented
96#2513C2214yescomplemented
97#2512C2214yes—
98#2497C2214yescomplemented
99#2496C2214yescomplemented
100#2495C2214yescomplemented
101#2492C2212yescomplemented
102#2491C2214yes—
103#2491C2214yes—
104#2491C2214yescomplemented
105#2490C2212yes—
106#2490C2214yescomplemented
107#2485C2214yescomplemented
108#2469C2218yescomplemented
109#2467C2218yescomplemented
110#2467C2218yescomplemented
111#2464C2214yescomplemented
112#2459C2218yescomplemented
113#2454C2214yescomplemented
114#2448C2218yescomplemented
115#2439C2214yescomplemented
116#2435C2214yes—
117#2433C2214yes—
118#2431C2218yescomplemented
119#2428C2212yes—
120#2428C2214yescomplemented
121#2428C2214yescomplemented
122#2427C2214yes—
123#2427C2212yescomplemented
124#2426C2214yes—
125#2426C2214yescomplemented
126#2424C2218yescomplemented
127#2422C2214yescomplemented
128#2421C2214yescomplemented
129#2420C2214yes—
130#2420C2214yescomplemented
131#2414C2214yes—
132#2414C2214yes—
133#2414C2214yescomplemented
134#2414C2214yescomplemented
135#2408C2214yes—
136#2408C2214yes—
137#2404C2214yescomplemented
138#2395C2214yescomplemented
139#2388C2214yescomplemented
140#2388C2214yescomplemented
141#2365C2214yescomplemented
142#2363C2214yescomplemented
143#2363C2214yescomplemented
144#2357C2212yescomplemented
145#2354C2212yes—
146Q8×C4⋊C4C2212yescomplemented
147#2347C2214yescomplemented
148#2341C2214yescomplemented
149D4×C22⋊C4C2214yes—
150#2324C2214yescomplemented
151#2312C2214yescomplemented
152C4×#127C2211yescharacteristic
153C4×#124C2212yes—
154C4×C22⋊Q8C2212yescomplemented
155C4×C22⋊Q8C2214yescomplemented
156C4×#121C2212yes—
157C4×#121C2214yescomplemented
158C4×#121C2214yescomplemented
159#2297C2214yescomplemented
160#2285C2212yescomplemented
161C42×D4C2211yescharacteristic, complemented
162C42×D4C2212yescomplemented
163C22×#41C2314yes—
164C22×#41C2314yes—
165C23×D4C2314yes—
166#559—44no—
167#556—416no—
168D42—44no—
169#535—416no—
170#532—48no—
171#532—416no—
172C2×C4⋊Q8C2314yes—
173C2×C4⋊Q8C2312yes—
174C2×#127C2311yescharacteristic
175C2×#127C2318yes—
176C2×#127C2312yes—
177C2×#127C2314yes—
178#529—48no—
179C2×#126C2318yes—
180C2×#126C2314yes—
181C2×#126C2318yes—
182C2×#125C2312yes—
183C2×#125C2312yes—
184C2×#124C2314yes—
185C2×#124C2318yes—
186C2×#124C2314yes—
187C2×#124C2318yes—
188C2×#124C2318yes—
189C2×#124C2312yes—
190C2×#124C2312yes—
191C2×#123C2314yes—
192C2×#123C2314yes—
193C2×#123C2318yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2312yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×#121C2314yes—
199C2×#121C2312yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2312yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2312yes—
209C2×#121C2314yes—
210C2×#121C2312yes—
211C2×#121C2318yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2318yes—
215C2×#120C2318yes—
216C2×#120C2318yes—
217C2×#120C2314yes—
218C2×#120C2318yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2318yes—
221C2×C4×Q8C2314yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2318yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2311yescharacteristic
235C2×#117C2314yes—
236C2×#117C2314yes—
237C2×#117C2314yes—
238C22×C22⋊C4C2314yes—
239C22×C42C2312yes—
240C22×C42C2314yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2314yes—
245#399C2318yes—
246#399C2314yes—
247#399C2318yes—
248#398C2314yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2314yes—
254#397C2318yes—
255#397C2314yes—
256#397C2314yes—
257#397C2314yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#395C2318yes—
265#395C2314yes—
266#395C2314yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2314yes—
281#394C2318yes—
282#394C2314yes—
283#394C2318yes—
284#394C2318yes—
285#394C2314yes—
286#394C2314yes—
287#394C2314yes—
288#394C2314yes—
289#394C2318yes—
290#393C2314yes—
291#393C2318yes—
292#393C2318yes—
293#393C2314yes—
294#393C2318yes—
295#392C2314yes—
296#392C2314yes—
297#392C2314yes—
298#392C2318yes—
299#392C2318yes—
300#392C2318yes—
301#392C2318yes—
302#392C2318yes—
303#392C2314yes—
304#392C2318yes—
305#392C2318yes—
306#392C2318yes—
307#392C2318yes—
308#392C2318yes—
309#392C2318yes—
310#392C2314yes—
311#391C2312yes—
312#391C2318yes—
313#391C2314yes—
314#391C2314yes—
315#391C2312yes—
316#390C2314yes—
317#390C2312yes—
318#390C2318yes—
319#390C2318yes—
320#390C2314yes—
321#390C2312yes—
322#390C2314yes—
323#390C2318yes—
324#390C2318yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2318yes—
330#390C2318yes—
331#390C2314yes—
332#390C2314yes—
333#390C2318yes—
334#390C2318yes—
335#390C2312yes—
336#390C2314yes—
337#390C2314yes—
338#389C2312yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2318yes—
344#389C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#388C2318yes—
349#388C2318yes—
350#388C2314yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2314yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2314yes—
372#386C2314yes—
373#386C2318yes—
374#386C2314yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2314yes—
381#386C2314yes—
382#386C2314yes—
383#386C2314yes—
384#386C2314yes—
385#385C2318yes—
386#385C2318yes—
387#385C2314yes—
388#384C2311yescharacteristic
389#384C2312yes—
390#384C2314yes—
391#383C2318yes—
392#382C2312yes—
393#382C2314yes—
394#382C2312yes—
395#381C2314yes—
396#381C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2318yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2312yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2312yes—
410#379C2318yes—
411#379C2318yes—
412#379C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2312yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2312yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2314yes—
437C43C2311yescharacteristic
438C25C2414yes—
439C2×#41—48no—
440C2×#41—48no—
441C2×#41—48no—
442C2×#41—48no—
443C2×#41—416no—
444C22×Q8C2412yes—
445C22×Q8C2414yes—
446C22×Q8C2414yes—
447C22×D4—48no—
448C22×D4—48no—
449C22×D4—48no—
450C22×D4C2412yes—
451C22×D4C2414yes—
452C22×D4C2412yes—
453C22×D4C2412yes—
454C22×D4C2414yes—
455C22×D4C2418yes—
456C22×D4C2411yescharacteristic
457C22×D4C2414yes—
458C22×D4C2418yes—
459C22×D4C2414yes—
460C22×D4C2418yes—
461C22×D4C2414yes—
462C22×D4C2414yes—
463C22×D4C2418yes—
464C22×D4C2418yes—
465C22×D4C2414yes—
466C22×D4C2414yes—
467C23×C4C2412yes—
468C23×C4C2414yes—
469C23×C4C2414yes—
470C23×C4C2412yes—
471C23×C4C2414yes—
472C23×C4C2414yes—
473C23×C4C2412yes—
474C23×C4C2414yes—
475C23×C4C2414yes—
476C4⋊Q8—216no—
477C4⋊Q8—44no—
478#127—24no—
479#127—44no—
480#127—48no—
481#127—416no—
482#126—48no—
483#126—416no—
484#126—416no—
485#125—44no—
486#125—82no—
487#124—48no—
488#124—416no—
489#124—44no—
490#124—44no—
491#124—48no—
492#124—416no—
493#124—416no—
494#123—48no—
495#123—48no—
496#123—88no—
497C22⋊Q8—28no—
498C22⋊Q8—48no—
499C22⋊Q8—44no—
500C22⋊Q8—48no—
501#121—216no—
502#121—28no—
503#121—48no—
504#121—48no—
505#121—416no—
506#121—48no—
507#121—48no—
508#121—48no—
509#121—44no—
510#121—48no—
511#121—44no—
512#121—44no—
513#121—48no—
514#121—48no—
515#121—48no—
516#121—84no—
517#121—88no—
518#120—416no—
519#120—416no—
520#120—48no—
521#120—88no—
522C4×Q8—28no—
523C4×Q8—48no—
524C4×Q8—416no—
525C4×D4—28no—
526C4×D4—28no—
527C4×D4—28no—
528C4×D4—42no—
529C4×D4—44no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—44no—
533C4×D4—44no—
534C4×D4—48no—
535C4×D4—48no—
536C4×D4—48no—
537C4×D4—416no—
538#117—216no—
539#117—48no—
540#117—48no—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2411yescharacteristic
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2412yes—
567C2×C22⋊C4—48no—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C42—28no—
612C2×C42—48no—
613C2×C42C2412yes—
614C2×C42C2414yes—
615C2×C42C2418yes—
616C2×C42C2411yescharacteristic
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2412yes—
620C2×C42C2414yes—
621C2×C42C2412yes—
622C2×C42C2418yes—
623C2×C42C2414yes—
624C2×C42C2418yes—
625C2×C42C2414yes—
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628#95C2411yescharacteristic
629#95C2414yes—
630#95C2414yes—
631#95C2411yescharacteristic
632#95C2414yes—
633#95C2414yes—
634#95C2412yes—
635#95C2414yes—
636#95C2412yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2414yes—
653#95C2418yes—
654#95C2418yes—
655#95C2414yes—
656C24—44no—
657C24—48no—
658C24—44no—
659C24—48no—
660C24—44no—
661C24C2514yes—
662C24C2514yes—
663C24C2512yes—
664C24C2514yes—
665#41—832no—
666#41—832no—
667C2×Q8—24no—
668C2×Q8—24no—
669C2×Q8—216no—
670C2×Q8—24no—
671C2×Q8—44no—
672C2×Q8—44no—
673C2×Q8—44no—
674C2×Q8—44no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—24no—
681C2×D4—28no—
682C2×D4—24no—
683C2×D4—216no—
684C2×D4—24no—
685C2×D4—28no—
686C2×D4—24no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—48no—
692C2×D4—44no—
693C2×D4—42no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—48no—
697C2×D4—44no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—48no—
706C2×D4—42no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—832no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—28no—
728C22×C4—28no—
729C22×C4—24no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—24no—
740C22×C4—28no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—48no—
744C22×C4—42no—
745C22×C4—44no—
746C22×C4—42no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4C2511yescharacteristic
752C22×C4C2512yes—
753C22×C4C2514yes—
754C22×C4C2512yes—
755C22×C4C2514yes—
756C22×C4C2514yes—
757C22×C4C2512yes—
758C22×C4C2518yes—
759C22×C4C2514yes—
760C22×C4C2514yes—
761C22×C4C2512yes—
762C22×C4C2514yes—
763C22×C4C2514yes—
764C22×C4C2511yescharacteristic
765C22×C4C2511yescharacteristic
766C22×C4C2512yes—
767C4⋊C4—28no—
768C4⋊C4—28no—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—216no—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—24no—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—42no—
780C4⋊C4—41no—
781C4⋊C4—42no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4—48no—
786C4⋊C4—48no—
787C4⋊C4—44no—
788C4⋊C4—48no—
789C4⋊C4—44no—
790C4⋊C4—48no—
791C4⋊C4—48no—
792C4⋊C4H(5,𝔽2)18yes—
793C22⋊C4—216no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—216no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—24no—
802C22⋊C4—48no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—48no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—42no—
809C22⋊C4—42no—
810C22⋊C4—44no—
811C22⋊C4—44no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—44no—
815C22⋊C4—48no—
816C22⋊C4—44no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—44no—
820C22⋊C4—48no—
821C22⋊C4—48no—
822C22⋊C4—44no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—44no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C42—24no—
837C42—24no—
838C42—24no—
839C42—24no—
840C42—28no—
841C42—216no—
842C42—28no—
843C42—22no—
844C42—24no—
845C42—44no—
846C42—44no—
847C42—48no—
848C42—48no—
849C42—41no—
850C42H(5,𝔽2)14yes—
851C23—22no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—28no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—22no—
860C23—24no—
861C23—22no—
862C23—24no—
863C23—22no—
864C23—24no—
865C23—24no—
866C23—28no—
867C23—24no—
868C23—24no—
869C23—22no—
870C23—22no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—22no—
876C23—24no—
877C23—816no—
878C23—88no—
879C23—164no—
880C23—168no—
881C23—164no—
882C23C2611yescharacteristic
883Q8—416no—
884Q8—48no—
885Q8—88no—
886D4—44no—
887D4—48no—
888D4—416no—
889D4—48no—
890D4—88no—
891D4—84no—
892D4—816no—
893D4—816no—
894D4—88no—
895D4—88no—
896D4—816no—
897D4—88no—
898D4—88no—
899D4—88no—
900D4—88no—
901D4—168no—
902D4—168no—
903C2×C4—24no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—24no—
907C2×C4—21no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—28no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—28no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—28no—
942C2×C4—416no—
943C2×C4—48no—
944C2×C4—416no—
945C2×C4—416no—
946C2×C4—48no—
947C2×C4—84no—
948C2×C4—88no—
949C2×C4—88no—
950C2×C4—164no—
951C2×C4C2×H(5,𝔽2)12yes—
952C2×C4C2×H(5,𝔽2)18yes—
953C2×C4C2×H(5,𝔽2)14yes—
954C2×C4C2×H(5,𝔽2)14yes—
955C2×C4#58512yes—
956C2×C4#58514yes—
957C22—42no—
958C22—44no—
959C22—44no—
960C22—42no—
961C22—44no—
962C22—48no—
963C22—44no—
964C22—44no—
965C22—44no—
966C22—42no—
967C22—44no—
968C22—42no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—48no—
975C22—42no—
976C22—44no—
977C22—42no—
978C22—44no—
979C22—42no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—1616no—
984C22C22×H(5,𝔽2)11yescharacteristic
985C22C22×H(5,𝔽2)12yes—
986C22C2×#58512yes—
987C22C2×#58511yescharacteristic
988C22H(7,𝔽2)11yescharacteristic
989C4—22no—
990C4—28no—
991C4—22no—
992C4—42no—
993C4—44no—
994C4—42no—
995C4—44no—
996C4—44no—
997C4—44no—
998C4—41no—
999C4—42no—
1000C4—44no—
1001C4—48no—
1002C4—42no—
1003C4—44no—
1004C4#354618yes—
1005C2—82no—
1006C2—84no—
1007C2—84no—
1008C2—84no—
1009C2C2×#354612yes—
1010C2#6276211yescharacteristic
1011C2#6292312yes—
1012C2#6293011yescharacteristic
1013C2#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. #59420C2semidirect
2. #59244C2semidirect
3. #59049C2semidirect
4. #58814C2semidirect
5. #53055C2semidirect
6. #52977C2semidirect
7. #52405C2semidirect
8. #42987C2semidirect
9. #42604C2semidirect
10. #40657C2semidirect
11. #39342C2semidirect
12. #39137C2semidirect
13. #39030C2semidirect
14. #37782C2semidirect
15. #37621C2semidirect
16. #37516C2semidirect
17. #36464C2semidirect
18. #36211C2semidirect
19. #34925C2semidirect
20. #34889C2semidirect
22. C2×#556C22semidirect
26. C2×#532C22semidirect
27. C2×#529C22semidirect
28. #2859C22semidirect
31. #2829C22semidirect
32. #2828C22semidirect
33. #2826C22semidirect
34. #2824C22semidirect
35. #2818C22semidirect
36. #2815C22semidirect
37. #2813C22semidirect
38. #2812C22semidirect
39. #2779C22semidirect
40. #2764C22semidirect
41. #2737C22semidirect
42. #2715C22semidirect
43. #2714C22semidirect
44. #2714C22semidirect
45. #2712C22semidirect
46. #2705C22semidirect
47. #2703C22semidirect
49. #2697C22semidirect
50. #2685C22semidirect
51. #2685C22semidirect
52. #2682C22semidirect
53. #2678C22semidirect
54. #2673C22semidirect
56. #2670C22semidirect
57. #2670C22semidirect
59. #2665C22semidirect
60. #2662C22semidirect
61. #2662C22semidirect
62. #2650C22semidirect
63. #2648C22semidirect
64. #2632C22semidirect
65. #2628C22semidirect
66. #2620C22semidirect
68. #2616C22semidirect
70. #2615C22semidirect
71. #2562C22semidirect
72. #2559C22semidirect
73. #2558C22semidirect
74. #2557C22semidirect
75. #2555C22semidirect
76. #2551C22semidirect
77. #2550C22semidirect
78. #2548C22semidirect
79. #2548C22semidirect
84. #2540C22semidirect
85. #2540C22semidirect
87. #2538C22semidirect
89. #2537C22semidirect
90. #2537C22semidirect
91. #2535C22semidirect
92. #2535C22semidirect
94. #2521C22semidirect
95. #2518C22semidirect
96. #2513C22semidirect
98. #2497C22semidirect
99. #2496C22semidirect
100. #2495C22semidirect
101. #2492C22semidirect
104. #2491C22semidirect
106. #2490C22semidirect
107. #2485C22semidirect
108. #2469C22semidirect
109. #2467C22semidirect
110. #2467C22semidirect
111. #2464C22semidirect
112. #2459C22semidirect
113. #2454C22semidirect
114. #2448C22semidirect
115. #2439C22semidirect
118. #2431C22semidirect
120. #2428C22semidirect
121. #2428C22semidirect
123. #2427C22semidirect
125. #2426C22semidirect
126. #2424C22semidirect
127. #2422C22semidirect
128. #2421C22semidirect
130. #2420C22semidirect
133. #2414C22semidirect
134. #2414C22semidirect
137. #2404C22semidirect
138. #2395C22semidirect
139. #2388C22semidirect
140. #2388C22semidirect
141. #2365C22semidirect
142. #2363C22semidirect
143. #2363C22semidirect
144. #2357C22semidirect
146. Q8×C4⋊C4C22semidirect
147. #2347C22semidirect
148. #2341C22semidirect
150. #2324C22semidirect
151. #2312C22semidirect
154. C4×C22⋊Q8C22semidirect
155. C4×C22⋊Q8C22semidirect
157. C4×#121C22semidirect
158. C4×#121C22semidirect
159. #2297C22semidirect
160. #2285C22semidirect
161. C42×D4C22semidirect
162. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#594202
#592442
#590492
#588142
#530552
#529772
#524052
#429872
#426042
#406572
#393422
#391372
#390302
#377822
#376212
#375162
#364642
#362112
#349252
#348892