Finite Group Databasebeta

← #8096185

Subgroups — #8096185

Order 512.

5083 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53000C214yesmaximal, complemented
2#52989C212yesmaximal, complemented
3#52693C214yesmaximal, complemented
4#52589C218yesmaximal, complemented
5#52304C211yesmaximal, characteristic, complemented
6#52163C212yesmaximal, complemented
7#46287C212yesmaximal, complemented
8#46013C212yesmaximal, complemented
9#45996C211yesmaximal, characteristic, complemented
10#45800C214yesmaximal, complemented
11#45718C214yesmaximal, complemented
12#45707C218yesmaximal, complemented
13#45697C212yesmaximal, complemented
14#45442C214yesmaximal, complemented
15#36463C212yesmaximal, complemented
16#36441C214yesmaximal, complemented
17#36406C211yesmaximal, characteristic, complemented
18#36102C212yesmaximal, complemented
19#35956C212yesmaximal, complemented
20#35880C214yesmaximal, complemented
21C2×H(3,𝔽4)C2212yes—
22C2×#559C2212yes—
23C2×#556C2211yescharacteristic, complemented
24C2×#547C2211yescharacteristic
25C2×#525C2214yes—
26C22×C4×D4C2212yescomplemented
27#2862C2211yescharacteristic, complemented
28#2858C2212yes—
29#2857C2212yescomplemented
30#2854C2212yescomplemented
31#2854C2214yescomplemented
32#2850C2214yes—
33#2849C2214yescomplemented
34#2849C2218yescomplemented
35#2832C2218yescomplemented
36#2832C2214yescomplemented
37#2830C2214yescomplemented
38#2828C2218yescomplemented
39#2827C2218yescomplemented
40#2826C2214yes—
41#2825C2218yescomplemented
42#2820C2214yescomplemented
43#2819C2212yes—
44#2813C2218yescomplemented
45#2812C2218yescomplemented
46#2808C2214yescomplemented
47#2805C2212yescomplemented
48#2795C2218yescomplemented
49#2789C2212yescomplemented
50#2765C2214yescomplemented
51#2761C2218yescomplemented
52#2752C2214yes—
53#2751C2218yescomplemented
54#2741C2218yescomplemented
55#2735C2218yescomplemented
56#2733C2212yes—
57#2732C2214yescomplemented
58#2728C2214yescomplemented
59#2724C2211yescharacteristic
60#2724C2214yescomplemented
61#2717C2212yes—
62#2710C2218yescomplemented
63#2708C2218yescomplemented
64#2703C2218yescomplemented
65#2700C2218yescomplemented
66#2697C2214yes—
67#2696C2218yescomplemented
68#2690C2214yescomplemented
69#2686C2218yescomplemented
70#2683C2211yescharacteristic
71#2679C2212yes—
72#2678C2218yescomplemented
73#2678C2218yescomplemented
74#2674C2218yescomplemented
75#2670C2218yes—
76#2668C2218yescomplemented
77#2662C2214yescomplemented
78#2657C2212yes—
79#2650C2218yescomplemented
80#2644C2214yescomplemented
81#2610C2214yescomplemented
82#2603C2214yescomplemented
83#2602C2218yescomplemented
84#2600C2218yescomplemented
85#2596C2218yescomplemented
86#2592C2212yescomplemented
87#2587C2218yescomplemented
88#2580C2214yescomplemented
89#2563C2212yescomplemented
90#2557C2218yescomplemented
91#2554C2218yescomplemented
92#2553C2218yescomplemented
93#2548C2212yes—
94#2548C2214yescomplemented
95#2546C2211yescharacteristic, complemented
96#2545C2214yescomplemented
97#2544C2214yes—
98#2542C2211yescharacteristic
99#2541C2212yes—
100#2527C2218yescomplemented
101#2526C2218yescomplemented
102#2513C2214yescomplemented
103#2509C2214yescomplemented
104#2499C2212yescomplemented
105#2491C2214yes—
106#2490C2214yescomplemented
107#2474C2218yescomplemented
108#2472C2218yescomplemented
109#2463C2218yescomplemented
110#2461C2218yescomplemented
111#2459C2218yescomplemented
112#2459C2218yescomplemented
113#2456C2218yes—
114#2455C2218yescomplemented
115#2452C2214yescomplemented
116#2451C2214yescomplemented
117#2448C2214yescomplemented
118#2447C2218yescomplemented
119#2447C2214yescomplemented
120#2445C2214yes—
121#2445C2214yescomplemented
122#2435C2214yescomplemented
123#2433C2214yes—
124#2433C2212yescomplemented
125#2432C2212yes—
126#2428C2214yes—
127#2427C2214yescomplemented
128#2426C2214yes—
129#2421C2214yescomplemented
130#2420C2214yescomplemented
131#2418C2218yescomplemented
132#2411C2214yescomplemented
133#2408C2212yes—
134#2404C2214yes—
135#2401C2214yescomplemented
136#2399C2212yescomplemented
137#2395C2218yescomplemented
138#2392C2214yescomplemented
139#2379C2214yescomplemented
140#2376C2218yescomplemented
141#2375C2214yes—
142#2369C2212yescomplemented
143#2367C2214yescomplemented
144#2366C2212yes—
145#2366C2214yescomplemented
146#2361C2214yes—
147#2360C2214yescomplemented
148#2357C2214yescomplemented
149#2344C2212yescomplemented
150C4×#125C2212yescomplemented
151C4×#124C2211yescharacteristic
152C4×C22⋊Q8C2214yescomplemented
153C4×#123C2212yes—
154C4×#121C2214yescomplemented
155C4×#120C2218yescomplemented
156#2297C2212yes—
157#2276C2212yescomplemented
158C42×D4C2211yescharacteristic, complemented
159C22×#41C2312yes—
160C23×D4C2312yes—
161C24×C4C2314yes—
162H(3,𝔽4)—48no—
163#559—48no—
164#556—44no—
165#547—44no—
166C2×C4⋊Q8C2312yes—
167C2×C4⋊Q8C2311yescharacteristic
168C2×C4⋊Q8C2311yescharacteristic
169C2×C4⋊Q8C2312yes—
170C2×#127C2312yes—
171C2×#127C2314yes—
172C2×#127C2312yes—
173C2×#126C2314yes—
174C2×#125C2312yes—
175C2×#124C2311yescharacteristic
176C2×#124C2314yes—
177C2×#124C2314yes—
178C2×#124C2312yes—
179C2×#124C2314yes—
180C2×#124C2314yes—
181C2×#124C2314yes—
182C2×#124C2318yes—
183C2×#124C2314yes—
184#525—416no—
185C2×#123C2312yes—
186C2×#123C2314yes—
187C2×#123C2318yes—
188C2×#123C2314yes—
189C2×#123C2318yes—
190C2×#123C2318yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2318yes—
195C2×C22⋊Q8C2314yes—
196C2×#121C2314yes—
197C2×#121C2312yes—
198C2×#121C2318yes—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#120C2314yes—
202C2×#120C2318yes—
203C2×#120C2314yes—
204C2×#120C2318yes—
205C2×#120C2314yes—
206C2×C4×Q8C2312yes—
207C2×C4×Q8C2312yes—
208C2×C4×Q8C2311yescharacteristic
209C2×C4×Q8C2314yes—
210C2×C4×D4—48no—
211C2×C4×D4C2314yes—
212C2×C4×D4C2311yescharacteristic
213C2×C4×D4C2312yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2318yes—
217C2×C4×D4C2318yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2314yes—
221C2×#117C2314yes—
222C2×#117C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C22⋊C4C2314yes—
225C22×C42C2312yes—
226C22×C42C2312yes—
227#401C2314yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2314yes—
232#400C2314yes—
233#400C2314yes—
234#399C2318yes—
235#399C2314yes—
236#399C2318yes—
237#398C2314yes—
238#398C2314yes—
239#398C2318yes—
240#398C2312yes—
241#398C2312yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#397C2314yes—
252#397C2314yes—
253#397C2318yes—
254#397C2314yes—
255#397C2314yes—
256#396C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2314yes—
262#395C2318yes—
263#395C2312yes—
264#395C2312yes—
265#395C2314yes—
266#394C2314yes—
267#394C2314yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2314yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#393C2318yes—
284#393C2318yes—
285#393C2318yes—
286#393C2314yes—
287#393C2318yes—
288#392C2318yes—
289#392C2314yes—
290#392C2318yes—
291#392C2318yes—
292#392C2314yes—
293#392C2314yes—
294#392C2318yes—
295#392C2318yes—
296#392C2318yes—
297#391C2314yes—
298#391C2312yes—
299#391C2314yes—
300#391C2311yescharacteristic
301#391C2312yes—
302#391C2314yes—
303#391C2312yes—
304#391C2318yes—
305#391C2318yes—
306#390C2314yes—
307#390C2318yes—
308#390C2314yes—
309#390C2314yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2314yes—
314#390C2314yes—
315#390C2314yes—
316#390C2318yes—
317#390C2314yes—
318#390C2314yes—
319#390C2318yes—
320#390C2312yes—
321#390C2318yes—
322#390C2311yescharacteristic
323#389C2312yes—
324#389C2312yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2318yes—
329#389C2318yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
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#388C2318yes—
350#388C2314yes—
351#388C2318yes—
352#388C2314yes—
353#387C2314yes—
354#387C2314yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2314yes—
360#387C2318yes—
361#387C2314yes—
362#387C2314yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2314yes—
373#386C2318yes—
374#386C2312yes—
375#386C2318yes—
376#386C2318yes—
377#385C2312yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2314yes—
384#385C2318yes—
385#385C2318yes—
386#385C2314yes—
387#384C2312yes—
388#382C2312yes—
389#382C2314yes—
390#382C2311yescharacteristic
391#382C2314yes—
392#381C2312yes—
393#381C2314yes—
394#381C2318yes—
395#381C2318yes—
396#380C2314yes—
397#380C2314yes—
398#380C2312yes—
399#380C2318yes—
400#380C2314yes—
401#379C2318yes—
402#379C2314yes—
403#379C2318yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2311yescharacteristic
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2312yes—
424#376C2314yes—
425#376C2312yes—
426C43C2311yescharacteristic
427C25C2414yes—
428C2×#41—28no—
429C2×#41—44no—
430C2×#41—82no—
431C22×Q8C2412yes—
432C22×Q8C2411yescharacteristic
433C22×Q8C2412yes—
434C22×Q8C2412yes—
435C22×Q8C2414yes—
436C22×D4—44no—
437C22×D4—48no—
438C22×D4C2411yescharacteristic
439C22×D4C2414yes—
440C22×D4C2418yes—
441C22×D4C2414yes—
442C22×D4C2414yes—
443C22×D4C2414yes—
444C22×D4C2414yes—
445C22×D4C2418yes—
446C22×D4C2414yes—
447C22×D4C2414yes—
448C22×D4C2418yes—
449C22×D4C2411yescharacteristic
450C23×C4—48no—
451C23×C4—48no—
452C23×C4—84no—
453C23×C4C2412yes—
454C23×C4C2414yes—
455C23×C4C2412yes—
456C23×C4C2418yes—
457C23×C4C2414yes—
458C23×C4C2412yes—
459C23×C4C2412yes—
460C23×C4C2418yes—
461C4⋊Q8—44no—
462C4⋊Q8—42no—
463C4⋊Q8—42no—
464C4⋊Q8—82no—
465#127—44no—
466#127—48no—
467#127—44no—
468#126—48no—
469#125—44no—
470#124—24no—
471#124—48no—
472#124—48no—
473#124—48no—
474#124—48no—
475#124—44no—
476#124—48no—
477#124—416no—
478#124—48no—
479#123—28no—
480#123—416no—
481#123—48no—
482#123—416no—
483#123—48no—
484#123—88no—
485C22⋊Q8—48no—
486C22⋊Q8—416no—
487C22⋊Q8—44no—
488C22⋊Q8—44no—
489C22⋊Q8—48no—
490#121—416no—
491#121—48no—
492#121—48no—
493#121—44no—
494#121—84no—
495#120—216no—
496#120—416no—
497#120—48no—
498#120—416no—
499#120—84no—
500C4×Q8—28no—
501C4×Q8—42no—
502C4×Q8—44no—
503C4×Q8—48no—
504C4×D4—216no—
505C4×D4—24no—
506C4×D4—48no—
507C4×D4—44no—
508C4×D4—42no—
509C4×D4—48no—
510C4×D4—416no—
511C4×D4—416no—
512C4×D4—416no—
513C4×D4—84no—
514#117—44no—
515#117—48no—
516C2×C4⋊C4—28no—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2411yescharacteristic
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2411yescharacteristic
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2411yescharacteristic
548C2×C22⋊C4—48no—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C42—44no—
585C2×C42—82no—
586C2×C42C2414yes—
587C2×C42C2414yes—
588C2×C42C2411yescharacteristic
589C2×C42C2412yes—
590C2×C42C2412yes—
591C2×C42C2414yes—
592C2×C42C2411yescharacteristic
593C2×C42C2412yes—
594C2×C42C2418yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2418yes—
598C2×C42C2414yes—
599C2×C42C2412yes—
600C2×C42C2411yescharacteristic
601#95C2412yes—
602#95C2418yes—
603#95C2414yes—
604#95C2412yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2412yes—
610#95C2414yes—
611#95C2418yes—
612#95C2418yes—
613#95C2414yes—
614#95C2418yes—
615#95C2414yes—
616#95C2418yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2414yes—
626#95C2418yes—
627#95C2414yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632C24—28no—
633C24—44no—
634C24—48no—
635C24—48no—
636C24—44no—
637C24C2518yes—
638C24C2512yes—
639C24C2512yes—
640#41—816no—
641C2×Q8—24no—
642C2×Q8—24no—
643C2×Q8—22no—
644C2×Q8—28no—
645C2×Q8—41no—
646C2×Q8—42no—
647C2×Q8—42no—
648C2×Q8—44no—
649C2×Q8—41no—
650C2×Q8—42no—
651C2×Q8—44no—
652C2×Q8—44no—
653C2×Q8—44no—
654C2×D4—216no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—28no—
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—44no—
663C2×D4—41no—
664C2×D4—48no—
665C2×D4—41no—
666C2×D4—48no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—48no—
670C2×D4—48no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—44no—
676C2×D4—48no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—44no—
681C2×D4—48no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—48no—
685C2×D4—44no—
686C2×D4—432no—
687C2×D4H(5,𝔽2)14yes—
688C22×C4—28no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—28no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—28no—
695C22×C4—216no—
696C22×C4—28no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—44no—
701C22×C4—42no—
702C22×C4—44no—
703C22×C4—48no—
704C22×C4—48no—
705C22×C4—44no—
706C22×C4—48no—
707C22×C4—48no—
708C22×C4—44no—
709C22×C4—48no—
710C22×C4—832no—
711C22×C4C2512yes—
712C22×C4C2514yes—
713C22×C4C2512yes—
714C22×C4C2512yes—
715C22×C4C2518yes—
716C22×C4C2514yes—
717C22×C4C2514yes—
718C22×C4C2514yes—
719C22×C4C2514yes—
720C22×C4C2514yes—
721C22×C4C2514yes—
722C22×C4C2511yescharacteristic
723C22×C4C2512yes—
724C22×C4C2512yes—
725C22×C4C2511yescharacteristic
726C22×C4C2512yes—
727C22×C4C2511yescharacteristic
728C4⋊C4—24no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—24no—
733C4⋊C4—28no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—28no—
737C4⋊C4—41no—
738C4⋊C4—48no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—41no—
742C4⋊C4—48no—
743C4⋊C4—42no—
744C4⋊C4—48no—
745C4⋊C4—44no—
746C4⋊C4—42no—
747C4⋊C4—42no—
748C4⋊C4—48no—
749C4⋊C4—44no—
750C4⋊C4—48no—
751C4⋊C4—42no—
752C4⋊C4—44no—
753C4⋊C4—48no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—42no—
757C4⋊C4—44no—
758C4⋊C4H(5,𝔽2)14yes—
759C22⋊C4—24no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—28no—
763C22⋊C4—216no—
764C22⋊C4—24no—
765C22⋊C4—216no—
766C22⋊C4—28no—
767C22⋊C4—216no—
768C22⋊C4—48no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—48no—
772C22⋊C4—48no—
773C22⋊C4—42no—
774C22⋊C4—48no—
775C22⋊C4—48no—
776C22⋊C4—48no—
777C22⋊C4—48no—
778C22⋊C4—48no—
779C22⋊C4—42no—
780C22⋊C4—48no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—44no—
784C22⋊C4—48no—
785C22⋊C4—48no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C42—28no—
795C42—28no—
796C42—22no—
797C42—24no—
798C42—22no—
799C42—24no—
800C42—28no—
801C42—24no—
802C42—44no—
803C42—41no—
804C42—44no—
805C42—42no—
806C42—48no—
807C42—48no—
808C42—44no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—22no—
813C23—22no—
814C23—28no—
815C23—28no—
816C23—22no—
817C23—28no—
818C23—24no—
819C23—28no—
820C23—28no—
821C23—24no—
822C23—28no—
823C23—28no—
824C23—22no—
825C23—416no—
826C23—88no—
827C23—816no—
828C23—88no—
829C23—816no—
830C23C2×H(5,𝔽2)14yes—
831C23C2611yescharacteristic
832Q8—48no—
833Q8—82no—
834Q8—84no—
835Q8—84no—
836Q8—164no—
837D4—44no—
838D4—416no—
839D4—44no—
840D4—416no—
841D4—88no—
842D4—816no—
843D4—88no—
844D4—816no—
845D4—88no—
846D4—164no—
847D4—164no—
848D4—168no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—24no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—28no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—28no—
875C2×C4—28no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—48no—
891C2×C4—416no—
892C2×C4—48no—
893C2×C4—48no—
894C2×C4—88no—
895C2×C4—816no—
896C2×C4—84no—
897C2×C4—816no—
898C2×C4C2×H(5,𝔽2)14yes—
899C2×C4C2×H(5,𝔽2)12yes—
900C2×C4C2×H(5,𝔽2)12yes—
901C2×C4#58514yes—
902C2×C4#58514yes—
903C22—28no—
904C22—24no—
905C22—42no—
906C22—42no—
907C22—44no—
908C22—44no—
909C22—48no—
910C22—48no—
911C22—48no—
912C22—42no—
913C22—42no—
914C22—48no—
915C22—48no—
916C22—42no—
917C22—44no—
918C22—48no—
919C22—48no—
920C22—832no—
921C22C22×H(5,𝔽2)11yescharacteristic
922C22C22×H(5,𝔽2)11yescharacteristic
923C22C2×#58512yes—
924C22C2×#58512yes—
925C22H(7,𝔽2)11yescharacteristic
926C4—24no—
927C4—22no—
928C4—24no—
929C4—44no—
930C4—48no—
931C4—42no—
932C4—41no—
933C4—44no—
934C4—42no—
935C4—44no—
936C4—44no—
937C4—42no—
938C4—42no—
939C4—44no—
940C4—44no—
941C4—44no—
942C4#352914yes—
943C2—44no—
944C2—82no—
945C2—88no—
946C2C2×#352911yescharacteristic
947C2#6289211yescharacteristic
948C2#6296512yes—
949C2#6302112yes—
950C2#6302211yescharacteristic
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. #53000C2semidirect
2. #52989C2semidirect
3. #52693C2semidirect
4. #52589C2semidirect
5. #52304C2semidirect
6. #52163C2semidirect
7. #46287C2semidirect
8. #46013C2semidirect
9. #45996C2semidirect
10. #45800C2semidirect
11. #45718C2semidirect
12. #45707C2semidirect
13. #45697C2semidirect
14. #45442C2semidirect
15. #36463C2semidirect
16. #36441C2semidirect
17. #36406C2semidirect
18. #36102C2semidirect
19. #35956C2semidirect
20. #35880C2semidirect
23. C2×#556C22semidirect
26. C22×C4×D4C22semidirect
27. #2862C22semidirect
29. #2857C22semidirect
30. #2854C22semidirect
31. #2854C22semidirect
33. #2849C22semidirect
34. #2849C22semidirect
35. #2832C22semidirect
36. #2832C22semidirect
37. #2830C22semidirect
38. #2828C22semidirect
39. #2827C22semidirect
41. #2825C22semidirect
42. #2820C22semidirect
44. #2813C22semidirect
45. #2812C22semidirect
46. #2808C22semidirect
47. #2805C22semidirect
48. #2795C22semidirect
49. #2789C22semidirect
50. #2765C22semidirect
51. #2761C22semidirect
53. #2751C22semidirect
54. #2741C22semidirect
55. #2735C22semidirect
57. #2732C22semidirect
58. #2728C22semidirect
60. #2724C22semidirect
62. #2710C22semidirect
63. #2708C22semidirect
64. #2703C22semidirect
65. #2700C22semidirect
67. #2696C22semidirect
68. #2690C22semidirect
69. #2686C22semidirect
72. #2678C22semidirect
73. #2678C22semidirect
74. #2674C22semidirect
76. #2668C22semidirect
77. #2662C22semidirect
79. #2650C22semidirect
80. #2644C22semidirect
81. #2610C22semidirect
82. #2603C22semidirect
83. #2602C22semidirect
84. #2600C22semidirect
85. #2596C22semidirect
86. #2592C22semidirect
87. #2587C22semidirect
88. #2580C22semidirect
89. #2563C22semidirect
90. #2557C22semidirect
91. #2554C22semidirect
92. #2553C22semidirect
94. #2548C22semidirect
95. #2546C22semidirect
96. #2545C22semidirect
100. #2527C22semidirect
101. #2526C22semidirect
102. #2513C22semidirect
103. #2509C22semidirect
104. #2499C22semidirect
106. #2490C22semidirect
107. #2474C22semidirect
108. #2472C22semidirect
109. #2463C22semidirect
110. #2461C22semidirect
111. #2459C22semidirect
112. #2459C22semidirect
114. #2455C22semidirect
115. #2452C22semidirect
116. #2451C22semidirect
117. #2448C22semidirect
118. #2447C22semidirect
119. #2447C22semidirect
121. #2445C22semidirect
122. #2435C22semidirect
124. #2433C22semidirect
127. #2427C22semidirect
129. #2421C22semidirect
130. #2420C22semidirect
131. #2418C22semidirect
132. #2411C22semidirect
135. #2401C22semidirect
136. #2399C22semidirect
137. #2395C22semidirect
138. #2392C22semidirect
139. #2379C22semidirect
140. #2376C22semidirect
142. #2369C22semidirect
143. #2367C22semidirect
145. #2366C22semidirect
147. #2360C22semidirect
148. #2357C22semidirect
149. #2344C22semidirect
150. C4×#125C22semidirect
152. C4×C22⋊Q8C22semidirect
154. C4×#121C22semidirect
155. C4×#120C22semidirect
157. #2276C22semidirect
158. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#530002
#529892
#526932
#525892
#523042
#521632
#462872
#460132
#459962
#458002
#457182
#457072
#456972
#454422
#364632
#364412
#364062
#361022
#359562
#358802