Finite Group Databasebeta

← #8701619

Subgroups — #8701619

Order 512.

5039 conjugacy classes of subgroups.

The subgroup lattice has 953 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59908C212yesmaximal, complemented
2#59885C212yesmaximal, complemented
3#59487C214yesmaximal, complemented
4#57577C218yesmaximal, complemented
5#55612C214yesmaximal, complemented
6#52306C211yesmaximal, characteristic, complemented
7#51749C214yesmaximal, complemented
8#49190C218yesmaximal, complemented
9#46013C212yesmaximal, complemented
10#45996C211yesmaximal, characteristic, complemented
11#45214C212yesmaximal, complemented
12#44876C214yesmaximal, complemented
13#42967C212yesmaximal, complemented
14#42735C214yesmaximal, complemented
15#40049C214yesmaximal, complemented
16#39363C212yesmaximal, complemented
17#37190C212yesmaximal, complemented
18#37154C214yesmaximal, complemented
19#36463C212yesmaximal, complemented
20#36303C211yesmaximal, characteristic, complemented
21C2×H(3,𝔽4)C2212yes—
22C2×#550C2212yes—
23C2×D4×Q8C2211yescharacteristic, complemented
24C2×#547C2211yescharacteristic
25C2×#536C2214yescomplemented
26C2×#535C2212yescomplemented
27#2862C2211yescharacteristic, complemented
28#2858C2212yes—
29#2858C2212yes—
30#2854C2214yescomplemented
31#2850C2212yes—
32#2831C2218yescomplemented
33#2820C2214yescomplemented
34#2819C2212yes—
35#2813C2214yes—
36#2809C2211yescharacteristic, complemented
37#2808C2214yescomplemented
38#2795C2214yescomplemented
39#2775C2214yescomplemented
40#2769C2212yescomplemented
41#2764C2218yescomplemented
42#2761C2218yescomplemented
43#2757C2218yescomplemented
44#2756C2218yescomplemented
45#2749C2218yes—
46#2749C2218yescomplemented
47#2737C2218yescomplemented
48#2735C2214yescomplemented
49#2734C2211yescharacteristic, complemented
50#2733C2212yes—
51#2732C2214yescomplemented
52#2731C2212yes—
53#2731C2214yescomplemented
54#2730C2218yescomplemented
55#2729C2218yescomplemented
56#2728C2214yescomplemented
57#2727C2212yes—
58#2721C2214yescomplemented
59#2700C2218yescomplemented
60#2700C2218yescomplemented
61#2699C2218yescomplemented
62#2697C2218yescomplemented
63#2688C2218yescomplemented
64#2685C2218yescomplemented
65#2684C2218yescomplemented
66#2681C2218yescomplemented
67#2681C2218yescomplemented
68#2679C2212yes—
69#2678C2218yes—
70#2678C2218yescomplemented
71#2670C2218yes—
72#2668C2218yescomplemented
73#2661C2214yes—
74#2651C2218yescomplemented
75#2648C2218yescomplemented
76#2640C2218yescomplemented
77#2625C2212yescomplemented
78#2620C2214yescomplemented
79#2618C2214yescomplemented
80#2610C2218yescomplemented
81#2592C2214yescomplemented
82#2591C2214yescomplemented
83#2572C2214yescomplemented
84#2572C2218yescomplemented
85#2572C2214yescomplemented
86#2568C2211yescharacteristic, complemented
87#2563C2212yescomplemented
88#2557C2218yescomplemented
89#2557C2218yescomplemented
90#2548C2212yes—
91#2547C2211yescharacteristic
92#2546C2212yescomplemented
93#2545C2214yescomplemented
94#2544C2214yes—
95#2544C2214yes—
96#2543C2218yescomplemented
97#2541C2212yes—
98#2532C2218yescomplemented
99#2526C2218yescomplemented
100#2518C2218yescomplemented
101#2513C2214yescomplemented
102#2503C2212yescomplemented
103#2498C2218yescomplemented
104#2495C2214yescomplemented
105#2492C2214yescomplemented
106#2491C2214yes—
107#2490C2214yescomplemented
108#2488C2218yescomplemented
109#2483C2214yescomplemented
110#2472C2218yes—
111#2472C2218yescomplemented
112#2467C2218yescomplemented
113#2459C2218yescomplemented
114#2459C2218yescomplemented
115#2452C2214yescomplemented
116#2452C2214yescomplemented
117#2451C2214yescomplemented
118#2448C2214yescomplemented
119#2447C2214yescomplemented
120#2445C2214yescomplemented
121#2445C2214yescomplemented
122#2436C2212yes—
123#2436C2214yescomplemented
124#2435C2212yescomplemented
125#2433C2214yes—
126#2432C2214yescomplemented
127#2431C2214yes—
128#2430C2218yescomplemented
129#2426C2214yes—
130#2424C2218yescomplemented
131#2420C2214yes—
132#2420C2214yescomplemented
133#2408C2212yes—
134#2404C2218yescomplemented
135#2396C2214yescomplemented
136#2395C2212yes—
137#2379C2214yescomplemented
138#2372C2214yescomplemented
139#2369C2212yescomplemented
140#2366C2212yes—
141#2366C2214yescomplemented
142#2357C2214yescomplemented
143#2356C2214yescomplemented
144#2353C2218yescomplemented
145#2341C2212yescomplemented
146#2339C2214yescomplemented
147D4×C22⋊C4C2214yescomplemented
148#2324C2214yes—
149#2321C2218yescomplemented
150C4×C4⋊Q8C2212yescomplemented
151C4×#125C2212yescomplemented
152C4×#126C2214yescomplemented
153C4×#124C2211yescharacteristic
154C4×#124C2214yescomplemented
155C4×#121C2214yescomplemented
156C2×#391C2212yescomplemented
157#2293C2212yescomplemented
158C42×D4C2211yescharacteristic, complemented
159C22×#41C2312yes—
160C22×#41C2314yes—
161C23×Q8C2312yes—
162C23×D4C2312yes—
163H(3,𝔽4)—48no—
164#550—48no—
165D4×Q8—44no—
166#547—44no—
167#536—416no—
168#535—48no—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2312yes—
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2311yescharacteristic
174C2×C4⋊Q8C2314yes—
175C2×#127C2314yes—
176C2×#127C2312yes—
177C2×#127C2312yes—
178C2×#126C2314yes—
179C2×#125C2312yes—
180C2×#124C2314yes—
181C2×#124C2311yescharacteristic
182C2×#124C2314yes—
183C2×#124C2314yes—
184C2×#124C2314yes—
185C2×#124C2314yes—
186C2×#124C2318yes—
187C2×#124C2314yes—
188C2×#124C2312yes—
189C2×#124C2314yes—
190C2×#123C2318yes—
191C2×#123C2314yes—
192C2×#123C2318yes—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2312yes—
196C2×C22⋊Q8C2318yes—
197C2×C22⋊Q8C2318yes—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2312yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2318yes—
205C2×#121C2314yes—
206C2×#120C2318yes—
207C2×#120C2318yes—
208C2×#120C2318yes—
209C2×#120C2314yes—
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2314yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2312yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2314yes—
221C2×#117C2312yes—
222C2×#117C2314yes—
223C22×C4⋊C4C2312yes—
224C22×C22⋊C4C2318yes—
225C22×C42C2312yes—
226#400C2314yes—
227#400C2312yes—
228#400C2318yes—
229#400C2314yes—
230#400C2318yes—
231#400C2314yes—
232#399C2318yes—
233#399C2312yes—
234#399C2314yes—
235#398C2314yes—
236#398C2318yes—
237#398C2312yes—
238#398C2314yes—
239#398C2318yes—
240#398C2314yes—
241#397C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2312yes—
250#397C2314yes—
251#397C2318yes—
252#397C2314yes—
253#396C2318yes—
254#396C2318yes—
255#396C2318yes—
256#396C2318yes—
257#396C2318yes—
258#396C2314yes—
259#396C2314yes—
260#395C2318yes—
261#395C2314yes—
262#394C2314yes—
263#394C2314yes—
264#394C2318yes—
265#394C2314yes—
266#394C2318yes—
267#394C2314yes—
268#394C2318yes—
269#394C2314yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2314yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#393C2318yes—
280#393C2318yes—
281#393C2318yes—
282#393C2318yes—
283#393C2314yes—
284#393C2318yes—
285#393C2318yes—
286#392C2318yes—
287#392C2318yes—
288#392C2318yes—
289#392C2318yes—
290#392C2314yes—
291#392C2318yes—
292#391C2312yes—
293#391C2312yes—
294#391C2314yes—
295#391C2312yes—
296#391C2312yes—
297#391C2318yes—
298#391C2318yes—
299#391C2314yes—
300#391C2312yes—
301#391C2314yes—
302#391C2312yes—
303#391C2314yes—
304#391C2318yes—
305#391C2311yescharacteristic
306#390C2314yes—
307#390C2318yes—
308#390C2318yes—
309#390C2314yes—
310#390C2318yes—
311#390C2314yes—
312#390C2314yes—
313#390C2311yescharacteristic
314#390C2318yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2314yes—
321#390C2318yes—
322#390C2314yes—
323#389C2312yes—
324#389C2312yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#388C2314yes—
332#388C2314yes—
333#388C2314yes—
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#388C2318yes—
353#387C2314yes—
354#387C2314yes—
355#387C2314yes—
356#387C2314yes—
357#387C2314yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#384C2312yes—
383#383C2314yes—
384#383C2318yes—
385#383C2318yes—
386#382C2312yes—
387#382C2314yes—
388#382C2311yescharacteristic
389#382C2314yes—
390#382C2312yes—
391#381C2318yes—
392#381C2318yes—
393#381C2318yes—
394#381C2318yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2312yes—
400#379C2318yes—
401#379C2318yes—
402#379C2314yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C22⋊C4C2312yes—
414C4×C22⋊C4C2314yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2312yes—
423#376C2318yes—
424C2×#95C2318yes—
425C43C2312yes—
426C43C2311yescharacteristic
427C25C2414yes—
428C2×#41—28no—
429C2×#41—48no—
430C2×#41—48no—
431C2×#41—48no—
432C2×#41—84no—
433C22×Q8—28no—
434C22×Q8—44no—
435C22×Q8—82no—
436C22×Q8C2412yes—
437C22×Q8C2412yes—
438C22×Q8C2412yes—
439C22×Q8C2414yes—
440C22×Q8C2414yes—
441C22×Q8C2411yescharacteristic
442C22×D4—44no—
443C22×D4—48no—
444C22×D4C2414yes—
445C22×D4C2411yescharacteristic
446C22×D4C2411yescharacteristic
447C22×D4C2414yes—
448C22×D4C2418yes—
449C22×D4C2414yes—
450C22×D4C2414yes—
451C22×D4C2418yes—
452C22×D4C2418yes—
453C22×D4C2414yes—
454C22×D4C2414yes—
455C22×D4C2414yes—
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2414yes—
459C23×C4C2414yes—
460C23×C4C2414yes—
461C23×C4C2418yes—
462C23×C4C2418yes—
463C4⋊Q8—28no—
464C4⋊Q8—44no—
465C4⋊Q8—42no—
466C4⋊Q8—44no—
467C4⋊Q8—48no—
468C4⋊Q8—42no—
469#127—216no—
470#127—44no—
471#127—44no—
472#126—48no—
473#125—44no—
474#124—216no—
475#124—24no—
476#124—48no—
477#124—416no—
478#124—48no—
479#124—48no—
480#124—48no—
481#124—48no—
482#124—82no—
483#124—84no—
484#123—416no—
485#123—416no—
486#123—48no—
487C22⋊Q8—44no—
488C22⋊Q8—48no—
489C22⋊Q8—416no—
490C22⋊Q8—416no—
491C22⋊Q8—44no—
492#121—416no—
493#121—48no—
494#121—48no—
495#121—48no—
496#121—48no—
497#121—44no—
498#121—48no—
499#121—84no—
500#120—416no—
501#120—416no—
502#120—48no—
503#120—416no—
504C4×Q8—42no—
505C4×Q8—44no—
506C4×Q8—48no—
507C4×D4—24no—
508C4×D4—28no—
509C4×D4—48no—
510C4×D4—44no—
511C4×D4—48no—
512C4×D4—42no—
513C4×D4—416no—
514C4×D4—84no—
515#117—44no—
516#117—48no—
517C2×C4⋊C4—44no—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2411yescharacteristic
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2411yescharacteristic
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2411yescharacteristic
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C22⋊C4—88no—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C42—82no—
585C2×C42C2412yes—
586C2×C42C2414yes—
587C2×C42C2414yes—
588C2×C42C2411yescharacteristic
589C2×C42C2412yes—
590C2×C42C2414yes—
591C2×C42C2412yes—
592C2×C42C2411yescharacteristic
593C2×C42C2412yes—
594C2×C42C2418yes—
595C2×C42C2414yes—
596C2×C42C2418yes—
597C2×C42C2412yes—
598C2×C42C2412yes—
599C2×C42C2414yes—
600C2×C42C2411yescharacteristic
601#95C2414yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2414yes—
606#95C2418yes—
607#95C2418yes—
608#95C2412yes—
609#95C2412yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2412yes—
614#95C2418yes—
615#95C2414yes—
616#95C2418yes—
617#95C2418yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2418yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632C24—44no—
633C24—48no—
634C24—44no—
635C24—48no—
636C24—44no—
637C24C2512yes—
638C24C2518yes—
639C24C2512yes—
640#41—816no—
641#41—832no—
642C2×Q8—24no—
643C2×Q8—24no—
644C2×Q8—24no—
645C2×Q8—28no—
646C2×Q8—28no—
647C2×Q8—41no—
648C2×Q8—42no—
649C2×Q8—41no—
650C2×Q8—42no—
651C2×Q8—42no—
652C2×Q8—44no—
653C2×Q8—42no—
654C2×Q8—44no—
655C2×Q8—44no—
656C2×Q8—44no—
657C2×Q8—44no—
658C2×Q8—816no—
659C2×Q8H(5,𝔽2)14yes—
660C2×D4—28no—
661C2×D4—216no—
662C2×D4—216no—
663C2×D4—28no—
664C2×D4—22no—
665C2×D4—28no—
666C2×D4—24no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—41no—
671C2×D4—48no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—44no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C2×D4—48no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—816no—
692C2×D4H(5,𝔽2)14yes—
693C22×C4—24no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—24no—
697C22×C4—28no—
698C22×C4—24no—
699C22×C4—28no—
700C22×C4—28no—
701C22×C4—42no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—44no—
707C22×C4—48no—
708C22×C4—48no—
709C22×C4—48no—
710C22×C4—48no—
711C22×C4—48no—
712C22×C4C2512yes—
713C22×C4C2514yes—
714C22×C4C2512yes—
715C22×C4C2514yes—
716C22×C4C2514yes—
717C22×C4C2518yes—
718C22×C4C2512yes—
719C22×C4C2514yes—
720C22×C4C2514yes—
721C22×C4C2514yes—
722C22×C4C2511yescharacteristic
723C22×C4C2514yes—
724C22×C4C2512yes—
725C22×C4C2512yes—
726C22×C4C2511yescharacteristic
727C22×C4C2512yes—
728C22×C4C2511yescharacteristic
729C4⋊C4—24no—
730C4⋊C4—22no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—24no—
734C4⋊C4—28no—
735C4⋊C4—28no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—41no—
739C4⋊C4—42no—
740C4⋊C4—44no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—48no—
744C4⋊C4—42no—
745C4⋊C4—48no—
746C4⋊C4—42no—
747C4⋊C4—44no—
748C4⋊C4—41no—
749C4⋊C4—42no—
750C4⋊C4—42no—
751C4⋊C4—42no—
752C4⋊C4—44no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—42no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C22⋊C4—28no—
761C22⋊C4—24no—
762C22⋊C4—28no—
763C22⋊C4—216no—
764C22⋊C4—216no—
765C22⋊C4—216no—
766C22⋊C4—28no—
767C22⋊C4—44no—
768C22⋊C4—48no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4—44no—
772C22⋊C4—48no—
773C22⋊C4—48no—
774C22⋊C4—44no—
775C22⋊C4—48no—
776C22⋊C4—48no—
777C22⋊C4—42no—
778C22⋊C4—48no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—44no—
784C22⋊C4—48no—
785C22⋊C4—48no—
786C22⋊C4—44no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C42—24no—
795C42—28no—
796C42—28no—
797C42—22no—
798C42—24no—
799C42—22no—
800C42—28no—
801C42—24no—
802C42—24no—
803C42—41no—
804C42—44no—
805C42—42no—
806C42—48no—
807C42—48no—
808C42—42no—
809C42—44no—
810C23—22no—
811C23—24no—
812C23—24no—
813C23—22no—
814C23—28no—
815C23—22no—
816C23—22no—
817C23—28no—
818C23—24no—
819C23—28no—
820C23—28no—
821C23—28no—
822C23—28no—
823C23—24no—
824C23—22no—
825C23—28no—
826C23—88no—
827C23—816no—
828C23—164no—
829C23—168no—
830C23—164no—
831C23C2×H(5,𝔽2)14yes—
832C23C2611yescharacteristic
833Q8—44no—
834Q8—48no—
835Q8—48no—
836Q8—88no—
837Q8—84no—
838Q8—164no—
839D4—28no—
840D4—416no—
841D4—82no—
842D4—88no—
843D4—88no—
844D4—816no—
845D4—88no—
846D4—816no—
847D4—88no—
848D4—164no—
849D4—164no—
850D4—168no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—28no—
859C2×C4—21no—
860C2×C4—22no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—28no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—28no—
883C2×C4—28no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—22no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—48no—
893C2×C4—416no—
894C2×C4—48no—
895C2×C4—88no—
896C2×C4—88no—
897C2×C4—816no—
898C2×C4—168no—
899C2×C4C2×H(5,𝔽2)14yes—
900C2×C4C2×H(5,𝔽2)12yes—
901C2×C4C2×H(5,𝔽2)12yes—
902C2×C4#58514yes—
903C2×C4#58514yes—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—44no—
908C22—44no—
909C22—42no—
910C22—48no—
911C22—48no—
912C22—42no—
913C22—44no—
914C22—48no—
915C22—48no—
916C22—48no—
917C22—42no—
918C22—48no—
919C22—48no—
920C22—44no—
921C22—1616no—
922C22C22×H(5,𝔽2)11yescharacteristic
923C22C22×H(5,𝔽2)11yescharacteristic
924C22C2×#58512yes—
925C22C2×#58512yes—
926C22H(7,𝔽2)11yescharacteristic
927C4—24no—
928C4—22no—
929C4—24no—
930C4—42no—
931C4—44no—
932C4—41no—
933C4—44no—
934C4—42no—
935C4—44no—
936C4—42no—
937C4—48no—
938C4—44no—
939C4—42no—
940C4—44no—
941C4—44no—
942C4—44no—
943C4#354514yes—
944C2—44no—
945C2—88no—
946C2—82no—
947C2C2×#354511yescharacteristic
948C2#6289211yescharacteristic
949C2#6296512yes—
950C2#6302411yescharacteristic
951C2#6303512yes—
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. #59908C2semidirect
2. #59885C2semidirect
3. #59487C2semidirect
4. #57577C2semidirect
5. #55612C2semidirect
6. #52306C2semidirect
7. #51749C2semidirect
8. #49190C2semidirect
9. #46013C2semidirect
10. #45996C2semidirect
11. #45214C2semidirect
12. #44876C2semidirect
13. #42967C2semidirect
14. #42735C2semidirect
15. #40049C2semidirect
16. #39363C2semidirect
17. #37190C2semidirect
18. #37154C2semidirect
19. #36463C2semidirect
20. #36303C2semidirect
23. C2×D4×Q8C22semidirect
25. C2×#536C22semidirect
26. C2×#535C22semidirect
27. #2862C22semidirect
30. #2854C22semidirect
32. #2831C22semidirect
33. #2820C22semidirect
36. #2809C22semidirect
37. #2808C22semidirect
38. #2795C22semidirect
39. #2775C22semidirect
40. #2769C22semidirect
41. #2764C22semidirect
42. #2761C22semidirect
43. #2757C22semidirect
44. #2756C22semidirect
46. #2749C22semidirect
47. #2737C22semidirect
48. #2735C22semidirect
49. #2734C22semidirect
51. #2732C22semidirect
53. #2731C22semidirect
54. #2730C22semidirect
55. #2729C22semidirect
56. #2728C22semidirect
58. #2721C22semidirect
59. #2700C22semidirect
60. #2700C22semidirect
61. #2699C22semidirect
62. #2697C22semidirect
63. #2688C22semidirect
64. #2685C22semidirect
65. #2684C22semidirect
66. #2681C22semidirect
67. #2681C22semidirect
70. #2678C22semidirect
72. #2668C22semidirect
74. #2651C22semidirect
75. #2648C22semidirect
76. #2640C22semidirect
77. #2625C22semidirect
78. #2620C22semidirect
79. #2618C22semidirect
80. #2610C22semidirect
81. #2592C22semidirect
82. #2591C22semidirect
83. #2572C22semidirect
84. #2572C22semidirect
85. #2572C22semidirect
86. #2568C22semidirect
87. #2563C22semidirect
88. #2557C22semidirect
89. #2557C22semidirect
92. #2546C22semidirect
93. #2545C22semidirect
96. #2543C22semidirect
98. #2532C22semidirect
99. #2526C22semidirect
100. #2518C22semidirect
101. #2513C22semidirect
102. #2503C22semidirect
103. #2498C22semidirect
104. #2495C22semidirect
105. #2492C22semidirect
107. #2490C22semidirect
108. #2488C22semidirect
109. #2483C22semidirect
111. #2472C22semidirect
112. #2467C22semidirect
113. #2459C22semidirect
114. #2459C22semidirect
115. #2452C22semidirect
116. #2452C22semidirect
117. #2451C22semidirect
118. #2448C22semidirect
119. #2447C22semidirect
120. #2445C22semidirect
121. #2445C22semidirect
123. #2436C22semidirect
124. #2435C22semidirect
126. #2432C22semidirect
128. #2430C22semidirect
130. #2424C22semidirect
132. #2420C22semidirect
134. #2404C22semidirect
135. #2396C22semidirect
137. #2379C22semidirect
138. #2372C22semidirect
139. #2369C22semidirect
141. #2366C22semidirect
142. #2357C22semidirect
143. #2356C22semidirect
144. #2353C22semidirect
145. #2341C22semidirect
146. #2339C22semidirect
147. D4×C22⋊C4C22semidirect
149. #2321C22semidirect
150. C4×C4⋊Q8C22semidirect
151. C4×#125C22semidirect
152. C4×#126C22semidirect
154. C4×#124C22semidirect
155. C4×#121C22semidirect
156. C2×#391C22semidirect
157. #2293C22semidirect
158. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#599082
#598852
#594872
#575772
#556122
#523062
#517492
#491902
#460132
#459962
#452142
#448762
#429672
#427352
#400492
#393632
#371902
#371542
#364632
#363032