Finite Group Databasebeta

← #8110574

Subgroups — #8110574

Order 512.

5364 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59056C211yesmaximal, characteristic, complemented
2#59041C211yesmaximal, characteristic, complemented
3#59040C212yesmaximal, complemented
4#53317C218yesmaximal, complemented
5#45741C214yesmaximal, complemented
6#45642C214yesmaximal, complemented
7#45593C214yesmaximal, complemented
8#39554C214yesmaximal, complemented
9#39515C212yesmaximal, complemented
10#39491C212yesmaximal, complemented
11#39419C214yesmaximal, complemented
12#39387C212yesmaximal, complemented
13#39362C212yesmaximal, complemented
14#39218C214yesmaximal, complemented
15#39024C214yesmaximal, complemented
16#37278C214yesmaximal, complemented
17#37277C214yesmaximal, complemented
18#36812C214yesmaximal, complemented
19#36639C211yesmaximal, characteristic, complemented
20#36631C212yesmaximal, complemented
21C2×#555C2211yescharacteristic, complemented
22C2×#547C2212yes—
23C2×D42C2211yescharacteristic
24C2×#542C2214yescomplemented
25C2×#535C2214yes—
26C2×#533C2211yescharacteristic, complemented
27C2×#532C2211yescharacteristic
28C2×#529C2214yescomplemented
29#2862C2212yescomplemented
30#2861C2214yescomplemented
31#2861C2214yescomplemented
32#2860C2212yes—
33#2860C2212yescomplemented
34#2860C2214yescomplemented
35#2859C2212yescomplemented
36#2858C2212yes—
37#2858C2212yes—
38#2857C2212yescomplemented
39#2856C2212yes—
40#2854C2212yes—
41#2854C2212yescomplemented
42#2854C2214yescomplemented
43#2850C2214yescomplemented
44#2850C2214yescomplemented
45#2850C2214yescomplemented
46#2825C2218yescomplemented
47#2803C2218yescomplemented
48#2801C2218yescomplemented
49#2798C2218yescomplemented
50#2778C2218yescomplemented
51#2759C2218yescomplemented
52#2757C2218yescomplemented
53#2756C2218yescomplemented
54#2735C2218yescomplemented
55#2733C2214yescomplemented
56#2730C2218yescomplemented
57#2725C2218yescomplemented
58#2715C2218yescomplemented
59#2714C2218yescomplemented
60#2711C2218yescomplemented
61#2710C2218yescomplemented
62#2710C2218yescomplemented
63#2705C2218yescomplemented
64#2705C2218yescomplemented
65#2703C2218yescomplemented
66#2702C2218yescomplemented
67#2694C2218yescomplemented
68#2693C2218yescomplemented
69#2685C2218yescomplemented
70#2685C2218yescomplemented
71#2684C2214yes—
72#2683C2214yescomplemented
73#2678C2218yes—
74#2678C2218yes—
75#2678C2218yescomplemented
76#2676C2218yescomplemented
77#2673C2218yescomplemented
78#2672C2218yescomplemented
79#2670C2218yescomplemented
80#2669C2214yescomplemented
81#2648C2218yescomplemented
82#2628C2214yescomplemented
83#2620C2214yes—
84#2620C2214yescomplemented
85#2619C2214yes—
86#2608C2214yescomplemented
87#2592C2214yes—
88#2581C2214yescomplemented
89#2576C2218yescomplemented
90#2563C2212yes—
91#2559C2218yescomplemented
92#2555C2218yescomplemented
93#2548C2214yescomplemented
94#2547C2212yes—
95#2542C2212yescomplemented
96#2541C2212yes—
97#2541C2214yescomplemented
98#2540C2214yes—
99#2539C2214yescomplemented
100#2538C2214yescomplemented
101#2538C2214yescomplemented
102#2535C2214yes—
103#2518C2218yescomplemented
104#2514C2214yescomplemented
105#2512C2214yescomplemented
106#2504C2214yescomplemented
107#2500C2214yes—
108#2495C2214yescomplemented
109#2494C2214yescomplemented
110#2472C2218yescomplemented
111#2471C2218yescomplemented
112#2448C2214yes—
113#2445C2214yescomplemented
114#2435C2214yes—
115#2431C2214yes—
116#2431C2214yescomplemented
117#2428C2214yescomplemented
118#2427C2214yescomplemented
119#2426C2214yes—
120#2426C2214yescomplemented
121#2423C2214yescomplemented
122#2420C2214yes—
123#2417C2214yescomplemented
124#2416C2214yes—
125#2416C2214yes—
126#2415C2214yescomplemented
127#2415C2214yescomplemented
128#2414C2214yescomplemented
129#2408C2214yes—
130#2408C2214yes—
131#2408C2214yes—
132#2407C2214yescomplemented
133#2407C2214yescomplemented
134#2407C2214yescomplemented
135#2404C2214yes—
136#2380C2214yescomplemented
137#2375C2214yescomplemented
138#2369C2211yescharacteristic, complemented
139#2366C2211yescharacteristic
140#2365C2212yescomplemented
141#2363C2214yescomplemented
142#2360C2214yescomplemented
143#2341C2214yescomplemented
144D4×C22⋊C4C2214yes—
145#2333C2214yescomplemented
146#2317C2214yescomplemented
147#2314C2214yescomplemented
148#2312C2214yescomplemented
149C4×C4⋊Q8C2212yescomplemented
150C4×#127C2212yes—
151C4×#124C2214yescomplemented
152C4×#124C2214yescomplemented
153C4×#124C2214yescomplemented
154C4×#121C2212yes—
155C4×#121C2214yescomplemented
156C4×#121C2212yescomplemented
157#2297C2212yescomplemented
158#2297C2212yescomplemented
159#2293C2212yes—
160#2293C2212yescomplemented
161#2293C2214yescomplemented
162C2×C43C2211yescharacteristic, complemented
163C22×#41C2314yes—
164C22×#41C2312yes—
165C23×D4C2314yes—
166#555—44no—
167#547—48no—
168D42—44no—
169#542—416no—
170#535—416no—
171#533—44no—
172#532—44no—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2311yescharacteristic
175C2×C4⋊Q8C2312yes—
176C2×#127C2312yes—
177C2×#127C2311yescharacteristic
178C2×#127C2314yes—
179C2×#127C2314yes—
180#529—416no—
181C2×#126C2314yes—
182C2×#126C2314yes—
183C2×#126C2318yes—
184C2×#125C2314yes—
185C2×#125C2312yes—
186C2×#124C2314yes—
187C2×#124C2314yes—
188C2×#124C2314yes—
189C2×#124C2314yes—
190C2×#124C2314yes—
191C2×#124C2312yes—
192C2×#124C2318yes—
193C2×#124C2314yes—
194C2×#123C2314yes—
195C2×#123C2314yes—
196C2×#123C2318yes—
197C2×#123C2318yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2318yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2312yes—
208C2×#121C2312yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2318yes—
216C2×#121C2318yes—
217C2×#120C2314yes—
218C2×#120C2314yes—
219C2×#120C2318yes—
220C2×#120C2318yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×#117C2314yes—
233C2×#117C2314yes—
234C2×#117C2314yes—
235C2×#117C2312yes—
236C22×C4⋊C4C2314yes—
237C22×C22⋊C4C2314yes—
238C22×C42C2312yes—
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2312yes—
242C22×C42C2311yescharacteristic
243#401C2318yes—
244#400C2318yes—
245#400C2318yes—
246#399C2318yes—
247#399C2318yes—
248#399C2318yes—
249#398C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#395C2318yes—
265#394C2318yes—
266#394C2318yes—
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#393C2318yes—
281#393C2318yes—
282#392C2318yes—
283#392C2318yes—
284#392C2318yes—
285#392C2318yes—
286#392C2318yes—
287#392C2318yes—
288#392C2318yes—
289#392C2318yes—
290#392C2318yes—
291#391C2314yes—
292#391C2314yes—
293#391C2314yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#391C2314yes—
298#391C2314yes—
299#391C2314yes—
300#390C2314yes—
301#390C2312yes—
302#390C2314yes—
303#390C2312yes—
304#390C2314yes—
305#390C2318yes—
306#390C2312yes—
307#390C2312yes—
308#390C2314yes—
309#390C2314yes—
310#390C2312yes—
311#390C2314yes—
312#390C2318yes—
313#390C2318yes—
314#390C2312yes—
315#390C2312yes—
316#390C2314yes—
317#390C2312yes—
318#390C2314yes—
319#390C2314yes—
320#390C2314yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2318yes—
325#390C2314yes—
326#390C2314yes—
327#390C2318yes—
328#389C2312yes—
329#389C2312yes—
330#389C2314yes—
331#389C2318yes—
332#389C2318yes—
333#389C2312yes—
334#389C2314yes—
335#389C2312yes—
336#389C2314yes—
337#389C2312yes—
338#389C2312yes—
339#389C2314yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2318yes—
344#389C2314yes—
345#388C2314yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2314yes—
352#388C2318yes—
353#388C2314yes—
354#388C2314yes—
355#388C2314yes—
356#388C2314yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#386C2314yes—
380#386C2314yes—
381#386C2314yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2314yes—
389#386C2318yes—
390#386C2314yes—
391#386C2314yes—
392#386C2314yes—
393#386C2314yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#384C2312yes—
401#384C2312yes—
402#384C2314yes—
403#383C2318yes—
404#382C2314yes—
405#382C2314yes—
406#382C2314yes—
407#382C2314yes—
408#381C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2318yes—
412#380C2314yes—
413#380C2314yes—
414#380C2318yes—
415#380C2312yes—
416#380C2312yes—
417#380C2314yes—
418#379C2318yes—
419#379C2318yes—
420#379C2318yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C43C2312yes—
436C43C2312yes—
437C43C2312yes—
438C43C2312yes—
439C25C2414yes—
440C2×#41—44no—
441C2×#41—44no—
442C2×#41—44no—
443C2×#41—48no—
444C2×#41—48no—
445C2×#41—48no—
446C22×Q8C2414yes—
447C22×Q8C2414yes—
448C22×Q8C2412yes—
449C22×D4—48no—
450C22×D4—48no—
451C22×D4—48no—
452C22×D4C2414yes—
453C22×D4C2412yes—
454C22×D4C2412yes—
455C22×D4C2414yes—
456C22×D4C2414yes—
457C22×D4C2414yes—
458C22×D4C2414yes—
459C22×D4C2412yes—
460C22×D4C2414yes—
461C22×D4C2418yes—
462C22×D4C2418yes—
463C22×D4C2418yes—
464C22×D4C2418yes—
465C22×D4C2414yes—
466C23×C4C2414yes—
467C23×C4C2411yescharacteristic
468C23×C4C2414yes—
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C23×C4C2412yes—
472C23×C4C2414yes—
473C23×C4C2414yes—
474C23×C4C2418yes—
475C23×C4C2411yescharacteristic
476C4⋊Q8—24no—
477C4⋊Q8—28no—
478C4⋊Q8—28no—
479#127—24no—
480#127—28no—
481#127—48no—
482#127—48no—
483#126—48no—
484#126—48no—
485#126—416no—
486#125—48no—
487#125—44no—
488#124—216no—
489#124—48no—
490#124—48no—
491#124—48no—
492#124—44no—
493#124—48no—
494#124—416no—
495#124—48no—
496#123—416no—
497#123—416no—
498#123—48no—
499#123—48no—
500C22⋊Q8—416no—
501C22⋊Q8—48no—
502C22⋊Q8—48no—
503C22⋊Q8—48no—
504C22⋊Q8—48no—
505C22⋊Q8—48no—
506#121—48no—
507#121—48no—
508#121—416no—
509#121—416no—
510#121—44no—
511#121—48no—
512#121—44no—
513#121—48no—
514#121—48no—
515#121—48no—
516#121—48no—
517#121—48no—
518#121—48no—
519#120—416no—
520#120—416no—
521#120—48no—
522#120—48no—
523C4×Q8—48no—
524C4×Q8—48no—
525C4×Q8—48no—
526C4×D4—28no—
527C4×D4—28no—
528C4×D4—48no—
529C4×D4—48no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—48no—
533C4×D4—48no—
534#117—216no—
535#117—216no—
536#117—44no—
537#117—48no—
538C2×C4⋊C4—48no—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C22⋊C4—48no—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C42—28no—
610C2×C42—24no—
611C2×C42—44no—
612C2×C42—42no—
613C2×C42—42no—
614C2×C42C2414yes—
615C2×C42C2414yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2411yescharacteristic
620C2×C42C2412yes—
621C2×C42C2412yes—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2414yes—
625C2×C42C2414yes—
626C2×C42C2418yes—
627C2×C42C2414yes—
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2412yes—
631C2×C42C2412yes—
632C2×C42C2412yes—
633C2×C42C2412yes—
634C2×C42C2412yes—
635C2×C42C2411yescharacteristic
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2418yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651#95C2414yes—
652#95C2414yes—
653#95C2418yes—
654#95C2414yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659C24—44no—
660C24—48no—
661C24—44no—
662C24—48no—
663C24—44no—
664C24C2514yes—
665C24C2514yes—
666C24C2514yes—
667C24C2511yescharacteristic
668#41—816no—
669#41—832no—
670C2×Q8—28no—
671C2×Q8—28no—
672C2×Q8—28no—
673C2×Q8—24no—
674C2×Q8—28no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—42no—
678C2×Q8—42no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—24no—
691C2×D4—28no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—44no—
702C2×D4—48no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—48no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—44no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—44no—
719C2×D4—48no—
720C2×D4—44no—
721C2×D4—832no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—24no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—42no—
739C22×C4—41no—
740C22×C4—42no—
741C22×C4—41no—
742C22×C4—48no—
743C22×C4—44no—
744C22×C4—48no—
745C22×C4—44no—
746C22×C4—48no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4C2514yes—
750C22×C4C2512yes—
751C22×C4C2514yes—
752C22×C4C2514yes—
753C22×C4C2512yes—
754C22×C4C2514yes—
755C22×C4C2514yes—
756C22×C4C2518yes—
757C22×C4C2514yes—
758C22×C4C2512yes—
759C22×C4C2514yes—
760C22×C4C2511yescharacteristic
761C22×C4C2512yes—
762C22×C4C2512yes—
763C22×C4C2511yescharacteristic
764C22×C4C2512yes—
765C4⋊C4—24no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—28no—
769C4⋊C4—28no—
770C4⋊C4—28no—
771C4⋊C4—24no—
772C4⋊C4—28no—
773C4⋊C4—28no—
774C4⋊C4—24no—
775C4⋊C4—24no—
776C4⋊C4—28no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—48no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4—48no—
786C4⋊C4—48no—
787C4⋊C4—44no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—48no—
792C4⋊C4—48no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—216no—
800C22⋊C4—216no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—48no—
809C22⋊C4—44no—
810C22⋊C4—44no—
811C22⋊C4—44no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C22⋊C4—44no—
815C22⋊C4—48no—
816C22⋊C4—48no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—48no—
820C22⋊C4—48no—
821C22⋊C4—44no—
822C22⋊C4—44no—
823C22⋊C4—44no—
824C22⋊C4—44no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C42—24no—
835C42—24no—
836C42—24no—
837C42—22no—
838C42—24no—
839C42—28no—
840C42—28no—
841C42—24no—
842C42—24no—
843C42—24no—
844C42—42no—
845C42—42no—
846C42—41no—
847C42—42no—
848C42—41no—
849C42—42no—
850C42—44no—
851C42—44no—
852C42—48no—
853C42—44no—
854C42H(5,𝔽2)18yes—
855C42H(5,𝔽2)14yes—
856C23—21no—
857C23—22no—
858C23—21no—
859C23—22no—
860C23—24no—
861C23—24no—
862C23—28no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—24no—
870C23—24no—
871C23—28no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—24no—
876C23—24no—
877C23—24no—
878C23—24no—
879C23—816no—
880C23—88no—
881C23—164no—
882C23—168no—
883C23—164no—
884C23#58512yes—
885C23C2611yescharacteristic
886Q8—416no—
887Q8—88no—
888Q8—84no—
889D4—416no—
890D4—48no—
891D4—48no—
892D4—88no—
893D4—88no—
894D4—84no—
895D4—88no—
896D4—88no—
897D4—88no—
898D4—816no—
899D4—816no—
900D4—164no—
901D4—168no—
902D4—168no—
903C2×C4—28no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—28no—
922C2×C4—24no—
923C2×C4—28no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—28no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—44no—
946C2×C4—48no—
947C2×C4—44no—
948C2×C4—48no—
949C2×C4—416no—
950C2×C4—416no—
951C2×C4—88no—
952C2×C4—816no—
953C2×C4—164no—
954C2×C4C2×H(5,𝔽2)14yes—
955C2×C4C2×H(5,𝔽2)12yes—
956C2×C4C2×H(5,𝔽2)14yes—
957C2×C4C2×H(5,𝔽2)14yes—
958C2×C4C2×H(5,𝔽2)14yes—
959C2×C4#58512yes—
960C2×C4#58514yes—
961C22—22no—
962C22—24no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—48no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—48no—
982C22—44no—
983C22—44no—
984C22—44no—
985C22—1616no—
986C22C22×H(5,𝔽2)11yescharacteristic
987C22C22×H(5,𝔽2)12yes—
988C22C2×#58512yes—
989C22C2×#58511yescharacteristic
990C22C2×#58511yescharacteristic
991C4—22no—
992C4—22no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—44no—
997C4—44no—
998C4—48no—
999C4—42no—
1000C4—44no—
1001C4—42no—
1002C4—44no—
1003C4—44no—
1004C4—44no—
1005C4—44no—
1006C4#354618yes—
1007C2—42no—
1008C2—84no—
1009C2—84no—
1010C2—84no—
1011C2C2×#354612yes—
1012C2#6276211yescharacteristic
1013C2#6282411yescharacteristic
1014C2#6283012yes—
1015C2#6283411yescharacteristic
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. #59056C2semidirect
2. #59041C2semidirect
3. #59040C2semidirect
4. #53317C2semidirect
5. #45741C2semidirect
6. #45642C2semidirect
7. #45593C2semidirect
8. #39554C2semidirect
9. #39515C2semidirect
10. #39491C2semidirect
11. #39419C2semidirect
12. #39387C2semidirect
13. #39362C2semidirect
14. #39218C2semidirect
15. #39024C2semidirect
16. #37278C2semidirect
17. #37277C2semidirect
18. #36812C2semidirect
19. #36639C2semidirect
20. #36631C2semidirect
21. C2×#555C22semidirect
24. C2×#542C22semidirect
26. C2×#533C22semidirect
28. C2×#529C22semidirect
29. #2862C22semidirect
30. #2861C22semidirect
31. #2861C22semidirect
33. #2860C22semidirect
34. #2860C22semidirect
35. #2859C22semidirect
38. #2857C22semidirect
41. #2854C22semidirect
42. #2854C22semidirect
43. #2850C22semidirect
44. #2850C22semidirect
45. #2850C22semidirect
46. #2825C22semidirect
47. #2803C22semidirect
48. #2801C22semidirect
49. #2798C22semidirect
50. #2778C22semidirect
51. #2759C22semidirect
52. #2757C22semidirect
53. #2756C22semidirect
54. #2735C22semidirect
55. #2733C22semidirect
56. #2730C22semidirect
57. #2725C22semidirect
58. #2715C22semidirect
59. #2714C22semidirect
60. #2711C22semidirect
61. #2710C22semidirect
62. #2710C22semidirect
63. #2705C22semidirect
64. #2705C22semidirect
65. #2703C22semidirect
66. #2702C22semidirect
67. #2694C22semidirect
68. #2693C22semidirect
69. #2685C22semidirect
70. #2685C22semidirect
72. #2683C22semidirect
75. #2678C22semidirect
76. #2676C22semidirect
77. #2673C22semidirect
78. #2672C22semidirect
79. #2670C22semidirect
80. #2669C22semidirect
81. #2648C22semidirect
82. #2628C22semidirect
84. #2620C22semidirect
86. #2608C22semidirect
88. #2581C22semidirect
89. #2576C22semidirect
91. #2559C22semidirect
92. #2555C22semidirect
93. #2548C22semidirect
95. #2542C22semidirect
97. #2541C22semidirect
99. #2539C22semidirect
100. #2538C22semidirect
101. #2538C22semidirect
103. #2518C22semidirect
104. #2514C22semidirect
105. #2512C22semidirect
106. #2504C22semidirect
108. #2495C22semidirect
109. #2494C22semidirect
110. #2472C22semidirect
111. #2471C22semidirect
113. #2445C22semidirect
116. #2431C22semidirect
117. #2428C22semidirect
118. #2427C22semidirect
120. #2426C22semidirect
121. #2423C22semidirect
123. #2417C22semidirect
126. #2415C22semidirect
127. #2415C22semidirect
128. #2414C22semidirect
132. #2407C22semidirect
133. #2407C22semidirect
134. #2407C22semidirect
136. #2380C22semidirect
137. #2375C22semidirect
138. #2369C22semidirect
140. #2365C22semidirect
141. #2363C22semidirect
142. #2360C22semidirect
143. #2341C22semidirect
145. #2333C22semidirect
146. #2317C22semidirect
147. #2314C22semidirect
148. #2312C22semidirect
149. C4×C4⋊Q8C22semidirect
151. C4×#124C22semidirect
152. C4×#124C22semidirect
153. C4×#124C22semidirect
155. C4×#121C22semidirect
156. C4×#121C22semidirect
157. #2297C22semidirect
158. #2297C22semidirect
160. #2293C22semidirect
161. #2293C22semidirect
162. C2×C43C22semidirect

Maximal subgroups

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

subgroupindex
#590562
#590412
#590402
#533172
#457412
#456422
#455932
#395542
#395152
#394912
#394192
#393872
#393622
#392182
#390242
#372782
#372772
#368122
#366392
#366312