Finite Group Databasebeta

← #8701635

Subgroups — #8701635

Order 512.

5175 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#59864C212yesmaximal, complemented
2#59002C214yesmaximal, complemented
3#59001C212yesmaximal, complemented
4#55492C214yesmaximal, complemented
5#54866C218yesmaximal, complemented
6#52301C211yesmaximal, characteristic, complemented
7#49876C218yesmaximal, complemented
8#49728C214yesmaximal, complemented
9#46016C212yesmaximal, complemented
10#46004C211yesmaximal, characteristic, complemented
11#45410C212yesmaximal, complemented
12#44993C214yesmaximal, complemented
13#42815C214yesmaximal, complemented
14#42683C212yesmaximal, complemented
15#39863C214yesmaximal, complemented
16#39594C212yesmaximal, complemented
17#37267C214yesmaximal, complemented
18#37249C212yesmaximal, complemented
19#36508C212yesmaximal, complemented
20#36496C211yesmaximal, characteristic, complemented
21C2×#559C2211yescharacteristic, complemented
22C2×#557C2212yescomplemented
23C2×#556C2212yes—
24C2×#554C2211yescharacteristic
25C2×#548C2214yes—
26C2×#547C2212yes—
27C2×#525C2214yescomplemented
28C22×C22⋊Q8C2212yescomplemented
29#2862C2212yescomplemented
30#2861C2214yes—
31#2861C2212yescomplemented
32#2858C2211yescharacteristic, complemented
33#2848C2212yescomplemented
34#2844C2212yescomplemented
35#2820C2218yescomplemented
36#2819C2214yes—
37#2813C2214yes—
38#2811C2212yescomplemented
39#2804C2212yes—
40#2804C2211yescharacteristic
41#2804C2212yes—
42#2804C2214yescomplemented
43#2795C2214yes—
44#2785C2214yes—
45#2782C2212yes—
46#2782C2214yes—
47#2781C2218yescomplemented
48#2775C2218yescomplemented
49#2763C2218yescomplemented
50#2756C2218yes—
51#2753C2218yescomplemented
52#2744C2218yescomplemented
53#2733C2214yes—
54#2731C2218yescomplemented
55#2720C2218yescomplemented
56#2720C2218yescomplemented
57#2720C2218yescomplemented
58#2718C2218yescomplemented
59#2712C2218yescomplemented
60#2711C2218yes—
61#2711C2218yes—
62#2710C2218yes—
63#2710C2218yescomplemented
64#2706C2218yescomplemented
65#2692C2218yes—
66#2685C2218yescomplemented
67#2684C2212yes—
68#2684C2214yes—
69#2680C2218yescomplemented
70#2679C2211yescharacteristic
71#2672C2218yes—
72#2670C2218yes—
73#2670C2214yescomplemented
74#2669C2214yes—
75#2658C2212yescomplemented
76#2636C2218yes—
77#2635C2214yes—
78#2633C2218yescomplemented
79#2632C2218yescomplemented
80#2626C2214yescomplemented
81#2623C2214yescomplemented
82#2612C2214yescomplemented
83#2603C2218yes—
84#2592C2214yescomplemented
85#2580C2218yescomplemented
86#2580C2218yescomplemented
87#2571C2214yescomplemented
88#2568C2212yescomplemented
89#2567C2211yescharacteristic, complemented
90#2566C2212yescomplemented
91#2565C2214yescomplemented
92#2563C2218yescomplemented
93#2546C2212yescomplemented
94#2545C2214yes—
95#2544C2212yes—
96#2542C2214yes—
97#2542C2212yes—
98#2541C2211yescharacteristic
99#2540C2212yes—
100#2532C2218yescomplemented
101#2532C2218yescomplemented
102#2531C2218yescomplemented
103#2519C2218yescomplemented
104#2519C2218yescomplemented
105#2502C2214yescomplemented
106#2492C2214yescomplemented
107#2492C2214yescomplemented
108#2491C2214yescomplemented
109#2487C2214yes—
110#2487C2214yescomplemented
111#2463C2214yescomplemented
112#2461C2218yes—
113#2461C2218yescomplemented
114#2461C2218yescomplemented
115#2459C2218yes—
116#2456C2218yes—
117#2449C2218yescomplemented
118#2443C2218yes—
119#2434C2212yescomplemented
120#2434C2214yescomplemented
121#2432C2214yescomplemented
122#2432C2214yescomplemented
123#2431C2214yescomplemented
124#2429C2214yescomplemented
125#2429C2214yescomplemented
126#2429C2214yescomplemented
127#2427C2214yescomplemented
128#2426C2214yescomplemented
129#2426C2214yescomplemented
130#2424C2218yes—
131#2418C2218yescomplemented
132#2417C2214yes—
133#2415C2214yes—
134#2414C2214yes—
135#2409C2212yes—
136#2407C2214yes—
137#2398C2214yes—
138#2398C2212yes—
139#2379C2212yes—
140#2379C2214yescomplemented
141#2366C2214yes—
142#2362C2214yescomplemented
143#2362C2214yescomplemented
144#2361C2214yescomplemented
145D4×C4⋊C4C2218yescomplemented
146#2346C2214yescomplemented
147#2345C2212yescomplemented
148#2326C2218yescomplemented
149#2321C2214yes—
150#2320C2214yescomplemented
151#2319C2212yescomplemented
152C4×C4⋊Q8C2214yescomplemented
153C4×#127C2212yes—
154C4×#124C2211yescharacteristic
155C4×#124C2212yes—
156C4×#120C2212yes—
157C4×#120C2214yes—
158C42×Q8C2211yescharacteristic, complemented
159C22×#41C2314yes—
160C23×Q8C2312yes—
161C24×C4C2312yes—
162#559—44no—
163#557—48no—
164#556—48no—
165#554—44no—
166#548—416no—
167#547—48no—
168C2×C4⋊Q8C2314yes—
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2312yes—
171C2×C4⋊Q8C2312yes—
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2314yes—
174C2×#127C2312yes—
175C2×#127C2311yescharacteristic
176C2×#126C2318yes—
177C2×#125C2318yes—
178C2×#125C2314yes—
179C2×#125C2312yes—
180C2×#124C2311yescharacteristic
181C2×#124C2312yes—
182C2×#124C2314yes—
183C2×#124C2318yes—
184C2×#124C2318yes—
185C2×#124C2314yes—
186C2×#124C2314yes—
187C2×#124C2312yes—
188C2×#124C2312yes—
189#525—416no—
190C2×#123C2314yes—
191C2×#123C2318yes—
192C2×#123C2318yes—
193C2×C22⋊Q8—48no—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2318yes—
202C2×C22⋊Q8C2318yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2318yes—
207C2×#120C2312yes—
208C2×#120C2318yes—
209C2×#120C2314yes—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2314yes—
214C2×C4×Q8C2314yes—
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2318yes—
222C2×C4×D4C2318yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2311yescharacteristic
228C2×#117C2314yes—
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2314yes—
231C22×C4⋊C4C2314yes—
232C22×C22⋊C4C2314yes—
233#400C2314yes—
234#400C2314yes—
235#400C2312yes—
236#400C2318yes—
237#400C2318yes—
238#400C2312yes—
239#400C2314yes—
240#400C2314yes—
241#399C2314yes—
242#399C2318yes—
243#399C2314yes—
244#399C2318yes—
245#399C2314yes—
246#399C2318yes—
247#399C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#397C2314yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2314yes—
258#397C2314yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#395C2318yes—
266#395C2318yes—
267#395C2314yes—
268#395C2314yes—
269#395C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2312yes—
278#394C2318yes—
279#394C2318yes—
280#394C2314yes—
281#394C2314yes—
282#394C2312yes—
283#394C2318yes—
284#394C2318yes—
285#393C2314yes—
286#393C2318yes—
287#393C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2314yes—
291#393C2314yes—
292#393C2314yes—
293#392C2318yes—
294#392C2318yes—
295#392C2318yes—
296#392C2314yes—
297#392C2318yes—
298#392C2314yes—
299#391C2312yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2312yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2314yes—
308#391C2318yes—
309#391C2314yes—
310#391C2311yescharacteristic
311#391C2318yes—
312#390C2311yescharacteristic
313#390C2318yes—
314#390C2312yes—
315#390C2318yes—
316#390C2318yes—
317#390C2312yes—
318#390C2312yes—
319#390C2314yes—
320#390C2318yes—
321#390C2318yes—
322#390C2314yes—
323#390C2312yes—
324#390C2314yes—
325#389C2318yes—
326#389C2318yes—
327#389C2314yes—
328#389C2318yes—
329#389C2318yes—
330#389C2314yes—
331#389C2314yes—
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#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2314yes—
353#388C2314yes—
354#388C2314yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#386C2314yes—
361#386C2318yes—
362#386C2314yes—
363#386C2318yes—
364#386C2318yes—
365#386C2312yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2314yes—
370#386C2314yes—
371#386C2314yes—
372#385C2318yes—
373#385C2314yes—
374#385C2314yes—
375#385C2314yes—
376#385C2314yes—
377#385C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2314yes—
382#385C2318yes—
383#385C2318yes—
384#385C2314yes—
385#385C2318yes—
386#385C2318yes—
387#385C2314yes—
388#385C2314yes—
389#385C2312yes—
390#384C2312yes—
391#384C2314yes—
392#384C2318yes—
393#383C2318yes—
394#382C2318yes—
395#382C2318yes—
396#382C2314yes—
397#382C2312yes—
398#382C2311yescharacteristic
399#382C2314yes—
400#382C2314yes—
401#381C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2318yes—
405#380C2318yes—
406#380C2312yes—
407#380C2314yes—
408#379C2314yes—
409#379C2312yes—
410#379C2314yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425#376C2312yes—
426#376C2318yes—
427C43C2312yes—
428C43C2311yescharacteristic
429C25C2412yes—
430C2×#41—48no—
431C2×#41—48no—
432C2×#41—48no—
433C22×Q8—44no—
434C22×Q8—48no—
435C22×Q8C2411yescharacteristic
436C22×Q8C2414yes—
437C22×Q8C2412yes—
438C22×Q8C2414yes—
439C22×Q8C2411yescharacteristic
440C22×Q8C2414yes—
441C22×Q8C2412yes—
442C22×D4C2412yes—
443C22×D4C2418yes—
444C22×D4C2414yes—
445C22×D4C2412yes—
446C22×D4C2412yes—
447C22×D4C2412yes—
448C22×D4C2418yes—
449C22×D4C2418yes—
450C22×D4C2412yes—
451C22×D4C2411yescharacteristic
452C23×C4—44no—
453C23×C4—48no—
454C23×C4C2412yes—
455C23×C4C2414yes—
456C23×C4C2414yes—
457C23×C4C2414yes—
458C23×C4C2414yes—
459C23×C4C2412yes—
460C23×C4C2418yes—
461C23×C4C2414yes—
462C4⋊Q8—42no—
463C4⋊Q8—44no—
464C4⋊Q8—48no—
465C4⋊Q8—44no—
466C4⋊Q8—48no—
467C4⋊Q8—44no—
468#127—28no—
469#127—42no—
470#126—416no—
471#125—44no—
472#125—416no—
473#125—48no—
474#124—24no—
475#124—48no—
476#124—416no—
477#124—48no—
478#124—44no—
479#124—44no—
480#124—48no—
481#124—44no—
482#124—416no—
483#123—416no—
484#123—416no—
485#123—48no—
486C22⋊Q8—216no—
487C22⋊Q8—216no—
488C22⋊Q8—416no—
489C22⋊Q8—416no—
490C22⋊Q8—48no—
491C22⋊Q8—48no—
492C22⋊Q8—48no—
493C22⋊Q8—44no—
494C22⋊Q8—48no—
495#121—216no—
496#121—48no—
497#121—416no—
498#121—48no—
499#120—28no—
500#120—48no—
501#120—416no—
502C4×Q8—216no—
503C4×Q8—24no—
504C4×Q8—28no—
505C4×Q8—48no—
506C4×Q8—48no—
507C4×Q8—44no—
508C4×Q8—42no—
509C4×D4—28no—
510C4×D4—416no—
511C4×D4—416no—
512C4×D4—416no—
513C4×D4—416no—
514C4×D4—44no—
515C4×D4—48no—
516C4×D4—44no—
517C4×D4—42no—
518C4×D4—44no—
519C4×D4—44no—
520#117—216no—
521C2×C4⋊C4—28no—
522C2×C4⋊C4—48no—
523C2×C4⋊C4—48no—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2411yescharacteristic
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2411yescharacteristic
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2411yescharacteristic
556C2×C4⋊C4C2412yes—
557C2×C22⋊C4—48no—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2418yes—
593C2×C42C2418yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2414yes—
597C2×C42C2418yes—
598C2×C42C2414yes—
599C2×C42C2411yescharacteristic
600C2×C42C2412yes—
601C2×C42C2414yes—
602C2×C42C2412yes—
603C2×C42C2411yescharacteristic
604C2×C42C2412yes—
605C2×C42C2418yes—
606C2×C42C2411yescharacteristic
607C2×C42C2414yes—
608#95C2414yes—
609#95C2412yes—
610#95C2418yes—
611#95C2412yes—
612#95C2414yes—
613#95C2418yes—
614#95C2418yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2418yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2412yes—
626#95C2414yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637C24—24no—
638C24—42no—
639C24—42no—
640C24—44no—
641C24—44no—
642C24C2514yes—
643C24C2514yes—
644C24C2512yes—
645#41—832no—
646C2×Q8—22no—
647C2×Q8—24no—
648C2×Q8—28no—
649C2×Q8—28no—
650C2×Q8—28no—
651C2×Q8—22no—
652C2×Q8—24no—
653C2×Q8—28no—
654C2×Q8—42no—
655C2×Q8—42no—
656C2×Q8—41no—
657C2×Q8—44no—
658C2×Q8—44no—
659C2×Q8—48no—
660C2×Q8—41no—
661C2×Q8—44no—
662C2×Q8—42no—
663C2×Q8—44no—
664C2×Q8—816no—
665C2×D4—216no—
666C2×D4—28no—
667C2×D4—24no—
668C2×D4—216no—
669C2×D4—28no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—41no—
673C2×D4—48no—
674C2×D4—41no—
675C2×D4—48no—
676C2×D4—44no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—48no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—48no—
689C2×D4—42no—
690C2×D4—44no—
691C2×D42−1+414yes—
692C22×C4—24no—
693C22×C4—28no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—28no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—44no—
700C22×C4—42no—
701C22×C4—48no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—48no—
707C22×C4—48no—
708C22×C4—48no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—816no—
712C22×C4C2512yes—
713C22×C4C2511yescharacteristic
714C22×C4C2514yes—
715C22×C4C2518yes—
716C22×C4C2512yes—
717C22×C4C2512yes—
718C22×C4C2514yes—
719C22×C4C2514yes—
720C22×C4C2514yes—
721C22×C4C2518yes—
722C22×C4C2512yes—
723C22×C4C2512yes—
724C22×C4C2514yes—
725C22×C4C2512yes—
726C22×C4C2511yescharacteristic
727C22×C4C2512yes—
728C22×C4C2511yescharacteristic
729C4⋊C4—28no—
730C4⋊C4—24no—
731C4⋊C4—216no—
732C4⋊C4—28no—
733C4⋊C4—216no—
734C4⋊C4—216no—
735C4⋊C4—24no—
736C4⋊C4—28no—
737C4⋊C4—42no—
738C4⋊C4—44no—
739C4⋊C4—48no—
740C4⋊C4—48no—
741C4⋊C4—41no—
742C4⋊C4—42no—
743C4⋊C4—44no—
744C4⋊C4—48no—
745C4⋊C4—41no—
746C4⋊C4—42no—
747C4⋊C4—48no—
748C4⋊C4—42no—
749C4⋊C4—42no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—48no—
757C4⋊C4—44no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4H(5,𝔽2)14yes—
761C4⋊C4H(5,𝔽2)18yes—
762C22⋊C4—24no—
763C22⋊C4—28no—
764C22⋊C4—216no—
765C22⋊C4—216no—
766C22⋊C4—28no—
767C22⋊C4—216no—
768C22⋊C4—216no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—216no—
772C22⋊C4—28no—
773C22⋊C4—48no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—48no—
777C22⋊C4—42no—
778C22⋊C4—44no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4—44no—
782C22⋊C4—42no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—48no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C42—216no—
798C42—24no—
799C42—24no—
800C42—216no—
801C42—28no—
802C42—22no—
803C42—24no—
804C42—28no—
805C42—22no—
806C42—24no—
807C42—28no—
808C42—24no—
809C42—41no—
810C42—44no—
811C42—48no—
812C23—22no—
813C23—24no—
814C23—24no—
815C23—22no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—28no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—28no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—48no—
829C23—88no—
830C23—84no—
831C23—84no—
832C23—88no—
833C23C2×2−1+414yes—
834C23C2611yescharacteristic
835Q8—48no—
836Q8—44no—
837Q8—416no—
838Q8—82no—
839Q8—88no—
840Q8—88no—
841Q8—162no—
842D4—44no—
843D4—432no—
844D4—48no—
845D4—84no—
846D4—84no—
847D4—88no—
848D4—84no—
849D4—816no—
850D4—816no—
851D4—162no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—22no—
862C2×C4—28no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—21no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—28no—
870C2×C4—24no—
871C2×C4—28no—
872C2×C4—28no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—24no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—22no—
888C2×C4—28no—
889C2×C4—24no—
890C2×C4—48no—
891C2×C4—416no—
892C2×C4—88no—
893C2×C4—88no—
894C2×C4—84no—
895C2×C4—88no—
896C2×C4—88no—
897C2×C4—816no—
898C2×C4C2×H(5,𝔽2)18yes—
899C2×C4C2×H(5,𝔽2)14yes—
900C2×C4C2×H(5,𝔽2)14yes—
901C2×C4C2×H(5,𝔽2)12yes—
902C2×C4C2×2−1+412yes—
903C2×C4#58514yes—
904C22—28no—
905C22—24no—
906C22—42no—
907C22—42no—
908C22—44no—
909C22—44no—
910C22—44no—
911C22—48no—
912C22—44no—
913C22—44no—
914C22—44no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—48no—
920C22—44no—
921C22—816no—
922C22C22×H(5,𝔽2)12yes—
923C22C22×H(5,𝔽2)11yescharacteristic
924C22C22×2−1+411yescharacteristic
925C22C2×#58512yes—
926C222−1+611yescharacteristic
927C4—28no—
928C4—24no—
929C4—22no—
930C4—24no—
931C4—44no—
932C4—42no—
933C4—48no—
934C4—42no—
935C4—42no—
936C4—44no—
937C4—42no—
938C4—44no—
939C4—41no—
940C4—42no—
941C4—48no—
942C4—44no—
943C4#354914yes—
944C2—44no—
945C2—84no—
946C2—84no—
947C2C2×#354911yescharacteristic
948C2#6289311yescharacteristic
949C2#6289712yes—
950C2#6301312yes—
951C2#6302111yescharacteristic
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. #59864C2semidirect
2. #59002C2semidirect
3. #59001C2semidirect
4. #55492C2semidirect
5. #54866C2semidirect
6. #52301C2semidirect
7. #49876C2semidirect
8. #49728C2semidirect
9. #46016C2semidirect
10. #46004C2semidirect
11. #45410C2semidirect
12. #44993C2semidirect
13. #42815C2semidirect
14. #42683C2semidirect
15. #39863C2semidirect
16. #39594C2semidirect
17. #37267C2semidirect
18. #37249C2semidirect
19. #36508C2semidirect
20. #36496C2semidirect
21. C2×#559C22semidirect
22. C2×#557C22semidirect
27. C2×#525C22semidirect
28. C22×C22⋊Q8C22semidirect
29. #2862C22semidirect
31. #2861C22semidirect
32. #2858C22semidirect
33. #2848C22semidirect
34. #2844C22semidirect
35. #2820C22semidirect
38. #2811C22semidirect
42. #2804C22semidirect
47. #2781C22semidirect
48. #2775C22semidirect
49. #2763C22semidirect
51. #2753C22semidirect
52. #2744C22semidirect
54. #2731C22semidirect
55. #2720C22semidirect
56. #2720C22semidirect
57. #2720C22semidirect
58. #2718C22semidirect
59. #2712C22semidirect
63. #2710C22semidirect
64. #2706C22semidirect
66. #2685C22semidirect
69. #2680C22semidirect
73. #2670C22semidirect
75. #2658C22semidirect
78. #2633C22semidirect
79. #2632C22semidirect
80. #2626C22semidirect
81. #2623C22semidirect
82. #2612C22semidirect
84. #2592C22semidirect
85. #2580C22semidirect
86. #2580C22semidirect
87. #2571C22semidirect
88. #2568C22semidirect
89. #2567C22semidirect
90. #2566C22semidirect
91. #2565C22semidirect
92. #2563C22semidirect
93. #2546C22semidirect
100. #2532C22semidirect
101. #2532C22semidirect
102. #2531C22semidirect
103. #2519C22semidirect
104. #2519C22semidirect
105. #2502C22semidirect
106. #2492C22semidirect
107. #2492C22semidirect
108. #2491C22semidirect
110. #2487C22semidirect
111. #2463C22semidirect
113. #2461C22semidirect
114. #2461C22semidirect
117. #2449C22semidirect
119. #2434C22semidirect
120. #2434C22semidirect
121. #2432C22semidirect
122. #2432C22semidirect
123. #2431C22semidirect
124. #2429C22semidirect
125. #2429C22semidirect
126. #2429C22semidirect
127. #2427C22semidirect
128. #2426C22semidirect
129. #2426C22semidirect
131. #2418C22semidirect
140. #2379C22semidirect
142. #2362C22semidirect
143. #2362C22semidirect
144. #2361C22semidirect
145. D4×C4⋊C4C22semidirect
146. #2346C22semidirect
147. #2345C22semidirect
148. #2326C22semidirect
150. #2320C22semidirect
151. #2319C22semidirect
152. C4×C4⋊Q8C22semidirect
158. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#598642
#590022
#590012
#554922
#548662
#523012
#498762
#497282
#460162
#460042
#454102
#449932
#428152
#426832
#398632
#395942
#372672
#372492
#365082
#364962