Finite Group Databasebeta

← #7656828

Subgroups — #7656828

Order 512.

5028 conjugacy classes of subgroups.

The subgroup lattice has 991 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42991C214yesmaximal, complemented
2#42921C214yesmaximal, complemented
3#42339C218yesmaximal, complemented
4#42229C218yesmaximal, complemented
5#39632C212yesmaximal, complemented
6#39422C214yesmaximal, complemented
7#39376C212yesmaximal, complemented
8#37942C214yesmaximal, complemented
9#37464C214yesmaximal, complemented
10#37442C212yesmaximal, complemented
11#36579C212yesmaximal, complemented
12#36176C212yesmaximal, complemented
13#36089C214yesmaximal, complemented
14#36006C214yesmaximal, complemented
15#35004C212yesmaximal, complemented
16#35002C211yesmaximal, characteristic, complemented
17#34595C212yesmaximal, complemented
18#34575C211yesmaximal, characteristic
19#34202C212yesmaximal, complemented
20C2×#2362C211yesmaximal, characteristic, complemented
21C2×#556C2212yescomplemented
22C2×#543C2212yes—
23C2×#539C2214yes—
24C2×#525C2212yes—
25C22×C22⋊Q8C2211yescharacteristic
26C2×#520C2212yes—
27C22×C4×Q8C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2857C2212yes—
30#2857C2212yes—
31#2854C2214yes—
32#2850C2214yes—
33#2839C2218yescomplemented
34#2830C2218yescomplemented
35#2814C2218yes—
36#2806C2214yescomplemented
37#2804C2214yescomplemented
38#2788C2218yescomplemented
39#2782C2218yes—
40#2781C2218yes—
41#2770C2218yes—
42#2749C2218yes—
43#2728C2218yes—
44#2726C2214yescomplemented
45#2724C2214yescomplemented
46#2702C2218yes—
47#2696C2218yes—
48#2690C2218yes—
49#2689C2218yescomplemented
50#2666C2218yescomplemented
51#2666C2218yescomplemented
52#2665C2218yescomplemented
53#2663C2214yes—
54#2661C2214yes—
55#2659C2211yescharacteristic
56#2659C2212yes—
57#2659C2214yes—
58#2659C2212yes—
59#2656C2211yescharacteristic
60#2652C2218yescomplemented
61#2650C2218yescomplemented
62#2646C2214yes—
63#2639C2212yes—
64#2639C2214yes—
65#2637C2218yescomplemented
66#2627C2214yes—
67#2627C2214yes—
68#2625C2214yes—
69#2618C2214yes—
70#2617C2212yes—
71#2617C2212yes—
72#2616C2214yes—
73#2603C2218yes—
74#2595C2218yes—
75#2592C2214yescomplemented
76#2581C2214yescomplemented
77#2571C2212yescomplemented
78#2568C2212yescomplemented
79#2563C2212yescomplemented
80#2560C2218yes—
81#2556C2218yescomplemented
82#2554C2218yescomplemented
83#2549C2218yes—
84#2538C2212yescomplemented
85#2536C2218yes—
86#2532C2218yescomplemented
87#2530C2218yes—
88#2520C2218yescomplemented
89#2519C2218yescomplemented
90#2513C2214yescomplemented
91#2511C2214yescomplemented
92#2508C2214yescomplemented
93#2506C2214yescomplemented
94#2502C2214yescomplemented
95#2496C2214yescomplemented
96#2495C2214yescomplemented
97#2492C2214yescomplemented
98#2489C2218yes—
99#2488C2218yes—
100#2486C2214yes—
101#2486C2214yescomplemented
102#2481C2218yes—
103#2469C2218yescomplemented
104#2468C2218yes—
105#2468C2218yescomplemented
106#2461C2218yes—
107#2461C2218yescomplemented
108#2450C2218yes—
109#2440C2214yes—
110#2440C2214yes—
111#2440C2214yescomplemented
112#2421C2214yescomplemented
113#2419C2218yes—
114#2417C2214yes—
115#2417C2214yes—
116#2417C2214yescomplemented
117#2412C2218yes—
118#2409C2214yes—
119#2402C2218yescomplemented
120#2399C2218yescomplemented
121#2395C2214yes—
122#2388C2214yes—
123#2369C2212yescomplemented
124#2362C2218yes—
125#2362C2214yes—
126#2362C2214yes—
127#2362C2214yescomplemented
128#2359C2218yes—
129#2358C2218yes—
130#2355C2212yescomplemented
131#2354C2214yes—
132#2354C2212yescomplemented
133#2352C2214yes—
134#2352C2214yes—
135D4×C4⋊C4C2214yes—
136#2346C2214yescomplemented
137#2325C2214yes—
138#2324C2214yes—
139#2323C2214yes—
140#2317C2212yes—
141#2315C2212yes—
142#2311C2212yes—
143C4×C22⋊Q8C2214yes—
144C4×C22⋊Q8C2214yes—
145C4×#121C2212yes—
146C4×#121C2212yes—
147C4×#121C2214yes—
148C2×#391C2211yescharacteristic
149C2×#389C2211yescharacteristic
150C2×#388C2212yes—
151C2×#388C2212yes—
152C2×#387C2212yes—
153#2283C2214yes—
154C2×#380C2212yes—
155#2274C2212yes—
156C2×C4×C4⋊C4C2212yes—
157C2×C4×C4⋊C4C2211yescharacteristic
158C2×C4×C22⋊C4C2211yescharacteristic
159C22×#41C2312yes—
160C23×Q8C2311yescharacteristic
161C24×C4C2311yescharacteristic
162#556—48no—
163#543—48no—
164#539—416no—
165C2×C4⋊Q8C2312yes—
166C2×C4⋊Q8C2312yes—
167C2×#126C2318yes—
168C2×#126C2318yes—
169C2×#125C2318yes—
170C2×#124C2314yes—
171#525—216no—
172C2×#123C2314yes—
173C2×#123C2318yes—
174C2×#123C2318yes—
175C2×C22⋊Q8—28no—
176C2×C22⋊Q8C2312yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2312yes—
181C2×C22⋊Q8C2318yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2314yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2318yes—
186C2×C22⋊Q8C2318yes—
187C2×#121C2312yes—
188C2×#121C2312yes—
189C2×#121C2312yes—
190C2×#121C2312yes—
191C2×#120C2314yes—
192#520—48no—
193C2×C4×Q8—44no—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2312yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2312yes—
206C2×#117—44no—
207C2×#117C2312yes—
208C2×#117C2314yes—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2314yes—
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2312yes—
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2314yes—
225C22×C22⋊C4C2312yes—
226C22×C42C2312yes—
227C22×C42C2312yes—
228C22×C42C2311yescharacteristic
229C22×C42C2311yescharacteristic
230C22×C42C2312yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2314yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#399C2314yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2314yes—
254#398C2318yes—
255#398C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2314yes—
263#397C2314yes—
264#397C2314yes—
265#397C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#396C2318yes—
270#395C2318yes—
271#395C2318yes—
272#395C2318yes—
273#395C2318yes—
274#395C2314yes—
275#395C2318yes—
276#394C2314yes—
277#394C2314yes—
278#394C2318yes—
279#394C2314yes—
280#394C2318yes—
281#394C2318yes—
282#394C2314yes—
283#394C2314yes—
284#393C2318yes—
285#393C2318yes—
286#393C2318yes—
287#393C2314yes—
288#392C2314yes—
289#392C2314yes—
290#392C2314yes—
291#391C2318yes—
292#391C2314yes—
293#391C2314yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#391C2314yes—
298#391C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2318yes—
302#390C2318yes—
303#390C2314yes—
304#390C2314yes—
305#390C2312yes—
306#390C2314yes—
307#390C2314yes—
308#390C2312yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2318yes—
314#389C2312yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2312yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2314yes—
342#388C2314yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2314yes—
362#386C2314yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#384C2312yes—
373#384C2314yes—
374#384C2312yes—
375#383C2318yes—
376#382C2314yes—
377#382C2314yes—
378#382C2314yes—
379#382C2314yes—
380#382C2318yes—
381#381C2318yes—
382#381C2318yes—
383#380C2314yes—
384#380C2314yes—
385#380C2314yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2312yes—
393#380C2312yes—
394#380C2314yes—
395#380C2318yes—
396#380C2318yes—
397#380C2318yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2312yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2318yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421#376C2318yes—
422C2×#95C2312yes—
423C2×#95C2314yes—
424C2×#95C2311yescharacteristic
425C2×#95C2311yescharacteristic
426C2×#95C2312yes—
427C2×#95C2312yes—
428C2×#95C2312yes—
429C25C2411yescharacteristic
430C2×#41—28no—
431C2×#41—44no—
432C2×#41—44no—
433C22×Q8—24no—
434C22×Q8—42no—
435C22×Q8—42no—
436C22×Q8C2412yes—
437C22×Q8C2412yes—
438C22×Q8C2412yes—
439C22×Q8C2414yes—
440C22×Q8C2414yes—
441C22×D4C2414yes—
442C22×D4C2414yes—
443C22×D4C2412yes—
444C22×D4C2414yes—
445C22×D4C2412yes—
446C22×D4C2412yes—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4#4118yes—
450C23×C4C2412yes—
451C23×C4C2414yes—
452C23×C4C2412yes—
453C23×C4C2411yescharacteristic
454C23×C4C2412yes—
455C23×C4C2412yes—
456C23×C4C2412yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2414yes—
460C23×C4C2414yes—
461C23×C4C2418yes—
462C23×C4C2411yescharacteristic
463C23×C4C2412yes—
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C4⋊Q8—44no—
467C4⋊Q8—44no—
468#126—416no—
469#126—416no—
470#125—416no—
471#124—48no—
472#123—216no—
473#123—416no—
474#123—416no—
475C22⋊Q8—216no—
476C22⋊Q8—216no—
477C22⋊Q8—28no—
478C22⋊Q8—28no—
479C22⋊Q8—216no—
480C22⋊Q8—48no—
481C22⋊Q8—416no—
482C22⋊Q8—416no—
483C22⋊Q8—416no—
484C22⋊Q8—48no—
485C22⋊Q8—48no—
486#121—28no—
487#121—28no—
488#121—28no—
489#121—28no—
490#120—216no—
491C4×Q8—28no—
492C4×Q8—48no—
493C4×Q8—48no—
494C4×Q8—48no—
495C4×Q8—44no—
496C4×D4—216no—
497C4×D4—216no—
498C4×D4—48no—
499C4×D4—416no—
500C4×D4—44no—
501C4×D4—44no—
502C4×D4—416no—
503#117—28no—
504#117—28no—
505#117—216no—
506#117—48no—
507#117—44no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—28no—
510C2×C4⋊C4—28no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—44no—
513C2×C4⋊C4—42no—
514C2×C4⋊C4—44no—
515C2×C4⋊C4—48no—
516C2×C4⋊C4—44no—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2411yescharacteristic
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2411yescharacteristic
557C2×C22⋊C4—28no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—44no—
561C2×C22⋊C4—48no—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C42—28no—
588C2×C42—44no—
589C2×C42—42no—
590C2×C42—44no—
591C2×C42—42no—
592C2×C42C2414yes—
593C2×C42C2414yes—
594C2×C42C2418yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2418yes—
602C2×C42C2412yes—
603C2×C42C2414yes—
604C2×C42C2418yes—
605C2×C42C2412yes—
606#95C2414yes—
607#95C2414yes—
608#95C2418yes—
609#95C2414yes—
610#95C2418yes—
611#95C2414yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2414yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2414yes—
625#95C2418yes—
626#95C2414yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2414yes—
633#95C2414yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637C24—22no—
638C24—22no—
639C24—41no—
640C24—41no—
641C24—41no—
642C24—41no—
643C24C2×#4114yes—
644C24C2514yes—
645C24C2512yes—
646C24C2511yescharacteristic
647#41—432no—
648C2×Q8—24no—
649C2×Q8—24no—
650C2×Q8—24no—
651C2×Q8—24no—
652C2×Q8—28no—
653C2×Q8—24no—
654C2×Q8—42no—
655C2×Q8—42no—
656C2×Q8—42no—
657C2×Q8—42no—
658C2×Q8—44no—
659C2×Q8—44no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8—416no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—42no—
673C2×D4—44no—
674C2×D4—42no—
675C2×D4—44no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—44no—
681C2×D4—44no—
682C22×C4—22no—
683C22×C4—24no—
684C22×C4—22no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—22no—
692C22×C4—24no—
693C22×C4—22no—
694C22×C4—28no—
695C22×C4—24no—
696C22×C4—28no—
697C22×C4—28no—
698C22×C4—416no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—42no—
702C22×C4—41no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—41no—
706C22×C4—42no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—41no—
712C22×C4—41no—
713C22×C4—41no—
714C22×C4—41no—
715C22×C4—42no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—48no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—48no—
722C22×C4—44no—
723C22×C4—48no—
724C22×C4—44no—
725C22×C4C2×#4114yes—
726C22×C4C2×#4118yes—
727C22×C4C2×#4114yes—
728C22×C4C2×#4118yes—
729C22×C4H(5,𝔽2)14yes—
730C22×C42−1+414yes—
731C22×C4C2514yes—
732C22×C4C2512yes—
733C22×C4C2512yes—
734C22×C4C2512yes—
735C22×C4C2514yes—
736C22×C4C2514yes—
737C22×C4C2518yes—
738C22×C4C2514yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2518yes—
742C22×C4C2511yescharacteristic
743C22×C4C2512yes—
744C22×C4C2512yes—
745C22×C4C2512yes—
746C22×C4C2512yes—
747C22×C4C2511yescharacteristic
748C4⋊C4—24no—
749C4⋊C4—24no—
750C4⋊C4—216no—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—24no—
756C4⋊C4—22no—
757C4⋊C4—216no—
758C4⋊C4—24no—
759C4⋊C4—28no—
760C4⋊C4—28no—
761C4⋊C4—24no—
762C4⋊C4—216no—
763C4⋊C4—28no—
764C4⋊C4—24no—
765C4⋊C4—28no—
766C4⋊C4—44no—
767C4⋊C4—42no—
768C4⋊C4—44no—
769C4⋊C4—48no—
770C4⋊C4—44no—
771C4⋊C4—42no—
772C4⋊C4—44no—
773C4⋊C4—42no—
774C4⋊C4—44no—
775C4⋊C4—48no—
776C4⋊C4—42no—
777C4⋊C4—42no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4—48no—
782C4⋊C4—44no—
783C4⋊C4—48no—
784C4⋊C4—48no—
785C4⋊C4—44no—
786C4⋊C4—44no—
787C4⋊C4H(5,𝔽2)14yes—
788C22⋊C4—216no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—216no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—216no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—48no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—48no—
806C22⋊C4—44no—
807C22⋊C4—48no—
808C22⋊C4—44no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C42—28no—
814C42—28no—
815C42—24no—
816C42—28no—
817C42—216no—
818C42—28no—
819C42—28no—
820C42—24no—
821C42—42no—
822C42—44no—
823C42—42no—
824C42—44no—
825C42—48no—
826C42—48no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—28no—
838C23—24no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—44no—
846C23—44no—
847C23—82no—
848C23—82no—
849C23—82no—
850C23—82no—
851C23C22×#4114yes—
852C23C22×#4112yes—
853C23C2×H(5,𝔽2)12yes—
854C23C2×2−1+412yes—
855C23C2611yescharacteristic
856Q8—48no—
857Q8—48no—
858Q8—48no—
859Q8—88no—
860Q8—164no—
861D4—48no—
862D4—416no—
863D4—416no—
864D4—84no—
865D4—84no—
866D4—88no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—28no—
878C2×C4—216no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—22no—
887C2×C4—24no—
888C2×C4—28no—
889C2×C4—22no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—28no—
893C2×C4—22no—
894C2×C4—28no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—28no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—28no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—28no—
912C2×C4—44no—
913C2×C4—48no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—48no—
917C2×C4—48no—
918C2×C4—48no—
919C2×C4—416no—
920C2×C4—84no—
921C2×C4—82no—
922C2×C4—82no—
923C2×C4—168no—
924C2×C4—164no—
925C2×C4—164no—
926C2×C4C22×#4112yes—
927C2×C4C22×#4114yes—
928C2×C4C22×#4112yes—
929C2×C4C2×H(5,𝔽2)14yes—
930C2×C4C2×H(5,𝔽2)14yes—
931C2×C4C2×H(5,𝔽2)12yes—
932C2×C4C2×2−1+414yes—
933C2×C4#58512yes—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—44no—
948C22—44no—
949C22—44no—
950C22—44no—
951C22—44no—
952C22—44no—
953C22—44no—
954C22—88no—
955C22#351114yes—
956C22C23×#4111yescharacteristic
957C22C22×H(5,𝔽2)11yescharacteristic
958C22C22×H(5,𝔽2)11yescharacteristic
959C22C22×2−1+411yescharacteristic
960C22C2×#58511yescharacteristic
961C222−1+611yescharacteristic
962C222−1+611yescharacteristic
963C4—24no—
964C4—24no—
965C4—24no—
966C4—24no—
967C4—22no—
968C4—44no—
969C4—44no—
970C4—44no—
971C4—44no—
972C4—48no—
973C4—42no—
974C4—42no—
975C4—44no—
976C4—44no—
977C4—42no—
978C4—48no—
979C4#345914yes—
980C2—24no—
981C2—44no—
982C2—84no—
983C2C2×#345911yescharacteristic
984C2C2×#351111yescharacteristic
985C2#6286011yescharacteristic
986C2#6289511yescharacteristic
987C2#6290411yescharacteristic
988C2#6291511yescharacteristic
989C2#6293111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34575C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42991C2semidirect
2. #42921C2semidirect
3. #42339C2semidirect
4. #42229C2semidirect
5. #39632C2semidirect
6. #39422C2semidirect
7. #39376C2semidirect
8. #37942C2semidirect
9. #37464C2semidirect
10. #37442C2semidirect
11. #36579C2semidirect
12. #36176C2semidirect
13. #36089C2semidirect
14. #36006C2semidirect
15. #35004C2semidirect
16. #35002C2semidirect
17. #34595C2semidirect
19. #34202C2semidirect
20. C2×#2362C2semidirect
21. C2×#556C22semidirect
33. #2839C22semidirect
34. #2830C22semidirect
36. #2806C22semidirect
37. #2804C22semidirect
38. #2788C22semidirect
44. #2726C22semidirect
45. #2724C22semidirect
49. #2689C22semidirect
50. #2666C22semidirect
51. #2666C22semidirect
52. #2665C22semidirect
60. #2652C22semidirect
61. #2650C22semidirect
65. #2637C22semidirect
75. #2592C22semidirect
76. #2581C22semidirect
77. #2571C22semidirect
78. #2568C22semidirect
79. #2563C22semidirect
81. #2556C22semidirect
82. #2554C22semidirect
84. #2538C22semidirect
86. #2532C22semidirect
88. #2520C22semidirect
89. #2519C22semidirect
90. #2513C22semidirect
91. #2511C22semidirect
92. #2508C22semidirect
93. #2506C22semidirect
94. #2502C22semidirect
95. #2496C22semidirect
96. #2495C22semidirect
97. #2492C22semidirect
101. #2486C22semidirect
103. #2469C22semidirect
105. #2468C22semidirect
107. #2461C22semidirect
111. #2440C22semidirect
112. #2421C22semidirect
116. #2417C22semidirect
119. #2402C22semidirect
120. #2399C22semidirect
123. #2369C22semidirect
127. #2362C22semidirect
130. #2355C22semidirect
132. #2354C22semidirect
136. #2346C22semidirect

Maximal subgroups

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

subgroupindex
#429912
#429212
#423392
#422292
#396322
#394222
#393762
#379422
#374642
#374422
#365792
#361762
#360892
#360062
#350042
#350022
#345952
#345752
#342022
C2×#23622