Finite Group Databasebeta

← #7699929

Subgroups — #7699929

Order 512.

5397 conjugacy classes of subgroups.

The subgroup lattice has 1129 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59904C214yesmaximal, complemented
2#59823C211yesmaximal, characteristic, complemented
3#59723C218yesmaximal, complemented
4#59660C212yesmaximal, complemented
5#59507C214yesmaximal, complemented
6#59437C212yesmaximal, complemented
7#59397C214yesmaximal, complemented
8#59064C212yesmaximal, complemented
9#36599C212yesmaximal, complemented
10#36598C211yesmaximal, characteristic, complemented
11#36560C211yesmaximal, characteristic, complemented
12#36505C214yesmaximal, complemented
13#36454C212yesmaximal, complemented
14#36453C212yesmaximal, complemented
15#36452C214yesmaximal, complemented
16#36450C212yesmaximal, complemented
17#36406C212yesmaximal, complemented
18#36299C212yesmaximal, complemented
19#36256C214yesmaximal, complemented
20#36127C211yesmaximal, characteristic
21C4×#559C211yesmaximal, characteristic, complemented
22C4×#554C211yesmaximal, characteristic, complemented
23C4×#554C212yesmaximal, complemented
24C4×#556C211yesmaximal, characteristic, complemented
25C4×#547C212yesmaximal, complemented
26#34141C212yesmaximal, complemented
27C2×#559C2211yescharacteristic
28C2×#557C2212yes—
29C2×#556C2211yescharacteristic
30C2×#554C2211yescharacteristic
31C2×#554C2212yes—
32C2×#547C2212yes—
33C2×#532C2212yes—
34C2×C4×#41C2214yes—
35#2868C2211yescharacteristic
36#2863C2214yes—
37#2862C2212yes—
38#2859C2212yes—
39#2857C2212yes—
40#2857C2214yes—
41#2855C2214yes—
42#2851C2218yes—
43#2787C2218yes—
44#2750C2218yes—
45#2732C2214yes—
46#2728C2218yes—
47#2708C2218yes—
48#2585C2218yes—
49#2582C2212yes—
50#2578C2218yes—
51#2577C2218yes—
52#2577C2218yes—
53#2576C2218yes—
54#2575C2218yes—
55#2573C2218yes—
56#2571C2212yes—
57#2570C2214yes—
58#2569C2218yes—
59#2568C2212yes—
60#2568C2212yes—
61#2565C2214yes—
62#2562C2218yes—
63#2553C2218yes—
64#2553C2218yes—
65#2552C2212yes—
66#2547C2212yes—
67#2547C2214yes—
68#2546C2212yes—
69#2546C2212yes—
70#2542C2212yes—
71#2538C2214yes—
72#2538C2212yes—
73#2537C2212yes—
74#2537C2212yes—
75#2536C2218yes—
76#2528C2218yes—
77#2517C2218yes—
78#2515C2218yes—
79#2514C2214yes—
80#2511C2214yes—
81#2511C2214yes—
82#2509C2214yes—
83#2506C2214yes—
84#2506C2214yes—
85#2499C2214yes—
86#2495C2214yes—
87#2494C2214yes—
88#2494C2214yes—
89#2493C2218yes—
90#2489C2214yes—
91#2489C2214yes—
92#2475C2218yes—
93#2475C2218yes—
94#2460C2218yes—
95#2460C2218yes—
96#2454C2214yes—
97#2447C2214yes—
98#2447C2214yes—
99#2446C2214yes—
100#2446C2214yes—
101#2442C2214yes—
102#2442C2214yes—
103#2432C2214yes—
104#2432C2214yes—
105#2427C2214yes—
106#2427C2214yes—
107#2427C2214yes—
108#2422C2214yes—
109#2422C2214yes—
110#2421C2214yes—
111#2420C2214yes—
112#2419C2218yes—
113#2417C2214yes—
114#2374C2214yes—
115#2373C2214yes—
116#2370C2214yes—
117#2370C2212yes—
118#2369C2211yescharacteristic
119#2368C2218yes—
120#2368C2214yes—
121#2367C2214yes—
122#2367C2212yes—
123#2367C2214yes—
124#2367C2212yes—
125#2367C2212yes—
126#2366C2211yescharacteristic
127#2366C2212yes—
128#2365C2212yes—
129#2365C2212yes—
130#2365C2211yescharacteristic
131#2365C2212yes—
132#2364C2218yes—
133#2362C2214yes—
134#2362C2212yes—
135#2361C2214yes—
136#2361C2214yes—
137#2361C2214yes—
138#2360C2214yes—
139#2360C2214yes—
140#2360C2212yes—
141#2359C2218yes—
142#2357C2212yes—
143#2357C2212yes—
144#2356C2212yes—
145#2355C2211yescharacteristic
146#2355C2211yescharacteristic
147#2355C2214yes—
148#2355C2212yes—
149#2355C2212yes—
150#2355C2211yescharacteristic
151#2355C2211yescharacteristic
152#2354C2211yescharacteristic
153#2349C2212yes—
154#2349C2214yes—
155D4×C4⋊C4C2212yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2211yescharacteristic
159#2347C2212yes—
160#2345C2214yes—
161#2345C2214yes—
162#2345C2212yes—
163#2344C2214yes—
164#2339C2214yes—
165C4×C4⋊Q8C2212yes—
166C4×C4⋊Q8C2212yes—
167C4×C4⋊Q8C2211yescharacteristic
168C4×C4⋊Q8C2211yescharacteristic
169C4×#127C2211yescharacteristic
170C4×#125C2212yes—
171C4×#125C2214yes—
172C4×#126C2214yes—
173C4×#124C2212yes—
174C4×#124C2212yes—
175C4×#124C2212yes—
176C4×C22⋊Q8C2214yes—
177C4×C22⋊Q8C2214yes—
178C4×C22⋊Q8C2214yes—
179C4×C22⋊Q8C2218yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×#123C2214yes—
183C4×#123C2218yes—
184C4×#121C2214yes—
185#2297C2214yes—
186#2293C2214yes—
187#2290C2218yes—
188C42×Q8C2212yes—
189C42×Q8C2211yescharacteristic
190C42×Q8C2211yescharacteristic
191C42×D4C2211yescharacteristic
192C42×D4C2212yes—
193C42×D4C2214yes—
194C42×D4C2212yes—
195C42×D4C2212yes—
196C4×#117C2212yes—
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2214yes—
199C22×#41C2314yes—
200#559—28no—
201#557—48no—
202#556—28no—
203#554—28no—
204#554—216no—
205#547—216no—
206#532—216no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#126C2314yes—
215C2×#125C2312yes—
216C2×#125C2314yes—
217C2×#125C2318yes—
218C2×#125C2314yes—
219C2×#124C2314yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#123C2318yes—
224C2×#123C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C4×#41—416no—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2318yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2318yes—
266C2×C4×D4C2311yescharacteristic
267C2×#117C2312yes—
268C2×#117C2312yes—
269C2×#117C2318yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2312yes—
274C22×C42C2312yes—
275C22×C42C2318yes—
276C22×C42C2314yes—
277C22×C42C2314yes—
278#401C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#399C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#396C2318yes—
300#396C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#391C2312yes—
306#391C2314yes—
307#391C2314yes—
308#391C2312yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2312yes—
315#391C2314yes—
316#391C2312yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#390C2312yes—
324#390C2312yes—
325#390C2312yes—
326#390C2312yes—
327#390C2312yes—
328#390C2312yes—
329#390C2314yes—
330#390C2314yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2312yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2318yes—
347#389C2318yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#388C2314yes—
356#388C2314yes—
357#388C2314yes—
358#388C2314yes—
359#388C2318yes—
360#388C2318yes—
361#388C2314yes—
362#388C2318yes—
363#388C2318yes—
364#388C2314yes—
365#388C2314yes—
366#388C2318yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2318yes—
371#388C2314yes—
372#387C2314yes—
373#387C2314yes—
374#387C2314yes—
375#387C2314yes—
376#387C2314yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2314yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2314yes—
391#387C2318yes—
392#387C2318yes—
393#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2314yes—
404#386C2318yes—
405#385C2314yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2314yes—
410#385C2314yes—
411#385C2318yes—
412#385C2314yes—
413#385C2314yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2312yes—
422#384C2311yescharacteristic
423#384C2312yes—
424#384C2312yes—
425#384C2314yes—
426#384C2312yes—
427#383C2314yes—
428#383C2318yes—
429#382C2314yes—
430#382C2312yes—
431#382C2314yes—
432#382C2314yes—
433#382C2314yes—
434#382C2318yes—
435#382C2312yes—
436#382C2312yes—
437#382C2312yes—
438#381C2318yes—
439#381C2318yes—
440#381C2314yes—
441#380C2314yes—
442#380C2318yes—
443#380C2318yes—
444#380C2318yes—
445#380C2314yes—
446#380C2318yes—
447#380C2318yes—
448#380C2312yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452#380C2312yes—
453#380C2314yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2318yes—
503C4×C22⋊C4C2318yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2318yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520#376C2314yes—
521C2×#95C2314yes—
522C2×#95C2318yes—
523C43C2314yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C43C2312yes—
527C2×#41—216no—
528C2×#41—216no—
529C2×#41—48no—
530C22×Q8C2412yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2414yes—
534C22×Q8C2412yes—
535C22×D4C2418yes—
536C22×D4C2411yescharacteristic
537C22×D4C2412yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C23×C4C2414yes—
541C23×C4C2412yes—
542C23×C4C2418yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2418yes—
546C23×C4C2414yes—
547C23×C4C2414yes—
548C23×C4C2414yes—
549C23×C4C2412yes—
550C4⋊Q8—28no—
551C4⋊Q8—28no—
552C4⋊Q8—24no—
553C4⋊Q8—48no—
554C4⋊Q8—44no—
555C4⋊Q8#4118yescomplemented
556#127#4118yes—
557#126—216no—
558#125—28no—
559#125—216no—
560#125—416no—
561#125—48no—
562#124—216no—
563#124—28no—
564#124—28no—
565#124—28no—
566#123—216no—
567#123—232no—
568C22⋊Q8—216no—
569C22⋊Q8—232no—
570C22⋊Q8—216no—
571C22⋊Q8—28no—
572C22⋊Q8—216no—
573C22⋊Q8—28no—
574C22⋊Q8—48no—
575#121—216no—
576#121—216no—
577#121—216no—
578C4×Q8—28no—
579C4×Q8—216no—
580C4×Q8—24no—
581C4×Q8—24no—
582C4×Q8—28no—
583C4×Q8—24no—
584C4×Q8—24no—
585C4×Q8—24no—
586C4×Q8—24no—
587C4×Q8—48no—
588C4×Q8—44no—
589C4×Q8—44no—
590C4×Q8—48no—
591C4×D4—216no—
592C4×D4—216no—
593C4×D4—28no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—216no—
597C4×D4—28no—
598C4×D4—28no—
599C4×D4—28no—
600C4×D4—28no—
601C4×D4—24no—
602C4×D4—416no—
603C4×D4—44no—
604C4×D4—42no—
605C4×D4—48no—
606C4×D4—44no—
607C4×D4—416no—
608C4×D4#4118yes—
609#117—28no—
610#117—28no—
611#117—416no—
612C2×C4⋊C4—216no—
613C2×C4⋊C4—216no—
614C2×C4⋊C4—28no—
615C2×C4⋊C4—28no—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2412yes—
690C2×C42—28no—
691C2×C42—416no—
692C2×C42—48no—
693C2×C42—48no—
694C2×C42C2414yes—
695C2×C42C2414yes—
696C2×C42C2411yescharacteristic
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2418yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2411yescharacteristic
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#95C2414yes—
729#95C2414yes—
730#95C2412yes—
731#95C2414yes—
732#95C2418yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2412yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2414yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2412yes—
750#95C2414yes—
751#95C2418yes—
752#95C2412yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2412yes—
762#95C2414yes—
763#95C2412yes—
764#95C2418yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772C24C2514yes—
773C24C2512yes—
774#41—464no—
775C2×Q8—24no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—22no—
780C2×Q8—24no—
781C2×Q8—28no—
782C2×Q8—28no—
783C2×Q8—28no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—24no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8C2×#4118yes—
790C2×D4—216no—
791C2×D4—216no—
792C2×D4—22no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—22no—
798C2×D4—48no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4C2×#4118yes—
802C2×D4C2×#4118yes—
803C2×D4C2×#4114yes—
804C2×D4C2×#4118yes—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—216no—
808C22×C4—28no—
809C22×C4—24no—
810C22×C4—28no—
811C22×C4—28no—
812C22×C4—24no—
813C22×C4—216no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—216no—
821C22×C4—28no—
822C22×C4—48no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—48no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—44no—
832C22×C4—48no—
833C22×C4—44no—
834C22×C4C2×#4118yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2518yes—
847C22×C4C2511yescharacteristic
848C22×C4C2512yes—
849C22×C4C2511yescharacteristic
850C22×C4C2512yes—
851C22×C4C2511yescharacteristic
852C22×C4C2514yes—
853C22×C4C2511yescharacteristic
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C4⋊C4—24no—
860C4⋊C4—22no—
861C4⋊C4—28no—
862C4⋊C4—216no—
863C4⋊C4—28no—
864C4⋊C4—216no—
865C4⋊C4—22no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—22no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—28no—
881C4⋊C4—216no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—216no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—22no—
891C4⋊C4—24no—
892C4⋊C4—42no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—42no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—42no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—44no—
904C4⋊C4C2×#4114yes—
905C4⋊C4C2×#4118yes—
906C4⋊C4C2×#4118yes—
907C4⋊C4H(5,𝔽2)14yes—
908C4⋊C42−1+414yes—
909C22⋊C4—28no—
910C22⋊C4—216no—
911C22⋊C4—216no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—216no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—216no—
919C22⋊C4—24no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—42no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4C2×#4118yes—
933C42—24no—
934C42—24no—
935C42—24no—
936C42—28no—
937C42—24no—
938C42—24no—
939C42—24no—
940C42—28no—
941C42—24no—
942C42—28no—
943C42—24no—
944C42—216no—
945C42—28no—
946C42—24no—
947C42—22no—
948C42—24no—
949C42—22no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—22no—
954C42—44no—
955C42—44no—
956C42—44no—
957C42—44no—
958C42—48no—
959C42—41no—
960C42—42no—
961C42—42no—
962C42—44no—
963C42—44no—
964C42C2×#4114yes—
965C42C2×#4114yes—
966C42C2×#4114yes—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—22no—
975C23—24no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23C22×#4114yes—
980C23C22×#4118yes—
981C23C2611yescharacteristic
982Q8—48no—
983Q8—48no—
984Q8—44no—
985Q8—416no—
986Q8—44no—
987D4—28no—
988D4—216no—
989D4—216no—
990D4—48no—
991D4—432no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—24no—
1006C2×C4—216no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—28no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—28no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—28no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—416no—
1050C2×C4—432no—
1051C2×C4—416no—
1052C2×C4—48no—
1053C2×C4—88no—
1054C2×C4—816no—
1055C2×C4—84no—
1056C2×C4—88no—
1057C2×C4—88no—
1058C2×C4C22×#4112yes—
1059C2×C4C22×#4114yes—
1060C2×C4C22×#4112yes—
1061C2×C4C22×#4112yes—
1062C2×C4C22×#4118yes—
1063C2×C4C22×#4112yes—
1064C2×C4C22×#4112yes—
1065C2×C4C22×#4112yes—
1066C2×C4C22×#4112yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4112yes—
1069C2×C4C2×H(5,𝔽2)14yes—
1070C2×C4C2×H(5,𝔽2)12yes—
1071C2×C4C2×2−1+414yes—
1072C2×C4C2×2−1+412yes—
1073C2×C4#58512yes—
1074C22—28no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—28no—
1079C22—28no—
1080C22—42no—
1081C22—44no—
1082C22—42no—
1083C22—44no—
1084C22—44no—
1085C22—42no—
1086C22—44no—
1087C22—42no—
1088C22C23×#4111yescharacteristic
1089C22C23×#4111yescharacteristic
1090C22C23×#4111yescharacteristic
1091C22C22×H(5,𝔽2)11yescharacteristic
1092C22C22×2−1+411yescharacteristic
1093C22C2×#58511yescharacteristic
1094C222−1+611yescharacteristic
1095C4—28no—
1096C4—22no—
1097C4—22no—
1098C4—22no—
1099C4—24no—
1100C4—24no—
1101C4—24no—
1102C4—42no—
1103C4—44no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—41no—
1109C4—44no—
1110C4—44no—
1111C4—44no—
1112C4—48no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4#348014yes—
1117C4#348114yes—
1118C4#348214yes—
1119C2—48no—
1120C2—44no—
1121C2C2×#348011yescharacteristic
1122C2C2×#348111yescharacteristic
1123C2C2×#348211yescharacteristic
1124C2#6298411yescharacteristic
1125C2#6299111yescharacteristic
1126C2#6300111yescharacteristic
1127C2#6301311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59904C2semidirect
2. #59823C2semidirect
3. #59723C2semidirect
4. #59660C2semidirect
5. #59507C2semidirect
6. #59437C2semidirect
7. #59397C2semidirect
8. #59064C2semidirect
9. #36599C2semidirect
10. #36598C2semidirect
11. #36560C2semidirect
12. #36505C2semidirect
13. #36454C2semidirect
14. #36453C2semidirect
15. #36452C2semidirect
16. #36450C2semidirect
17. #36406C2semidirect
18. #36299C2semidirect
19. #36256C2semidirect
21. C4×#559C2semidirect
22. C4×#554C2semidirect
23. C4×#554C2semidirect
24. C4×#556C2semidirect
25. C4×#547C2semidirect
26. #34141C2semidirect
555. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599042
#598232
#597232
#596602
#595072
#594372
#593972
#590642
#365992
#365982
#365602
#365052
#364542
#364532
#364522
#364502
#364062
#362992
#362562
#361272
C4×#5592
C4×#5542
C4×#5562
C4×#5472
#341412