Finite Group Databasebeta

← #7688589

Subgroups — #7688589

Order 512.

5141 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59482C214yesmaximal, complemented
3#59410C212yesmaximal, complemented
4#59309C214yesmaximal, complemented
5#59212C212yesmaximal, complemented
6#59033C212yesmaximal, complemented
7#45406C214yesmaximal, complemented
8#43707C218yesmaximal, complemented
9#39906C214yesmaximal, complemented
10#39009C214yesmaximal, complemented
11#38933C212yesmaximal, complemented
12#38930C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36534C212yesmaximal, complemented
15#36504C212yesmaximal, complemented
16#36315C212yesmaximal, complemented
17#36188C211yesmaximal, characteristic, complemented
18#36164C212yesmaximal, complemented
19#36127C211yesmaximal, characteristic, complemented
20#36044C214yesmaximal, complemented
21#34945C212yesmaximal, complemented
22#34943C211yesmaximal, characteristic, complemented
23#34232C212yesmaximal, complemented
24#34191C212yesmaximal, complemented
25C4×#556C211yesmaximal, characteristic, complemented
26C4×#550C211yesmaximal, characteristic, complemented
27C2×#556C2211yescharacteristic
28C2×#556C2212yes—
29C2×#554C2212yes—
30C2×#550C2211yescharacteristic
31C2×#547C2212yes—
32C2×#532C2212yes—
33C2×C4×#41C2212yes—
34#2868C2211yescharacteristic
35#2862C2212yes—
36#2861C2214yes—
37#2857C2212yes—
38#2857C2212yes—
39#2850C2214yes—
40#2778C2218yes—
41#2766C2218yes—
42#2761C2218yes—
43#2756C2218yes—
44#2743C2218yes—
45#2740C2218yes—
46#2738C2218yes—
47#2738C2218yes—
48#2732C2214yes—
49#2705C2218yes—
50#2688C2218yes—
51#2648C2218yes—
52#2647C2214yes—
53#2595C2218yes—
54#2582C2212yes—
55#2573C2218yes—
56#2572C2214yes—
57#2571C2212yes—
58#2571C2211yescharacteristic
59#2570C2214yes—
60#2569C2218yes—
61#2568C2212yes—
62#2568C2212yes—
63#2565C2214yes—
64#2563C2211yescharacteristic
65#2563C2211yescharacteristic
66#2560C2218yes—
67#2560C2218yes—
68#2554C2218yes—
69#2552C2212yes—
70#2547C2212yes—
71#2547C2212yes—
72#2547C2212yes—
73#2544C2214yes—
74#2542C2212yes—
75#2540C2214yes—
76#2538C2212yes—
77#2538C2214yes—
78#2537C2211yescharacteristic
79#2537C2212yes—
80#2537C2212yes—
81#2536C2214yes—
82#2536C2214yes—
83#2535C2214yes—
84#2531C2218yes—
85#2531C2218yes—
86#2529C2218yes—
87#2515C2218yes—
88#2514C2214yes—
89#2511C2214yes—
90#2510C2218yes—
91#2504C2214yes—
92#2503C2214yes—
93#2499C2214yes—
94#2497C2214yes—
95#2496C2214yes—
96#2496C2214yes—
97#2495C2212yes—
98#2495C2212yes—
99#2494C2214yes—
100#2494C2214yes—
101#2489C2214yes—
102#2489C2214yes—
103#2488C2218yes—
104#2488C2218yes—
105#2485C2214yes—
106#2479C2218yes—
107#2467C2218yes—
108#2454C2214yes—
109#2447C2214yes—
110#2446C2214yes—
111#2444C2218yes—
112#2432C2214yes—
113#2431C2214yes—
114#2426C2214yes—
115#2423C2214yes—
116#2423C2214yes—
117#2422C2214yes—
118#2422C2214yes—
119#2421C2214yes—
120#2420C2214yes—
121#2420C2212yes—
122#2420C2212yes—
123#2417C2214yes—
124#2417C2214yes—
125#2414C2214yes—
126#2407C2214yes—
127#2401C2218yes—
128#2398C2214yes—
129#2373C2214yes—
130#2367C2212yes—
131#2366C2212yes—
132#2366C2211yescharacteristic
133#2366C2212yes—
134#2365C2211yescharacteristic
135#2365C2212yes—
136#2365C2212yes—
137#2365C2212yes—
138#2363C2214yes—
139#2363C2214yes—
140#2363C2212yes—
141#2363C2214yes—
142#2362C2212yes—
143#2356C2212yes—
144#2355C2211yescharacteristic
145#2355C2212yes—
146#2355C2212yes—
147#2354C2211yescharacteristic
148#2354C2212yes—
149#2354C2211yescharacteristic
150#2354C2214yes—
151#2353C2218yes—
152#2352C2214yes—
153#2352C2214yes—
154#2352C2214yes—
155Q8×C4⋊C4C2211yescharacteristic
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159#2347C2212yes—
160#2346C2214yes—
161#2343C2218yes—
162#2341C2214yes—
163#2341C2212yes—
164#2339C2214yes—
165#2339C2214yes—
166#2339C2214yes—
167#2333C2218yes—
168#2320C2214yes—
169#2319C2214yes—
170#2318C2218yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×#127C2212yes—
175C4×#127C2211yescharacteristic
176C4×#126C2214yes—
177C4×#124C2212yes—
178C4×#124C2214yes—
179C4×#124C2214yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2214yes—
182C4×#121C2212yes—
183C4×#121C2212yes—
184C4×#121C2214yes—
185C4×#121C2212yes—
186#2295C2214yes—
187#2285C2212yes—
188#2283C2212yes—
189#2283C2212yes—
190#2283C2214yes—
191C2×#382C2214yes—
192#2275C2214yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2212yes—
195C42×D4C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C22×#41C2312yes—
200C22×#41C2314yes—
201#556—28no—
202#556—48no—
203#554—48no—
204#550—28no—
205#547—48no—
206#532—216no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×#127C2312yes—
213C2×#127C2311yescharacteristic
214C2×#126C2314yes—
215C2×#126C2318yes—
216C2×#125C2314yes—
217C2×#124C2312yes—
218C2×#124C2314yes—
219C2×#124C2314yes—
220C2×#123C2318yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2312yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C4×#41—216no—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×#117C2314yes—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2314yes—
269C2×#117C2312yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2314yes—
272C22×C42C2314yes—
273C22×C42C2312yes—
274C22×C42C2312yes—
275#401C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#400C2318yes—
280#400C2314yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#399C2318yes—
285#399C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2314yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2314yes—
306#394C2318yes—
307#394C2314yes—
308#394C2318yes—
309#394C2318yes—
310#393C2314yes—
311#393C2314yes—
312#392C2318yes—
313#392C2318yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2312yes—
326#391C2314yes—
327#391C2312yes—
328#390C2314yes—
329#390C2314yes—
330#390C2312yes—
331#390C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2314yes—
339#390C2318yes—
340#390C2318yes—
341#390C2314yes—
342#390C2314yes—
343#390C2312yes—
344#390C2318yes—
345#389C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2314yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2314yes—
362#389C2314yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2314yes—
373#388C2314yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2318yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#386C2318yes—
401#386C2318yes—
402#386C2314yes—
403#386C2314yes—
404#386C2318yes—
405#386C2314yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2314yes—
412#386C2314yes—
413#386C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#384C2312yes—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2312yes—
424#384C2312yes—
425#384C2312yes—
426#384C2314yes—
427#384C2312yes—
428#383C2314yes—
429#383C2314yes—
430#383C2314yes—
431#383C2318yes—
432#382C2312yes—
433#382C2312yes—
434#382C2314yes—
435#382C2314yes—
436#382C2314yes—
437#382C2314yes—
438#382C2312yes—
439#382C2312yes—
440#382C2318yes—
441#382C2318yes—
442#382C2312yes—
443#381C2314yes—
444#381C2314yes—
445#381C2318yes—
446#381C2318yes—
447#381C2318yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451#380C2312yes—
452#380C2314yes—
453#380C2318yes—
454#380C2318yes—
455#380C2314yes—
456#380C2314yes—
457#380C2312yes—
458#380C2312yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2312yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2318yes—
498C4×C4⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2318yes—
503C4×C22⋊C4C2318yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518#376C2314yes—
519#376C2318yes—
520#376C2314yes—
521C2×#95C2318yes—
522C2×#95C2318yes—
523C43C2314yes—
524C43C2311yescharacteristic
525C43C2312yes—
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—216no—
529C2×#41—44no—
530C2×#41—48no—
531C2×#41—48no—
532C22×Q8C2412yes—
533C22×Q8C2414yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2412yes—
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2414yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2414yes—
542C22×D4C2418yes—
543C22×D4C2414yes—
544C22×D4C2412yes—
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2418yes—
552C23×C4C2414yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2418yes—
556C4⋊Q8—28no—
557C4⋊Q8—24no—
558C4⋊Q8—28no—
559C4⋊Q8—24no—
560C4⋊Q8—44no—
561#127—28no—
562#127#4118yes—
563#126—216no—
564#126—416no—
565#125—48no—
566#124—216no—
567#124—28no—
568#124—48no—
569#123—416no—
570C22⋊Q8—28no—
571C22⋊Q8—416no—
572C22⋊Q8—48no—
573C22⋊Q8—48no—
574C22⋊Q8—48no—
575C22⋊Q8—48no—
576#121—216no—
577#121—216no—
578#121—28no—
579#121—216no—
580#121—44no—
581#121—44no—
582#121—48no—
583C4×Q8—28no—
584C4×Q8—24no—
585C4×Q8—28no—
586C4×Q8—28no—
587C4×Q8—44no—
588C4×Q8—44no—
589C4×Q8—48no—
590C4×Q8—42no—
591C4×Q8—48no—
592C4×Q8#4118yescomplemented
593C4×D4—216no—
594C4×D4—216no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—216no—
598C4×D4—28no—
599C4×D4—216no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—28no—
604C4×D4—24no—
605C4×D4—42no—
606C4×D4—48no—
607C4×D4—44no—
608C4×D4—42no—
609C4×D4—48no—
610C4×D4—44no—
611C4×D4—48no—
612C4×D4—48no—
613#117—28no—
614#117—216no—
615#117—28no—
616#117—44no—
617#117—48no—
618C2×C4⋊C4—48no—
619C2×C4⋊C4—48no—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2412yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C42—28no—
698C2×C42—216no—
699C2×C42—28no—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2414yes—
703C2×C42C2411yescharacteristic
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2414yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2418yes—
718C2×C42C2414yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2418yes—
722C2×C42C2414yes—
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2412yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2412yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2412yes—
747#95C2414yes—
748#95C2414yes—
749#95C2412yes—
750#95C2414yes—
751#95C2412yes—
752#95C2412yes—
753#95C2412yes—
754#95C2412yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2412yes—
762#95C2412yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2414yes—
767#95C2418yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771C24C2512yes—
772C24C2512yes—
773C24C2514yes—
774#41—432no—
775#41—832no—
776C2×Q8—22no—
777C2×Q8—24no—
778C2×Q8—28no—
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—24no—
782C2×Q8—22no—
783C2×Q8—24no—
784C2×Q8—28no—
785C2×Q8—42no—
786C2×Q8—42no—
787C2×Q8C2×#4114yes—
788C2×D4—28no—
789C2×D4—28no—
790C2×D4—216no—
791C2×D4—24no—
792C2×D4—28no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—24no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—48no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—48no—
812C2×D4C2×#4118yes—
813C2×D4C2×#4118yes—
814C2×D4C2×#4118yes—
815C22×C4—28no—
816C22×C4—216no—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—28no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—28no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—28no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—44no—
837C22×C4—48no—
838C22×C4—44no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—44no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2514yes—
856C22×C4C2514yes—
857C22×C4C2518yes—
858C22×C4C2512yes—
859C22×C4C2511yescharacteristic
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2511yescharacteristic
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C22×C4C2511yescharacteristic
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C4⋊C4—28no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—22no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—22no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—22no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—22no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4C2×#4114yes—
914C4⋊C4C2×#4118yes—
915C22⋊C4—28no—
916C22⋊C4—216no—
917C22⋊C4—216no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—24no—
927C22⋊C4—24no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—42no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—42no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C42—24no—
949C42—28no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—28no—
954C42—24no—
955C42—24no—
956C42—28no—
957C42—24no—
958C42—28no—
959C42—22no—
960C42—24no—
961C42—28no—
962C42—24no—
963C42—22no—
964C42—22no—
965C42—42no—
966C42—44no—
967C42—41no—
968C42—44no—
969C42—48no—
970C42—48no—
971C42—42no—
972C42—44no—
973C42C2×#4114yes—
974C42C2×#4118yes—
975C42C2×#4114yes—
976C42H(5,𝔽2)14yes—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23C22×#4118yes—
998C23C2611yescharacteristic
999Q8—28no—
1000Q8—416no—
1001Q8—48no—
1002Q8—84no—
1003D4—216no—
1004D4—216no—
1005D4—48no—
1006D4—416no—
1007D4—44no—
1008D4—44no—
1009D4—88no—
1010D4—816no—
1011D4—88no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—28no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—28no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—28no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—416no—
1068C2×C4—48no—
1069C2×C4—48no—
1070C2×C4—48no—
1071C2×C4—416no—
1072C2×C4—48no—
1073C2×C4—84no—
1074C2×C4—88no—
1075C2×C4—84no—
1076C2×C4—816no—
1077C2×C4—168no—
1078C2×C4C22×#4114yes—
1079C2×C4C22×#4112yes—
1080C2×C4C22×#4112yes—
1081C2×C4C22×#4114yes—
1082C2×C4C22×#4112yes—
1083C2×C4C22×#4112yes—
1084C2×C4C22×#4112yes—
1085C2×C4C22×#4112yes—
1086C2×C4C2×H(5,𝔽2)12yes—
1087C2×C4C2×H(5,𝔽2)12yes—
1088C2×C4C2×H(5,𝔽2)12yes—
1089C2×C4#58512yes—
1090C2×C4#58512yes—
1091C2×C4#58512yes—
1092C22—28no—
1093C22—28no—
1094C22—28no—
1095C22—44no—
1096C22—44no—
1097C22—44no—
1098C22—44no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22C23×#4111yescharacteristic
1114C22C23×#4111yescharacteristic
1115C22C22×H(5,𝔽2)11yescharacteristic
1116C22C2×#58511yescharacteristic
1117C22C2×#58511yescharacteristic
1118C22C2×#58511yescharacteristic
1119C222−1+611yescharacteristic
1120C4—22no—
1121C4—24no—
1122C4—22no—
1123C4—22no—
1124C4—24no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—41no—
1130C4—44no—
1131C4—42no—
1132C4—48no—
1133C4—42no—
1134C4—44no—
1135C4—44no—
1136C4—44no—
1137C4—44no—
1138C4—42no—
1139C4—42no—
1140C4#347514yes—
1141C4#351414yes—
1142C4#351714yes—
1143C2—48no—
1144C2—82no—
1145C2—82no—
1146C2C2×#347511yescharacteristic
1147C2C2×#351411yescharacteristic
1148C2C2×#351711yescharacteristic
1149C2#6293111yescharacteristic
1150C2#6299111yescharacteristic
1151C2#6300911yescharacteristic
1152C2#6303111yescharacteristic
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. #59823C2semidirect
2. #59482C2semidirect
3. #59410C2semidirect
4. #59309C2semidirect
5. #59212C2semidirect
6. #59033C2semidirect
7. #45406C2semidirect
8. #43707C2semidirect
9. #39906C2semidirect
10. #39009C2semidirect
11. #38933C2semidirect
12. #38930C2semidirect
13. #36598C2semidirect
14. #36534C2semidirect
15. #36504C2semidirect
16. #36315C2semidirect
17. #36188C2semidirect
18. #36164C2semidirect
19. #36127C2semidirect
20. #36044C2semidirect
21. #34945C2semidirect
22. #34943C2semidirect
23. #34232C2semidirect
24. #34191C2semidirect
25. C4×#556C2semidirect
26. C4×#550C2semidirect
592. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598232
#594822
#594102
#593092
#592122
#590332
#454062
#437072
#399062
#390092
#389332
#389302
#365982
#365342
#365042
#363152
#361882
#361642
#361272
#360442
#349452
#349432
#342322
#341912
C4×#5562
C4×#5502