Finite Group Databasebeta

← #7987060

Subgroups — #7987060

Order 512.

4323 conjugacy classes of subgroups.

The subgroup lattice has 1075 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59435C212yesmaximal, complemented
3#59227C212yesmaximal, complemented
4#59065C212yesmaximal, complemented
5#50246C218yesmaximal, complemented
6#46109C214yesmaximal, complemented
7#45304C214yesmaximal, complemented
8#44983C214yesmaximal, complemented
9#42904C214yesmaximal, complemented
10#42711C214yesmaximal, complemented
11#39479C212yesmaximal, complemented
12#39194C212yesmaximal
13#39157C212yesmaximal, complemented
14#39157C212yesmaximal, complemented
15#39011C214yesmaximal, complemented
16#36584C212yesmaximal, complemented
17#36563C211yesmaximal, characteristic, complemented
18#36459C212yesmaximal, complemented
19#36194C211yesmaximal, characteristic, complemented
20#36134C211yesmaximal, characteristic, complemented
21#35202C212yesmaximal, complemented
22#35185C212yesmaximal, complemented
23#34943C211yesmaximal, characteristic
24#34941C211yesmaximal, characteristic, complemented
25#34394C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×#556C2211yescharacteristic
28C2×#533C2212yes—
29#2868C2211yescharacteristic
30#2864C2214yes—
31#2860C2214yes—
32#2859C2212yes—
33#2859C2214yes—
34#2857C2212yes—
35#2857C2212yes—
36#2837C2218yes—
37#2806C2214yes—
38#2801C2218yes—
39#2800C2218yes—
40#2783C2218yes—
41#2781C2218yes—
42#2777C2218yes—
43#2775C2218yes—
44#2773C2218yes—
45#2766C2218yes—
46#2762C2218yes—
47#2762C2218yes—
48#2754C2218yes—
49#2727C2218yes—
50#2723C2218yes—
51#2702C2218yes—
52#2689C2218yes—
53#2689C2218yes—
54#2667C2218yes—
55#2654C2218yes—
56#2650C2218yes—
57#2645C2214yes—
58#2624C2214yes—
59#2606C2218yes—
60#2604C2218yes—
61#2584C2214yes—
62#2582C2214yes—
63#2582C2212yes—
64#2574C2214yes—
65#2572C2214yes—
66#2571C2214yes—
67#2571C2214yes—
68#2571C2214yes—
69#2571C2212yes—
70#2571C2211yescharacteristic
71#2567C2212yes—
72#2567C2211yescharacteristic
73#2567C2212yes—
74#2563C2211yescharacteristic
75#2563C2212yes—
76#2563C2211yescharacteristic
77#2563C2211yescharacteristic
78#2562C2214yes—
79#2560C2218yes—
80#2552C2212yes—
81#2552C2212yes—
82#2552C2212yes—
83#2552C2212yes—
84#2552C2211yescharacteristic
85#2550C2214yes—
86#2542C2212yes—
87#2538C2212yes—
88#2538C2211yescharacteristic
89#2538C2212yes—
90#2537C2211yescharacteristic
91#2533C2218yes—
92#2532C2218yes—
93#2529C2218yes—
94#2513C2214yes—
95#2512C2214yes—
96#2509C2214yes—
97#2509C2218yes—
98#2509C2218yes—
99#2509C2214yes—
100#2509C2214yes—
101#2508C2212yes—
102#2507C2214yes—
103#2507C2214yes—
104#2500C2214yes—
105#2497C2214yes—
106#2497C2212yes—
107#2496C2214yes—
108#2496C2214yes—
109#2496C2214yes—
110#2496C2214yes—
111#2495C2214yes—
112#2495C2212yes—
113#2495C2212yes—
114#2494C2214yes—
115#2494C2214yes—
116#2492C2214yes—
117#2490C2214yes—
118#2489C2214yes—
119#2489C2214yes—
120#2485C2214yes—
121#2469C2218yes—
122#2469C2218yes—
123#2454C2212yes—
124#2451C2214yes—
125#2448C2214yes—
126#2441C2214yes—
127#2441C2214yes—
128#2441C2214yes—
129#2441C2214yes—
130#2441C2214yes—
131#2439C2214yes—
132#2429C2214yes—
133#2426C2214yes—
134#2423C2214yes—
135#2423C2212yes—
136#2421C2214yes—
137#2420C2212yes—
138#2420C2212yes—
139#2415C2214yes—
140#2398C2214yes—
141#2396C2214yes—
142#2378C2218yes—
143#2373C2214yes—
144#2369C2212yes—
145#2369C2212yes—
146#2369C2212yes—
147#2367C2212yes—
148#2365C2212yes—
149#2365C2211yescharacteristic
150#2365C2212yes—
151#2362C2212yes—
152#2356C2214yes—
153#2356C2212yes—
154#2355C2212yes—
155#2355C2212yes—
156#2355C2211yescharacteristic
157#2354C2212yes—
158#2354C2212yes—
159#2354C2211yescharacteristic
160#2354C2214yes—
161#2351C2214yes—
162#2351C2214yes—
163Q8×C4⋊C4C2212yes—
164Q8×C4⋊C4C2212yes—
165Q8×C4⋊C4C2212yes—
166#2347C2214yes—
167#2347C2212yes—
168#2346C2214yes—
169#2346C2214yes—
170#2330C2214yes—
171#2330C2214yes—
172#2330C2214yes—
173#2323C2214yes—
174#2323C2214yes—
175#2320C2218yes—
176#2314C2214yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×#125C2212yes—
182C4×#125C2214yes—
183C4×#126C2214yes—
184C4×#124C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189#2293C2212yes—
190#2285C2212yes—
191#2285C2212yes—
192#2283C2212yes—
193#2283C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199#556—28no—
200#533—216no—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×#126C2314yes—
208C2×#126C2318yes—
209C2×#126C2318yes—
210C2×#125C2314yes—
211C2×#125C2312yes—
212C2×#125C2314yes—
213C2×#125C2314yes—
214C2×#124C2312yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×#121C2312yes—
222C2×#121C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2314yes—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2314yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117C2314yes—
243C2×#117C2312yes—
244C2×#117C2314yes—
245C2×#117C2314yes—
246C2×#117C2312yes—
247C22×C42C2312yes—
248C22×C42C2312yes—
249#401C2318yes—
250#400C2318yes—
251#400C2314yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2314yes—
261#400C2314yes—
262#399C2314yes—
263#399C2318yes—
264#399C2318yes—
265#399C2318yes—
266#398C2318yes—
267#398C2314yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#398C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2314yes—
280#397C2314yes—
281#397C2318yes—
282#396C2314yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2314yes—
287#396C2318yes—
288#395C2314yes—
289#395C2318yes—
290#395C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2314yes—
294#394C2314yes—
295#394C2318yes—
296#393C2314yes—
297#393C2314yes—
298#393C2314yes—
299#393C2318yes—
300#391C2318yes—
301#391C2312yes—
302#391C2312yes—
303#391C2312yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2312yes—
308#391C2318yes—
309#391C2318yes—
310#391C2312yes—
311#391C2314yes—
312#391C2314yes—
313#391C2312yes—
314#390C2318yes—
315#390C2312yes—
316#390C2312yes—
317#390C2314yes—
318#390C2312yes—
319#390C2314yes—
320#390C2312yes—
321#390C2312yes—
322#389C2312yes—
323#389C2312yes—
324#389C2314yes—
325#389C2312yes—
326#389C2314yes—
327#389C2312yes—
328#389C2312yes—
329#389C2312yes—
330#389C2314yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2312yes—
338#389C2314yes—
339#389C2318yes—
340#389C2318yes—
341#389C2314yes—
342#389C2312yes—
343#389C2318yes—
344#389C2318yes—
345#389C2318yes—
346#389C2314yes—
347#389C2318yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2318yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2318yes—
365#389C2312yes—
366#389C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2314yes—
385#388C2318yes—
386#388C2318yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2318yes—
394#387C2314yes—
395#387C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2314yes—
411#387C2318yes—
412#386C2314yes—
413#386C2314yes—
414#385C2314yes—
415#385C2314yes—
416#384C2311yescharacteristic
417#384C2312yes—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2314yes—
421#384C2312yes—
422#384C2314yes—
423#384C2314yes—
424#384C2314yes—
425#384C2312yes—
426#384C2312yes—
427#384C2312yes—
428#384C2312yes—
429#383C2314yes—
430#383C2314yes—
431#383C2314yes—
432#383C2318yes—
433#382C2312yes—
434#382C2314yes—
435#382C2312yes—
436#382C2312yes—
437#382C2312yes—
438#382C2314yes—
439#382C2314yes—
440#382C2312yes—
441#382C2318yes—
442#382C2318yes—
443#382C2312yes—
444#382C2318yes—
445#382C2314yes—
446#381C2314yes—
447#381C2314yes—
448#380C2312yes—
449#380C2312yes—
450#380C2314yes—
451#380C2314yes—
452#380C2312yes—
453#380C2312yes—
454#380C2314yes—
455#380C2312yes—
456#380C2312yes—
457#380C2312yes—
458#380C2312yes—
459#380C2314yes—
460#380C2314yes—
461#380C2312yes—
462#380C2314yes—
463#380C2314yes—
464#380C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515#376C2318yes—
516#376C2314yes—
517#376C2314yes—
518C43C2314yes—
519C43C2312yes—
520C43C2311yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×Q8C2412yes—
523C22×Q8C2412yes—
524C22×Q8C2414yes—
525C22×Q8C2412yes—
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2414yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C4⋊Q8—28no—
536C4⋊Q8—24no—
537C4⋊Q8—24no—
538C4⋊Q8—44no—
539C4⋊Q8—82no—
540C4⋊Q8#4118yes—
541#126—216no—
542#126—88no—
543#126—88no—
544#125—216no—
545#125—48no—
546#125—44no—
547#125—48no—
548#124—28no—
549C22⋊Q8—216no—
550C22⋊Q8—216no—
551C22⋊Q8—28no—
552C22⋊Q8—44no—
553C22⋊Q8—84no—
554C22⋊Q8—84no—
555#121—44no—
556#121—44no—
557C4×Q8—216no—
558C4×Q8—28no—
559C4×Q8—216no—
560C4×Q8—24no—
561C4×Q8—24no—
562C4×Q8—28no—
563C4×Q8—44no—
564C4×Q8—44no—
565C4×Q8—44no—
566C4×Q8—48no—
567C4×Q8—42no—
568C4×Q8—84no—
569C4×D4—24no—
570C4×D4—24no—
571C4×D4—24no—
572C4×D4—24no—
573C4×D4—42no—
574C4×D4—42no—
575C4×D4—48no—
576#117—216no—
577#117—28no—
578#117—48no—
579#117—44no—
580#117—48no—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C42—28no—
662C2×C42—28no—
663C2×C42C2412yes—
664C2×C42C2418yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2411yescharacteristic
668C2×C42C2414yes—
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2414yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2412yes—
684C2×C42C2418yes—
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2418yes—
688C2×C42C2414yes—
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693#95C2412yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2412yes—
706#95C2412yes—
707#95C2412yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2412yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2412yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2414yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737#95C2414yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741C24C2512yes—
742C24C2512yes—
743C2×Q8—22no—
744C2×Q8—28no—
745C2×Q8—24no—
746C2×Q8—22no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—24no—
750C2×Q8—22no—
751C2×Q8—42no—
752C2×Q8—42no—
753C2×Q8—42no—
754C2×Q8—42no—
755C2×Q8—44no—
756C2×Q8—44no—
757C2×Q8C2×#4118yes—
758C2×D4—22no—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2512yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2511yescharacteristic
798C22×C4C2514yes—
799C22×C4C2518yes—
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2511yescharacteristic
803C22×C4C2514yes—
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C4⋊C4—22no—
810C4⋊C4—28no—
811C4⋊C4—22no—
812C4⋊C4—216no—
813C4⋊C4—216no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—24no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—28no—
821C4⋊C4—24no—
822C4⋊C4—22no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—22no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—44no—
843C4⋊C4—48no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—42no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—42no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C4⋊C4C2×#4118yes—
864C4⋊C4C2×#4118yes—
865C22⋊C4—216no—
866C22⋊C4—28no—
867C22⋊C4—24no—
868C22⋊C4—28no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—48no—
876C22⋊C4—42no—
877C22⋊C4—42no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—216no—
893C42—28no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—28no—
899C42—24no—
900C42—24no—
901C42—28no—
902C42—22no—
903C42—28no—
904C42—22no—
905C42—22no—
906C42—24no—
907C42—48no—
908C42—44no—
909C42—42no—
910C42—44no—
911C42—48no—
912C42—42no—
913C42—48no—
914C42—44no—
915C42—41no—
916C42C2×#4114yes—
917C422−1+414yes—
918C422−1+414yes—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23C2611yescharacteristic
934Q8—216no—
935Q8—48no—
936Q8—44no—
937Q8—88no—
938Q8—84no—
939D4—44no—
940D4—44no—
941D4—88no—
942C2×C4—24no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—24no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—28no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—28no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—48no—
1002C2×C4—48no—
1003C2×C4—48no—
1004C2×C4—48no—
1005C2×C4—84no—
1006C2×C4—84no—
1007C2×C4C22×#4118yes—
1008C2×C4C22×#4112yes—
1009C2×C4C22×#4112yes—
1010C2×C4C22×#4112yes—
1011C2×C4C2×2−1+412yes—
1012C2×C4C2×2−1+412yes—
1013C2×C4C2×2−1+412yes—
1014C2×C4C2×2−1+412yes—
1015C2×C4C2×2−1+412yes—
1016C2×C4C2×2−1+412yes—
1017C2×C4#58512yes—
1018C2×C4#58512yes—
1019C2×C4#58512yes—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22C23×#4111yescharacteristic
1035C22C22×2−1+411yescharacteristic
1036C22C22×2−1+411yescharacteristic
1037C22C2×#58511yescharacteristic
1038C22C2×#58511yescharacteristic
1039C22C2×#58511yescharacteristic
1040C22H(7,𝔽2)11yescharacteristic
1041C4—22no—
1042C4—28no—
1043C4—22no—
1044C4—22no—
1045C4—42no—
1046C4—42no—
1047C4—48no—
1048C4—42no—
1049C4—42no—
1050C4—41no—
1051C4—44no—
1052C4—44no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—44no—
1058C4—44no—
1059C4—42no—
1060C4—42no—
1061C4—44no—
1062C4#351514yes—
1063C4#351814yes—
1064C4#355514yes—
1065C2—82no—
1066C2—82no—
1067C2C2×#355511yescharacteristic
1068C2C2×#351511yescharacteristic
1069C2C2×#351811yescharacteristic
1070C2#6292611yescharacteristic
1071C2#6292911yescharacteristic
1072C2#6300611yescharacteristic
1073C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59435C2semidirect
3. #59227C2semidirect
4. #59065C2semidirect
5. #50246C2semidirect
6. #46109C2semidirect
7. #45304C2semidirect
8. #44983C2semidirect
9. #42904C2semidirect
10. #42711C2semidirect
11. #39479C2semidirect
13. #39157C2semidirect
14. #39157C2semidirect
15. #39011C2semidirect
16. #36584C2semidirect
17. #36563C2semidirect
18. #36459C2semidirect
19. #36194C2semidirect
20. #36134C2semidirect
21. #35202C2semidirect
22. #35185C2semidirect
24. #34941C2semidirect
25. #34394C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#594352
#592272
#590652
#502462
#461092
#453042
#449832
#429042
#427112
#394792
#391942
#391572
#390112
#365842
#365632
#364592
#361942
#361342
#352022
#351852
#349432
#349412
#343942
C4×#5562