Finite Group Databasebeta

← #8095351

Subgroups — #8095351

Order 512.

4362 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53118C214yesmaximal, complemented
2#53091C214yesmaximal, complemented
3#53038C214yesmaximal, complemented
4#53034C214yesmaximal, complemented
5#52322C218yesmaximal, complemented
6#46117C214yesmaximal, complemented
7#46113C214yesmaximal, complemented
8#46006C214yesmaximal, complemented
9#46001C214yesmaximal, complemented
10#45750C218yesmaximal, complemented
11#35630C211yesmaximal, characteristic, complemented
12#35619C211yesmaximal, characteristic
13#35576C211yesmaximal, characteristic, complemented
14#35574C211yesmaximal, characteristic
15#35557C211yesmaximal, characteristic
16#35532C211yesmaximal, characteristic
17#35313C211yesmaximal, characteristic, complemented
18#35312C211yesmaximal, characteristic
19#35286C211yesmaximal, characteristic, complemented
20#35275C211yesmaximal, characteristic, complemented
21#35182C211yesmaximal, characteristic
22#35154C211yesmaximal, characteristic, complemented
23C2×#2567C211yesmaximal, characteristic, complemented
24#34816C211yesmaximal, characteristic
25#34815C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32#2868C2212yes—
33#2863C2214yes—
34#2862C2212yes—
35#2861C2212yes—
36#2859C2214yes—
37#2859C2212yes—
38#2855C2214yes—
39#2853C2214yes—
40#2844C2218yes—
41#2843C2218yes—
42#2839C2218yes—
43#2838C2218yes—
44#2838C2218yes—
45#2838C2218yes—
46#2833C2218yes—
47#2833C2218yes—
48#2821C2218yes—
49#2817C2218yes—
50#2805C2218yes—
51#2791C2218yes—
52#2777C2218yes—
53#2776C2218yes—
54#2776C2218yes—
55#2775C2218yes—
56#2774C2218yes—
57#2774C2218yes—
58#2765C2218yes—
59#2758C2218yes—
60#2734C2218yes—
61#2729C2218yes—
62#2725C2218yes—
63#2725C2218yes—
64#2720C2218yes—
65#2713C2218yes—
66#2713C2218yes—
67#2698C2218yes—
68#2689C2218yes—
69#2677C2218yes—
70#2660C2212yes—
71#2660C2212yes—
72#2647C2214yes—
73#2645C2214yes—
74#2642C2212yes—
75#2640C2212yes—
76#2627C2214yes—
77#2623C2214yes—
78#2583C2214yes—
79#2579C2214yes—
80#2571C2214yes—
81#2567C2214yes—
82#2567C2214yes—
83#2567C2214yes—
84#2567C2214yes—
85#2567C2212yes—
86#2566C2212yes—
87#2565C2212yes—
88#2552C2214yes—
89#2552C2214yes—
90#2551C2214yes—
91#2551C2214yes—
92#2551C2214yes—
93#2550C2214yes—
94#2550C2214yes—
95#2542C2212yes—
96#2514C2212yes—
97#2514C2214yes—
98#2514C2214yes—
99#2514C2214yes—
100#2513C2212yes—
101#2512C2212yes—
102#2512C2214yes—
103#2511C2212yes—
104#2511C2214yes—
105#2511C2214yes—
106#2511C2214yes—
107#2511C2214yes—
108#2510C2214yes—
109#2509C2212yes—
110#2508C2212yes—
111#2507C2212yes—
112#2506C2212yes—
113#2505C2214yes—
114#2503C2212yes—
115#2502C2212yes—
116#2499C2212yes—
117#2499C2212yes—
118#2497C2214yes—
119#2496C2214yes—
120#2493C2218yes—
121#2493C2218yes—
122#2492C2214yes—
123#2489C2214yes—
124#2488C2218yes—
125#2481C2214yes—
126#2481C2218yes—
127#2473C2214yes—
128#2453C2214yes—
129#2453C2214yes—
130#2452C2214yes—
131#2451C2214yes—
132#2451C2214yes—
133#2451C2214yes—
134#2449C2218yes—
135#2448C2214yes—
136#2447C2214yes—
137#2446C2214yes—
138#2446C2214yes—
139#2442C2218yes—
140#2441C2214yes—
141#2440C2214yes—
142#2440C2214yes—
143#2440C2218yes—
144#2439C2214yes—
145#2434C2214yes—
146#2423C2214yes—
147#2421C2214yes—
148#2419C2218yes—
149#2409C2214yes—
150#2402C2214yes—
151#2401C2214yes—
152C2×#395C2214yes—
153#2383C2218yes—
154#2382C2218yes—
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2317C2211yescharacteristic
159#2316C2211yescharacteristic
160#2316C2211yescharacteristic
161#2311C2211yescharacteristic
162#2311C2211yescharacteristic
163#2310C2211yescharacteristic
164#2310C2211yescharacteristic
165#2310C2211yescharacteristic
166C4×#125C2214yes—
167C4×#126C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#391C2211yescharacteristic
178C2×#389C2214yes—
179#2285C2211yescharacteristic
180#2285C2211yescharacteristic
181C2×#384C2211yescharacteristic
182C2×#384C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2312yes—
190#544—44no—
191#544—44no—
192#536—44no—
193C2×C4⋊Q8—44no—
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2318yes—
202C2×C4⋊Q8C2318yes—
203C2×#126C2314yes—
204C2×#126C2318yes—
205C2×#125C2314yes—
206C2×#125C2312yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#125C2318yes—
211C2×#124C2312yes—
212C2×#123C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2318yes—
219#520—44no—
220C2×C4×Q8—44no—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2314yes—
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2312yes—
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2314yes—
242C22×C4⋊C4C2314yes—
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2312yes—
247#401C2314yes—
248#401C2318yes—
249#401C2318yes—
250#400C2314yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2314yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2314yes—
265#400C2314yes—
266#400C2318yes—
267#400C2314yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2314yes—
272#399C2318yes—
273#399C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2314yes—
286#398C2318yes—
287#398C2314yes—
288#398C2314yes—
289#397C2314yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2314yes—
295#397C2314yes—
296#397C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2314yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#393C2318yes—
314#393C2318yes—
315#391C2311yescharacteristic
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2311yescharacteristic
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2314yes—
332#391C2314yes—
333#391C2318yes—
334#391C2318yes—
335#391C2318yes—
336#391C2318yes—
337#391C2312yes—
338#391C2312yes—
339#390C2311yescharacteristic
340#390C2312yes—
341#390C2312yes—
342#390C2311yescharacteristic
343#390C2312yes—
344#390C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2318yes—
348#389C2318yes—
349#389C2318yes—
350#389C2318yes—
351#389C2318yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2318yes—
365#389C2318yes—
366#389C2318yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#386C2314yes—
409#386C2314yes—
410#386C2312yes—
411#386C2312yes—
412#386C2314yes—
413#386C2314yes—
414#385C2318yes—
415#385C2314yes—
416#385C2314yes—
417#385C2314yes—
418#385C2314yes—
419#385C2312yes—
420#385C2318yes—
421#385C2312yes—
422#385C2312yes—
423#385C2312yes—
424#385C2312yes—
425#385C2312yes—
426#385C2318yes—
427#385C2314yes—
428#385C2314yes—
429#384C2312yes—
430#384C2312yes—
431#384C2314yes—
432#384C2312yes—
433#384C2312yes—
434#384C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2318yes—
440#384C2311yescharacteristic
441#384C2312yes—
442#384C2311yescharacteristic
443#383C2314yes—
444#383C2318yes—
445#383C2318yes—
446#382C2314yes—
447#382C2312yes—
448#382C2312yes—
449#382C2312yes—
450#382C2318yes—
451#382C2312yes—
452#382C2318yes—
453#382C2312yes—
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#381C2318yes—
457#381C2314yes—
458#381C2314yes—
459#381C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491#376C2312yes—
492#376C2312yes—
493C2×#95C2312yes—
494C2×#95C2314yes—
495C2×#95C2314yes—
496C43C2312yes—
497C43C2312yes—
498C2×#41—24no—
499C2×#41—24no—
500C2×#41—24no—
501C22×Q8—24no—
502C22×Q8—24no—
503C22×Q8—24no—
504C22×Q8—44no—
505C22×Q8—84no—
506C22×Q8C2412yes—
507C22×Q8C2412yes—
508C22×Q8C2411yescharacteristic
509C22×Q8C2414yes—
510C22×Q8C2414yes—
511C22×Q8C2418yes—
512C22×D4C2412yes—
513C22×D4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2411yescharacteristic
523C23×C4C2414yes—
524C23×C4C2411yescharacteristic
525C4⋊Q8—48no—
526C4⋊Q8—48no—
527C4⋊Q8—44no—
528C4⋊Q8—44no—
529C4⋊Q8—44no—
530C4⋊Q8—44no—
531C4⋊Q8—44no—
532C4⋊Q8—88no—
533C4⋊Q8—88no—
534#126—216no—
535#126—88no—
536#125—216no—
537#125—44no—
538#125—44no—
539#125—44no—
540#125—44no—
541#125—88no—
542#124—44no—
543#123—48no—
544C22⋊Q8—48no—
545C22⋊Q8—48no—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548C22⋊Q8—88no—
549C22⋊Q8—88no—
550C4×Q8—48no—
551C4×Q8—48no—
552C4×Q8—44no—
553C4×D4—44no—
554C4×D4—48no—
555#117—24no—
556#117—24no—
557#117—24no—
558#117—24no—
559#117—24no—
560#117—24no—
561#117—24no—
562#117—44no—
563C2×C4⋊C4—24no—
564C2×C4⋊C4—24no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—28no—
567C2×C4⋊C4—44no—
568C2×C4⋊C4—44no—
569C2×C4⋊C4—44no—
570C2×C4⋊C4—84no—
571C2×C4⋊C4—84no—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2414yes—
645C2×C42—24no—
646C2×C42—24no—
647C2×C42—24no—
648C2×C42—44no—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2414yes—
667C2×C42C2418yes—
668C2×C42C2414yes—
669C2×C42C2418yes—
670C2×C42C2414yes—
671#95C2412yes—
672#95C2412yes—
673#95C2412yes—
674#95C2412yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718C24C2512yes—
719C24C2511yescharacteristic
720#41—416no—
721C2×Q8—24no—
722C2×Q8—24no—
723C2×Q8—22no—
724C2×Q8—24no—
725C2×Q8—24no—
726C2×Q8—24no—
727C2×Q8—24no—
728C2×Q8—22no—
729C2×Q8—22no—
730C2×Q8—48no—
731C2×Q8—48no—
732C2×Q8—48no—
733C2×Q8—44no—
734C2×Q8—44no—
735C2×Q8—48no—
736C2×Q8—48no—
737C2×Q8—416no—
738C2×Q8—816no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C22×C4—22no—
746C22×C4—24no—
747C22×C4—22no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—48no—
769C22×C4H(5,𝔽2)14yes—
770C22×C42−1+414yes—
771C22×C42−1+414yes—
772C22×C4C2514yes—
773C22×C4C2512yes—
774C22×C4C2512yes—
775C22×C4C2512yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2512yes—
785C22×C4C2514yes—
786C22×C4C2512yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—22no—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—44no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—44no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C42−1+418yes—
850C22⋊C4—24no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—28no—
858C22⋊C4—28no—
859C22⋊C4—28no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—44no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—24no—
872C42—24no—
873C42—22no—
874C42—22no—
875C42—24no—
876C42—24no—
877C42—22no—
878C42—22no—
879C42—24no—
880C42—24no—
881C42—24no—
882C42—24no—
883C42—28no—
884C42—28no—
885C42—48no—
886C42—44no—
887C42—44no—
888C42—48no—
889C42—44no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—24no—
894C23—22no—
895C23—22no—
896C23—24no—
897C23C2×H(5,𝔽2)12yes—
898C23C2×2−1+412yes—
899C23C2×2−1+412yes—
900C23C2611yescharacteristic
901Q8—48no—
902Q8—48no—
903Q8—44no—
904Q8—816no—
905Q8—164no—
906Q8—164no—
907D4—48no—
908D4—44no—
909C2×C4—28no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—28no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—28no—
958C2×C4—28no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—48no—
962C2×C4—48no—
963C2×C4—44no—
964C2×C4—48no—
965C2×C4—48no—
966C2×C4—84no—
967C2×C4—84no—
968C2×C4—84no—
969C2×C4—164no—
970C2×C4#563116yes—
971C2×C4C2×H(5,𝔽2)12yes—
972C2×C4C2×H(5,𝔽2)12yes—
973C2×C4C2×2−1+414yes—
974C2×C4C2×2−1+414yes—
975C2×C4C2×2−1+414yes—
976C2×C4C2×2−1+412yes—
977C2×C4C2×2−1+412yes—
978C2×C4C2×2−1+412yes—
979C2×C4C2×2−1+412yes—
980C22—22no—
981C22—22no—
982C22—24no—
983C22—24no—
984C22—42no—
985C22—42no—
986C22—44no—
987C22—44no—
988C22—42no—
989C22C2×#56314yes—
990C22C22×H(5,𝔽2)11yescharacteristic
991C22C22×2−1+412yes—
992C22C22×2−1+411yescharacteristic
993C22C22×2−1+411yescharacteristic
994C22H(7,𝔽2)12yes—
995C4—24no—
996C4—24no—
997C4—24no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—44no—
1003C4—44no—
1004C4—44no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—44no—
1009C4—44no—
1010C4—44no—
1011C4—44no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—44no—
1016C4C2×#56314yes—
1017C4C2×#56314yes—
1018C2—24no—
1019C2—82no—
1020C2C22×#56311yescharacteristic
1021C2#6283311yescharacteristic
1022C2#6287611yescharacteristic
1023C2#6294312yes—
1024C2#6294512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53118C2semidirect
2. #53091C2semidirect
3. #53038C2semidirect
4. #53034C2semidirect
5. #52322C2semidirect
6. #46117C2semidirect
7. #46113C2semidirect
8. #46006C2semidirect
9. #46001C2semidirect
10. #45750C2semidirect
11. #35630C2semidirect
13. #35576C2semidirect
17. #35313C2semidirect
19. #35286C2semidirect
20. #35275C2semidirect
22. #35154C2semidirect
23. C2×#2567C2semidirect
25. #34815C2semidirect

Maximal subgroups

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

subgroupindex
#531182
#530912
#530382
#530342
#523222
#461172
#461132
#460062
#460012
#457502
#356302
#356192
#355762
#355742
#355572
#355322
#353132
#353122
#352862
#352752
#351822
#351542
C2×#25672
#348162
#348152