Finite Group Databasebeta

← #7987476

Subgroups — #7987476

Order 512.

4541 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59832C211yesmaximal, characteristic, complemented
2#59711C214yesmaximal, complemented
3#59659C211yesmaximal, characteristic
4#59659C211yesmaximal, characteristic
5#51999C214yesmaximal, complemented
6#51882C214yesmaximal, complemented
7#46269C214yesmaximal, complemented
8#45000C214yesmaximal, complemented
9#44997C214yesmaximal, complemented
10#42738C214yesmaximal, complemented
11#42735C214yesmaximal, complemented
12#39633C212yesmaximal, complemented
13#39192C212yesmaximal, complemented
14#39162C214yesmaximal, complemented
15#39077C214yesmaximal, complemented
16#36560C211yesmaximal, characteristic, complemented
17#36311C214yesmaximal, complemented
18#36299C212yesmaximal, complemented
19#35194C214yesmaximal, complemented
20#34902C212yesmaximal, complemented
21#34491C211yesmaximal, characteristic, complemented
22#34485C211yesmaximal, characteristic
23C4×Q82C211yesmaximal, characteristic, complemented
24C2×Q82C2211yescharacteristic
25C2×Q82C2211yescharacteristic
26C2×#557C2212yes—
27C2×#556C2214yes—
28C2×#555C2211yescharacteristic
29#2868C2211yescharacteristic
30#2865C2218yes—
31#2863C2214yes—
32#2861C2214yes—
33#2859C2211yescharacteristic
34#2859C2211yescharacteristic
35#2831C2218yes—
36#2791C2218yes—
37#2790C2218yes—
38#2790C2218yes—
39#2772C2218yes—
40#2765C2218yes—
41#2764C2218yes—
42#2762C2218yes—
43#2757C2218yes—
44#2755C2218yes—
45#2734C2214yes—
46#2731C2214yes—
47#2731C2214yes—
48#2729C2218yes—
49#2729C2218yes—
50#2725C2218yes—
51#2725C2218yes—
52#2716C2218yes—
53#2700C2218yes—
54#2651C2218yes—
55#2650C2218yes—
56#2647C2214yes—
57#2642C2214yes—
58#2640C2214yes—
59#2625C2214yes—
60#2599C2218yes—
61#2597C2218yes—
62#2596C2214yes—
63#2594C2214yes—
64#2592C2212yes—
65#2589C2218yes—
66#2582C2212yes—
67#2581C2212yes—
68#2570C2212yes—
69#2568C2212yes—
70#2567C2214yes—
71#2566C2214yes—
72#2565C2212yes—
73#2565C2214yes—
74#2565C2212yes—
75#2551C2214yes—
76#2546C2214yes—
77#2546C2214yes—
78#2545C2214yes—
79#2545C2214yes—
80#2545C2212yes—
81#2538C2212yes—
82#2538C2212yes—
83#2533C2218yes—
84#2532C2218yes—
85#2525C2218yes—
86#2525C2214yes—
87#2524C2218yes—
88#2520C2218yes—
89#2515C2218yes—
90#2514C2212yes—
91#2513C2214yes—
92#2512C2214yes—
93#2512C2212yes—
94#2509C2214yes—
95#2509C2214yes—
96#2507C2214yes—
97#2506C2214yes—
98#2506C2214yes—
99#2502C2214yes—
100#2497C2214yes—
101#2496C2214yes—
102#2495C2214yes—
103#2492C2214yes—
104#2491C2214yes—
105#2491C2214yes—
106#2475C2218yes—
107#2475C2218yes—
108#2474C2218yes—
109#2469C2218yes—
110#2469C2214yes—
111#2466C2218yes—
112#2465C2218yes—
113#2452C2214yes—
114#2451C2214yes—
115#2451C2214yes—
116#2451C2214yes—
117#2448C2212yes—
118#2447C2214yes—
119#2446C2212yes—
120#2440C2214yes—
121#2439C2214yes—
122#2439C2214yes—
123#2429C2214yes—
124#2426C2214yes—
125#2426C2214yes—
126#2421C2214yes—
127#2401C2214yes—
128#2396C2214yes—
129#2381C2214yes—
130#2379C2214yes—
131#2369C2214yes—
132#2369C2211yescharacteristic
133#2369C2214yes—
134#2365C2214yes—
135#2365C2214yes—
136#2365C2214yes—
137#2362C2214yes—
138#2362C2214yes—
139#2361C2214yes—
140#2360C2214yes—
141#2356C2214yes—
142#2355C2212yes—
143Q8×C4⋊C4C2212yes—
144Q8×C4⋊C4C2214yes—
145D4×C4⋊C4C2212yes—
146#2346C2214yes—
147#2344C2214yes—
148#2331C2214yes—
149#2327C2214yes—
150#2326C2214yes—
151#2326C2214yes—
152#2324C2214yes—
153#2323C2214yes—
154#2320C2214yes—
155#2317C2214yes—
156C4×C4⋊Q8C2211yescharacteristic
157C4×C4⋊Q8C2211yescharacteristic
158C4×C4⋊Q8C2212yes—
159C4×C4⋊Q8C2214yes—
160C4×C4⋊Q8C2214yes—
161C4×C4⋊Q8C2211yescharacteristic
162C4×#126C2214yes—
163C4×#124C2212yes—
164C4×#124C2212yes—
165#2298C2214yes—
166#2295C2212yes—
167#2295C2214yes—
168#2293C2212yes—
169#2293C2214yes—
170C42×Q8C2211yescharacteristic
171C42×Q8C2212yes—
172C42×Q8C2214yes—
173Q82—28no—
174Q82—28no—
175#557—48no—
176#556—416no—
177#555—28no—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2312yes—
185C2×C4⋊Q8C2314yes—
186C2×C4⋊Q8C2314yes—
187C2×C4⋊Q8C2311yescharacteristic
188C2×#126C2314yes—
189C2×#126C2318yes—
190C2×#125C2312yes—
191C2×#125C2312yes—
192C2×#125C2314yes—
193C2×#125C2314yes—
194C2×#124C2312yes—
195C2×#124C2314yes—
196C2×#124C2312yes—
197C2×#124C2314yes—
198C2×#124C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2318yes—
202C2×#121C2314yes—
203C2×C4×Q8C2312yes—
204C2×C4×Q8C2312yes—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2314yes—
208C2×C4×Q8C2312yes—
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2312yes—
214C2×C4×Q8C2314yes—
215C2×C4×Q8C2314yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2312yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×#117C2314yes—
222C2×#117C2314yes—
223C2×#117C2318yes—
224C22×C4⋊C4C2314yes—
225#401C2314yes—
226#400C2318yes—
227#400C2314yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2314yes—
232#400C2318yes—
233#400C2314yes—
234#400C2314yes—
235#400C2318yes—
236#400C2318yes—
237#399C2314yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2314yes—
243#398C2318yes—
244#398C2314yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#397C2314yes—
250#397C2318yes—
251#397C2318yes—
252#397C2314yes—
253#397C2314yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#396C2314yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2314yes—
262#396C2318yes—
263#396C2314yes—
264#396C2318yes—
265#396C2318yes—
266#395C2314yes—
267#395C2318yes—
268#395C2318yes—
269#395C2318yes—
270#394C2318yes—
271#394C2318yes—
272#393C2318yes—
273#393C2318yes—
274#393C2314yes—
275#393C2318yes—
276#391C2312yes—
277#391C2312yes—
278#391C2312yes—
279#391C2314yes—
280#391C2312yes—
281#391C2314yes—
282#391C2312yes—
283#391C2318yes—
284#391C2314yes—
285#391C2314yes—
286#391C2314yes—
287#391C2314yes—
288#391C2318yes—
289#391C2312yes—
290#391C2314yes—
291#391C2312yes—
292#391C2314yes—
293#391C2314yes—
294#391C2314yes—
295#391C2318yes—
296#391C2312yes—
297#391C2312yes—
298#391C2318yes—
299#390C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2312yes—
303#390C2314yes—
304#390C2312yes—
305#390C2312yes—
306#390C2314yes—
307#390C2312yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2318yes—
316#389C2318yes—
317#389C2318yes—
318#389C2318yes—
319#389C2318yes—
320#389C2312yes—
321#389C2312yes—
322#389C2312yes—
323#389C2314yes—
324#389C2314yes—
325#389C2312yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2318yes—
334#389C2318yes—
335#388C2314yes—
336#388C2314yes—
337#388C2314yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2314yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2314yes—
347#388C2314yes—
348#388C2314yes—
349#388C2314yes—
350#388C2314yes—
351#388C2314yes—
352#388C2318yes—
353#388C2314yes—
354#388C2318yes—
355#388C2314yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2314yes—
361#387C2314yes—
362#387C2314yes—
363#387C2314yes—
364#387C2314yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2314yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2314yes—
374#387C2314yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2314yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2314yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#386C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#384C2314yes—
397#384C2312yes—
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2314yes—
402#384C2312yes—
403#384C2314yes—
404#384C2314yes—
405#383C2314yes—
406#383C2318yes—
407#383C2318yes—
408#382C2314yes—
409#382C2312yes—
410#382C2312yes—
411#382C2312yes—
412#382C2312yes—
413#382C2318yes—
414#382C2314yes—
415#381C2318yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2318yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2318yes—
446C4×C4⋊C4C2312yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453#376C2314yes—
454#376C2314yes—
455#376C2314yes—
456C43C2314yes—
457C43C2311yescharacteristic
458C43C2311yescharacteristic
459C43C2314yes—
460C43C2311yescharacteristic
461C22×Q8C2412yes—
462C22×Q8C2412yes—
463C22×Q8C2411yescharacteristic
464C22×Q8C2414yes—
465C22×Q8C2414yes—
466C22×Q8C2414yes—
467C22×Q8C2412yes—
468C22×D4C2412yes—
469C22×D4C2414yes—
470C23×C4C2414yes—
471C23×C4C2418yes—
472C4⋊Q8—216no—
473C4⋊Q8—216no—
474C4⋊Q8—28no—
475C4⋊Q8—216no—
476C4⋊Q8—216no—
477C4⋊Q8—48no—
478C4⋊Q8—48no—
479C4⋊Q8—48no—
480C4⋊Q8—44no—
481C4⋊Q8#4118yes—
482#126—216no—
483#126—416no—
484#125—48no—
485#125—48no—
486#125—44no—
487#125—44no—
488#124—216no—
489#124—28no—
490#124—48no—
491#124—48no—
492#124—44no—
493C22⋊Q8—216no—
494C22⋊Q8—416no—
495C22⋊Q8—48no—
496#121—216no—
497C4×Q8—28no—
498C4×Q8—216no—
499C4×Q8—216no—
500C4×Q8—216no—
501C4×Q8—24no—
502C4×Q8—28no—
503C4×Q8—28no—
504C4×Q8—44no—
505C4×Q8—48no—
506C4×Q8—44no—
507C4×Q8—44no—
508C4×Q8—44no—
509C4×Q8—48no—
510C4×Q8—48no—
511C4×Q8—44no—
512C4×D4—28no—
513C4×D4—48no—
514C4×D4—48no—
515#117—216no—
516#117—48no—
517#117—416no—
518C2×C4⋊C4—48no—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2411yescharacteristic
526C2×C4⋊C4C2411yescharacteristic
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2411yescharacteristic
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C42C2414yes—
587C2×C42C2412yes—
588C2×C42C2414yes—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2414yes—
592C2×C42C2414yes—
593C2×C42C2411yescharacteristic
594C2×C42C2411yescharacteristic
595C2×C42C2411yescharacteristic
596C2×C42C2412yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2414yes—
604C2×C42C2412yes—
605C2×C42C2412yes—
606C2×C42C2418yes—
607C2×C42C2414yes—
608C2×C42C2418yes—
609C2×C42C2414yes—
610C2×C42C2411yescharacteristic
611C2×C42C2414yes—
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615#95C2414yes—
616#95C2414yes—
617#95C2418yes—
618#95C2414yes—
619#95C2418yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2418yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2412yes—
637#95C2414yes—
638#95C2412yes—
639#95C2412yes—
640#95C2418yes—
641#95C2418yes—
642#95C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2414yes—
647#95C2418yes—
648#95C2414yes—
649#95C2418yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657C24C2514yes—
658C2×Q8—24no—
659C2×Q8—24no—
660C2×Q8—28no—
661C2×Q8—28no—
662C2×Q8—22no—
663C2×Q8—28no—
664C2×Q8—24no—
665C2×Q8—24no—
666C2×Q8—24no—
667C2×Q8—42no—
668C2×Q8—42no—
669C2×Q8—42no—
670C2×Q8—44no—
671C2×Q8—44no—
672C2×Q8—48no—
673C2×Q8—44no—
674C2×Q8—44no—
675C2×Q8C2×#4118yes—
676C2×Q82−1+418yes—
677C2×D4—24no—
678C2×D4—28no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—44no—
682C2×D4—44no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4C2514yes—
690C22×C4C2512yes—
691C22×C4C2512yes—
692C22×C4C2512yes—
693C22×C4C2514yes—
694C22×C4C2514yes—
695C22×C4C2514yes—
696C22×C4C2511yescharacteristic
697C22×C4C2514yes—
698C22×C4C2514yes—
699C22×C4C2514yes—
700C22×C4C2514yes—
701C22×C4C2514yes—
702C22×C4C2511yescharacteristic
703C22×C4C2511yescharacteristic
704C22×C4C2514yes—
705C22×C4C2511yescharacteristic
706C22×C4C2511yescharacteristic
707C22×C4C2511yescharacteristic
708C22×C4C2511yescharacteristic
709C22×C4C2514yes—
710C22×C4C2512yes—
711C4⋊C4—24no—
712C4⋊C4—216no—
713C4⋊C4—28no—
714C4⋊C4—216no—
715C4⋊C4—28no—
716C4⋊C4—24no—
717C4⋊C4—24no—
718C4⋊C4—28no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—24no—
726C4⋊C4—28no—
727C4⋊C4—216no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—24no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—48no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—48no—
739C4⋊C4—44no—
740C4⋊C4—42no—
741C4⋊C4—44no—
742C4⋊C4—48no—
743C4⋊C4—42no—
744C4⋊C4—42no—
745C4⋊C4—48no—
746C4⋊C4—42no—
747C4⋊C4—44no—
748C4⋊C4—42no—
749C4⋊C4—42no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—48no—
757C4⋊C4C2×#41116yes—
758C4⋊C4H(5,𝔽2)14yes—
759C22⋊C4—216no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—28no—
763C22⋊C4—28no—
764C22⋊C4—216no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—48no—
773C22⋊C4—48no—
774C22⋊C4—48no—
775C22⋊C4—48no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C42—28no—
779C42—28no—
780C42—28no—
781C42—28no—
782C42—28no—
783C42—28no—
784C42—28no—
785C42—28no—
786C42—28no—
787C42—22no—
788C42—22no—
789C42—22no—
790C42—28no—
791C42—24no—
792C42—24no—
793C42—24no—
794C42—24no—
795C42—28no—
796C42—24no—
797C42—24no—
798C42—41no—
799C42—41no—
800C42—41no—
801C42—44no—
802C42—44no—
803C42—48no—
804C42—48no—
805C42—44no—
806C42C2×#4114yes—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23C2611yescharacteristic
815Q8—216no—
816Q8—48no—
817Q8—44no—
818Q8—48no—
819Q8—88no—
820Q8—88no—
821Q8—88no—
822D4—48no—
823D4—88no—
824C2×C4—24no—
825C2×C4—21no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—21no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—28no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—22no—
861C2×C4—28no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—416no—
873C2×C4—816no—
874C2×C4C22×#4118yes—
875C2×C4C22×#4112yes—
876C2×C4C22×#4114yes—
877C2×C4C2×H(5,𝔽2)12yes—
878C2×C4C2×H(5,𝔽2)12yes—
879C2×C4C2×H(5,𝔽2)12yes—
880C2×C4C2×2−1+418yes—
881C2×C4C2×2−1+414yes—
882C2×C4#58514yes—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22C23×#4111yescharacteristic
891C22C22×H(5,𝔽2)11yescharacteristic
892C22C22×2−1+412yes—
893C22C2×#58512yes—
894C222−1+611yescharacteristic
895C4—28no—
896C4—22no—
897C4—22no—
898C4—22no—
899C4—22no—
900C4—28no—
901C4—44no—
902C4—44no—
903C4—44no—
904C4—44no—
905C4—41no—
906C4—41no—
907C4—44no—
908C4—44no—
909C4—41no—
910C4—44no—
911C4—44no—
912C4—42no—
913C4—44no—
914C4—42no—
915C4—42no—
916C4#351618yes—
917C2—84no—
918C2#6275911yescharacteristic
919C2C2×#351612yes—
920C2#6295312yes—
921C2#6298411yescharacteristic
922C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#555C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59832C2semidirect
2. #59711C2semidirect
5. #51999C2semidirect
6. #51882C2semidirect
7. #46269C2semidirect
8. #45000C2semidirect
9. #44997C2semidirect
10. #42738C2semidirect
11. #42735C2semidirect
12. #39633C2semidirect
13. #39192C2semidirect
14. #39162C2semidirect
15. #39077C2semidirect
16. #36560C2semidirect
17. #36311C2semidirect
18. #36299C2semidirect
19. #35194C2semidirect
20. #34902C2semidirect
21. #34491C2semidirect
23. C4×Q82C2semidirect

Maximal subgroups

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

subgroupindex
#598322
#597112
#596592
#519992
#518822
#462692
#450002
#449972
#427382
#427352
#396332
#391922
#391622
#390772
#365602
#363112
#362992
#351942
#349022
#344912
#344852
C4×Q822