Finite Group Databasebeta

← #7680449

Subgroups — #7680449

Order 512.

4443 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59766C214yesmaximal, complemented
2#59699C214yesmaximal
3#59695C214yesmaximal, complemented
4#59682C214yesmaximal, complemented
5#44740C218yesmaximal, complemented
6#44722C218yesmaximal, complemented
7#39513C211yesmaximal, characteristic, complemented
8#39510C212yesmaximal, complemented
9#39379C211yesmaximal, characteristic, complemented
10#39379C212yesmaximal, complemented
11#39127C212yesmaximal
12#38279C214yesmaximal, complemented
13#36584C211yesmaximal, characteristic, complemented
14#36560C211yesmaximal, characteristic, complemented
15#36314C212yesmaximal, complemented
16#35657C214yesmaximal, complemented
17#35345C212yesmaximal, complemented
18#35284C211yesmaximal, characteristic, complemented
19#34945C212yesmaximal, complemented
20#34337C212yesmaximal, complemented
21#34281C212yesmaximal, complemented
22#34151C211yesmaximal, characteristic
23C4×#541C211yesmaximal, characteristic, complemented
24C2×#557C2212yes—
25C2×#541C2211yescharacteristic
26C2×#541C2212yes—
27C2×#529C2211yescharacteristic
28#2868C2211yescharacteristic
29#2864C2214yes—
30#2859C2212yes—
31#2859C2212yes—
32#2859C2211yescharacteristic
33#2857C2212yes—
34#2800C2218yes—
35#2794C2218yes—
36#2793C2218yes—
37#2793C2218yes—
38#2776C2218yes—
39#2772C2218yes—
40#2766C2218yes—
41#2725C2218yes—
42#2725C2218yes—
43#2725C2218yes—
44#2725C2218yes—
45#2707C2218yes—
46#2647C2212yes—
47#2629C2212yes—
48#2629C2212yes—
49#2629C2214yes—
50#2629C2212yes—
51#2608C2218yes—
52#2608C2218yes—
53#2606C2218yes—
54#2606C2218yes—
55#2597C2218yes—
56#2594C2218yes—
57#2590C2218yes—
58#2587C2218yes—
59#2573C2218yes—
60#2571C2214yes—
61#2571C2212yes—
62#2568C2212yes—
63#2565C2214yes—
64#2562C2214yes—
65#2547C2212yes—
66#2546C2214yes—
67#2545C2214yes—
68#2545C2214yes—
69#2538C2214yes—
70#2538C2212yes—
71#2533C2218yes—
72#2533C2218yes—
73#2533C2218yes—
74#2530C2218yes—
75#2529C2218yes—
76#2529C2218yes—
77#2528C2218yes—
78#2526C2218yes—
79#2525C2218yes—
80#2525C2218yes—
81#2525C2218yes—
82#2515C2218yes—
83#2514C2214yes—
84#2512C2214yes—
85#2512C2218yes—
86#2511C2214yes—
87#2509C2214yes—
88#2509C2218yes—
89#2507C2214yes—
90#2506C2214yes—
91#2506C2218yes—
92#2506C2218yes—
93#2499C2214yes—
94#2497C2214yes—
95#2497C2214yes—
96#2495C2214yes—
97#2494C2214yes—
98#2453C2214yes—
99#2447C2214yes—
100#2446C2214yes—
101#2446C2214yes—
102#2429C2214yes—
103#2429C2214yes—
104#2426C2214yes—
105#2421C2214yes—
106#2421C2214yes—
107#2421C2214yes—
108#2401C2218yes—
109#2374C2214yes—
110#2373C2218yes—
111#2373C2218yes—
112#2373C2214yes—
113#2371C2218yes—
114#2370C2214yes—
115#2370C2218yes—
116#2370C2218yes—
117#2370C2212yes—
118#2367C2212yes—
119#2365C2214yes—
120#2365C2212yes—
121#2365C2214yes—
122#2363C2212yes—
123#2362C2212yes—
124#2362C2214yes—
125#2356C2214yes—
126#2351C2214yes—
127Q8×C4⋊C4C2214yes—
128Q8×C4⋊C4C2214yes—
129Q8×C4⋊C4C2212yes—
130Q8×C4⋊C4C2212yes—
131#2336C2214yes—
132#2334C2214yes—
133#2330C2211yescharacteristic
134#2330C2214yes—
135#2330C2212yes—
136#2330C2218yes—
137#2327C2211yescharacteristic
138#2323C2212yes—
139#2323C2214yes—
140#2320C2212yes—
141#2314C2211yescharacteristic
142#2314C2212yes—
143#2314C2212yes—
144C4×C4⋊Q8C2214yes—
145C4×C4⋊Q8C2212yes—
146C4×C4⋊Q8C2211yescharacteristic
147C4×C4⋊Q8C2212yes—
148C4×#125C2214yes—
149C4×#125C2211yescharacteristic
150C4×#125C2212yes—
151C4×#126C2214yes—
152C4×#124C2214yes—
153C4×C22⋊Q8C2212yes—
154C4×C22⋊Q8C2214yes—
155#2298C2212yes—
156#2295C2211yescharacteristic
157#2295C2214yes—
158#2295C2214yes—
159#2295C2214yes—
160#2293C2212yes—
161#2293C2211yescharacteristic
162#2290C2212yes—
163#2283C2214yes—
164#2276C2214yes—
165C42×Q8C2212yes—
166C42×Q8C2211yescharacteristic
167C42×D4C2211yescharacteristic
168C4×#117C2212yes—
169C4×#117C2211yescharacteristic
170C4×#117C2211yescharacteristic
171#557—216no—
172#541—28no—
173#541—216no—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2311yescharacteristic
178#529—28no—
179C2×#126C2314yes—
180C2×#126C2312yes—
181C2×#126C2318yes—
182C2×#125C2311yescharacteristic
183C2×#125C2312yes—
184C2×#125C2314yes—
185C2×#125C2314yes—
186C2×#125C2318yes—
187C2×#125C2311yescharacteristic
188C2×#125C2318yes—
189C2×#124C2311yescharacteristic
190C2×#124C2314yes—
191C2×#123C2312yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2311yescharacteristic
195C2×C22⋊Q8C2314yes—
196C2×#121C2311yescharacteristic
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2312yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2312yes—
207C2×C4×Q8C2311yescharacteristic
208C2×C4×D4C2312yes—
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2312yes—
211C2×#117C2311yescharacteristic
212C2×#117C2311yescharacteristic
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218#401C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#397C2318yes—
243#397C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#396C2318yes—
253#394C2318yes—
254#391C2312yes—
255#391C2314yes—
256#391C2312yes—
257#391C2314yes—
258#391C2314yes—
259#391C2314yes—
260#391C2312yes—
261#391C2314yes—
262#391C2314yes—
263#391C2314yes—
264#390C2318yes—
265#390C2312yes—
266#390C2314yes—
267#390C2314yes—
268#389C2312yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#389C2318yes—
274#389C2314yes—
275#389C2314yes—
276#389C2318yes—
277#389C2318yes—
278#389C2318yes—
279#389C2314yes—
280#389C2312yes—
281#389C2314yes—
282#389C2318yes—
283#389C2318yes—
284#389C2318yes—
285#389C2314yes—
286#389C2314yes—
287#389C2318yes—
288#389C2318yes—
289#389C2318yes—
290#389C2318yes—
291#389C2318yes—
292#389C2314yes—
293#389C2318yes—
294#389C2318yes—
295#389C2318yes—
296#389C2314yes—
297#389C2314yes—
298#389C2312yes—
299#389C2314yes—
300#389C2312yes—
301#389C2314yes—
302#389C2314yes—
303#389C2318yes—
304#388C2314yes—
305#388C2314yes—
306#388C2314yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2314yes—
317#388C2318yes—
318#388C2318yes—
319#388C2314yes—
320#388C2318yes—
321#388C2314yes—
322#388C2314yes—
323#388C2314yes—
324#388C2314yes—
325#387C2314yes—
326#387C2314yes—
327#387C2314yes—
328#387C2314yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2314yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2314yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2314yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2314yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2314yes—
360#387C2314yes—
361#387C2318yes—
362#386C2314yes—
363#385C2318yes—
364#385C2314yes—
365#385C2314yes—
366#384C2311yescharacteristic
367#384C2312yes—
368#384C2312yes—
369#384C2314yes—
370#384C2312yes—
371#384C2314yes—
372#384C2318yes—
373#384C2314yes—
374#383C2314yes—
375#383C2318yes—
376#383C2318yes—
377#382C2311yescharacteristic
378#382C2314yes—
379#382C2314yes—
380#382C2312yes—
381#382C2314yes—
382#382C2314yes—
383#382C2318yes—
384#381C2318yes—
385#380C2312yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2312yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2318yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2314yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2312yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2312yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2312yes—
438#376C2311yescharacteristic
439#376C2311yescharacteristic
440#376C2312yes—
441#376C2318yes—
442#376C2318yes—
443#376C2318yes—
444#376C2312yes—
445C43C2314yes—
446C43C2312yes—
447C43C2311yescharacteristic
448C43C2311yescharacteristic
449C43C2312yes—
450C22×Q8C2414yes—
451C22×Q8C2412yes—
452C22×Q8C2411yescharacteristic
453C22×D4C2411yescharacteristic
454C22×D4C2412yes—
455C23×C4C2411yescharacteristic
456C23×C4C2412yes—
457C23×C4C2411yescharacteristic
458C23×C4C2414yes—
459C23×C4C2411yescharacteristic
460C4⋊Q8—216no—
461C4⋊Q8—28no—
462C4⋊Q8—48no—
463C4⋊Q8#4118yes—
464#126—28no—
465#126—216no—
466#126—232no—
467#125—24no—
468#125—216no—
469#125—232no—
470#125—232no—
471#125—24no—
472#125—28no—
473#125—216no—
474#124—24no—
475#124—48no—
476#123—28no—
477C22⋊Q8—24no—
478C22⋊Q8—28no—
479C22⋊Q8—216no—
480C22⋊Q8—48no—
481#121—24no—
482C4×Q8—28no—
483C4×Q8—216no—
484C4×Q8—216no—
485C4×Q8—216no—
486C4×Q8—28no—
487C4×Q8—28no—
488C4×Q8—48no—
489C4×Q8—48no—
490C4×Q8—48no—
491C4×Q8—44no—
492C4×Q8#4118yes—
493C4×D4—24no—
494C4×D4—28no—
495C4×D4—44no—
496#117—28no—
497#117—24no—
498#117—28no—
499#117—24no—
500#117—44no—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2411yescharacteristic
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2411yescharacteristic
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C22⋊C4C2412yes—
547C2×C22⋊C4C2412yes—
548C2×C22⋊C4C2412yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C42—24no—
565C2×C42—28no—
566C2×C42C2411yescharacteristic
567C2×C42C2411yescharacteristic
568C2×C42C2412yes—
569C2×C42C2411yescharacteristic
570C2×C42C2412yes—
571C2×C42C2414yes—
572C2×C42C2418yes—
573C2×C42C2414yes—
574C2×C42C2414yes—
575C2×C42C2418yes—
576C2×C42C2412yes—
577C2×C42C2414yes—
578C2×C42C2411yescharacteristic
579C2×C42C2411yescharacteristic
580C2×C42C2412yes—
581C2×C42C2414yes—
582C2×C42C2414yes—
583C2×C42C2414yes—
584C2×C42C2418yes—
585C2×C42C2418yes—
586C2×C42C2418yes—
587C2×C42C2414yes—
588C2×C42C2414yes—
589C2×C42C2412yes—
590C2×C42C2414yes—
591C2×C42C2412yes—
592C2×C42C2414yes—
593C2×C42C2411yescharacteristic
594C2×C42C2412yes—
595C2×C42C2411yescharacteristic
596C2×C42C2411yescharacteristic
597#95C2414yes—
598#95C2414yes—
599#95C2412yes—
600#95C2412yes—
601#95C2412yes—
602#95C2414yes—
603#95C2418yes—
604#95C2412yes—
605#95C2414yes—
606#95C2412yes—
607#95C2412yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2414yes—
618#95C2414yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2418yes—
631#95C2414yes—
632#95C2418yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2414yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640C24C2512yes—
641C24C2511yescharacteristic
642C2×Q8—24no—
643C2×Q8—28no—
644C2×Q8—24no—
645C2×Q8—24no—
646C2×Q8—28no—
647C2×Q8—28no—
648C2×Q8C2×#4118yes—
649C2×Q8C2×#4114yes—
650C2×D4—22no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—44no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—24no—
657C22×C4—22no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—22no—
661C22×C4—24no—
662C22×C4—22no—
663C22×C4—28no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—42no—
667C22×C4C2514yes—
668C22×C4C2514yes—
669C22×C4C2511yescharacteristic
670C22×C4C2512yes—
671C22×C4C2511yescharacteristic
672C22×C4C2512yes—
673C22×C4C2514yes—
674C22×C4C2512yes—
675C22×C4C2514yes—
676C22×C4C2511yescharacteristic
677C22×C4C2514yes—
678C22×C4C2518yes—
679C22×C4C2518yes—
680C22×C4C2514yes—
681C22×C4C2512yes—
682C22×C4C2511yescharacteristic
683C22×C4C2512yes—
684C22×C4C2512yes—
685C22×C4C2512yes—
686C22×C4C2511yescharacteristic
687C22×C4C2511yescharacteristic
688C4⋊C4—24no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—28no—
692C4⋊C4—22no—
693C4⋊C4—24no—
694C4⋊C4—24no—
695C4⋊C4—28no—
696C4⋊C4—28no—
697C4⋊C4—24no—
698C4⋊C4—216no—
699C4⋊C4—28no—
700C4⋊C4—216no—
701C4⋊C4—216no—
702C4⋊C4—28no—
703C4⋊C4—28no—
704C4⋊C4—216no—
705C4⋊C4—28no—
706C4⋊C4—216no—
707C4⋊C4—216no—
708C4⋊C4—28no—
709C4⋊C4—24no—
710C4⋊C4—28no—
711C4⋊C4—24no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—28no—
715C4⋊C4—44no—
716C4⋊C4—44no—
717C4⋊C4—44no—
718C4⋊C4—48no—
719C4⋊C4—44no—
720C4⋊C4—48no—
721C4⋊C4—44no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—44no—
725C4⋊C4—48no—
726C4⋊C4—48no—
727C4⋊C4—48no—
728C4⋊C4—48no—
729C4⋊C4—48no—
730C4⋊C4C2×#4114yes—
731C4⋊C4C2×#4118yes—
732C4⋊C4C2×#41116yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—28no—
737C22⋊C4—24no—
738C22⋊C4—24no—
739C22⋊C4—24no—
740C22⋊C4—28no—
741C22⋊C4—216no—
742C22⋊C4—24no—
743C22⋊C4—44no—
744C22⋊C4—48no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—48no—
749C22⋊C4—48no—
750C22⋊C4—48no—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—24no—
756C42—216no—
757C42—28no—
758C42—28no—
759C42—216no—
760C42—28no—
761C42—24no—
762C42—22no—
763C42—28no—
764C42—24no—
765C42—28no—
766C42—24no—
767C42—42no—
768C42—44no—
769C42—42no—
770C42—44no—
771C42—44no—
772C42—44no—
773C42—44no—
774C42—48no—
775C42—44no—
776C42—48no—
777C42—48no—
778C42C2×#4114yes—
779C42C2×#4114yes—
780C42C2×#4118yes—
781C422−1+414yes—
782C23—21no—
783C23—22no—
784C23—22no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—22no—
789C23—24no—
790C23—24no—
791C23—22no—
792C23C2611yescharacteristic
793Q8—216no—
794Q8—28no—
795Q8—416no—
796D4—44no—
797D4—84no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—24no—
813C2×C4—28no—
814C2×C4—24no—
815C2×C4—28no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—21no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—28no—
831C2×C4—22no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—44no—
845C2×C4—48no—
846C2×C4—44no—
847C2×C4—82no—
848C2×C4—88no—
849C2×C4C22×#4114yes—
850C2×C4C22×#4118yes—
851C2×C4C22×#4112yes—
852C2×C4C22×#4114yes—
853C2×C4C22×#4114yes—
854C2×C4C22×#4112yes—
855C2×C4C22×#4112yes—
856C2×C4C22×#4112yes—
857C2×C4C2×2−1+414yes—
858C2×C4C2×2−1+412yes—
859C2×C4#58514yes—
860C22—42no—
861C22—44no—
862C22—41no—
863C22—42no—
864C22—41no—
865C22—42no—
866C22—44no—
867C22—42no—
868C22—42no—
869C22—41no—
870C22C23×#4111yescharacteristic
871C22C23×#4111yescharacteristic
872C22C22×2−1+411yescharacteristic
873C22C2×#58512yes—
874C222−1+612yes—
875C4—24no—
876C4—24no—
877C4—22no—
878C4—24no—
879C4—24no—
880C4—28no—
881C4—42no—
882C4—44no—
883C4—44no—
884C4—48no—
885C4—41no—
886C4—48no—
887C4—44no—
888C4—41no—
889C4—42no—
890C4—44no—
891C4—44no—
892C4—41no—
893C4—42no—
894C4#348214yes—
895C4#351214yes—
896C2—81no—
897C2—82no—
898C2C2×#348211yescharacteristic
899C2C2×#351211yescharacteristic
900C2#6286111yescharacteristic
901C2#6295912yes—
902C2#6300712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59766C2semidirect
3. #59695C2semidirect
4. #59682C2semidirect
5. #44740C2semidirect
6. #44722C2semidirect
7. #39513C2semidirect
8. #39510C2semidirect
9. #39379C2semidirect
10. #39379C2semidirect
12. #38279C2semidirect
13. #36584C2semidirect
14. #36560C2semidirect
15. #36314C2semidirect
16. #35657C2semidirect
17. #35345C2semidirect
18. #35284C2semidirect
19. #34945C2semidirect
20. #34337C2semidirect
21. #34281C2semidirect
23. C4×#541C2semidirect

Maximal subgroups

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

subgroupindex
#597662
#596992
#596952
#596822
#447402
#447222
#395132
#395102
#393792
#391272
#382792
#365842
#365602
#363142
#356572
#353452
#352842
#349452
#343372
#342812
#341512
C4×#5412