Finite Group Databasebeta

← #7638440

Subgroups — #7638440

Order 512.

4638 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#52240C218yesmaximal, complemented
2#40031C214yesmaximal
3#40028C214yesmaximal, complemented
4#39769C211yesmaximal, characteristic, complemented
5#39641C211yesmaximal, characteristic, complemented
6#39513C211yesmaximal, characteristic, complemented
7#39385C211yesmaximal, characteristic, complemented
8#39200C212yesmaximal, complemented
9#38984C212yesmaximal, complemented
10#38496C218yesmaximal, complemented
11#38128C214yesmaximal, complemented
12#37897C212yesmaximal, complemented
13#37709C212yesmaximal, complemented
14#36645C211yesmaximal, characteristic, complemented
15#34979C212yesmaximal
16#34951C214yesmaximal, complemented
17#34916C214yesmaximal, complemented
18#34902C214yesmaximal, complemented
19#34629C212yesmaximal, complemented
20#34154C212yesmaximal, complemented
21C4×#541C212yesmaximal, complemented
22C4×#533C211yesmaximal, characteristic, complemented
23#34026C211yesmaximal, characteristic
24C2×#541C2212yes—
25C2×#533C2212yes—
26C2×#533C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28#2868C2211yescharacteristic
29#2868C2211yescharacteristic
30#2862C2212yes—
31#2859C2214yes—
32#2857C2212yes—
33#2857C2214yes—
34#2857C2212yes—
35#2794C2218yes—
36#2793C2218yes—
37#2791C2218yes—
38#2787C2218yes—
39#2781C2218yes—
40#2779C2218yes—
41#2773C2218yes—
42#2770C2218yes—
43#2767C2218yes—
44#2762C2218yes—
45#2754C2218yes—
46#2747C2218yes—
47#2741C2218yes—
48#2721C2218yes—
49#2702C2218yes—
50#2690C2218yes—
51#2655C2218yes—
52#2652C2218yes—
53#2647C2212yes—
54#2645C2214yes—
55#2642C2212yes—
56#2629C2212yes—
57#2625C2214yes—
58#2621C2212yes—
59#2611C2218yes—
60#2596C2218yes—
61#2594C2218yes—
62#2592C2214yes—
63#2590C2218yes—
64#2589C2218yes—
65#2588C2218yes—
66#2587C2218yes—
67#2585C2218yes—
68#2585C2218yes—
69#2582C2214yes—
70#2581C2214yes—
71#2570C2214yes—
72#2568C2212yes—
73#2568C2214yes—
74#2552C2214yes—
75#2547C2212yes—
76#2546C2212yes—
77#2546C2214yes—
78#2545C2214yes—
79#2542C2212yes—
80#2525C2218yes—
81#2514C2214yes—
82#2512C2214yes—
83#2511C2214yes—
84#2511C2214yes—
85#2511C2214yes—
86#2509C2218yes—
87#2507C2214yes—
88#2499C2214yes—
89#2497C2214yes—
90#2492C2214yes—
91#2469C2218yes—
92#2453C2218yes—
93#2451C2214yes—
94#2448C2214yes—
95#2446C2214yes—
96#2446C2214yes—
97#2446C2214yes—
98#2446C2214yes—
99#2432C2214yes—
100#2429C2214yes—
101#2423C2214yes—
102#2415C2214yes—
103#2415C2214yes—
104#2402C2218yes—
105#2402C2218yes—
106#2401C2218yes—
107#2396C2218yes—
108#2395C2218yes—
109#2371C2218yes—
110#2365C2212yes—
111#2365C2212yes—
112#2365C2212yes—
113#2365C2212yes—
114#2362C2214yes—
115#2362C2214yes—
116#2362C2214yes—
117#2362C2214yes—
118#2336C2218yes—
119#2334C2218yes—
120#2330C2212yes—
121#2327C2212yes—
122#2323C2214yes—
123#2320C2214yes—
124#2314C2212yes—
125C4×C4⋊Q8C2212yes—
126C4×C4⋊Q8C2212yes—
127C4×C4⋊Q8C2214yes—
128C4×C4⋊Q8C2212yes—
129C4×C4⋊Q8C2212yes—
130C4×C4⋊Q8C2214yes—
131C4×#125C2218yes—
132C4×#125C2211yescharacteristic
133C4×#125C2211yescharacteristic
134C4×#125C2211yescharacteristic
135C4×#125C2211yescharacteristic
136C4×#126C2218yes—
137C4×#124C2214yes—
138C4×C22⋊Q8C2214yes—
139C4×C22⋊Q8C2214yes—
140C4×C22⋊Q8C2214yes—
141C4×C22⋊Q8C2214yes—
142#2298C2218yes—
143#2298C2218yes—
144#2298C2214yes—
145#2297C2212yes—
146#2296C2212yes—
147#2296C2212yes—
148#2295C2218yes—
149#2295C2214yes—
150#2295C2211yescharacteristic
151#2295C2214yes—
152#2295C2211yescharacteristic
153#2295C2214yes—
154#2295C2212yes—
155#2293C2211yescharacteristic
156#2293C2212yes—
157#2293C2211yescharacteristic
158#2290C2212yes—
159#2290C2214yes—
160#2290C2212yes—
161#2285C2211yescharacteristic
162#2285C2214yes—
163C42×Q8C2214yes—
164C42×Q8C2214yes—
165C42×Q8C2214yes—
166C4×#117C2212yes—
167C4×#117C2212yes—
168C4×#117C2211yescharacteristic
169C4×#117C2212yes—
170C2×C43C2211yescharacteristic
171C22×#41C2311yescharacteristic
172#541—216no—
173#533—28no—
174#533—216no—
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2312yes—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2314yes—
182C2×#126C2318yes—
183C2×#125C2311yescharacteristic
184C2×#125C2318yes—
185C2×#125C2314yes—
186C2×#125C2311yescharacteristic
187C2×#124C2314yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C4×#41—28no—
194C2×C4×Q8C2311yescharacteristic
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2311yescharacteristic
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2314yes—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2311yescharacteristic
208C2×C4×D4C2311yescharacteristic
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2312yes—
212C2×#117C2314yes—
213C2×#117C2314yes—
214C2×#117C2311yescharacteristic
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220C22×C42C2312yes—
221C22×C42C2311yescharacteristic
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224#401C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#399C2318yes—
239#399C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#395C2318yes—
261#394C2318yes—
262#394C2318yes—
263#393C2318yes—
264#391C2314yes—
265#391C2314yes—
266#391C2314yes—
267#391C2314yes—
268#391C2314yes—
269#391C2314yes—
270#391C2314yes—
271#391C2314yes—
272#391C2312yes—
273#391C2314yes—
274#391C2318yes—
275#391C2314yes—
276#391C2314yes—
277#391C2314yes—
278#391C2318yes—
279#391C2314yes—
280#391C2314yes—
281#391C2314yes—
282#391C2312yes—
283#390C2312yes—
284#390C2314yes—
285#390C2312yes—
286#389C2312yes—
287#389C2312yes—
288#389C2312yes—
289#389C2312yes—
290#389C2318yes—
291#389C2318yes—
292#389C2318yes—
293#389C2318yes—
294#389C2318yes—
295#389C2318yes—
296#389C2314yes—
297#389C2318yes—
298#389C2318yes—
299#389C2314yes—
300#389C2312yes—
301#389C2314yes—
302#389C2314yes—
303#389C2312yes—
304#389C2314yes—
305#389C2312yes—
306#389C2318yes—
307#389C2318yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2312yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2314yes—
320#388C2318yes—
321#388C2318yes—
322#388C2314yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2314yes—
328#388C2314yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2314yes—
337#387C2314yes—
338#387C2314yes—
339#387C2314yes—
340#387C2318yes—
341#387C2318yes—
342#387C2314yes—
343#387C2314yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2314yes—
361#387C2314yes—
362#386C2314yes—
363#386C2314yes—
364#385C2318yes—
365#385C2318yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#385C2314yes—
370#384C2312yes—
371#384C2312yes—
372#384C2314yes—
373#384C2314yes—
374#384C2312yes—
375#384C2314yes—
376#384C2314yes—
377#383C2318yes—
378#382C2311yescharacteristic
379#382C2311yescharacteristic
380#382C2318yes—
381#382C2314yes—
382#382C2314yes—
383#382C2314yes—
384#380C2314yes—
385#380C2318yes—
386#380C2318yes—
387#380C2314yes—
388#380C2314yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2318yes—
391C4×C4⋊C4C2318yes—
392C4×C4⋊C4C2318yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2312yes—
397C4×C4⋊C4C2312yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2312yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2318yes—
432C4×C22⋊C4C2312yes—
433C4×C22⋊C4C2312yes—
434C4×C22⋊C4C2312yes—
435#376C2312yes—
436#376C2312yes—
437#376C2314yes—
438#376C2312yes—
439#376C2318yes—
440#376C2314yes—
441C43C2318yes—
442C43C2311yescharacteristic
443C43C2311yescharacteristic
444C43C2311yescharacteristic
445C43C2311yescharacteristic
446C43C2312yes—
447C43C2314yes—
448C43C2312yes—
449C43C2312yes—
450C2×#41—24no—
451C2×#41—44no—
452C22×Q8C2414yes—
453C22×Q8C2414yes—
454C22×Q8C2411yescharacteristic
455C22×Q8C2414yes—
456C22×D4C2411yescharacteristic
457C22×D4C2412yes—
458C23×C4C2412yes—
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2412yes—
466C4⋊Q8—28no—
467C4⋊Q8—28no—
468C4⋊Q8—28no—
469C4⋊Q8—28no—
470C4⋊Q8—44no—
471C4⋊Q8—48no—
472C4⋊Q8—48no—
473#126—232no—
474#125—232no—
475#125—24no—
476#125—216no—
477#125#4118yescomplemented
478#124—48no—
479C22⋊Q8—216no—
480C22⋊Q8—216no—
481C22⋊Q8—216no—
482C22⋊Q8—216no—
483C22⋊Q8—48no—
484C4×Q8—216no—
485C4×Q8—216no—
486C4×Q8—24no—
487C4×Q8—24no—
488C4×Q8—216no—
489C4×Q8—216no—
490C4×Q8—216no—
491C4×Q8—48no—
492C4×Q8—48no—
493C4×Q8—48no—
494C4×Q8—48no—
495C4×D4—28no—
496C4×D4—28no—
497C4×D4—24no—
498C4×D4—24no—
499#117—24no—
500#117—216no—
501#117—28no—
502#117—28no—
503#117—28no—
504#117—216no—
505#117—44no—
506#117—44no—
507#117—44no—
508C2×C4⋊C4C2411yescharacteristic
509C2×C4⋊C4C2411yescharacteristic
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2414yes—
549C2×C22⋊C4C2412yes—
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C42—28no—
565C2×C42—24no—
566C2×C42—28no—
567C2×C42—42no—
568C2×C42—44no—
569C2×C42#4118yes—
570C2×C42C2411yescharacteristic
571C2×C42C2412yes—
572C2×C42C2412yes—
573C2×C42C2412yes—
574C2×C42C2414yes—
575C2×C42C2412yes—
576C2×C42C2414yes—
577C2×C42C2414yes—
578C2×C42C2412yes—
579C2×C42C2412yes—
580C2×C42C2418yes—
581C2×C42C2411yescharacteristic
582C2×C42C2411yescharacteristic
583C2×C42C2412yes—
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2418yes—
587C2×C42C2414yes—
588C2×C42C2412yes—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2412yes—
592C2×C42C2414yes—
593C2×C42C2414yes—
594C2×C42C2418yes—
595C2×C42C2418yes—
596C2×C42C2418yes—
597C2×C42C2412yes—
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2412yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2412yes—
618#95C2412yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2414yes—
630#95C2414yes—
631#95C2418yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647C24C2512yes—
648C24C2511yescharacteristic
649#41—416no—
650C2×Q8—22no—
651C2×Q8—28no—
652C2×Q8—28no—
653C2×Q8—28no—
654C2×Q8—28no—
655C2×Q8—28no—
656C2×Q8—28no—
657C2×Q8—28no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—44no—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—24no—
664C2×D4—44no—
665C22×C4—22no—
666C22×C4—24no—
667C22×C4—22no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—28no—
677C22×C4—24no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—44no—
682C22×C4C2×#4114yes—
683C22×C4C2×#4114yes—
684C22×C4C2×#4114yes—
685C22×C4C2512yes—
686C22×C4C2512yes—
687C22×C4C2514yes—
688C22×C4C2512yes—
689C22×C4C2514yes—
690C22×C4C2514yes—
691C22×C4C2514yes—
692C22×C4C2514yes—
693C22×C4C2518yes—
694C22×C4C2518yes—
695C22×C4C2512yes—
696C22×C4C2511yescharacteristic
697C22×C4C2511yescharacteristic
698C22×C4C2514yes—
699C22×C4C2512yes—
700C22×C4C2511yescharacteristic
701C22×C4C2512yes—
702C22×C4C2512yes—
703C22×C4C2511yescharacteristic
704C22×C4C2511yescharacteristic
705C22×C4C2511yescharacteristic
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—28no—
713C4⋊C4—24no—
714C4⋊C4—216no—
715C4⋊C4—28no—
716C4⋊C4—216no—
717C4⋊C4—28no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—216no—
721C4⋊C4—216no—
722C4⋊C4—216no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—28no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—24no—
732C4⋊C4—44no—
733C4⋊C4—44no—
734C4⋊C4—44no—
735C4⋊C4—48no—
736C4⋊C4—44no—
737C4⋊C4—48no—
738C4⋊C4—48no—
739C4⋊C4—48no—
740C4⋊C4—48no—
741C4⋊C4—48no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4C2×#4118yes—
746C4⋊C4C2×#41116yes—
747C22⋊C4—24no—
748C22⋊C4—216no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—28no—
752C22⋊C4—28no—
753C22⋊C4—216no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—48no—
760C22⋊C4—48no—
761C22⋊C4—48no—
762C42—24no—
763C42—24no—
764C42—24no—
765C42—24no—
766C42—22no—
767C42—28no—
768C42—24no—
769C42—216no—
770C42—216no—
771C42—24no—
772C42—24no—
773C42—24no—
774C42—28no—
775C42—28no—
776C42—28no—
777C42—22no—
778C42—24no—
779C42—24no—
780C42—22no—
781C42—24no—
782C42—28no—
783C42—28no—
784C42—42no—
785C42—42no—
786C42—42no—
787C42—44no—
788C42—44no—
789C42—48no—
790C42—48no—
791C42—48no—
792C42C2×#4114yes—
793C42C2×#4114yes—
794C42C2×#4114yes—
795C42C2×#4114yes—
796C42C2×#4114yes—
797C422−1+418yes—
798C23—21no—
799C23—22no—
800C23—21no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—24no—
805C23—22no—
806C23—24no—
807C23C22×#4112yes—
808C23C2611yescharacteristic
809Q8—416no—
810Q8—416no—
811Q8—44no—
812Q8—416no—
813D4—48no—
814D4—44no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—28no—
836C2×C4—28no—
837C2×C4—28no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—28no—
857C2×C4—28no—
858C2×C4—28no—
859C2×C4—22no—
860C2×C4—24no—
861C2×C4—48no—
862C2×C4—48no—
863C2×C4—48no—
864C2×C4—48no—
865C2×C4—48no—
866C2×C4C22×#4118yes—
867C2×C4C22×#4112yes—
868C2×C4C22×#4114yes—
869C2×C4C22×#4112yes—
870C2×C4C22×#4112yes—
871C2×C4C22×#4112yes—
872C2×C4C22×#4112yes—
873C2×C4C22×#4112yes—
874C2×C4C22×#4112yes—
875C2×C4C2×2−1+414yes—
876C2×C4C2×2−1+414yes—
877C2×C4C2×2−1+414yes—
878C2×C4#58514yes—
879C2×C4#58512yes—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—42no—
884C22—42no—
885C22—44no—
886C22—42no—
887C22—44no—
888C22—42no—
889C22—42no—
890C22C23×#4111yescharacteristic
891C22C23×#4111yescharacteristic
892C22C22×2−1+412yes—
893C22C2×#58511yescharacteristic
894C22C2×#58512yes—
895C4—24no—
896C4—22no—
897C4—24no—
898C4—24no—
899C4—28no—
900C4—22no—
901C4—22no—
902C4—44no—
903C4—44no—
904C4—44no—
905C4—42no—
906C4—42no—
907C4—44no—
908C4—44no—
909C4—42no—
910C4—48no—
911C4—42no—
912C4—48no—
913C4#345514yes—
914C4#348014yes—
915C4#350914yes—
916C2—42no—
917C2—82no—
918C2C2×#345511yescharacteristic
919C2C2×#348011yescharacteristic
920C2#6276112yes—
921C2C2×#350911yescharacteristic
922C2#6280512yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52240C2semidirect
3. #40028C2semidirect
4. #39769C2semidirect
5. #39641C2semidirect
6. #39513C2semidirect
7. #39385C2semidirect
8. #39200C2semidirect
9. #38984C2semidirect
10. #38496C2semidirect
11. #38128C2semidirect
12. #37897C2semidirect
13. #37709C2semidirect
14. #36645C2semidirect
16. #34951C2semidirect
17. #34916C2semidirect
18. #34902C2semidirect
19. #34629C2semidirect
20. #34154C2semidirect
21. C4×#541C2semidirect
22. C4×#533C2semidirect
477. #125#41semidirect

Maximal subgroups

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

subgroupindex
#522402
#400312
#400282
#397692
#396412
#395132
#393852
#392002
#389842
#384962
#381282
#378972
#377092
#366452
#349792
#349512
#349162
#349022
#346292
#341542
C4×#5412
C4×#5332
#340262