Finite Group Databasebeta

← #7672602

Subgroups — #7672602

Order 512.

4628 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59682C214yesmaximal, complemented
2#59447C214yesmaximal, complemented
3#59327C218yesmaximal, complemented
4#39826C218yesmaximal, complemented
5#39769C211yesmaximal, characteristic, complemented
6#39641C211yesmaximal, characteristic, complemented
7#39513C211yesmaximal, characteristic, complemented
8#39385C211yesmaximal, characteristic, complemented
9#37894C212yesmaximal, complemented
10#37705C212yesmaximal, complemented
11#36645C211yesmaximal, characteristic, complemented
12#36605C214yesmaximal
13#36599C214yesmaximal, complemented
14#36454C212yesmaximal, complemented
15#36313C212yesmaximal, complemented
16#36278C214yesmaximal, complemented
17#35650C214yesmaximal, complemented
18#35321C212yesmaximal, complemented
19#35241C212yesmaximal
20#34281C212yesmaximal, complemented
21#34235C212yesmaximal, complemented
22C4×#529C211yesmaximal, characteristic
23C2×C4×#125C211yesmaximal, characteristic, complemented
24C2×#541C2212yes—
25C2×#533C2212yes—
26C2×#529C2211yescharacteristic
27C22×#125C2211yescharacteristic
28#2868C2211yescharacteristic
29#2868C2211yescharacteristic
30#2863C2214yes—
31#2862C2212yes—
32#2859C2214yes—
33#2857C2212yes—
34#2857C2212yes—
35#2857C2214yes—
36#2857C2214yes—
37#2855C2214yes—
38#2850C2214yes—
39#2794C2218yes—
40#2793C2218yes—
41#2791C2218yes—
42#2772C2218yes—
43#2766C2218yes—
44#2725C2218yes—
45#2721C2218yes—
46#2719C2218yes—
47#2664C2218yes—
48#2647C2212yes—
49#2642C2212yes—
50#2629C2212yes—
51#2621C2212yes—
52#2608C2218yes—
53#2606C2218yes—
54#2594C2218yes—
55#2590C2218yes—
56#2587C2218yes—
57#2585C2218yes—
58#2585C2218yes—
59#2579C2218yes—
60#2575C2218yes—
61#2573C2218yes—
62#2570C2214yes—
63#2569C2218yes—
64#2569C2218yes—
65#2568C2212yes—
66#2565C2214yes—
67#2552C2214yes—
68#2547C2212yes—
69#2546C2214yes—
70#2546C2212yes—
71#2545C2214yes—
72#2545C2214yes—
73#2542C2212yes—
74#2529C2218yes—
75#2528C2218yes—
76#2528C2218yes—
77#2525C2218yes—
78#2525C2218yes—
79#2524C2218yes—
80#2524C2218yes—
81#2524C2218yes—
82#2517C2218yes—
83#2515C2218yes—
84#2514C2214yes—
85#2514C2214yes—
86#2512C2214yes—
87#2511C2214yes—
88#2511C2214yes—
89#2510C2218yes—
90#2509C2218yes—
91#2507C2214yes—
92#2498C2218yes—
93#2497C2214yes—
94#2489C2214yes—
95#2481C2218yes—
96#2453C2214yes—
97#2447C2214yes—
98#2446C2214yes—
99#2446C2214yes—
100#2446C2214yes—
101#2446C2214yes—
102#2442C2218yes—
103#2429C2214yes—
104#2421C2214yes—
105#2417C2214yes—
106#2417C2214yes—
107#2373C2218yes—
108#2373C2218yes—
109#2371C2218yes—
110#2370C2218yes—
111#2367C2214yes—
112#2365C2214yes—
113#2365C2212yes—
114#2365C2212yes—
115#2365C2212yes—
116#2365C2212yes—
117#2360C2214yes—
118#2360C2214yes—
119#2356C2214yes—
120#2356C2214yes—
121#2355C2214yes—
122#2353C2218yes—
123#2351C2214yes—
124#2345C2218yes—
125#2343C2218yes—
126#2336C2218yes—
127#2330C2212yes—
128#2327C2212yes—
129#2323C2214yes—
130#2323C2214yes—
131#2320C2214yes—
132#2314C2212yes—
133C4×C4⋊Q8C2214yes—
134C4×C4⋊Q8C2212yes—
135C4×C4⋊Q8C2212yes—
136C4×#125C2214yes—
137C4×#125C2212yes—
138C4×#125C2212yes—
139C4×#125C2211yescharacteristic
140C4×#125C2212yes—
141C4×#125C2214yes—
142C4×#125C2211yescharacteristic
143C4×#125C2211yescharacteristic
144C4×#125C2211yescharacteristic
145C4×#126C2214yes—
146C4×#124C2212yes—
147C4×C22⋊Q8C2214yes—
148C4×C22⋊Q8C2214yes—
149C4×C22⋊Q8C2214yes—
150C4×C22⋊Q8C2212yes—
151C4×#123C2214yes—
152C4×#121C2212yes—
153#2298C2212yes—
154#2295C2211yescharacteristic
155#2295C2214yes—
156#2293C2211yescharacteristic
157C2×#389C2212yes—
158#2290C2212yes—
159C2×#387C2214yes—
160#2285C2214yes—
161#2283C2211yescharacteristic
162C2×#382C2211yescharacteristic
163#2276C2214yes—
164C42×Q8C2211yescharacteristic
165C42×D4C2211yescharacteristic
166C42×D4C2212yes—
167C4×#117C2212yes—
168C2×C4×C4⋊C4C2212yes—
169C2×C4×C4⋊C4C2214yes—
170C2×C43C2211yescharacteristic
171#541—216no—
172#533—216no—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2314yes—
179#529—28no—
180C2×#126C2312yes—
181C2×#126C2318yes—
182C2×#125—28no—
183C2×#125C2311yescharacteristic
184C2×#125C2311yescharacteristic
185C2×#125C2312yes—
186C2×#125C2314yes—
187C2×#125C2314yes—
188C2×#125C2318yes—
189C2×#125C2311yescharacteristic
190C2×#124C2311yescharacteristic
191C2×#124C2314yes—
192C2×#123C2312yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2311yescharacteristic
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×#121C2311yescharacteristic
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2314yes—
201C2×C4×Q8C2311yescharacteristic
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2312yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2312yes—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2314yes—
214C22×C4⋊C4C2314yes—
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2314yes—
217C22×C4⋊C4C2312yes—
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220C22×C42C2314yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225#401C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#399C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#396C2318yes—
253#396C2318yes—
254#396C2318yes—
255#396C2318yes—
256#396C2318yes—
257#391C2314yes—
258#391C2314yes—
259#391C2314yes—
260#391C2314yes—
261#391C2314yes—
262#391C2314yes—
263#391C2314yes—
264#391C2314yes—
265#391C2314yes—
266#391C2314yes—
267#391C2314yes—
268#391C2314yes—
269#391C2314yes—
270#391C2312yes—
271#390C2314yes—
272#390C2312yes—
273#389C2314yes—
274#389C2312yes—
275#389C2314yes—
276#389C2312yes—
277#389C2312yes—
278#389C2312yes—
279#389C2312yes—
280#389C2312yes—
281#389C2318yes—
282#389C2318yes—
283#389C2318yes—
284#389C2318yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2318yes—
289#389C2318yes—
290#389C2314yes—
291#389C2314yes—
292#389C2318yes—
293#389C2318yes—
294#389C2318yes—
295#389C2318yes—
296#389C2318yes—
297#389C2314yes—
298#389C2318yes—
299#388C2314yes—
300#388C2314yes—
301#388C2314yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2314yes—
312#387C2314yes—
313#387C2314yes—
314#387C2314yes—
315#387C2314yes—
316#387C2314yes—
317#387C2314yes—
318#387C2314yes—
319#387C2314yes—
320#387C2314yes—
321#387C2314yes—
322#387C2314yes—
323#387C2314yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2314yes—
356#385C2318yes—
357#385C2314yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#384C2312yes—
362#384C2314yes—
363#384C2312yes—
364#384C2314yes—
365#384C2314yes—
366#384C2314yes—
367#383C2312yes—
368#383C2318yes—
369#383C2318yes—
370#383C2318yes—
371#382C2311yescharacteristic
372#382C2311yescharacteristic
373#382C2312yes—
374#382C2314yes—
375#382C2312yes—
376#382C2314yes—
377#382C2314yes—
378#382C2318yes—
379#382C2314yes—
380#382C2318yes—
381#381C2318yes—
382#381C2312yes—
383#380C2318yes—
384#380C2318yes—
385#380C2318yes—
386#380C2318yes—
387#380C2314yes—
388#380C2314yes—
389#380C2312yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2312yes—
398C4×C4⋊C4C2312yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2318yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2318yes—
432C4×C22⋊C4C2312yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2312yes—
435C4×C22⋊C4C2312yes—
436#376C2312yes—
437#376C2312yes—
438#376C2318yes—
439#376C2318yes—
440C2×#95C2314yes—
441C2×#95C2314yes—
442C2×#95C2314yes—
443C43C2312yes—
444C43C2312yes—
445C43C2311yescharacteristic
446C43C2311yescharacteristic
447C43C2311yescharacteristic
448C43C2311yescharacteristic
449C43C2312yes—
450C22×Q8C2414yes—
451C22×Q8C2411yescharacteristic
452C22×Q8C2414yes—
453C22×D4C2412yes—
454C22×D4C2411yescharacteristic
455C23×C4C2412yes—
456C23×C4C2414yes—
457C23×C4C2412yes—
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2414yes—
462C23×C4C2414yes—
463C23×C4C2412yes—
464C4⋊Q8—28no—
465C4⋊Q8—28no—
466C4⋊Q8—28no—
467C4⋊Q8—48no—
468C4⋊Q8—48no—
469C4⋊Q8—44no—
470#126—232no—
471#126—28no—
472#125—28no—
473#125—216no—
474#125—232no—
475#125—24no—
476#125—24no—
477#125—216no—
478#125#4118yes—
479#124—24no—
480#124—48no—
481#123—28no—
482C22⋊Q8—24no—
483C22⋊Q8—216no—
484C22⋊Q8—216no—
485C22⋊Q8—216no—
486C22⋊Q8—48no—
487#121—24no—
488C4×Q8—216no—
489C4×Q8—24no—
490C4×Q8—216no—
491C4×Q8—216no—
492C4×Q8—44no—
493C4×Q8—48no—
494C4×Q8—48no—
495C4×Q8—48no—
496C4×D4—28no—
497C4×D4—216no—
498C4×D4—24no—
499C4×D4—44no—
500#117—216no—
501#117—28no—
502#117—28no—
503C2×C4⋊C4—216no—
504C2×C4⋊C4—28no—
505C2×C4⋊C4—216no—
506C2×C4⋊C4—44no—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2411yescharacteristic
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2411yescharacteristic
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2414yes—
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C42—28no—
565C2×C42—24no—
566C2×C42—44no—
567C2×C42—42no—
568C2×C42—44no—
569C2×C42—48no—
570C2×C42#4118yes—
571C2×C42C2412yes—
572C2×C42C2412yes—
573C2×C42C2418yes—
574C2×C42C2412yes—
575C2×C42C2414yes—
576C2×C42C2412yes—
577C2×C42C2414yes—
578C2×C42C2418yes—
579C2×C42C2414yes—
580C2×C42C2411yescharacteristic
581C2×C42C2412yes—
582C2×C42C2411yescharacteristic
583C2×C42C2412yes—
584C2×C42C2411yescharacteristic
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2412yes—
589C2×C42C2414yes—
590C2×C42C2418yes—
591C2×C42C2418yes—
592C2×C42C2418yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604#95C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2412yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2412yes—
636#95C2414yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647C24C2512yes—
648C24C2511yescharacteristic
649C2×Q8—22no—
650C2×Q8—28no—
651C2×Q8—28no—
652C2×Q8—28no—
653C2×Q8—28no—
654C2×Q8—28no—
655C2×Q8—24no—
656C2×Q8—28no—
657C2×D4—24no—
658C2×D4—28no—
659C2×D4—22no—
660C2×D4—24no—
661C22×C4—24no—
662C22×C4—22no—
663C22×C4—24no—
664C22×C4—22no—
665C22×C4—24no—
666C22×C4—28no—
667C22×C4—28no—
668C22×C4—24no—
669C22×C4—28no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—28no—
674C22×C4—44no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4C2×#4114yes—
683C22×C4C2×#4114yes—
684C22×C4C2×#4114yes—
685C22×C42−1+418yes—
686C22×C4C2512yes—
687C22×C4C2512yes—
688C22×C4C2514yes—
689C22×C4C2514yes—
690C22×C4C2514yes—
691C22×C4C2514yes—
692C22×C4C2514yes—
693C22×C4C2512yes—
694C22×C4C2518yes—
695C22×C4C2518yes—
696C22×C4C2512yes—
697C22×C4C2511yescharacteristic
698C22×C4C2511yescharacteristic
699C22×C4C2512yes—
700C22×C4C2514yes—
701C22×C4C2511yescharacteristic
702C22×C4C2511yescharacteristic
703C22×C4C2512yes—
704C22×C4C2512yes—
705C22×C4C2511yescharacteristic
706C22×C4C2511yescharacteristic
707C4⋊C4—28no—
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—24no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—22no—
718C4⋊C4—24no—
719C4⋊C4—22no—
720C4⋊C4—216no—
721C4⋊C4—216no—
722C4⋊C4—28no—
723C4⋊C4—28no—
724C4⋊C4—24no—
725C4⋊C4—216no—
726C4⋊C4—216no—
727C4⋊C4—216no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—44no—
738C4⋊C4—48no—
739C4⋊C4—48no—
740C4⋊C4—44no—
741C4⋊C4—48no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4—48no—
748C4⋊C4C2×#4118yes—
749C4⋊C4C2×#41116yes—
750C22⋊C4—216no—
751C22⋊C4—24no—
752C22⋊C4—28no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—28no—
756C22⋊C4—24no—
757C22⋊C4—24no—
758C22⋊C4—216no—
759C22⋊C4—28no—
760C22⋊C4—44no—
761C22⋊C4—48no—
762C22⋊C4—48no—
763C22⋊C4—48no—
764C42—24no—
765C42—22no—
766C42—24no—
767C42—24no—
768C42—216no—
769C42—216no—
770C42—24no—
771C42—24no—
772C42—24no—
773C42—24no—
774C42—28no—
775C42—22no—
776C42—24no—
777C42—24no—
778C42—28no—
779C42—28no—
780C42—22no—
781C42—24no—
782C42—44no—
783C42—42no—
784C42—42no—
785C42—44no—
786C42—42no—
787C42—44no—
788C42—48no—
789C42—44no—
790C42—48no—
791C42—48no—
792C42C2×#4114yes—
793C42C2×#4114yes—
794C42C2×#4114yes—
795C42C2×#4114yes—
796C42C2×#4114yes—
797C23—21no—
798C23—22no—
799C23—21no—
800C23—22no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—22no—
805C23C22×#4112yes—
806C23C2×2−1+414yes—
807C23C2611yescharacteristic
808Q8—416no—
809Q8—44no—
810Q8—416no—
811D4—48no—
812D4—44no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—24no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—22no—
837C2×C4—24no—
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—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—22no—
855C2×C4—28no—
856C2×C4—28no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—48no—
861C2×C4—48no—
862C2×C4—416no—
863C2×C4—48no—
864C2×C4—88no—
865C2×C4—88no—
866C2×C4C22×#4112yes—
867C2×C4C22×#4118yes—
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×C4#58512yes—
878C2×C4#58514yes—
879C22—24no—
880C22—22no—
881C22—24no—
882C22—22no—
883C22—42no—
884C22—44no—
885C22—42no—
886C22—44no—
887C22—42no—
888C22#350914yes—
889C22C23×#4111yescharacteristic
890C22C23×#4111yescharacteristic
891C22C22×2−1+412yes—
892C22C2×#58512yes—
893C22C2×#58511yescharacteristic
894C4—22no—
895C4—22no—
896C4—24no—
897C4—28no—
898C4—22no—
899C4—24no—
900C4—24no—
901C4—22no—
902C4—42no—
903C4—44no—
904C4—42no—
905C4—44no—
906C4—42no—
907C4—48no—
908C4—44no—
909C4—44no—
910C4—44no—
911C4—42no—
912C4—48no—
913C4#348014yes—
914C4#351214yes—
915C2—24no—
916C2—82no—
917C2C2×#348011yescharacteristic
918C2C2×#350911yescharacteristic
919C2#6280512yes—
920C2C2×#351211yescharacteristic
921C2#6282312yes—
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. #59682C2semidirect
2. #59447C2semidirect
3. #59327C2semidirect
4. #39826C2semidirect
5. #39769C2semidirect
6. #39641C2semidirect
7. #39513C2semidirect
8. #39385C2semidirect
9. #37894C2semidirect
10. #37705C2semidirect
11. #36645C2semidirect
13. #36599C2semidirect
14. #36454C2semidirect
15. #36313C2semidirect
16. #36278C2semidirect
17. #35650C2semidirect
18. #35321C2semidirect
20. #34281C2semidirect
21. #34235C2semidirect
23. C2×C4×#125C2semidirect

Maximal subgroups

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

subgroupindex
#596822
#594472
#593272
#398262
#397692
#396412
#395132
#393852
#378942
#377052
#366452
#366052
#365992
#364542
#363132
#362782
#356502
#353212
#352412
#342812
#342352
C4×#5292
C2×C4×#1252