Finite Group Databasebeta

← #7680483

Subgroups — #7680483

Order 512.

4465 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59963C214yesmaximal, complemented
2#59695C214yesmaximal, complemented
3#59575C214yesmaximal
4#59437C214yesmaximal, complemented
5#43884C218yesmaximal, complemented
6#43856C218yesmaximal, complemented
7#39762C211yesmaximal, characteristic, complemented
8#39641C211yesmaximal, characteristic, complemented
9#39082C214yesmaximal, complemented
10#38923C212yesmaximal
11#37889C212yesmaximal, complemented
12#37705C212yesmaximal, complemented
13#36450C212yesmaximal, complemented
14#36188C211yesmaximal, characteristic, complemented
15D4×#125C211yesmaximal, characteristic, complemented
16#35652C214yesmaximal, complemented
17#35323C212yesmaximal, complemented
18#35284C211yesmaximal, characteristic, complemented
19#34951C212yesmaximal, complemented
20#34322C212yesmaximal, complemented
21#34217C212yesmaximal, complemented
22#34151C211yesmaximal, characteristic
23C4×#541C211yesmaximal, characteristic, complemented
24C2×#556C2212yes—
25C2×#541C2211yescharacteristic
26C2×#529C2211yescharacteristic
27C22×#125C2212yes—
28#2868C2211yescharacteristic
29#2863C2214yes—
30#2859C2211yescharacteristic
31#2857C2212yes—
32#2857C2212yes—
33#2851C2212yes—
34#2791C2218yes—
35#2787C2218yes—
36#2787C2218yes—
37#2779C2218yes—
38#2776C2218yes—
39#2767C2218yes—
40#2766C2218yes—
41#2747C2218yes—
42#2725C2218yes—
43#2722C2218yes—
44#2719C2218yes—
45#2695C2218yes—
46#2647C2212yes—
47#2647C2212yes—
48#2642C2212yes—
49#2629C2212yes—
50#2625C2214yes—
51#2606C2218yes—
52#2595C2218yes—
53#2594C2218yes—
54#2590C2218yes—
55#2585C2218yes—
56#2585C2218yes—
57#2582C2212yes—
58#2577C2218yes—
59#2577C2218yes—
60#2577C2218yes—
61#2577C2218yes—
62#2568C2212yes—
63#2552C2212yes—
64#2547C2214yes—
65#2547C2214yes—
66#2546C2212yes—
67#2546C2214yes—
68#2533C2218yes—
69#2533C2218yes—
70#2531C2218yes—
71#2530C2218yes—
72#2529C2218yes—
73#2528C2218yes—
74#2528C2218yes—
75#2528C2218yes—
76#2525C2218yes—
77#2514C2214yes—
78#2514C2214yes—
79#2514C2214yes—
80#2511C2214yes—
81#2509C2214yes—
82#2509C2214yes—
83#2507C2214yes—
84#2507C2214yes—
85#2506C2214yes—
86#2499C2214yes—
87#2499C2214yes—
88#2497C2214yes—
89#2496C2218yes—
90#2495C2218yes—
91#2494C2214yes—
92#2494C2218yes—
93#2489C2214yes—
94#2485C2214yes—
95#2481C2218yes—
96#2473C2218yes—
97#2453C2214yes—
98#2453C2214yes—
99#2446C2214yes—
100#2446C2214yes—
101#2446C2214yes—
102#2442C2214yes—
103#2442C2218yes—
104#2429C2214yes—
105#2429C2214yes—
106#2427C2214yes—
107#2417C2214yes—
108#2402C2218yes—
109#2374C2214yes—
110#2373C2218yes—
111#2373C2214yes—
112#2370C2218yes—
113#2370C2212yes—
114#2370C2218yes—
115#2367C2214yes—
116#2367C2212yes—
117#2365C2212yes—
118#2365C2214yes—
119#2363C2212yes—
120#2362C2212yes—
121#2362C2214yes—
122#2360C2214yes—
123#2355C2212yes—
124#2355C2214yes—
125#2351C2214yes—
126D4×C4⋊C4C2212yes—
127D4×C4⋊C4C2214yes—
128#2346C2214yes—
129#2345C2218yes—
130#2345C2218yes—
131#2336C2214yes—
132#2334C2218yes—
133#2334C2214yes—
134#2330C2212yes—
135#2330C2211yescharacteristic
136#2330C2212yes—
137#2330C2212yes—
138#2327C2211yescharacteristic
139#2323C2214yes—
140#2323C2212yes—
141#2320C2212yes—
142#2316C2214yes—
143#2314C2211yescharacteristic
144#2314C2212yes—
145C4×C4⋊Q8C2212yes—
146C4×C4⋊Q8C2214yes—
147C4×C4⋊Q8C2211yescharacteristic
148C4×#125C2211yescharacteristic
149C4×#125C2214yes—
150C4×#125C2214yes—
151C4×#125C2214yes—
152C4×#126C2214yes—
153C4×#124C2214yes—
154C4×C22⋊Q8C2212yes—
155#2298C2212yes—
156#2295C2214yes—
157#2295C2214yes—
158#2295C2214yes—
159#2295C2211yescharacteristic
160#2293C2211yescharacteristic
161#2293C2212yes—
162#2290C2212yes—
163#2285C2212yes—
164#2274C2214yes—
165C42×Q8C2212yes—
166C42×Q8C2211yescharacteristic
167C42×D4C2211yescharacteristic
168C4×#117C2211yescharacteristic
169C4×#117C2211yescharacteristic
170C4×#117C2212yes—
171#556—216no—
172#541—28no—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2311yescharacteristic
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177#529—28no—
178C2×#126C2314yes—
179C2×#126C2318yes—
180C2×#126C2312yes—
181C2×#125—216no—
182C2×#125C2314yes—
183C2×#125C2314yes—
184C2×#125C2312yes—
185C2×#125C2318yes—
186C2×#125C2311yescharacteristic
187C2×#125C2311yescharacteristic
188C2×#124C2311yescharacteristic
189C2×#124C2314yes—
190C2×#123C2312yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2311yescharacteristic
194C2×C22⋊Q8C2314yes—
195C2×#121C2311yescharacteristic
196C2×C4×Q8C2312yes—
197C2×C4×Q8C2312yes—
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2311yescharacteristic
200C2×C4×Q8C2314yes—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2314yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2311yescharacteristic
208C2×#117C2311yescharacteristic
209C2×#117C2311yescharacteristic
210C2×#117C2312yes—
211C2×#117C2314yes—
212C2×#117C2312yes—
213C2×#117C2312yes—
214C22×C4⋊C4C2314yes—
215C22×C4⋊C4C2318yes—
216C22×C42C2312yes—
217C22×C42C2311yescharacteristic
218#401C2318yes—
219#401C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#396C2318yes—
252#396C2318yes—
253#394C2318yes—
254#391C2314yes—
255#391C2312yes—
256#391C2314yes—
257#391C2314yes—
258#391C2314yes—
259#391C2314yes—
260#391C2312yes—
261#391C2314yes—
262#391C2314yes—
263#391C2314yes—
264#391C2312yes—
265#391C2314yes—
266#391C2314yes—
267#390C2314yes—
268#390C2312yes—
269#389C2312yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#389C2312yes—
274#389C2314yes—
275#389C2314yes—
276#389C2314yes—
277#389C2318yes—
278#389C2318yes—
279#389C2314yes—
280#389C2314yes—
281#389C2318yes—
282#389C2318yes—
283#389C2318yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2318yes—
288#389C2318yes—
289#389C2318yes—
290#389C2318yes—
291#389C2318yes—
292#389C2318yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2312yes—
300#389C2312yes—
301#389C2314yes—
302#388C2314yes—
303#388C2314yes—
304#388C2314yes—
305#388C2318yes—
306#388C2318yes—
307#388C2314yes—
308#388C2314yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2314yes—
314#388C2314yes—
315#388C2318yes—
316#388C2318yes—
317#388C2314yes—
318#388C2314yes—
319#387C2314yes—
320#387C2314yes—
321#387C2314yes—
322#387C2314yes—
323#387C2314yes—
324#387C2314yes—
325#387C2314yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2314yes—
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#387C2314yes—
352#387C2314yes—
353#387C2318yes—
354#387C2318yes—
355#387C2314yes—
356#387C2314yes—
357#387C2314yes—
358#386C2318yes—
359#386C2314yes—
360#385C2314yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2314yes—
366#384C2311yescharacteristic
367#384C2312yes—
368#384C2314yes—
369#384C2312yes—
370#384C2312yes—
371#384C2314yes—
372#383C2314yes—
373#383C2318yes—
374#383C2318yes—
375#382C2314yes—
376#382C2311yescharacteristic
377#382C2314yes—
378#382C2312yes—
379#382C2318yes—
380#382C2314yes—
381#382C2318yes—
382#380C2312yes—
383#380C2314yes—
384#380C2318yes—
385#380C2318yes—
386#380C2314yes—
387#380C2318yes—
388#380C2318yes—
389#380C2314yes—
390#380C2318yes—
391#380C2318yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2312yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2318yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2318yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2312yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2318yes—
432C4×C22⋊C4C2312yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2312yes—
438C4×C22⋊C4C2312yes—
439#376C2311yescharacteristic
440#376C2311yescharacteristic
441#376C2312yes—
442#376C2318yes—
443#376C2312yes—
444#376C2318yes—
445C43C2314yes—
446C43C2312yes—
447C43C2312yes—
448C43C2311yescharacteristic
449C43C2311yescharacteristic
450C22×Q8C2412yes—
451C22×Q8C2411yescharacteristic
452C22×Q8C2414yes—
453C22×D4C2411yescharacteristic
454C22×D4C2412yes—
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2412yes—
458C23×C4C2418yes—
459C23×C4C2414yes—
460C23×C4C2411yescharacteristic
461C4⋊Q8—24no—
462C4⋊Q8—28no—
463C4⋊Q8—48no—
464C4⋊Q8—48no—
465#126—216no—
466#126—28no—
467#126—232no—
468#125—216no—
469#125—232no—
470#125—24no—
471#125—216no—
472#125—28no—
473#125#4118yes—
474#124—24no—
475#124—216no—
476#123—28no—
477C22⋊Q8—216no—
478C22⋊Q8—24no—
479C22⋊Q8—28no—
480C22⋊Q8—48no—
481#121—24no—
482C4×Q8—28no—
483C4×Q8—216no—
484C4×Q8—24no—
485C4×Q8—28no—
486C4×Q8—28no—
487C4×Q8—48no—
488C4×Q8—44no—
489C4×Q8—48no—
490C4×D4—28no—
491C4×D4—48no—
492C4×D4—44no—
493C4×D4#4118yes—
494#117—28no—
495#117—216no—
496#117—24no—
497#117—28no—
498#117—24no—
499#117—44no—
500C2×C4⋊C4—216no—
501C2×C4⋊C4—232no—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2411yescharacteristic
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2411yescharacteristic
546C2×C22⋊C4C2412yes—
547C2×C22⋊C4C2412yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2412yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2412yes—
563C2×C42—28no—
564C2×C42—24no—
565C2×C42C2411yescharacteristic
566C2×C42C2412yes—
567C2×C42C2411yescharacteristic
568C2×C42C2418yes—
569C2×C42C2412yes—
570C2×C42C2411yescharacteristic
571C2×C42C2414yes—
572C2×C42C2412yes—
573C2×C42C2412yes—
574C2×C42C2414yes—
575C2×C42C2414yes—
576C2×C42C2414yes—
577C2×C42C2411yescharacteristic
578C2×C42C2412yes—
579C2×C42C2414yes—
580C2×C42C2411yescharacteristic
581C2×C42C2414yes—
582C2×C42C2414yes—
583C2×C42C2418yes—
584C2×C42C2418yes—
585C2×C42C2414yes—
586C2×C42C2414yes—
587C2×C42C2412yes—
588C2×C42C2414yes—
589C2×C42C2414yes—
590C2×C42C2412yes—
591C2×C42C2418yes—
592C2×C42C2411yescharacteristic
593C2×C42C2411yescharacteristic
594C2×C42C2411yescharacteristic
595#95C2414yes—
596#95C2412yes—
597#95C2412yes—
598#95C2412yes—
599#95C2414yes—
600#95C2412yes—
601#95C2412yes—
602#95C2414yes—
603#95C2414yes—
604#95C2412yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2418yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2418yes—
639#95C2418yes—
640C24C2511yescharacteristic
641C24C2512yes—
642C2×Q8—24no—
643C2×Q8—22no—
644C2×Q8—24no—
645C2×Q8—28no—
646C2×Q8—24no—
647C2×Q8—28no—
648C2×Q8—24no—
649C2×Q8—28no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—44no—
653C2×D4C2×#4114yes—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—28no—
662C22×C4—22no—
663C22×C4—216no—
664C22×C4—48no—
665C22×C4—44no—
666C22×C4—42no—
667C22×C4—44no—
668C22×C4—48no—
669C22×C4C2×#4118yes—
670C22×C4C2514yes—
671C22×C4C2511yescharacteristic
672C22×C4C2512yes—
673C22×C4C2514yes—
674C22×C4C2514yes—
675C22×C4C2512yes—
676C22×C4C2511yescharacteristic
677C22×C4C2514yes—
678C22×C4C2514yes—
679C22×C4C2518yes—
680C22×C4C2512yes—
681C22×C4C2511yescharacteristic
682C22×C4C2512yes—
683C22×C4C2518yes—
684C22×C4C2512yes—
685C22×C4C2511yescharacteristic
686C22×C4C2514yes—
687C22×C4C2512yes—
688C22×C4C2512yes—
689C22×C4C2511yescharacteristic
690C22×C4C2511yescharacteristic
691C4⋊C4—216no—
692C4⋊C4—216no—
693C4⋊C4—216no—
694C4⋊C4—216no—
695C4⋊C4—28no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—28no—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—24no—
702C4⋊C4—22no—
703C4⋊C4—216no—
704C4⋊C4—24no—
705C4⋊C4—28no—
706C4⋊C4—28no—
707C4⋊C4—28no—
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—24no—
712C4⋊C4—24no—
713C4⋊C4—28no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—28no—
717C4⋊C4—44no—
718C4⋊C4—44no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—44no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—44no—
726C4⋊C4—48no—
727C4⋊C4—48no—
728C4⋊C4—48no—
729C4⋊C4—48no—
730C4⋊C4—48no—
731C4⋊C4—48no—
732C4⋊C4C2×#4118yes—
733C4⋊C4C2×#41116yes—
734C4⋊C4C2×#4114yes—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—216no—
738C22⋊C4—24no—
739C22⋊C4—216no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—24no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C22⋊C4—48no—
750C22⋊C4—48no—
751C22⋊C4C2×#4118yes—
752C42—22no—
753C42—22no—
754C42—28no—
755C42—24no—
756C42—22no—
757C42—24no—
758C42—22no—
759C42—216no—
760C42—28no—
761C42—28no—
762C42—24no—
763C42—22no—
764C42—28no—
765C42—28no—
766C42—24no—
767C42—24no—
768C42—42no—
769C42—44no—
770C42—44no—
771C42—42no—
772C42—44no—
773C42—48no—
774C42—44no—
775C42—44no—
776C42—44no—
777C42—48no—
778C42—48no—
779C42C2×#4114yes—
780C42C2×#4114yes—
781C422−1+414yes—
782C23—22no—
783C23—22no—
784C23—24no—
785C23—24no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—22no—
790C23—22no—
791C23C22×#4114yes—
792C23C2611yescharacteristic
793Q8—48no—
794Q8—44no—
795Q8—416no—
796D4—28no—
797D4—84no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—216no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—28no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—28no—
820C2×C4—21no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—21no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—24no—
835C2×C4—28no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—28no—
845C2×C4—24no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—88no—
849C2×C4—816no—
850C2×C4—82no—
851C2×C4C22×#4114yes—
852C2×C4C22×#4114yes—
853C2×C4C22×#4112yes—
854C2×C4C22×#4118yes—
855C2×C4C22×#4112yes—
856C2×C4C22×#4112yes—
857C2×C4C22×#4112yes—
858C2×C4C2×2−1+414yes—
859C2×C4C2×2−1+412yes—
860C2×C4#58514yes—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—44no—
865C22—44no—
866C22—42no—
867C22—41no—
868C22—41no—
869C22—42no—
870C22—41no—
871C22C23×#4111yescharacteristic
872C22C23×#4111yescharacteristic
873C22C22×2−1+411yescharacteristic
874C22C2×#58512yes—
875C222−1+612yes—
876C4—28no—
877C4—24no—
878C4—22no—
879C4—24no—
880C4—24no—
881C4—42no—
882C4—44no—
883C4—48no—
884C4—41no—
885C4—42no—
886C4—48no—
887C4—44no—
888C4—41no—
889C4—42no—
890C4—42no—
891C4—44no—
892C4—44no—
893C4—41no—
894C4—44no—
895C4#348214yes—
896C4#351214yes—
897C2—44no—
898C2—81no—
899C2C2×#348211yescharacteristic
900C2C2×#351211yescharacteristic
901C2#6286111yescharacteristic
902C2#6295612yes—
903C2#6300912yes—
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. #59963C2semidirect
2. #59695C2semidirect
4. #59437C2semidirect
5. #43884C2semidirect
6. #43856C2semidirect
7. #39762C2semidirect
8. #39641C2semidirect
9. #39082C2semidirect
11. #37889C2semidirect
12. #37705C2semidirect
13. #36450C2semidirect
14. #36188C2semidirect
15. D4×#125C2semidirect
16. #35652C2semidirect
17. #35323C2semidirect
18. #35284C2semidirect
19. #34951C2semidirect
20. #34322C2semidirect
21. #34217C2semidirect
23. C4×#541C2semidirect

Maximal subgroups

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

subgroupindex
#599632
#596952
#595752
#594372
#438842
#438562
#397622
#396412
#390822
#389232
#378892
#377052
#364502
#361882
D4×#1252
#356522
#353232
#352842
#349512
#343222
#342172
#341512
C4×#5412