Finite Group Databasebeta

← #7643263

Subgroups — #7643263

Order 512.

4312 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39987C214yesmaximal, complemented
2#39984C214yesmaximal
3#39970C218yesmaximal, complemented
4#39182C212yesmaximal, complemented
5#39181C212yesmaximal, complemented
6#38967C212yesmaximal, complemented
7#38964C212yesmaximal, complemented
8#38106C214yesmaximal, complemented
9#38105C214yesmaximal, complemented
10#36755C218yesmaximal, complemented
11#36640C211yesmaximal, characteristic, complemented
12#36635C211yesmaximal, characteristic, complemented
13#35643C214yesmaximal, complemented
14#35602C214yesmaximal, complemented
15#35344C212yesmaximal, complemented
16#35339C212yesmaximal, complemented
17#35192C211yesmaximal, characteristic, complemented
18#35192C211yesmaximal, characteristic, complemented
19#35192C212yesmaximal, complemented
20#35132C212yesmaximal, complemented
21#34193C211yesmaximal, characteristic
22#34191C211yesmaximal, characteristic
23#34026C211yesmaximal, characteristic
24C2×C4×#41C2211yescharacteristic
25#2864C2211yescharacteristic
26#2864C2212yes—
27#2864C2212yes—
28#2864C2212yes—
29#2864C2211yescharacteristic
30#2864C2212yes—
31#2863C2214yes—
32#2862C2212yes—
33#2862C2212yes—
34#2862C2211yescharacteristic
35#2859C2212yes—
36#2859C2212yes—
37#2859C2211yescharacteristic
38#2857C2212yes—
39#2855C2214yes—
40#2851C2212yes—
41#2851C2214yes—
42#2851C2214yes—
43#2805C2218yes—
44#2804C2218yes—
45#2790C2218yes—
46#2788C2218yes—
47#2788C2218yes—
48#2784C2218yes—
49#2780C2218yes—
50#2774C2218yes—
51#2763C2218yes—
52#2763C2218yes—
53#2755C2218yes—
54#2742C2218yes—
55#2729C2218yes—
56#2720C2218yes—
57#2713C2218yes—
58#2692C2218yes—
59#2666C2218yes—
60#2665C2218yes—
61#2665C2214yes—
62#2665C2214yes—
63#2647C2214yes—
64#2647C2214yes—
65#2628C2214yes—
66#2628C2214yes—
67#2612C2218yes—
68#2607C2218yes—
69#2607C2218yes—
70#2605C2218yes—
71#2605C2218yes—
72#2605C2214yes—
73#2605C2214yes—
74#2605C2218yes—
75#2589C2218yes—
76#2588C2218yes—
77#2586C2218yes—
78#2581C2214yes—
79#2580C2214yes—
80#2574C2218yes—
81#2571C2212yes—
82#2571C2212yes—
83#2571C2214yes—
84#2570C2218yes—
85#2570C2218yes—
86#2570C2214yes—
87#2569C2218yes—
88#2569C2218yes—
89#2568C2214yes—
90#2567C2214yes—
91#2563C2214yes—
92#2551C2212yes—
93#2551C2214yes—
94#2551C2212yes—
95#2550C2214yes—
96#2550C2214yes—
97#2550C2214yes—
98#2546C2214yes—
99#2522C2218yes—
100#2520C2218yes—
101#2511C2218yes—
102#2509C2214yes—
103#2509C2214yes—
104#2508C2214yes—
105#2508C2214yes—
106#2492C2218yes—
107#2454C2214yes—
108#2453C2214yes—
109#2452C2214yes—
110#2451C2214yes—
111#2442C2214yes—
112#2440C2214yes—
113#2439C2218yes—
114#2439C2214yes—
115#2439C2214yes—
116#2439C2214yes—
117#2439C2214yes—
118#2439C2214yes—
119#2439C2214yes—
120#2438C2218yes—
121#2355C2212yes—
122#2354C2212yes—
123#2354C2214yes—
124#2352C2214yes—
125Q8×C4⋊C4C2212yes—
126D4×C4⋊C4C2212yes—
127#2347C2214yes—
128#2347C2212yes—
129#2346C2212yes—
130#2343C2214yes—
131#2341C2212yes—
132#2339C2212yes—
133#2331C2214yes—
134#2331C2214yes—
135#2331C2214yes—
136#2331C2214yes—
137#2331C2218yes—
138#2329C2218yes—
139#2320C2212yes—
140#2319C2212yes—
141#2319C2214yes—
142#2318C2214yes—
143#2317C2214yes—
144#2316C2214yes—
145C4×C4⋊Q8C2212yes—
146C4×#125C2212yes—
147C4×#125C2214yes—
148C4×#125C2214yes—
149C4×C22⋊Q8C2214yes—
150#2298C2214yes—
151#2297C2212yes—
152#2296C2212yes—
153#2296C2212yes—
154#2296C2212yes—
155#2295C2211yescharacteristic
156#2295C2211yescharacteristic
157#2295C2214yes—
158#2295C2212yes—
159#2293C2212yes—
160#2293C2211yescharacteristic
161#2293C2211yescharacteristic
162#2290C2214yes—
163#2290C2212yes—
164#2290C2212yes—
165#2285C2212yes—
166#2285C2211yescharacteristic
167#2285C2211yescharacteristic
168#2283C2212yes—
169#2283C2212yes—
170#2283C2211yescharacteristic
171#2283C2211yescharacteristic
172C2×#382C2212yes—
173#2276C2212yes—
174#2275C2212yes—
175C4×#117C2212yes—
176C4×#117C2212yes—
177C4×#117C2211yescharacteristic
178C2×C43C2211yescharacteristic
179C22×#41C2311yescharacteristic
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2318yes—
186C2×#125C2312yes—
187C2×#125C2314yes—
188C2×#125C2314yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2314yes—
191C4×#41Q8116yescomplemented
192C2×C4×Q8C2314yes—
193C2×C4×Q8C2314yes—
194C2×C4×Q8C2311yescharacteristic
195C2×C4×Q8C2311yescharacteristic
196C2×C4×D4C2314yes—
197C2×C4×D4C2312yes—
198C2×C4×D4C2311yescharacteristic
199C2×C4×D4C2311yescharacteristic
200C2×C4×D4C2312yes—
201C2×#117C2312yes—
202C2×#117C2314yes—
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2314yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2311yescharacteristic
210C22×C4⋊C4C2314yes—
211C22×C42C2312yes—
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#399C2318yes—
230#399C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#396C2318yes—
240#396C2318yes—
241#396C2318yes—
242#396C2318yes—
243#395C2318yes—
244#395C2318yes—
245#395C2318yes—
246#395C2318yes—
247#395C2318yes—
248#395C2318yes—
249#395C2318yes—
250#395C2318yes—
251#393C2318yes—
252#393C2318yes—
253#393C2318yes—
254#393C2318yes—
255#393C2318yes—
256#393C2318yes—
257#391C2314yes—
258#391C2318yes—
259#391C2312yes—
260#391C2314yes—
261#391C2318yes—
262#391C2318yes—
263#391C2318yes—
264#391C2312yes—
265#391C2318yes—
266#391C2318yes—
267#391C2314yes—
268#391C2318yes—
269#391C2318yes—
270#391C2318yes—
271#391C2318yes—
272#391C2318yes—
273#391C2318yes—
274#391C2318yes—
275#391C2314yes—
276#391C2314yes—
277#390C2312yes—
278#390C2314yes—
279#390C2318yes—
280#390C2312yes—
281#389C2314yes—
282#389C2312yes—
283#389C2314yes—
284#389C2312yes—
285#389C2314yes—
286#389C2314yes—
287#389C2312yes—
288#389C2312yes—
289#389C2314yes—
290#389C2312yes—
291#389C2314yes—
292#389C2314yes—
293#389C2318yes—
294#389C2318yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2318yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2318yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2318yes—
311#389C2314yes—
312#389C2318yes—
313#389C2314yes—
314#389C2312yes—
315#389C2312yes—
316#389C2312yes—
317#388C2318yes—
318#388C2314yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2314yes—
323#388C2314yes—
324#388C2314yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2314yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2314yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2314yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2314yes—
352#387C2314yes—
353#387C2314yes—
354#387C2314yes—
355#387C2314yes—
356#387C2314yes—
357#386C2318yes—
358#386C2314yes—
359#386C2314yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2314yes—
368#385C2314yes—
369#385C2314yes—
370#385C2314yes—
371#384C2312yes—
372#384C2318yes—
373#384C2312yes—
374#384C2312yes—
375#384C2314yes—
376#383C2314yes—
377#383C2312yes—
378#383C2312yes—
379#383C2314yes—
380#382C2314yes—
381#382C2312yes—
382#382C2314yes—
383#382C2314yes—
384#382C2314yes—
385#382C2318yes—
386#382C2314yes—
387#382C2314yes—
388#382C2314yes—
389#382C2314yes—
390#382C2314yes—
391#382C2318yes—
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2312yes—
396#382C2312yes—
397#382C2311yescharacteristic
398#381C2312yes—
399#381C2312yes—
400#381C2314yes—
401#381C2314yes—
402#380C2318yes—
403#380C2318yes—
404#380C2318yes—
405#380C2314yes—
406#380C2314yes—
407#380C2312yes—
408#380C2312yes—
409#380C2312yes—
410#380C2312yes—
411#380C2312yes—
412#380C2312yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2318yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2318yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2312yes—
449C4×C22⋊C4C2312yes—
450C4×C22⋊C4C2312yes—
451C4×C22⋊C4C2312yes—
452C4×C22⋊C4C2312yes—
453C4×C22⋊C4C2312yes—
454#376C2312yes—
455#376C2314yes—
456#376C2312yes—
457#376C2314yes—
458#376C2312yes—
459#376C2312yes—
460#376C2312yes—
461#376C2314yes—
462C2×#95C2314yes—
463C2×#95C2314yes—
464C43C2311yescharacteristic
465C43C2312yes—
466C43C2312yes—
467C43C2311yescharacteristic
468C43C2311yescharacteristic
469C43C2312yes—
470C43C2311yescharacteristic
471C2×#41—44no—
472C2×#41C2×Q818yes—
473C22×Q8C2411yescharacteristic
474C22×Q8C2414yes—
475C22×Q8C2418yes—
476C22×Q8C2418yes—
477C22×D4C2411yescharacteristic
478C22×D4C2412yes—
479C23×C4C2412yes—
480C23×C4C2411yescharacteristic
481C23×C4C2411yescharacteristic
482C23×C4C2412yes—
483C23×C4C2418yes—
484C23×C4C2412yes—
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2411yescharacteristic
488C4⋊Q8—44no—
489C4⋊Q8—48no—
490C4⋊Q8—48no—
491C4⋊Q8—48no—
492C4⋊Q8—48no—
493C4⋊Q8—416no—
494#125—44no—
495#125—48no—
496#125—48no—
497C22⋊Q8—416no—
498C22⋊Q8—48no—
499C4×Q8—48no—
500C4×Q8—48no—
501C4×Q8C2×Q818yes—
502C4×Q8C2×Q818yes—
503C4×D4—48no—
504C4×D4C2×Q818yes—
505C4×D4C2×Q8116yes—
506C4×D4C2×Q818yes—
507C4×D4C2×Q8116yes—
508#117—44no—
509#117—44no—
510#117—48no—
511#117—44no—
512#117—44no—
513#117—48no—
514#117—44no—
515#117C2×Q818yes—
516#117C2×Q8116yes—
517C2×C4⋊C4—48no—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2411yescharacteristic
559C2×C4⋊C4C2412yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2412yes—
575C2×C42—42no—
576C2×C42—44no—
577C2×C42—42no—
578C2×C42—44no—
579C2×C42C2×Q818yes—
580C2×C42C2×Q8116yes—
581C2×C42C2412yes—
582C2×C42C2411yescharacteristic
583C2×C42C2411yescharacteristic
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2414yes—
587C2×C42C2414yes—
588C2×C42C2412yes—
589C2×C42C2411yescharacteristic
590C2×C42C2412yes—
591C2×C42C2412yes—
592C2×C42C2411yescharacteristic
593C2×C42C2414yes—
594C2×C42C2414yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2418yes—
598C2×C42C2418yes—
599C2×C42C2418yes—
600C2×C42C2412yes—
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2412yes—
604C2×C42C2412yes—
605C2×C42C2412yes—
606C2×C42C2411yescharacteristic
607C2×C42C2412yes—
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2412yes—
611C2×C42C2412yes—
612C2×C42C2411yescharacteristic
613#95C2412yes—
614#95C2412yes—
615#95C2414yes—
616#95C2414yes—
617#95C2418yes—
618#95C2418yes—
619#95C2412yes—
620#95C2412yes—
621#95C2414yes—
622#95C2412yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2412yes—
633#95C2412yes—
634#95C2412yes—
635#95C2414yes—
636#95C2414yes—
637#95C2418yes—
638#95C2418yes—
639#95C2412yes—
640#95C2414yes—
641#95C2412yes—
642#95C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2418yes—
648#95C2414yes—
649#95C2418yes—
650#95C2414yes—
651#95C2414yes—
652#95C2418yes—
653#95C2418yes—
654#95C2414yes—
655#95C2414yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664C24C2512yes—
665C24C2511yescharacteristic
666#41—416no—
667C2×Q8—24no—
668C2×Q8—28no—
669C2×Q8—44no—
670C2×Q8—44no—
671C2×Q8—48no—
672C2×Q8—48no—
673C2×Q8—48no—
674C2×Q8—48no—
675C2×Q8—48no—
676C2×Q8—48no—
677C2×Q8C22×Q814yes—
678C2×D4—24no—
679C2×D4—44no—
680C2×D4C22×Q814yes—
681C2×D4C22×Q818yes—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—48no—
697C22×C4—48no—
698C22×C4—48no—
699C22×C4C22×Q814yes—
700C22×C4C22×Q818yes—
701C22×C4C22×Q814yes—
702C22×C4C22×Q818yes—
703C22×C4C22×Q818yes—
704C22×C4C22×Q814yes—
705C22×C4C2514yes—
706C22×C4C2514yes—
707C22×C4C2514yes—
708C22×C4C2514yes—
709C22×C4C2518yes—
710C22×C4C2514yes—
711C22×C4C2512yes—
712C22×C4C2512yes—
713C22×C4C2512yes—
714C22×C4C2514yes—
715C22×C4C2518yes—
716C22×C4C2511yescharacteristic
717C22×C4C2511yescharacteristic
718C22×C4C2512yes—
719C22×C4C2511yescharacteristic
720C22×C4C2511yescharacteristic
721C22×C4C2512yes—
722C22×C4C2512yes—
723C22×C4C2512yes—
724C22×C4C2511yescharacteristic
725C22×C4C2511yescharacteristic
726C4⋊C4—24no—
727C4⋊C4—28no—
728C4⋊C4—24no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—24no—
732C4⋊C4—24no—
733C4⋊C4—28no—
734C4⋊C4—28no—
735C4⋊C4—28no—
736C4⋊C4—216no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—48no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C4⋊C4—48no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—48no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—44no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—48no—
763C4⋊C4—48no—
764C4⋊C4C22×Q818yes—
765C4⋊C4C22×Q818yes—
766C4⋊C4C22×Q814yes—
767C4⋊C4C22×Q814yes—
768C22⋊C4—28no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—48no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—48no—
777C22⋊C4—44no—
778C22⋊C4—48no—
779C22⋊C4—44no—
780C22⋊C4C22×Q818yes—
781C22⋊C4C22×Q818yes—
782C22⋊C4C22×Q818yes—
783C42—24no—
784C42—22no—
785C42—22no—
786C42—24no—
787C42—24no—
788C42—24no—
789C42—22no—
790C42—22no—
791C42—24no—
792C42—24no—
793C42—28no—
794C42—28no—
795C42—42no—
796C42—42no—
797C42—42no—
798C42—42no—
799C42—42no—
800C42—42no—
801C42—44no—
802C42—44no—
803C42—44no—
804C42—48no—
805C42—44no—
806C42—48no—
807C42—48no—
808C42C22×Q814yes—
809C42C22×Q814yes—
810C42C22×Q818yes—
811C42C22×Q818yes—
812C42C22×Q814yes—
813C42C22×Q818yes—
814C42C22×Q814yes—
815C23—24no—
816C23—22no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—24no—
823C23C23×Q812yes—
824C23C23×Q814yes—
825C23C2611yescharacteristic
826Q8—28no—
827Q8—88no—
828Q8—168no—
829Q8—168no—
830D4—28no—
831D4—48no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—28no—
844C2×C4—28no—
845C2×C4—216no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—28no—
862C2×C4—24no—
863C2×C4—22no—
864C2×C4—24no—
865C2×C4—28no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—24no—
872C2×C4—28no—
873C2×C4—24no—
874C2×C4—28no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—44no—
880C2×C4—48no—
881C2×C4—48no—
882C2×C4—48no—
883C2×C4—48no—
884C2×C4—168no—
885C2×C4C23×Q812yes—
886C2×C4C23×Q812yes—
887C2×C4C23×Q812yes—
888C2×C4C23×Q814yes—
889C2×C4C23×Q812yes—
890C2×C4C23×Q814yes—
891C2×C4C23×Q814yes—
892C2×C4C23×Q812yes—
893C2×C4C23×Q812yes—
894C2×C4#58514yes—
895C2×C4#58514yes—
896C2×C4#58512yes—
897C2×C4#58512yes—
898C22—24no—
899C22—22no—
900C22—24no—
901C22—22no—
902C22—22no—
903C22—24no—
904C22—42no—
905C22—44no—
906C22—42no—
907C22—44no—
908C22C24×Q811yescharacteristic
909C22C2×#58511yescharacteristic
910C22C2×#58511yescharacteristic
911C22C2×#58512yes—
912C22C2×#58512yes—
913C4—22no—
914C4—24no—
915C4—22no—
916C4—22no—
917C4—24no—
918C4—24no—
919C4—22no—
920C4—24no—
921C4—42no—
922C4—44no—
923C4—44no—
924C4—48no—
925C4—44no—
926C4—42no—
927C4—42no—
928C4—44no—
929C4—48no—
930C4—44no—
931C4—44no—
932C4#345814yes—
933C4#350414yes—
934C2—42no—
935C2—44no—
936C2C2×#345811yescharacteristic
937C2C2×#350411yescharacteristic
938C2#6281311yescharacteristic
939C2#6282712yes—
940C2#6284112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39987C2semidirect
3. #39970C2semidirect
4. #39182C2semidirect
5. #39181C2semidirect
6. #38967C2semidirect
7. #38964C2semidirect
8. #38106C2semidirect
9. #38105C2semidirect
10. #36755C2semidirect
11. #36640C2semidirect
12. #36635C2semidirect
13. #35643C2semidirect
14. #35602C2semidirect
15. #35344C2semidirect
16. #35339C2semidirect
17. #35192C2semidirect
18. #35192C2semidirect
19. #35192C2semidirect
20. #35132C2semidirect
191. C4×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#399872
#399842
#399702
#391822
#391812
#389672
#389642
#381062
#381052
#367552
#366402
#366352
#356432
#356022
#353442
#353392
#351922
#351322
#341932
#341912
#340262