Finite Group Databasebeta

← #7632101

Subgroups — #7632101

Order 512.

4744 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36286C214yesmaximal, complemented
2#36285C214yesmaximal, complemented
3#36283C214yesmaximal, complemented
4#36283C214yesmaximal, complemented
5#35972C214yesmaximal, complemented
6#35958C214yesmaximal, complemented
7#35936C214yesmaximal, complemented
8#35867C214yesmaximal, complemented
9#35668C212yesmaximal
10#35662C212yesmaximal
11#35403C218yesmaximal
12#35339C211yesmaximal, characteristic
13#35330C211yesmaximal, characteristic
14#35146C214yesmaximal
15#34948C211yesmaximal, characteristic
16#34938C211yesmaximal, characteristic
17#34878C214yesmaximal
18#34271C212yesmaximal
19#34213C212yesmaximal
20#34187C211yesmaximal, characteristic
21C2×#2356C211yesmaximal, characteristic
22C4×#519C211yesmaximal, characteristic
23C2×#544C2212yes—
24C2×#533C2212yes—
25C2×#519C2211yescharacteristic
26C2×#519C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28#2864C2212yes—
29#2864C2212yes—
30#2863C2218yes—
31#2863C2218yes—
32#2862C2212yes—
33#2859C2212yes—
34#2666C2218yes—
35#2666C2218yes—
36#2660C2214yes—
37#2647C2214yes—
38#2612C2218yes—
39#2612C2218yes—
40#2606C2218yes—
41#2606C2218yes—
42#2606C2218yes—
43#2605C2218yes—
44#2605C2218yes—
45#2605C2218yes—
46#2590C2218yes—
47#2590C2218yes—
48#2588C2218yes—
49#2588C2218yes—
50#2586C2218yes—
51#2586C2218yes—
52#2585C2218yes—
53#2585C2218yes—
54#2582C2214yes—
55#2582C2214yes—
56#2581C2214yes—
57#2581C2214yes—
58#2571C2212yes—
59#2570C2214yes—
60#2570C2214yes—
61#2570C2212yes—
62#2570C2212yes—
63#2569C2214yes—
64#2569C2214yes—
65#2569C2212yes—
66#2569C2212yes—
67#2568C2214yes—
68#2567C2214yes—
69#2565C2214yes—
70#2565C2214yes—
71#2552C2212yes—
72#2552C2212yes—
73#2551C2212yes—
74#2550C2214yes—
75#2550C2214yes—
76#2550C2212yes—
77#2550C2212yes—
78#2549C2214yes—
79#2549C2214yes—
80#2549C2212yes—
81#2549C2212yes—
82#2520C2218yes—
83#2520C2218yes—
84#2511C2218yes—
85#2507C2218yes—
86#2462C2218yes—
87#2462C2218yes—
88#2453C2214yes—
89#2453C2214yes—
90#2453C2214yes—
91#2453C2214yes—
92#2451C2218yes—
93#2451C2214yes—
94#2451C2214yes—
95#2451C2214yes—
96#2451C2214yes—
97#2446C2218yes—
98#2442C2214yes—
99#2440C2214yes—
100#2438C2218yes—
101#2438C2218yes—
102#2438C2218yes—
103#2438C2218yes—
104#2402C2212yes—
105#2402C2218yes—
106#2402C2212yes—
107#2399C2218yes—
108#2399C2212yes—
109#2399C2212yes—
110#2370C2214yes—
111#2370C2214yes—
112#2370C2214yes—
113#2370C2214yes—
114#2370C2214yes—
115#2370C2214yes—
116#2369C2214yes—
117#2369C2214yes—
118#2369C2214yes—
119#2365C2214yes—
120#2365C2214yes—
121#2365C2214yes—
122#2356C2212yes—
123#2356C2212yes—
124#2356C2212yes—
125#2356C2212yes—
126#2356C2214yes—
127#2356C2214yes—
128#2356C2212yes—
129#2356C2212yes—
130#2356C2212yes—
131#2356C2212yes—
132#2355C2214yes—
133#2355C2214yes—
134#2355C2214yes—
135#2355C2214yes—
136#2355C2214yes—
137Q8×C4⋊C4C2214yes—
138#2329C2218yes—
139#2329C2218yes—
140#2317C2212yes—
141#2317C2212yes—
142#2316C2212yes—
143#2313C2214yes—
144#2310C2212yes—
145C4×C4⋊Q8C2214yes—
146C4×#125C2214yes—
147C4×C22⋊Q8C2218yes—
148C4×C22⋊Q8C2218yes—
149#2296C2212yes—
150#2296C2212yes—
151#2295C2218yes—
152#2295C2218yes—
153C2×#391C2212yes—
154C2×#387C2214yes—
155#2285C2211yescharacteristic
156#2285C2211yescharacteristic
157#2285C2212yes—
158#2283C2214yes—
159C2×#383C2212yes—
160C2×#382C2211yescharacteristic
161#2276C2214yes—
162#2276C2214yes—
163#2274C2214yes—
164#2274C2212yes—
165#2274C2211yescharacteristic
166#2274C2211yescharacteristic
167C42×Q8C2214yes—
168C42×Q8C2214yes—
169C4×#117C2211yescharacteristic
170C4×#117C2211yescharacteristic
171C4×#117C2214yes—
172C2×C4×C4⋊C4C2211yescharacteristic
173C2×C4×C4⋊C4C2212yes—
174C2×#376C2212yes—
175C23×Q8C2311yescharacteristic
176#544—216no—
177#533—216no—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2312yes—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2314yes—
183C2×#125C2314yes—
184C2×#125C2312yes—
185C2×#125C2312yes—
186C2×#125C2314yes—
187C2×#125C2314yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2314yes—
191#519—28no—
192#519—28no—
193C2×C4×Q8Q8116yescomplemented
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2318yes—
201C2×C4×Q8C2318yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2312yes—
204C2×C4×Q8C2312yes—
205C2×C4×Q8C2312yes—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2311yescharacteristic
209C2×#117C2311yescharacteristic
210C2×#117C2314yes—
211C2×#117C2314yes—
212C2×#117C2311yescharacteristic
213C2×#117C2311yescharacteristic
214C22×C4⋊C4C2312yes—
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2314yes—
220C22×C42C2312yes—
221C22×C42C2311yescharacteristic
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2314yes—
227#400C2314yes—
228#400C2314yes—
229#400C2314yes—
230#400C2318yes—
231#400C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2314yes—
239#398C2314yes—
240#398C2314yes—
241#398C2314yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2314yes—
247#398C2314yes—
248#398C2318yes—
249#398C2314yes—
250#398C2318yes—
251#398C2314yes—
252#395C2318yes—
253#395C2318yes—
254#395C2318yes—
255#395C2318yes—
256#395C2314yes—
257#395C2314yes—
258#395C2318yes—
259#395C2314yes—
260#395C2318yes—
261#395C2314yes—
262#391C2314yes—
263#391C2314yes—
264#391C2314yes—
265#391C2314yes—
266#391C2314yes—
267#391C2314yes—
268#391C2314yes—
269#391C2314yes—
270#391C2318yes—
271#391C2318yes—
272#391C2318yes—
273#391C2318yes—
274#391C2318yes—
275#391C2318yes—
276#391C2318yes—
277#391C2318yes—
278#391C2318yes—
279#391C2318yes—
280#391C2318yes—
281#391C2318yes—
282#391C2314yes—
283#391C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2314yes—
289#389C2314yes—
290#389C2318yes—
291#389C2318yes—
292#389C2314yes—
293#389C2314yes—
294#389C2312yes—
295#389C2312yes—
296#389C2312yes—
297#389C2312yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2318yes—
305#389C2318yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C2318yes—
310#389C2318yes—
311#389C2318yes—
312#389C2318yes—
313#389C2318yes—
314#389C2312yes—
315#389C2312yes—
316#389C2312yes—
317#389C2312yes—
318#387C2314yes—
319#387C2314yes—
320#387C2314yes—
321#387C2314yes—
322#387C2318yes—
323#387C2318yes—
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#387C2318yes—
354#385C2318yes—
355#385C2314yes—
356#385C2314yes—
357#385C2318yes—
358#385C2314yes—
359#385C2314yes—
360#384C2314yes—
361#384C2312yes—
362#384C2314yes—
363#384C2312yes—
364#384C2312yes—
365#384C2314yes—
366#384C2312yes—
367#383C2314yes—
368#383C2314yes—
369#383C2318yes—
370#383C2314yes—
371#383C2314yes—
372#382C2314yes—
373#382C2312yes—
374#382C2314yes—
375#382C2312yes—
376#382C2311yescharacteristic
377#382C2312yes—
378#382C2311yescharacteristic
379#382C2312yes—
380#382C2314yes—
381#382C2312yes—
382#382C2311yescharacteristic
383#382C2311yescharacteristic
384#382C2318yes—
385#382C2312yes—
386#381C2318yes—
387#380C2312yes—
388#380C2312yes—
389#380C2318yes—
390#380C2312yes—
391#380C2312yes—
392#380C2314yes—
393#380C2314yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2318yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2318yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2318yes—
436C4×C4⋊C4C2318yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C22⋊C4C2318yes—
440C4×C22⋊C4C2312yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2312yes—
445C4×C22⋊C4C2312yes—
446#376C2314yes—
447#376C2318yes—
448#376C2318yes—
449#376C2314yes—
450#376C2314yes—
451#376C2314yes—
452#376C2312yes—
453#376C2312yes—
454C2×#95C2311yescharacteristic
455C2×#95C2312yes—
456C2×#95C2311yescharacteristic
457C2×#95C2312yes—
458C2×#95C2314yes—
459C2×#95C2314yes—
460C2×#95C2314yes—
461C43C2312yes—
462C43C2312yes—
463C43C2318yes—
464C22×Q8—24no—
465C22×Q8—24no—
466C22×Q8C2×Q818yes—
467C22×Q8C2414yes—
468C22×Q8C2412yes—
469C22×Q8C2412yes—
470C22×Q8C2414yes—
471C22×Q8C2418yes—
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2412yes—
475C23×C4C2414yes—
476C23×C4C2411yescharacteristic
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C4⋊Q8—28no—
481C4⋊Q8—28no—
482C4⋊Q8—216no—
483C4⋊Q8—216no—
484C4⋊Q8—48no—
485#125—28no—
486#125—28no—
487#125—216no—
488#125—216no—
489#125—48no—
490C22⋊Q8—216no—
491C22⋊Q8—216no—
492C22⋊Q8—232no—
493C4×Q8—216no—
494C4×Q8—216no—
495C4×Q8—216no—
496C4×Q8—216no—
497C4×Q8—216no—
498C4×Q8—216no—
499C4×Q8—416no—
500C4×Q8—416no—
501C4×Q8C2×Q8116yes—
502C4×Q8C2×Q8116yes—
503C4×Q8C2×Q8116yes—
504C4×Q8C2×Q8116yes—
505#117—24no—
506#117—24no—
507#117—28no—
508#117—28no—
509#117—216no—
510#117—216no—
511#117#4118yes—
512#117#4118yes—
513C2×C4⋊C4—28no—
514C2×C4⋊C4—44no—
515C2×C4⋊C4C2×Q8116yes—
516C2×C4⋊C4C2×Q818yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2412yes—
574C2×C42—28no—
575C2×C42—48no—
576C2×C42C2×Q8116yes—
577C2×C42C2×Q818yes—
578C2×C42C2412yes—
579C2×C42C2412yes—
580C2×C42C2418yes—
581C2×C42C2418yes—
582C2×C42C2414yes—
583C2×C42C2414yes—
584C2×C42C2418yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2412yes—
589C2×C42C2418yes—
590C2×C42C2418yes—
591C2×C42C2418yes—
592C2×C42C2418yes—
593C2×C42C2414yes—
594C2×C42C2414yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2418yes—
598C2×C42C2414yes—
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601C2×C42C2414yes—
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2412yes—
605C2×C42C2412yes—
606#95C2412yes—
607#95C2411yescharacteristic
608#95C2411yescharacteristic
609#95C2414yes—
610#95C2414yes—
611#95C2418yes—
612#95C2418yes—
613#95C2412yes—
614#95C2411yescharacteristic
615#95C2411yescharacteristic
616#95C2418yes—
617#95C2418yes—
618#95C2414yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2412yes—
625#95C2412yes—
626#95C2412yes—
627#95C2412yes—
628#95C2418yes—
629#95C2418yes—
630#95C2414yes—
631#95C2414yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2412yes—
644#95C2412yes—
645#95C2414yes—
646#95C2412yes—
647#95C2412yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2414yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660C24C2511yescharacteristic
661C2×Q8—232no—
662C2×Q8—24no—
663C2×Q8—24no—
664C2×Q8—24no—
665C2×Q8—24no—
666C2×Q8—28no—
667C2×Q8—28no—
668C2×Q8—216no—
669C2×Q8—28no—
670C2×Q8—44no—
671C2×Q8—48no—
672C2×Q8—44no—
673C2×Q8—44no—
674C2×Q8—48no—
675C2×Q8C22×Q818yes—
676C2×Q8C22×Q818yes—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—28no—
682C22×C4—24no—
683C22×C4—44no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—44no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—44no—
691C22×C4C22×Q818yes—
692C22×C4C22×Q814yes—
693C22×C4C22×Q814yes—
694C22×C4C22×Q818yes—
695C22×C4C22×Q814yes—
696C22×C4C2×#4114yes—
697C22×C4C2×#4114yes—
698C22×C4C2512yes—
699C22×C4C2514yes—
700C22×C4C2518yes—
701C22×C4C2512yes—
702C22×C4C2514yes—
703C22×C4C2514yes—
704C22×C4C2512yes—
705C22×C4C2514yes—
706C22×C4C2514yes—
707C22×C4C2514yes—
708C22×C4C2511yescharacteristic
709C22×C4C2511yescharacteristic
710C22×C4C2514yes—
711C22×C4C2514yes—
712C22×C4C2511yescharacteristic
713C22×C4C2511yescharacteristic
714C22×C4C2514yes—
715C22×C4C2514yes—
716C22×C4C2512yes—
717C22×C4C2511yescharacteristic
718C22×C4C2511yescharacteristic
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—216no—
722C4⋊C4—216no—
723C4⋊C4—24no—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—28no—
734C4⋊C4—28no—
735C4⋊C4—216no—
736C4⋊C4—216no—
737C4⋊C4—216no—
738C4⋊C4—24no—
739C4⋊C4—24no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—42no—
744C4⋊C4—42no—
745C4⋊C4—48no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—44no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4C22×Q8116yes—
765C4⋊C4C22×Q8116yes—
766C4⋊C4C22×Q818yes—
767C4⋊C4C22×Q818yes—
768C4⋊C4C2×#4118yes—
769C4⋊C4C2×#4118yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—28no—
773C22⋊C4—28no—
774C22⋊C4C2×#4118yes—
775C22⋊C4C2×#4118yes—
776C42—24no—
777C42—24no—
778C42—24no—
779C42—24no—
780C42—216no—
781C42—216no—
782C42—24no—
783C42—24no—
784C42—28no—
785C42—28no—
786C42—216no—
787C42—48no—
788C42—44no—
789C42—44no—
790C42—48no—
791C42—48no—
792C42—48no—
793C42—48no—
794C42—44no—
795C42—44no—
796C42C22×Q8116yes—
797C42C22×Q8116yes—
798C42C22×Q814yes—
799C42C22×Q814yes—
800C42C22×Q814yes—
801C42C22×Q814yes—
802C42C2×#4118yes—
803C42C2×#4118yes—
804C23—22no—
805C23—22no—
806C23C23×Q812yes—
807C23C22×#4112yes—
808C23C22×#4112yes—
809C23C2611yescharacteristic
810Q8—216no—
811Q8—216no—
812Q8—416no—
813Q8—88no—
814Q8—816no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—216no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—28no—
839C2×C4—28no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—28no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—48no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—48no—
863C2×C4—84no—
864C2×C4—88no—
865C2×C4#533116yes—
866C2×C4C23×Q812yes—
867C2×C4C23×Q812yes—
868C2×C4C23×Q818yes—
869C2×C4C23×Q812yes—
870C2×C4C23×Q812yes—
871C2×C4C23×Q818yes—
872C2×C4C23×Q812yes—
873C2×C4C23×Q812yes—
874C2×C4C22×#4118yes—
875C2×C4C22×#4118yes—
876C2×C4C22×#4112yes—
877C2×C4C22×#4112yes—
878C2×C4C22×#4112yes—
879C2×C4C22×#4112yes—
880C2×C4#58514yes—
881C22—24no—
882C22—24no—
883C22—22no—
884C22—22no—
885C22C2×#53314yes—
886C22C24×Q811yescharacteristic
887C22C23×#4111yescharacteristic
888C22C23×#4111yescharacteristic
889C22C2×#58512yes—
890C222−1+612yes—
891C4—24no—
892C4—28no—
893C4—28no—
894C4—28no—
895C4—22no—
896C4—22no—
897C4—22no—
898C4—22no—
899C4—28no—
900C4—44no—
901C4—42no—
902C4—42no—
903C4—42no—
904C4—44no—
905C4—44no—
906C4—44no—
907C4—44no—
908C4—48no—
909C4—44no—
910C4C2×#53314yes—
911C4C2×#53314yes—
912C2—24no—
913C2C22×#53311yescharacteristic
914C2#6281311yescharacteristic
915C2#6284911yescharacteristic
916C2#6299312yes—
917C2#6299512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36286C2semidirect
2. #36285C2semidirect
3. #36283C2semidirect
4. #36283C2semidirect
5. #35972C2semidirect
6. #35958C2semidirect
7. #35936C2semidirect
8. #35867C2semidirect
193. C2×C4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#362862
#362852
#362832
#359722
#359582
#359362
#358672
#356682
#356622
#354032
#353392
#353302
#351462
#349482
#349382
#348782
#342712
#342132
#341872
C2×#23562
C4×#5192