Finite Group Databasebeta

← #7679780

Subgroups — #7679780

Order 512.

4672 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59856C214yesmaximal, complemented
2#59393C214yesmaximal, complemented
3#59291C214yesmaximal, complemented
4#59214C214yesmaximal, complemented
5#43139C218yesmaximal, complemented
6#43131C218yesmaximal, complemented
7#39692C214yesmaximal, complemented
8#39642C211yesmaximal, characteristic, complemented
9#39638C212yesmaximal, complemented
10#39634C211yesmaximal, characteristic, complemented
11#39634C212yesmaximal, complemented
12#39598C212yesmaximal, complemented
13#36559C211yesmaximal, characteristic, complemented
14#36551C212yesmaximal, complemented
15Q8×#125C211yesmaximal, characteristic, complemented
16#35612C214yesmaximal, complemented
17#35336C212yesmaximal, complemented
18#35284C211yesmaximal, characteristic, complemented
19#34941C212yesmaximal, complemented
20#34332C212yesmaximal, complemented
21#34280C212yesmaximal
22#34145C211yesmaximal, characteristic, complemented
23C4×#540C211yesmaximal, characteristic
24C2×#554C2212yes—
25C2×#540C2211yescharacteristic
26C2×#533C2211yescharacteristic
27#2868C2211yescharacteristic
28#2859C2212yes—
29#2859C2212yes—
30#2859C2211yescharacteristic
31#2857C2212yes—
32#2851C2214yes—
33#2802C2218yes—
34#2790C2218yes—
35#2780C2218yes—
36#2780C2218yes—
37#2780C2218yes—
38#2780C2218yes—
39#2780C2218yes—
40#2774C2218yes—
41#2768C2218yes—
42#2713C2218yes—
43#2704C2218yes—
44#2683C2218yes—
45#2647C2212yes—
46#2647C2212yes—
47#2647C2212yes—
48#2629C2214yes—
49#2629C2212yes—
50#2608C2218yes—
51#2590C2218yes—
52#2590C2218yes—
53#2589C2218yes—
54#2587C2218yes—
55#2587C2218yes—
56#2587C2218yes—
57#2585C2218yes—
58#2584C2214yes—
59#2579C2218yes—
60#2574C2218yes—
61#2569C2218yes—
62#2567C2212yes—
63#2566C2214yes—
64#2566C2218yes—
65#2563C2212yes—
66#2556C2218yes—
67#2552C2214yes—
68#2552C2214yes—
69#2552C2212yes—
70#2538C2214yes—
71#2538C2214yes—
72#2538C2214yes—
73#2538C2212yes—
74#2522C2218yes—
75#2522C2218yes—
76#2511C2214yes—
77#2509C2214yes—
78#2509C2218yes—
79#2508C2214yes—
80#2507C2214yes—
81#2507C2218yes—
82#2507C2214yes—
83#2506C2214yes—
84#2497C2218yes—
85#2497C2214yes—
86#2497C2214yes—
87#2497C2214yes—
88#2487C2214yes—
89#2487C2214yes—
90#2487C2218yes—
91#2473C2218yes—
92#2454C2214yes—
93#2454C2214yes—
94#2454C2214yes—
95#2452C2218yes—
96#2450C2218yes—
97#2446C2214yes—
98#2441C2218yes—
99#2440C2214yes—
100#2438C2218yes—
101#2429C2214yes—
102#2429C2214yes—
103#2423C2214yes—
104#2417C2214yes—
105#2417C2218yes—
106#2417C2214yes—
107#2396C2218yes—
108#2374C2218yes—
109#2370C2214yes—
110#2370C2214yes—
111#2369C2212yes—
112#2369C2212yes—
113#2368C2214yes—
114#2365C2212yes—
115#2364C2218yes—
116#2363C2218yes—
117#2360C2214yes—
118#2360C2218yes—
119#2360C2212yes—
120#2360C2212yes—
121#2359C2218yes—
122Q8×C4⋊C4C2214yes—
123Q8×C4⋊C4C2212yes—
124D4×C4⋊C4C2214yes—
125D4×C4⋊C4C2212yes—
126D4×C4⋊C4C2214yes—
127D4×C4⋊C4C2214yes—
128#2345C2214yes—
129#2345C2214yes—
130#2335C2214yes—
131#2333C2214yes—
132#2330C2214yes—
133#2330C2212yes—
134#2330C2211yescharacteristic
135#2330C2212yes—
136#2329C2218yes—
137#2328C2211yescharacteristic
138#2328C2212yes—
139#2324C2212yes—
140#2324C2214yes—
141#2319C2212yes—
142#2314C2211yescharacteristic
143#2314C2212yes—
144C4×C4⋊Q8C2212yes—
145C4×#127C2211yescharacteristic
146C4×#127C2212yes—
147C4×#125C2214yes—
148C4×#125C2211yescharacteristic
149C4×#125C2212yes—
150C4×C22⋊Q8C2214yes—
151C4×C22⋊Q8C2214yes—
152C4×#123C2214yes—
153C4×#121C2214yes—
154C4×#121C2214yes—
155C4×#121C2212yes—
156#2296C2212yes—
157#2295C2211yescharacteristic
158#2295C2212yes—
159#2295C2212yes—
160#2295C2211yescharacteristic
161#2293C2214yes—
162C2×#389C2214yes—
163#2285C2214yes—
164#2275C2214yes—
165C42×Q8C2211yescharacteristic
166C42×Q8C2211yescharacteristic
167C42×D4C2212yes—
168C4×#117C2212yes—
169C4×#117C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171#554—216no—
172#540Q8116yescomplemented
173#533—28no—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2311yescharacteristic
176C2×C4⋊Q8C2311yescharacteristic
177C2×C4⋊Q8C2314yes—
178C2×#127C2311yescharacteristic
179C2×#125C2314yes—
180C2×#125C2312yes—
181C2×#125C2314yes—
182C2×#125C2312yes—
183C2×#125C2318yes—
184C2×#125C2311yescharacteristic
185C2×#123C2314yes—
186C2×C22⋊Q8C2318yes—
187C2×C22⋊Q8C2311yescharacteristic
188C2×C22⋊Q8C2311yescharacteristic
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2312yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2318yes—
194C2×#121C2312yes—
195C2×#121C2314yes—
196C2×C4×Q8C2311yescharacteristic
197C2×C4×Q8C2312yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2312yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2311yescharacteristic
203C2×C4×D4C2312yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2312yes—
212C2×#117C2312yes—
213C2×#117C2311yescharacteristic
214C2×#117C2318yes—
215C2×#117C2311yescharacteristic
216C22×C4⋊C4C2314yes—
217C22×C4⋊C4C2314yes—
218C22×C4⋊C4C2312yes—
219C22×C4⋊C4C2318yes—
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2314yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#399C2318yes—
231#399C2318yes—
232#399C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#396C2318yes—
253#396C2318yes—
254#396C2318yes—
255#396C2318yes—
256#395C2318yes—
257#395C2318yes—
258#393C2318yes—
259#391C2314yes—
260#391C2314yes—
261#391C2318yes—
262#391C2314yes—
263#391C2312yes—
264#391C2312yes—
265#391C2314yes—
266#391C2314yes—
267#390C2314yes—
268#390C2312yes—
269#390C2314yes—
270#390C2318yes—
271#390C2314yes—
272#390C2318yes—
273#390C2312yes—
274#390C2314yes—
275#389C2314yes—
276#389C2312yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2312yes—
283#389C2318yes—
284#389C2314yes—
285#389C2318yes—
286#389C2318yes—
287#389C2318yes—
288#389C2318yes—
289#389C2318yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2318yes—
294#389C2318yes—
295#389C2314yes—
296#389C2318yes—
297#389C2318yes—
298#389C2318yes—
299#389C2318yes—
300#389C2318yes—
301#389C2312yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2312yes—
308#389C2314yes—
309#389C2314yes—
310#389C2318yes—
311#389C2314yes—
312#389C2314yes—
313#388C2314yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2314yes—
318#388C2314yes—
319#388C2314yes—
320#388C2318yes—
321#388C2314yes—
322#388C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2314yes—
326#387C2318yes—
327#387C2314yes—
328#387C2318yes—
329#387C2318yes—
330#387C2314yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2314yes—
336#387C2318yes—
337#387C2318yes—
338#387C2314yes—
339#387C2314yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2314yes—
345#387C2314yes—
346#387C2314yes—
347#386C2314yes—
348#386C2318yes—
349#386C2314yes—
350#386C2314yes—
351#386C2318yes—
352#386C2318yes—
353#386C2314yes—
354#386C2318yes—
355#385C2314yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2314yes—
364#385C2314yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#384C2311yescharacteristic
370#384C2312yes—
371#384C2312yes—
372#384C2312yes—
373#384C2318yes—
374#384C2314yes—
375#384C2314yes—
376#384C2314yes—
377#384C2314yes—
378#382C2314yes—
379#382C2311yescharacteristic
380#382C2312yes—
381#382C2318yes—
382#381C2314yes—
383#380C2314yes—
384#380C2314yes—
385#380C2314yes—
386#380C2318yes—
387#380C2318yes—
388#380C2312yes—
389#380C2314yes—
390#380C2318yes—
391#380C2318yes—
392#380C2314yes—
393#380C2318yes—
394#380C2314yes—
395#380C2314yes—
396C4×C4⋊C4C2312yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2312yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2318yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2312yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2318yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2312yes—
439#376C2311yescharacteristic
440#376C2312yes—
441#376C2311yescharacteristic
442#376C2312yes—
443C2×#95C2318yes—
444C2×#95C2312yes—
445C43C2312yes—
446C43C2312yes—
447C43C2311yescharacteristic
448C43C2311yescharacteristic
449C22×Q8C2411yescharacteristic
450C22×Q8C2411yescharacteristic
451C22×Q8C2412yes—
452C22×Q8C2414yes—
453C22×D4C2412yes—
454C22×D4C2414yes—
455C22×D4C2414yes—
456C23×C4C2411yescharacteristic
457C23×C4C2414yes—
458C23×C4C2411yescharacteristic
459C23×C4C2418yes—
460C23×C4C2411yescharacteristic
461C23×C4C2418yes—
462C23×C4C2414yes—
463C23×C4C2414yes—
464C23×C4C2414yes—
465C4⋊Q8—24no—
466C4⋊Q8—24no—
467C4⋊Q8—28no—
468C4⋊Q8—84no—
469#127C2×Q818yes—
470#125—28no—
471#125—216no—
472#125—48no—
473#125—44no—
474#125—88no—
475#125C2×Q818yes—
476#123C2×Q8132yes—
477C22⋊Q8—24no—
478C22⋊Q8—216no—
479C22⋊Q8—24no—
480C22⋊Q8—28no—
481C22⋊Q8—232no—
482C22⋊Q8—48no—
483C22⋊Q8—88no—
484C22⋊Q8—84no—
485#121C2×Q8132yes—
486#121C2×Q8116yes—
487C4×Q8—28no—
488C4×Q8—24no—
489C4×Q8—44no—
490C4×Q8—48no—
491C4×Q8—44no—
492C4×Q8—84no—
493C4×Q8#4118yes—
494C4×D4—28no—
495C4×D4—216no—
496C4×D4—48no—
497C4×D4—44no—
498C4×D4—48no—
499C4×D4—48no—
500C4×D4—88no—
501C4×D4—88no—
502C4×D4C2×Q8116yes—
503#117—28no—
504#117—42no—
505#117—88no—
506#117C2×Q818yes—
507C2×C4⋊C4—216no—
508C2×C4⋊C4—44no—
509C2×C4⋊C4—48no—
510C2×C4⋊C4—88no—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2411yescharacteristic
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2411yescharacteristic
557C2×C4⋊C4C2412yes—
558C2×C22⋊C4C2412yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C42—24no—
579C2×C42—48no—
580C2×C42—44no—
581C2×C42C2411yescharacteristic
582C2×C42C2412yes—
583C2×C42C2411yescharacteristic
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2414yes—
587C2×C42C2411yescharacteristic
588C2×C42C2412yes—
589C2×C42C2412yes—
590C2×C42C2411yescharacteristic
591C2×C42C2411yescharacteristic
592C2×C42C2414yes—
593C2×C42C2418yes—
594C2×C42C2414yes—
595C2×C42C2418yes—
596C2×C42C2412yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2418yes—
600C2×C42C2412yes—
601C2×C42C2414yes—
602C2×C42C2414yes—
603C2×C42C2414yes—
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606C2×C42C2412yes—
607C2×C42C2411yescharacteristic
608#95C2414yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2412yes—
613#95C2414yes—
614#95C2412yes—
615#95C2414yes—
616#95C2412yes—
617#95C2412yes—
618#95C2414yes—
619#95C2412yes—
620#95C2412yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2414yes—
626#95C2414yes—
627#95C2418yes—
628#95C2414yes—
629#95C2418yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2414yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2414yes—
642#95C2418yes—
643#95C2414yes—
644#95C2418yes—
645C24C2511yescharacteristic
646C24C2514yes—
647C2×Q8—22no—
648C2×Q8—24no—
649C2×Q8—28no—
650C2×Q8—24no—
651C2×Q8—24no—
652C2×Q8—44no—
653C2×Q8—44no—
654C2×Q8—44no—
655C2×Q8C2×#4114yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—44no—
659C2×D4—44no—
660C2×D4—44no—
661C2×D4—44no—
662C2×D4C22×Q818yes—
663C2×D4C22×Q8116yes—
664C2×D4C22×Q8116yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—24no—
671C22×C4—28no—
672C22×C4—22no—
673C22×C4—216no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—48no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—48no—
684C22×C4—42no—
685C22×C4—48no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4C22×Q814yes—
689C22×C4C22×Q8116yes—
690C22×C4C2514yes—
691C22×C4C2512yes—
692C22×C4C2512yes—
693C22×C4C2511yescharacteristic
694C22×C4C2514yes—
695C22×C4C2511yescharacteristic
696C22×C4C2514yes—
697C22×C4C2514yes—
698C22×C4C2518yes—
699C22×C4C2518yes—
700C22×C4C2512yes—
701C22×C4C2512yes—
702C22×C4C2512yes—
703C22×C4C2512yes—
704C22×C4C2511yescharacteristic
705C22×C4C2514yes—
706C22×C4C2511yescharacteristic
707C22×C4C2512yes—
708C22×C4C2512yes—
709C22×C4C2511yescharacteristic
710C22×C4C2511yescharacteristic
711C4⋊C4—216no—
712C4⋊C4—28no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—28no—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—22no—
722C4⋊C4—216no—
723C4⋊C4—24no—
724C4⋊C4—24no—
725C4⋊C4—28no—
726C4⋊C4—24no—
727C4⋊C4—28no—
728C4⋊C4—48no—
729C4⋊C4—44no—
730C4⋊C4—44no—
731C4⋊C4—48no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C4⋊C4—42no—
735C4⋊C4—48no—
736C4⋊C4—48no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C4⋊C4—48no—
740C4⋊C4—48no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4—48no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4C22×Q818yes—
754C4⋊C4C22×Q818yes—
755C4⋊C4C22×Q8116yes—
756C4⋊C4C2×#4114yes—
757C4⋊C4C2×#4118yes—
758C22⋊C4—24no—
759C22⋊C4—24no—
760C22⋊C4—28no—
761C22⋊C4—216no—
762C22⋊C4—42no—
763C22⋊C4—48no—
764C22⋊C4—48no—
765C22⋊C4—44no—
766C22⋊C4—44no—
767C22⋊C4—48no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—48no—
772C22⋊C4—48no—
773C22⋊C4—48no—
774C22⋊C4—44no—
775C22⋊C4C22×Q818yes—
776C22⋊C4C22×Q8116yes—
777C22⋊C4C22×Q8116yes—
778C42—22no—
779C42—22no—
780C42—22no—
781C42—24no—
782C42—24no—
783C42—24no—
784C42—28no—
785C42—24no—
786C42—22no—
787C42—22no—
788C42—24no—
789C42—44no—
790C42—44no—
791C42—44no—
792C42—44no—
793C42—48no—
794C42—44no—
795C42—48no—
796C42—44no—
797C42—48no—
798C42—44no—
799C42—42no—
800C42—42no—
801C42C22×Q814yes—
802C42C22×Q814yes—
803C42C2×#4114yes—
804C42C2×#4118yes—
805C23—21no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—21no—
810C23—22no—
811C23—24no—
812C23—24no—
813C23—22no—
814C23—24no—
815C23C23×Q818yes—
816C23C23×Q812yes—
817C23C2611yescharacteristic
818Q8—28no—
819Q8—44no—
820Q8—84no—
821Q8—88no—
822D4—216no—
823D4—416no—
824D4—416no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—28no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—28no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—28no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—28no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—28no—
862C2×C4—24no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—416no—
870C2×C4—44no—
871C2×C4—416no—
872C2×C4—816no—
873C2×C4—82no—
874C2×C4—88no—
875C2×C4—88no—
876C2×C4—168no—
877C2×C4C23×Q814yes—
878C2×C4C23×Q814yes—
879C2×C4C23×Q812yes—
880C2×C4C23×Q818yes—
881C2×C4C23×Q812yes—
882C2×C4C22×#4112yes—
883C2×C4C22×#4114yes—
884C2×C4C22×#4114yes—
885C2×C4C22×#4112yes—
886C2×C4C22×#4112yes—
887C2×C4#58512yes—
888C2×C4#58514yes—
889C22—28no—
890C22—28no—
891C22—24no—
892C22—22no—
893C22—28no—
894C22—41no—
895C22—44no—
896C22—44no—
897C22—41no—
898C22—42no—
899C22—44no—
900C22—44no—
901C22C24×Q811yescharacteristic
902C22C23×#4111yescharacteristic
903C22C2×#58512yes—
904C22C2×#58511yescharacteristic
905C22H(7,𝔽2)12yes—
906C4—24no—
907C4—28no—
908C4—24no—
909C4—24no—
910C4—24no—
911C4—22no—
912C4—22no—
913C4—41no—
914C4—44no—
915C4—42no—
916C4—48no—
917C4—41no—
918C4—42no—
919C4—42no—
920C4—44no—
921C4—44no—
922C4—42no—
923C4—44no—
924C4—48no—
925C4Q8×#4114yes—
926C4#351214yes—
927C2—48no—
928C2—42no—
929C2C2×Q8×#4111yescharacteristic
930C2C2×#351211yescharacteristic
931C2#6285811yescharacteristic
932C2#6293712yes—
933C2#6298912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#540C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59856C2semidirect
2. #59393C2semidirect
3. #59291C2semidirect
4. #59214C2semidirect
5. #43139C2semidirect
6. #43131C2semidirect
7. #39692C2semidirect
8. #39642C2semidirect
9. #39638C2semidirect
10. #39634C2semidirect
11. #39634C2semidirect
12. #39598C2semidirect
13. #36559C2semidirect
14. #36551C2semidirect
15. Q8×#125C2semidirect
16. #35612C2semidirect
17. #35336C2semidirect
18. #35284C2semidirect
19. #34941C2semidirect
20. #34332C2semidirect
22. #34145C2semidirect
172. #540Q8semidirect

Maximal subgroups

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

subgroupindex
#598562
#593932
#592912
#592142
#431392
#431312
#396922
#396422
#396382
#396342
#395982
#365592
#365512
Q8×#1252
#356122
#353362
#352842
#349412
#343322
#342802
#341452
C4×#5402