Finite Group Databasebeta

← #7632265

Subgroups — #7632265

Order 512.

5050 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36599C214yesmaximal, complemented
2#36564C214yesmaximal, complemented
3#36519C214yesmaximal, complemented
4#36519C214yesmaximal, complemented
5#35843C214yesmaximal, complemented
6#35788C214yesmaximal, complemented
7#35783C214yesmaximal, complemented
8#35708C214yesmaximal, complemented
9#35585C212yesmaximal, complemented
10#35566C212yesmaximal, complemented
11#35403C218yesmaximal, complemented
12#35253C212yesmaximal
13#35079C214yesmaximal
14#34958C214yesmaximal
15#34739C212yesmaximal
16#34271C212yesmaximal, complemented
17#34213C212yesmaximal, complemented
18#34178C211yesmaximal, characteristic
19C2×#2345C211yesmaximal, characteristic
20C2×#2274C211yesmaximal, characteristic
21C2×#544C2212yes—
22C2×#533C2212yes—
23C22×#117C2212yes—
24C23×C4⋊C4C2211yescharacteristic
25#2857C2218yes—
26#2857C2214yes—
27#2851C2218yes—
28#2851C2214yes—
29#2667C2214yes—
30#2667C2214yes—
31#2665C2214yes—
32#2665C2214yes—
33#2629C2214yes—
34#2628C2214yes—
35#2608C2218yes—
36#2607C2218yes—
37#2590C2218yescomplemented
38#2590C2218yescomplemented
39#2588C2218yescomplemented
40#2588C2218yescomplemented
41#2586C2218yescomplemented
42#2586C2218yescomplemented
43#2585C2218yescomplemented
44#2585C2218yescomplemented
45#2584C2214yescomplemented
46#2584C2214yescomplemented
47#2569C2218yes—
48#2569C2218yes—
49#2569C2214yes—
50#2569C2214yes—
51#2567C2214yescomplemented
52#2552C2214yescomplemented
53#2551C2214yescomplemented
54#2550C2214yescomplemented
55#2550C2214yescomplemented
56#2549C2218yes—
57#2549C2218yes—
58#2549C2214yes—
59#2549C2214yes—
60#2546C2214yescomplemented
61#2520C2218yescomplemented
62#2520C2218yescomplemented
63#2511C2218yescomplemented
64#2509C2214yescomplemented
65#2509C2214yescomplemented
66#2508C2214yescomplemented
67#2508C2214yescomplemented
68#2507C2214yescomplemented
69#2507C2214yescomplemented
70#2507C2218yescomplemented
71#2506C2214yescomplemented
72#2506C2214yescomplemented
73#2462C2218yescomplemented
74#2462C2218yescomplemented
75#2451C2218yescomplemented
76#2446C2218yescomplemented
77#2442C2218yes—
78#2442C2212yes—
79#2442C2214yes—
80#2442C2212yes—
81#2441C2218yes—
82#2441C2212yes—
83#2441C2214yes—
84#2441C2212yes—
85#2440C2218yes—
86#2440C2212yes—
87#2440C2214yes—
88#2440C2212yes—
89#2439C2212yes—
90#2439C2218yes—
91#2439C2214yes—
92#2439C2212yes—
93#2438C2214yes—
94#2438C2214yes—
95#2438C2218yes—
96#2437C2214yes—
97#2437C2218yes—
98#2437C2214yes—
99#2396C2218yes—
100#2396C2214yes—
101#2396C2218yes—
102#2396C2214yes—
103#2370C2214yescomplemented
104#2370C2214yescomplemented
105#2370C2214yescomplemented
106#2370C2214yescomplemented
107#2370C2214yescomplemented
108#2370C2214yescomplemented
109#2369C2214yescomplemented
110#2369C2214yescomplemented
111#2369C2214yescomplemented
112#2365C2214yescomplemented
113#2365C2214yescomplemented
114#2365C2214yescomplemented
115#2355C2214yescomplemented
116#2355C2214yescomplemented
117#2355C2214yescomplemented
118Q8×C4⋊C4C2214yescomplemented
119#2345C2214yes—
120#2345C2214yes—
121#2345C2214yes—
122#2345C2214yes—
123#2345C2214yes—
124#2345C2214yes—
125#2344C2214yes—
126#2344C2214yes—
127#2329C2218yes—
128#2329C2218yes—
129#2317C2212yes—
130#2317C2212yes—
131#2316C2212yes—
132#2316C2212yes—
133#2313C2214yes—
134C4×C22⋊Q8C2218yes—
135C4×C22⋊Q8C2218yes—
136C4×C22⋊Q8C2218yes—
137C4×C22⋊Q8C2218yes—
138C4×C22⋊Q8C2214yes—
139C4×C22⋊Q8C2214yes—
140#2296C2212yes—
141#2296C2212yes—
142C2×#389C2212yes—
143C2×#387C2214yes—
144#2285C2212yes—
145#2280C2214yes—
146#2280C2212yes—
147C2×#380C2212yes—
148C2×#380C2211yescharacteristic
149#2274C2211yescharacteristic
150#2274C2214yes—
151#2274C2214yes—
152#2274C2214yes—
153#2274C2211yescharacteristic
154#2274C2211yescharacteristic
155#2274C2212yes—
156#2274C2211yescharacteristic
157C2×C4×C4⋊C4C2212yes—
158C2×C4×C4⋊C4C2214yes—
159C2×C4×C4⋊C4C2214yes—
160C2×C4×C22⋊C4C2214yes—
161C2×C4×C22⋊C4C2212yes—
162C2×C4×C22⋊C4C2211yescharacteristic
163C24×C4C2311yescharacteristic
164C24×C4C2312yes—
165#544—216no—
166#533—216no—
167C2×C4⋊Q8C2314yes—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2314yes—
170C2×C4⋊Q8C2312yes—
171C2×C4⋊Q8C2318yes—
172C2×#125C2314yes—
173C2×#125C2312yes—
174C2×#125C2312yes—
175C2×#125C2314yes—
176C2×#125C2318yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2318yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2318yes—
183C2×C4×Q8C2314yes—
184C2×C4×Q8C2314yes—
185C2×C4×Q8C2318yes—
186C2×C4×Q8C2318yes—
187C2×#117—216no—
188C2×#117C2312yes—
189C2×#117C2312yes—
190C2×#117C2312yes—
191C2×#117C2314yes—
192C2×#117C2314yes—
193C2×#117C2312yes—
194C2×#117C2312yes—
195C2×#117C2318yes—
196C2×#117C2312yes—
197C22×C4⋊C4Q8116yescomplemented
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2314yes—
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2314yes—
205C22×C4⋊C4C2314yes—
206C22×C4⋊C4C2311yescharacteristic
207C22×C22⋊C4C2314yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C42C2314yes—
212C22×C42C2312yes—
213C22×C42C2318yes—
214C22×C42C2314yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2314yes—
220#400C2318yes—
221#400C2314yes—
222#399C2314yes—
223#399C2318yes—
224#399C2314yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2314yes—
232#398C2318yes—
233#398C2314yes—
234#398C2318yes—
235#398C2318yes—
236#398C2314yes—
237#398C2314yes—
238#398C2318yes—
239#396C2314yes—
240#396C2314yes—
241#396C2318yes—
242#396C2318yes—
243#396C2314yes—
244#396C2314yes—
245#395C2318yes—
246#395C2318yes—
247#395C2318yes—
248#395C2318yes—
249#395C2314yes—
250#395C2318yes—
251#395C2314yes—
252#393C2314yes—
253#393C2318yes—
254#393C2314yes—
255#391C2318yes—
256#391C2318yes—
257#391C2318yes—
258#391C2318yes—
259#391C2318yes—
260#391C2318yes—
261#391C2318yes—
262#391C2318yes—
263#391C2318yes—
264#391C2314yes—
265#391C2314yes—
266#389C2312yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#389C2314yes—
274#389C2314yes—
275#389C2314yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2312yes—
281#389C2312yes—
282#389C2318yes—
283#389C2318yes—
284#389C2318yes—
285#389C2318yes—
286#389C2314yes—
287#389C2318yes—
288#389C2318yes—
289#389C2318yes—
290#389C2318yes—
291#389C2318yes—
292#389C2318yes—
293#389C2318yes—
294#389C2318yes—
295#389C2318yes—
296#389C2314yes—
297#389C2314yes—
298#389C2312yes—
299#389C2312yes—
300#389C2312yes—
301#389C2312yes—
302#389C2312yes—
303#389C2314yes—
304#389C2314yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2318yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2314yes—
326#387C2314yes—
327#387C2318yes—
328#387C2318yes—
329#387C2314yes—
330#387C2314yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#385C2314yes—
336#385C2314yes—
337#385C2314yes—
338#385C2318yes—
339#385C2318yes—
340#385C2318yes—
341#385C2318yes—
342#385C2314yes—
343#385C2314yes—
344#385C2314yes—
345#385C2314yes—
346#385C2314yes—
347#384C2318yes—
348#384C2314yes—
349#384C2314yes—
350#384C2312yes—
351#384C2312yes—
352#382C2314yes—
353#382C2314yes—
354#382C2318yes—
355#382C2312yes—
356#382C2312yes—
357#381C2314yes—
358#381C2314yes—
359#381C2314yes—
360#380C2318yes—
361#380C2314yes—
362#380C2318yes—
363#380C2314yes—
364#380C2314yes—
365#380C2318yes—
366#380C2314yes—
367#380C2318yes—
368#380C2314yes—
369#380C2314yes—
370#380C2312yes—
371#380C2314yes—
372#380C2312yes—
373#380C2312yes—
374#380C2312yes—
375#380C2314yes—
376#380C2314yes—
377#380C2314yes—
378#379C2314yes—
379C4×C4⋊C4C2314yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2318yes—
383C4×C4⋊C4C2318yes—
384C4×C4⋊C4C2318yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2318yes—
387C4×C4⋊C4C2318yes—
388C4×C4⋊C4C2318yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C22⋊C4C2314yes—
412C4×C22⋊C4C2314yes—
413C4×C22⋊C4C2314yes—
414C4×C22⋊C4C2314yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2312yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C2×#95C2314yes—
430C2×#95C2314yes—
431C2×#95C2314yes—
432C2×#95C2314yes—
433C2×#95C2312yes—
434C2×#95C2312yes—
435C25C2411yescharacteristic
436C22×Q8C2414yes—
437C22×Q8C2414yes—
438C22×Q8C2418yes—
439C23×C4—28no—
440C23×C4—84no—
441C23×C4C2×Q818yes—
442C23×C4C2×Q8116yes—
443C23×C4C2414yes—
444C23×C4C2414yes—
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2414yes—
451C23×C4C2412yes—
452C23×C4C2414yes—
453C23×C4C2412yes—
454C23×C4C2414yes—
455C23×C4C2411yescharacteristic
456C4⋊Q8—28no—
457C4⋊Q8—28no—
458C4⋊Q8—216no—
459C4⋊Q8—216no—
460C4⋊Q8—88no—
461#125—28no—
462#125—28no—
463#125—216no—
464#125—216no—
465#125—88no—
466C22⋊Q8—216no—
467C22⋊Q8—216no—
468C22⋊Q8—232no—
469C22⋊Q8—216no—
470C22⋊Q8—48no—
471C22⋊Q8—416no—
472C4×Q8—216no—
473C4×Q8—216no—
474C4×Q8—88no—
475C4×Q8—88no—
476#117—28no—
477#117—28no—
478#117—28no—
479#117—28no—
480#117—28no—
481#117—216no—
482#117—216no—
483#117—88no—
484#117#41116yes—
485C2×C4⋊C4—28no—
486C2×C4⋊C4—28no—
487C2×C4⋊C4—28no—
488C2×C4⋊C4—84no—
489C2×C4⋊C4C2×Q8116yes—
490C2×C4⋊C4C2×Q8132yes—
491C2×C4⋊C4C2×Q8132yes—
492C2×C4⋊C4C2×Q818yes—
493C2×C4⋊C4C2×Q818yes—
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2412yes—
540C2×C22⋊C4—216no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—44no—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2412yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2411yescharacteristic
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2411yescharacteristic
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2411yescharacteristic
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2411yescharacteristic
562C2×C42—28no—
563C2×C42—216no—
564C2×C42—84no—
565C2×C42—88no—
566C2×C42C2414yes—
567C2×C42C2414yes—
568C2×C42C2414yes—
569C2×C42C2414yes—
570C2×C42C2414yes—
571C2×C42C2412yes—
572C2×C42C2412yes—
573C2×C42C2412yes—
574C2×C42C2412yes—
575C2×C42C2418yes—
576C2×C42C2418yes—
577C2×C42C2418yes—
578C2×C42C2418yes—
579C2×C42C2418yes—
580C2×C42C2418yes—
581C2×C42C2418yes—
582C2×C42C2418yes—
583C2×C42C2414yes—
584#95C2418yes—
585#95C2418yes—
586#95C2414yes—
587#95C2414yes—
588#95C2414yes—
589#95C2414yes—
590#95C2412yes—
591#95C2412yes—
592#95C2412yes—
593#95C2412yes—
594#95C2418yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C2418yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2418yes—
607#95C2418yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2418yes—
617#95C2414yes—
618#95C2418yes—
619#95C2418yes—
620#95C2414yes—
621#95C2418yes—
622#95C2414yes—
623#95C2418yes—
624#95C2418yes—
625#95C2414yes—
626#95C2414yes—
627C24—24no—
628C24—22no—
629C24—22no—
630C24—42no—
631C24C22×Q814yes—
632C24C2511yescharacteristic
633C24C2511yescharacteristic
634C24C2511yescharacteristic
635C2×Q8—28no—
636C2×Q8—28no—
637C2×Q8—216no—
638C2×Q8—28no—
639C2×Q8—44no—
640C2×Q8—48no—
641C2×Q8—48no—
642C2×Q8—44no—
643C2×Q8—44no—
644C22×C4—24no—
645C22×C4—232no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—24no—
654C22×C4—28no—
655C22×C4—28no—
656C22×C4—28no—
657C22×C4—24no—
658C22×C4—44no—
659C22×C4—42no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—48no—
663C22×C4—44no—
664C22×C4—48no—
665C22×C4—44no—
666C22×C4—42no—
667C22×C4—44no—
668C22×C4—42no—
669C22×C4—816no—
670C22×C4C22×Q814yes—
671C22×C4C22×Q818yes—
672C22×C4C22×Q818yes—
673C22×C4C22×Q8116yes—
674C22×C4C22×Q818yes—
675C22×C4C22×Q818yes—
676C22×C4C22×Q8116yes—
677C22×C4C22×Q814yes—
678C22×C4C2×#4118yes—
679C22×C4C2514yes—
680C22×C4C2512yes—
681C22×C4C2514yes—
682C22×C4C2512yes—
683C22×C4C2514yes—
684C22×C4C2514yes—
685C22×C4C2518yes—
686C22×C4C2514yes—
687C22×C4C2514yes—
688C22×C4C2512yes—
689C22×C4C2512yes—
690C22×C4C2514yes—
691C22×C4C2514yes—
692C22×C4C2514yes—
693C22×C4C2514yes—
694C22×C4C2512yes—
695C22×C4C2512yes—
696C4⋊C4—28no—
697C4⋊C4—28no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—28no—
701C4⋊C4—28no—
702C4⋊C4—24no—
703C4⋊C4—24no—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—28no—
707C4⋊C4—28no—
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—216no—
713C4⋊C4—216no—
714C4⋊C4—216no—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—28no—
718C4⋊C4—48no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—48no—
722C4⋊C4—44no—
723C4⋊C4—44no—
724C4⋊C4—44no—
725C4⋊C4—48no—
726C4⋊C4—48no—
727C4⋊C4—48no—
728C4⋊C4—44no—
729C4⋊C4—48no—
730C4⋊C4—44no—
731C4⋊C4—48no—
732C4⋊C4—48no—
733C4⋊C4—44no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4C22×Q8132yes—
738C4⋊C4C22×Q8116yes—
739C4⋊C4C22×Q8116yes—
740C4⋊C4C2×#4118yes—
741C4⋊C4C2×#4118yes—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—28no—
745C22⋊C4—22no—
746C22⋊C4—28no—
747C22⋊C4—24no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—28no—
751C22⋊C4—28no—
752C22⋊C4—24no—
753C22⋊C4—41no—
754C22⋊C4—44no—
755C22⋊C4—41no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C22⋊C4C2×#41116yes—
759C22⋊C42−1+414yes—
760C42—28no—
761C42—28no—
762C42—28no—
763C42—24no—
764C42—24no—
765C42—24no—
766C42—24no—
767C42—28no—
768C42—28no—
769C42—48no—
770C42—48no—
771C42—48no—
772C42—48no—
773C42—48no—
774C42—48no—
775C42—48no—
776C42—48no—
777C42C2×#41116yes—
778C23—22no—
779C23—21no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—28no—
788C23—28no—
789C23—44no—
790C23—48no—
791C23—48no—
792C23C23×Q812yes—
793C23C23×Q812yes—
794C23C23×Q812yes—
795C23C22×#4114yes—
796C23C2×2−1+412yes—
797C23#58512yes—
798C23C2611yescharacteristic
799Q8—416no—
800Q8—816no—
801Q8—88no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—28no—
813C2×C4—216no—
814C2×C4—216no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—28no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—28no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—28no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—48no—
846C2×C4—416no—
847C2×C4—48no—
848C2×C4—416no—
849C2×C4—416no—
850C2×C4—48no—
851C2×C4—416no—
852C2×C4—84no—
853C2×C4—88no—
854C2×C4#533116yes—
855C2×C4C23×Q818yes—
856C2×C4C23×Q818yes—
857C2×C4C23×Q814yes—
858C2×C4C23×Q814yes—
859C2×C4C22×#4118yes—
860C2×C4C22×#4118yes—
861C2×C4C22×#4114yes—
862C2×C4C22×#4114yes—
863C2×C4C2×2−1+414yes—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—416no—
876C22—42no—
877C22—42no—
878C22C2×#53314yes—
879C22#350214yes—
880C22C24×Q811yescharacteristic
881C22C23×#4112yes—
882C22C22×2−1+411yescharacteristic
883C22C2×#58511yescharacteristic
884C22H(7,𝔽2)12yes—
885C4—28no—
886C4—24no—
887C4—28no—
888C4—28no—
889C4—28no—
890C4—24no—
891C4—44no—
892C4—44no—
893C4—42no—
894C4—44no—
895C4—44no—
896C4—42no—
897C4—48no—
898C4—42no—
899C4—44no—
900C4—44no—
901C4C2×#53318yes—
902C2—24no—
903C2—24no—
904C2—42no—
905C2C22×#53311yescharacteristic
906C2C2×#350211yescharacteristic
907C2#6284311yescharacteristic
908C2#6300012yes—
909C2#6300812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36599C2semidirect
2. #36564C2semidirect
3. #36519C2semidirect
4. #36519C2semidirect
5. #35843C2semidirect
6. #35788C2semidirect
7. #35783C2semidirect
8. #35708C2semidirect
9. #35585C2semidirect
10. #35566C2semidirect
11. #35403C2semidirect
16. #34271C2semidirect
17. #34213C2semidirect
37. #2590C22semidirect
38. #2590C22semidirect
39. #2588C22semidirect
40. #2588C22semidirect
41. #2586C22semidirect
42. #2586C22semidirect
43. #2585C22semidirect
44. #2585C22semidirect
45. #2584C22semidirect
46. #2584C22semidirect
51. #2567C22semidirect
52. #2552C22semidirect
53. #2551C22semidirect
54. #2550C22semidirect
55. #2550C22semidirect
60. #2546C22semidirect
61. #2520C22semidirect
62. #2520C22semidirect
63. #2511C22semidirect
64. #2509C22semidirect
65. #2509C22semidirect
66. #2508C22semidirect
67. #2508C22semidirect
68. #2507C22semidirect
69. #2507C22semidirect
70. #2507C22semidirect
71. #2506C22semidirect
72. #2506C22semidirect
73. #2462C22semidirect
74. #2462C22semidirect
75. #2451C22semidirect
76. #2446C22semidirect
103. #2370C22semidirect
104. #2370C22semidirect
105. #2370C22semidirect
106. #2370C22semidirect
107. #2370C22semidirect
108. #2370C22semidirect
109. #2369C22semidirect
110. #2369C22semidirect
111. #2369C22semidirect
112. #2365C22semidirect
113. #2365C22semidirect
114. #2365C22semidirect
115. #2355C22semidirect
116. #2355C22semidirect
117. #2355C22semidirect
118. Q8×C4⋊C4C22semidirect
197. C22×C4⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
#365992
#365642
#365192
#358432
#357882
#357832
#357082
#355852
#355662
#354032
#352532
#350792
#349582
#347392
#342712
#342132
#341782
C2×#23452
C2×#22742