Finite Group Databasebeta

← #7682803

Subgroups — #7682803

Order 512.

5224 conjugacy classes of subgroups.

The subgroup lattice has 1091 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59914C218yesmaximal, complemented
2#59460C214yesmaximal, complemented
3#59457C214yesmaximal, complemented
4#59326C214yesmaximal, complemented
5#59214C214yesmaximal, complemented
6#45233C214yesmaximal, complemented
7#44951C214yesmaximal, complemented
8#44942C214yesmaximal, complemented
9#44908C214yesmaximal, complemented
10#43123C218yesmaximal, complemented
11#35640C211yesmaximal, characteristic, complemented
12#35639C211yesmaximal, characteristic, complemented
13#35627C211yesmaximal, characteristic, complemented
14#35532C211yesmaximal, characteristic, complemented
15#35529C211yesmaximal, characteristic, complemented
16#35515C211yesmaximal, characteristic, complemented
17C2×#2566C211yesmaximal, characteristic, complemented
18#34815C211yesmaximal, characteristic, complemented
19#34745C211yesmaximal, characteristic, complemented
20#34275C211yesmaximal, characteristic
21#34269C211yesmaximal, characteristic
22#34265C211yesmaximal, characteristic
23#34248C211yesmaximal, characteristic, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34184C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#535C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#518C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36#2807C2218yescomplemented
37#2790C2218yescomplemented
38#2780C2218yescomplemented
39#2780C2218yescomplemented
40#2780C2218yescomplemented
41#2780C2218yescomplemented
42#2768C2218yescomplemented
43#2768C2218yescomplemented
44#2763C2218yescomplemented
45#2748C2218yescomplemented
46#2732C2218yescomplemented
47#2704C2218yescomplemented
48#2587C2218yescomplemented
49#2587C2218yescomplemented
50#2587C2218yescomplemented
51#2583C2214yes—
52#2583C2218yescomplemented
53#2580C2214yes—
54#2580C2218yescomplemented
55#2579C2214yes—
56#2574C2218yescomplemented
57#2571C2214yescomplemented
58#2570C2214yescomplemented
59#2567C2212yescomplemented
60#2566C2214yes—
61#2566C2214yes—
62#2566C2214yes—
63#2566C2214yes—
64#2566C2212yes—
65#2566C2212yes—
66#2566C2212yescomplemented
67#2566C2218yescomplemented
68#2565C2212yescomplemented
69#2564C2218yescomplemented
70#2563C2212yes—
71#2552C2214yescomplemented
72#2552C2214yescomplemented
73#2550C2214yescomplemented
74#2550C2214yescomplemented
75#2542C2212yes—
76#2542C2212yescomplemented
77#2538C2214yes—
78#2538C2218yescomplemented
79#2509C2214yescomplemented
80#2509C2212yescomplemented
81#2508C2214yescomplemented
82#2508C2212yescomplemented
83#2507C2212yescomplemented
84#2506C2212yescomplemented
85#2505C2214yes—
86#2505C2218yes—
87#2505C2218yescomplemented
88#2505C2218yescomplemented
89#2502C2214yes—
90#2497C2218yescomplemented
91#2487C2214yes—
92#2487C2218yescomplemented
93#2473C2214yes—
94#2465C2218yescomplemented
95#2454C2214yes—
96#2454C2214yes—
97#2454C2214yescomplemented
98#2454C2212yescomplemented
99#2453C2214yescomplemented
100#2453C2212yescomplemented
101#2452C2214yes—
102#2452C2214yes—
103#2452C2212yescomplemented
104#2451C2212yescomplemented
105#2450C2214yes—
106#2450C2218yescomplemented
107#2450C2218yescomplemented
108#2450C2218yescomplemented
109#2449C2218yes—
110#2449C2214yes—
111#2449C2218yescomplemented
112#2442C2214yescomplemented
113#2441C2214yescomplemented
114#2441C2214yescomplemented
115#2440C2214yescomplemented
116#2437C2218yes—
117#2437C2218yes—
118#2402C2214yescomplemented
119#2396C2214yescomplemented
120C2×#396C2214yes—
121#2367C2214yes—
122#2367C2214yes—
123#2366C2214yes—
124#2366C2214yes—
125#2363C2214yes—
126#2363C2214yes—
127#2361C2214yes—
128#2361C2214yes—
129#2360C2218yes—
130#2360C2218yescomplemented
131#2358C2218yes—
132#2358C2218yes—
133#2355C2214yescomplemented
134#2351C2214yescomplemented
135Q8×C4⋊C4C2214yescomplemented
136#2349C2218yes—
137#2349C2214yes—
138#2349C2214yes—
139#2349C2218yescomplemented
140#2349C2214yescomplemented
141D4×C4⋊C4C2214yes—
142D4×C4⋊C4C2214yes—
143#2330C2214yescomplemented
144#2328C2212yes—
145#2326C2212yes—
146#2324C2214yes—
147#2321C2214yes—
148#2317C2211yescharacteristic
149#2317C2211yescharacteristic
150#2317C2211yescharacteristic
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2212yescomplemented
154#2317C2212yescomplemented
155#2316C2211yescharacteristic
156#2315C2214yes—
157#2311C2211yescharacteristic
158#2309C2211yescharacteristic
159C4×C4⋊Q8C2214yescomplemented
160C4×#127C2212yes—
161C4×#125C2214yescomplemented
162C4×#124C2212yes—
163C4×C22⋊Q8C2214yescomplemented
164C4×#121C2214yes—
165C4×#120C2214yes—
166#2297C2211yescharacteristic
167#2297C2211yescharacteristic
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174C2×#390C2211yescharacteristic
175C2×#390C2211yescharacteristic
176C2×#385C2214yes—
177C2×#385C2214yes—
178#2285C2211yescharacteristic
179#2285C2212yescomplemented
180C2×#384C2211yescharacteristic
181C2×#382C2211yescharacteristic
182C2×#382C2212yescomplemented
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×D4C2311yescharacteristic
189C24×C4C2312yes—
190#544—44no—
191#535Q8116yescomplemented
192#533—28no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×#127C2312yes—
197C2×#125—44no—
198C2×#125C2312yes—
199C2×#125C2314yes—
200C2×#125C2312yes—
201C2×#125C2314yes—
202C2×#125C2314yes—
203C2×#125C2312yes—
204C2×#124C2312yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2318yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C2318yes—
211C2×#121C2314yes—
212C2×#120C2314yes—
213#520—44no—
214#520—44no—
215#518—28no—
216#518—44no—
217C4×#41—28no—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2318yes—
223C2×C4×D4—44no—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2318yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2318yes—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2318yes—
260C22×C4⋊C4C2314yes—
261C22×C22⋊C4C2314yes—
262C22×C22⋊C4C2312yes—
263C22×C22⋊C4C2314yes—
264C22×C22⋊C4C2314yes—
265C22×C22⋊C4C2314yes—
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2312yes—
269C22×C42C2311yescharacteristic
270#400C2314yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2314yes—
275#400C2318yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#399C2318yes—
280#399C2318yes—
281#399C2318yes—
282#399C2314yes—
283#399C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2314yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2314yes—
308#395C2318yes—
309#395C2318yes—
310#395C2314yes—
311#393C2318yes—
312#393C2318yes—
313#393C2314yes—
314#391C2318yes—
315#391C2311yescharacteristic
316#391C2312yes—
317#391C2311yescharacteristic
318#391C2318yes—
319#391C2314yes—
320#391C2312yes—
321#390C2311yescharacteristic
322#390C2312yes—
323#390C2318yes—
324#390C2312yes—
325#390C2312yes—
326#390C2312yes—
327#390C2314yes—
328#390C2312yes—
329#390C2314yes—
330#390C2312yes—
331#390C2314yes—
332#390C2312yes—
333#390C2318yes—
334#390C2318yes—
335#390C2311yescharacteristic
336#390C2312yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2318yes—
342#389C2318yes—
343#389C2312yes—
344#389C2314yes—
345#389C2312yes—
346#389C2318yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2318yes—
353#389C2312yes—
354#389C2312yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2314yes—
368#389C2312yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#387C2314yes—
376#387C2314yes—
377#387C2314yes—
378#387C2314yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2314yes—
384#387C2318yes—
385#387C2318yes—
386#387C2314yes—
387#386C2318yes—
388#386C2318yes—
389#386C2314yes—
390#386C2312yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2314yes—
395#386C2318yes—
396#386C2312yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2312yes—
409#385C2312yes—
410#385C2314yes—
411#385C2314yes—
412#385C2318yes—
413#385C2314yes—
414#385C2314yes—
415#385C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2312yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2312yes—
424#385C2312yes—
425#385C2318yes—
426#385C2314yes—
427#385C2314yes—
428#385C2314yes—
429#385C2314yes—
430#385C2314yes—
431#385C2312yes—
432#384C2312yes—
433#384C2312yes—
434#384C2312yes—
435#384C2311yescharacteristic
436#384C2314yes—
437#384C2312yes—
438#384C2318yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#384C2311yescharacteristic
443#382C2314yes—
444#382C2311yescharacteristic
445#382C2312yes—
446#382C2312yes—
447#382C2314yes—
448#382C2312yes—
449#382C2312yes—
450#382C2311yescharacteristic
451#382C2318yes—
452#382C2312yes—
453#382C2312yes—
454#382C2312yes—
455#382C2318yes—
456#380C2318yes—
457#380C2314yes—
458#380C2318yes—
459#380C2314yes—
460#380C2318yes—
461#380C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2318yes—
465#380C2318yes—
466#379C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496#376C2312yes—
497C2×#95C2318yes—
498C2×#95C2318yes—
499C2×#95C2314yes—
500C2×#95C2312yes—
501C43C2312yes—
502C25C2412yes—
503C2×#41—24no—
504C2×#41—24no—
505C2×#41C2×Q818yes—
506C22×Q8C2414yes—
507C22×Q8C2411yescharacteristic
508C22×Q8C2414yes—
509C22×D4—24no—
510C22×D4—24no—
511C22×D4C2×Q818yes—
512C22×D4C2412yes—
513C22×D4C2412yes—
514C22×D4C2412yes—
515C22×D4C2411yescharacteristic
516C22×D4C2418yes—
517C23×C4—44no—
518C23×C4—84no—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2411yescharacteristic
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2418yes—
527C23×C4C2411yescharacteristic
528C23×C4C2414yes—
529C23×C4C2414yes—
530C23×C4C2414yes—
531C23×C4C2414yes—
532C23×C4C2414yes—
533C23×C4C2418yes—
534C23×C4C2411yescharacteristic
535C4⋊Q8—28no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538#127C2×Q8116yes—
539#125—28no—
540#125—48no—
541#125—48no—
542#125—48no—
543#125—44no—
544#125—44no—
545#124C2×Q8116yes—
546C22⋊Q8—216no—
547C22⋊Q8—48no—
548C22⋊Q8—416no—
549C22⋊Q8—48no—
550C22⋊Q8—88no—
551C22⋊Q8—88no—
552#121C2×Q8132yes—
553#120C2×Q8132yes—
554C4×Q8—28no—
555C4×Q8—216no—
556C4×Q8—44no—
557C4×Q8—44no—
558C4×Q8—88no—
559C4×D4—28no—
560C4×D4—216no—
561C4×D4—216no—
562C4×D4—216no—
563C4×D4—416no—
564C4×D4—48no—
565C4×D4—48no—
566C4×D4—44no—
567C4×D4—44no—
568C4×D4—44no—
569C4×D4—44no—
570C4×D4—44no—
571C4×D4—44no—
572C4×D4—48no—
573C4×D4—48no—
574C4×D4—88no—
575C4×D4—88no—
576#117—24no—
577#117—24no—
578#117—24no—
579#117—24no—
580#117—24no—
581#117—28no—
582#117—44no—
583#117—44no—
584#117C2×Q818yes—
585#117#4118yes—
586C2×C4⋊C4—24no—
587C2×C4⋊C4—24no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—44no—
590C2×C4⋊C4—44no—
591C2×C4⋊C4—44no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—44no—
594C2×C4⋊C4—88no—
595C2×C4⋊C4—84no—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C22⋊C4—216no—
650C2×C22⋊C4—48no—
651C2×C22⋊C4—48no—
652C2×C22⋊C4—44no—
653C2×C22⋊C4—84no—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2412yes—
680C2×C42—24no—
681C2×C42—24no—
682C2×C42—24no—
683C2×C42—28no—
684C2×C42C2411yescharacteristic
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2418yes—
702C2×C42C2418yes—
703C2×C42C2414yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2418yes—
741C24—24no—
742C24—24no—
743C24—44no—
744C24—44no—
745C24C22×Q818yes—
746C24C2514yes—
747C24C2512yes—
748C24C2511yescharacteristic
749#41—232no—
750C2×Q8—22no—
751C2×Q8—28no—
752C2×Q8—22no—
753C2×Q8—28no—
754C2×Q8—44no—
755C2×Q8—44no—
756C2×Q8—48no—
757C2×Q8C22×Q814yes—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—232no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—22no—
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—22no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4C22×Q818yes—
770C2×D4C22×Q818yes—
771C2×D4C22×Q818yes—
772C2×D4C22×Q814yes—
773C2×D4C22×Q8132yes—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—28no—
785C22×C4—216no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—44no—
790C22×C4—42no—
791C22×C4—44no—
792C22×C4—42no—
793C22×C4—48no—
794C22×C4—44no—
795C22×C4—48no—
796C22×C4—48no—
797C22×C4—44no—
798C22×C4—48no—
799C22×C4—48no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—816no—
810C22×C4C22×Q818yes—
811C22×C4C22×Q814yes—
812C22×C4C2×#4114yes—
813C22×C4H(5,𝔽2)14yes—
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2514yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2514yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C4⋊C4—24no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—44no—
875C4⋊C4—48no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4C22×Q818yes—
888C4⋊C4C2×#4118yes—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—216no—
895C22⋊C4—28no—
896C22⋊C4—216no—
897C22⋊C4—28no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4C22×Q818yes—
913C22⋊C4C22×Q8132yes—
914C22⋊C4C2×#4118yes—
915C42—22no—
916C42—22no—
917C42—28no—
918C42—24no—
919C42—24no—
920C42—22no—
921C42—22no—
922C42—24no—
923C42—24no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—28no—
930C42—44no—
931C42—44no—
932C42—48no—
933C42—48no—
934C42—44no—
935C42C22×Q818yes—
936C42C2×#4118yes—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—24no—
941C23—22no—
942C23—24no—
943C23—28no—
944C23—24no—
945C23—24no—
946C23—28no—
947C23—216no—
948C23—416no—
949C23—84no—
950C23—88no—
951C23—84no—
952C23C23×Q818yes—
953C23C23×Q814yes—
954C23C23×Q812yes—
955C23C22×#4112yes—
956C23C2×H(5,𝔽2)12yes—
957C23C2611yescharacteristic
958Q8—28no—
959Q8—416no—
960Q8—164no—
961D4—216no—
962D4—216no—
963D4—216no—
964D4—28no—
965D4—432no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—216no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—28no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—24no—
1005C2×C4—28no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—44no—
1017C2×C4—816no—
1018C2×C4—88no—
1019C2×C4—84no—
1020C2×C4—84no—
1021C2×C4—84no—
1022C2×C4—84no—
1023C2×C4—816no—
1024C2×C4—164no—
1025C2×C4—164no—
1026C2×C4—164no—
1027C2×C4—164no—
1028C2×C4#554116yes—
1029C2×C4C23×Q818yes—
1030C2×C4C23×Q814yes—
1031C2×C4C23×Q812yes—
1032C2×C4C23×Q812yes—
1033C2×C4C22×#4118yes—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4112yes—
1036C2×C4C2×H(5,𝔽2)12yes—
1037C2×C4C2×H(5,𝔽2)12yes—
1038C2×C4#58514yes—
1039C22—24no—
1040C22—24no—
1041C22—22no—
1042C22—22no—
1043C22—28no—
1044C22—216no—
1045C22—24no—
1046C22—28no—
1047C22—44no—
1048C22—48no—
1049C22—42no—
1050C22—44no—
1051C22—44no—
1052C22—42no—
1053C22—816no—
1054C22C2×#55414yes—
1055C22C24×Q811yescharacteristic
1056C22C23×#4111yescharacteristic
1057C22C22×H(5,𝔽2)11yescharacteristic
1058C22C2×#58512yes—
1059C22H(7,𝔽2)12yes—
1060C4—28no—
1061C4—24no—
1062C4—28no—
1063C4—24no—
1064C4—42no—
1065C4—42no—
1066C4—44no—
1067C4—42no—
1068C4—44no—
1069C4—42no—
1070C4—42no—
1071C4—44no—
1072C4—42no—
1073C4—42no—
1074C4—42no—
1075C4—44no—
1076C4—44no—
1077C4—42no—
1078C4—42no—
1079C4—42no—
1080C4C2×#55414yes—
1081C4C2×#55414yes—
1082C2—24no—
1083C2—44no—
1084C2—48no—
1085C2C22×#55411yescharacteristic
1086C2#6283611yescharacteristic
1087C2#6287611yescharacteristic
1088C2#6298912yes—
1089C2#6300812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59914C2semidirect
2. #59460C2semidirect
3. #59457C2semidirect
4. #59326C2semidirect
5. #59214C2semidirect
6. #45233C2semidirect
7. #44951C2semidirect
8. #44942C2semidirect
9. #44908C2semidirect
10. #43123C2semidirect
11. #35640C2semidirect
12. #35639C2semidirect
13. #35627C2semidirect
14. #35532C2semidirect
15. #35529C2semidirect
16. #35515C2semidirect
17. C2×#2566C2semidirect
18. #34815C2semidirect
19. #34745C2semidirect
23. #34248C2semidirect
24. #34214C2semidirect
25. #34184C2semidirect
36. #2807C22semidirect
37. #2790C22semidirect
38. #2780C22semidirect
39. #2780C22semidirect
40. #2780C22semidirect
41. #2780C22semidirect
42. #2768C22semidirect
43. #2768C22semidirect
44. #2763C22semidirect
45. #2748C22semidirect
46. #2732C22semidirect
47. #2704C22semidirect
48. #2587C22semidirect
49. #2587C22semidirect
50. #2587C22semidirect
52. #2583C22semidirect
54. #2580C22semidirect
56. #2574C22semidirect
57. #2571C22semidirect
58. #2570C22semidirect
59. #2567C22semidirect
66. #2566C22semidirect
67. #2566C22semidirect
68. #2565C22semidirect
69. #2564C22semidirect
71. #2552C22semidirect
72. #2552C22semidirect
73. #2550C22semidirect
74. #2550C22semidirect
76. #2542C22semidirect
78. #2538C22semidirect
79. #2509C22semidirect
80. #2509C22semidirect
81. #2508C22semidirect
82. #2508C22semidirect
83. #2507C22semidirect
84. #2506C22semidirect
87. #2505C22semidirect
88. #2505C22semidirect
90. #2497C22semidirect
92. #2487C22semidirect
94. #2465C22semidirect
97. #2454C22semidirect
98. #2454C22semidirect
99. #2453C22semidirect
100. #2453C22semidirect
103. #2452C22semidirect
104. #2451C22semidirect
106. #2450C22semidirect
107. #2450C22semidirect
108. #2450C22semidirect
111. #2449C22semidirect
112. #2442C22semidirect
113. #2441C22semidirect
114. #2441C22semidirect
115. #2440C22semidirect
118. #2402C22semidirect
119. #2396C22semidirect
130. #2360C22semidirect
133. #2355C22semidirect
134. #2351C22semidirect
135. Q8×C4⋊C4C22semidirect
139. #2349C22semidirect
140. #2349C22semidirect
143. #2330C22semidirect
153. #2317C22semidirect
154. #2317C22semidirect
159. C4×C4⋊Q8C22semidirect
161. C4×#125C22semidirect
163. C4×C22⋊Q8C22semidirect
179. #2285C22semidirect
182. C2×#382C22semidirect
191. #535Q8semidirect

Maximal subgroups

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

subgroupindex
#599142
#594602
#594572
#593262
#592142
#452332
#449512
#449422
#449082
#431232
#356402
#356392
#356272
#355322
#355292
#355152
C2×#25662
#348152
#347452
#342752
#342692
#342652
#342482
#342142
#341842