Finite Group Databasebeta

← #7681816

Subgroups — #7681816

Order 512.

4962 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59328C218yesmaximal, complemented
2#59264C214yesmaximal, complemented
3#59260C214yesmaximal, complemented
4#45132C214yesmaximal, complemented
5#44910C214yesmaximal, complemented
6#43509C214yesmaximal, complemented
7#43078C214yesmaximal, complemented
8#38971C212yesmaximal, complemented
9#38969C212yesmaximal, complemented
10#38230C214yesmaximal, complemented
11#38226C214yesmaximal, complemented
12#36394C212yesmaximal, complemented
13#36370C212yesmaximal, complemented
14#35585C212yesmaximal, complemented
15#35541C212yesmaximal
16#35339C211yesmaximal, characteristic, complemented
17#35267C212yesmaximal, complemented
18#34952C211yesmaximal, characteristic, complemented
19C2×#2580C211yesmaximal, characteristic, complemented
20#34255C212yesmaximal, complemented
21#34189C211yesmaximal, characteristic, complemented
22#34181C211yesmaximal, characteristic, complemented
23Q8×#117C211yesmaximal, characteristic, complemented
24C4×#535C211yesmaximal, characteristic
25C2×#535C2211yescharacteristic
26C2×#518C2212yes—
27C2×C4×#41C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30#2864C2212yescomplemented
31#2864C2212yescomplemented
32#2863C2214yescomplemented
33#2860C2214yescomplemented
34#2787C2218yescomplemented
35#2781C2218yescomplemented
36#2779C2218yescomplemented
37#2771C2218yescomplemented
38#2770C2218yescomplemented
39#2764C2218yescomplemented
40#2751C2218yescomplemented
41#2745C2218yescomplemented
42#2743C2218yescomplemented
43#2738C2218yescomplemented
44#2694C2218yescomplemented
45#2687C2218yescomplemented
46#2647C2214yescomplemented
47#2645C2214yescomplemented
48#2644C2214yescomplemented
49#2611C2218yescomplemented
50#2599C2218yescomplemented
51#2582C2212yescomplemented
52#2581C2211yescharacteristic, complemented
53#2581C2211yescharacteristic, complemented
54#2580C2212yes—
55#2580C2212yes—
56#2580C2212yes—
57#2580C2214yes—
58#2580C2212yes—
59#2580C2214yes—
60#2580C2211yescharacteristic, complemented
61#2580C2211yescharacteristic, complemented
62#2579C2214yes—
63#2577C2218yescomplemented
64#2575C2218yescomplemented
65#2570C2214yescomplemented
66#2570C2214yescomplemented
67#2569C2218yes—
68#2569C2214yes—
69#2569C2214yes—
70#2553C2218yescomplemented
71#2538C2212yescomplemented
72#2530C2218yescomplemented
73#2527C2218yescomplemented
74#2510C2218yes—
75#2509C2214yescomplemented
76#2509C2214yescomplemented
77#2508C2214yescomplemented
78#2508C2214yescomplemented
79#2507C2214yescomplemented
80#2507C2214yescomplemented
81#2506C2214yescomplemented
82#2506C2214yescomplemented
83#2497C2214yescomplemented
84#2496C2214yescomplemented
85#2495C2214yescomplemented
86#2494C2214yescomplemented
87#2493C2218yescomplemented
88#2487C2212yes—
89#2484C2218yescomplemented
90#2481C2218yes—
91#2481C2218yescomplemented
92#2479C2218yescomplemented
93#2477C2218yescomplemented
94#2473C2218yescomplemented
95#2468C2218yescomplemented
96#2460C2218yescomplemented
97#2458C2218yescomplemented
98#2447C2214yes—
99#2447C2214yes—
100#2445C2214yes—
101#2445C2214yes—
102#2442C2218yes—
103#2422C2214yes—
104#2422C2214yes—
105#2420C2214yes—
106#2420C2214yes—
107#2419C2218yescomplemented
108#2413C2218yescomplemented
109#2412C2218yes—
110#2412C2218yes—
111#2409C2212yes—
112#2396C2212yescomplemented
113#2396C2212yescomplemented
114C2×#399C2212yes—
115C2×#393C2212yes—
116#2359C2218yescomplemented
117#2357C2214yes—
118#2357C2214yes—
119#2357C2212yescomplemented
120#2357C2212yescomplemented
121#2356C2212yescomplemented
122#2356C2212yescomplemented
123#2355C2212yescomplemented
124#2355C2212yescomplemented
125#2355C2212yescomplemented
126#2354C2214yes—
127#2354C2214yes—
128#2353C2214yes—
129#2353C2214yes—
130Q8×C4⋊C4C2212yescomplemented
131#2349C2212yes—
132#2349C2212yes—
133#2349C2212yes—
134#2349C2212yes—
135D4×C4⋊C4C2214yes—
136D4×C4⋊C4C2214yes—
137#2345C2214yes—
138#2345C2212yes—
139#2343C2218yescomplemented
140#2342C2218yes—
141#2342C2218yes—
142Q8×C22⋊C4C2212yes—
143#2328C2212yes—
144#2326C2212yes—
145#2324C2214yes—
146#2321C2214yes—
147#2319C2214yes—
148#2319C2214yes—
149#2317C2211yescharacteristic
150#2317C2212yes—
151#2316C2212yes—
152#2316C2212yes—
153#2315C2214yes—
154#2314C2214yescomplemented
155#2311C2211yescharacteristic
156#2311C2212yes—
157#2309C2211yescharacteristic
158C4×#127C2212yes—
159C4×#124C2212yes—
160C4×C22⋊Q8C2214yescomplemented
161C4×#121C2214yes—
162C4×#120C2214yes—
163#2297C2212yes—
164#2296C2212yes—
165#2295C2212yescomplemented
166#2295C2214yescomplemented
167#2293C2214yes—
168#2293C2214yes—
169C2×#390C2212yes—
170C2×#389C2212yes—
171C2×#385C2214yes—
172#2285C2212yes—
173#2285C2211yescharacteristic
174#2285C2211yescharacteristic
175#2283C2212yescomplemented
176#2283C2212yescomplemented
177C2×#382C2211yescharacteristic
178C2×#380C2214yes—
179#2274C2212yes—
180C42×Q8C2212yescomplemented
181C4×#117C2211yescharacteristic
182C4×#117C2212yes—
183C22×#41C2311yescharacteristic
184C23×Q8C2311yescharacteristic
185C23×D4C2311yescharacteristic
186C24×C4C2312yes—
187#535—28no—
188C2×#127C2312yes—
189C2×#126C2318yes—
190C2×#125C2318yes—
191C2×#124C2312yes—
192C2×#123C2318yes—
193C2×#123C2318yes—
194C2×C22⋊Q8C2314yes—
195C2×#121C2314yes—
196C2×#120C2314yes—
197#518—216no—
198C4×#41—28no—
199C2×C4×Q8—28no—
200C2×C4×Q8C2311yescharacteristic
201C2×C4×Q8C2311yescharacteristic
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2311yescharacteristic
204C2×C4×Q8C2311yescharacteristic
205C2×C4×Q8C2312yes—
206C2×C4×Q8C2311yescharacteristic
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2314yes—
209C2×C4×D4—28no—
210C2×C4×D4C2311yescharacteristic
211C2×C4×D4C2312yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2318yes—
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2312yes—
226C2×#117C2312yes—
227C2×#117C2312yes—
228C2×#117C2311yescharacteristic
229C2×#117C2318yes—
230C2×#117C2318yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2318yes—
236C22×C4⋊C4C2314yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2318yes—
239C22×C22⋊C4C2314yes—
240C22×C22⋊C4C2314yes—
241C22×C42C2312yes—
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244#401C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2312yes—
250#400C2318yes—
251#400C2312yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#399C2314yes—
257#399C2318yes—
258#399C2314yes—
259#399C2312yes—
260#399C2312yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2314yes—
266#398C2314yes—
267#398C2318yes—
268#398C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#396C2314yes—
277#396C2314yes—
278#396C2318yes—
279#395C2312yes—
280#395C2312yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#393C2314yes—
286#393C2318yes—
287#393C2314yes—
288#393C2312yes—
289#393C2312yes—
290#391C2312yes—
291#391C2314yes—
292#391C2312yes—
293#391C2312yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#391C2314yes—
298#390C2312yes—
299#390C2312yes—
300#390C2318yes—
301#390C2312yes—
302#390C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2314yes—
306#390C2314yes—
307#390C2314yes—
308#390C2312yes—
309#390C2312yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2312yes—
322#389C2312yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2312yes—
328#389C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2318yes—
334#389C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2314yes—
363#387C2318yes—
364#387C2314yes—
365#387C2314yes—
366#387C2314yes—
367#387C2314yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
371#386C2314yes—
372#386C2318yes—
373#386C2318yes—
374#386C2314yes—
375#386C2314yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#385C2314yes—
380#385C2318yes—
381#385C2314yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2314yes—
388#385C2314yes—
389#385C2314yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#384C2312yes—
397#384C2312yes—
398#384C2314yes—
399#384C2312yes—
400#384C2312yes—
401#384C2312yes—
402#383C2314yes—
403#383C2318yes—
404#383C2314yes—
405#382C2312yes—
406#382C2314yes—
407#382C2312yes—
408#382C2312yes—
409#382C2318yes—
410#382C2312yes—
411#382C2312yes—
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2312yes—
417#382C2312yes—
418#381C2318yes—
419#381C2318yes—
420#381C2318yes—
421#381C2314yes—
422#381C2314yes—
423#381C2318yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2318yes—
428#380C2312yes—
429#380C2312yes—
430#380C2314yes—
431#380C2318yes—
432#380C2312yes—
433#380C2318yes—
434#380C2318yes—
435#380C2314yes—
436#380C2312yes—
437#380C2314yes—
438#380C2318yes—
439#380C2314yes—
440#380C2314yes—
441#379C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2314yes—
475#376C2314yes—
476#376C2312yes—
477#376C2314yes—
478#376C2314yes—
479C2×#95C2312yes—
480C2×#95C2312yes—
481C2×#95C2314yes—
482C2×#95C2314yes—
483C2×#95C2314yes—
484C43C2312yes—
485C43C2314yes—
486C25C2412yes—
487C2×#41—24no—
488C2×#41—24no—
489C2×#41—24no—
490C22×Q8—24no—
491C22×Q8—44no—
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2412yes—
495C22×Q8C2411yescharacteristic
496C22×D4—24no—
497C22×D4—24no—
498C22×D4#4118yes—
499C22×D4C2412yes—
500C22×D4C2411yescharacteristic
501C22×D4C2412yes—
502C22×D4C2412yes—
503C22×D4C2418yes—
504C23×C4—28no—
505C23×C4—84no—
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2414yes—
510C23×C4C2412yes—
511C23×C4C2418yes—
512C23×C4C2418yes—
513C23×C4C2414yes—
514C23×C4C2412yes—
515C23×C4C2414yes—
516C23×C4C2412yes—
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520#127—28no—
521#126—88no—
522#125—88no—
523#124—28no—
524#123—416no—
525#123—88no—
526C22⋊Q8—48no—
527#121—216no—
528#120—216no—
529C4×Q8—28no—
530C4×Q8—24no—
531C4×Q8—24no—
532C4×Q8—24no—
533C4×Q8—24no—
534C4×Q8—28no—
535C4×Q8—24no—
536C4×Q8—24no—
537C4×Q8—48no—
538C4×D4—216no—
539C4×D4—216no—
540C4×D4—216no—
541C4×D4—216no—
542C4×D4—28no—
543C4×D4—28no—
544C4×D4—28no—
545C4×D4—28no—
546C4×D4—28no—
547C4×D4—28no—
548C4×D4—24no—
549C4×D4—24no—
550C4×D4—88no—
551#117—24no—
552#117—28no—
553#117—28no—
554#117—24no—
555#117—24no—
556#117—28no—
557#117—416no—
558#117—88no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—28no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—28no—
563C2×C4⋊C4—88no—
564C2×C4⋊C4—84no—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C22⋊C4—232no—
608C2×C22⋊C4—28no—
609C2×C22⋊C4—48no—
610C2×C22⋊C4—84no—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C42—28no—
637C2×C42—28no—
638C2×C42#4118yes—
639C2×C42C2414yes—
640C2×C42C2412yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2414yes—
652C2×C42C2418yes—
653C2×C42C2418yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662#95C2412yes—
663#95C2412yes—
664#95C2412yes—
665#95C2412yes—
666#95C2414yes—
667#95C2414yes—
668#95C2418yes—
669#95C2418yes—
670#95C2414yes—
671#95C2414yes—
672#95C2418yes—
673#95C2418yes—
674#95C2412yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2418yes—
682#95C2418yes—
683#95C2414yes—
684#95C2412yes—
685#95C2414yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2414yes—
690#95C2414yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2412yes—
701#95C2412yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2418yes—
706C24—24no—
707C24—24no—
708C24—44no—
709C24—44no—
710C24C2×#4118yes—
711C24C2512yes—
712C24C2514yes—
713C24C2511yescharacteristic
714#41—416no—
715C2×Q8—22no—
716C2×Q8—24no—
717C2×Q8—22no—
718C2×Q8—22no—
719C2×Q8—22no—
720C2×Q8—22no—
721C2×Q8—24no—
722C2×Q8—24no—
723C2×Q8—42no—
724C2×Q8—42no—
725C2×Q8—416no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—24no—
729C2×D4—216no—
730C2×D4—232no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—22no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4C2×#4118yes—
741C2×D4C2×#4118yes—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—216no—
746C22×C4—216no—
747C22×C4—28no—
748C22×C4—24no—
749C22×C4—28no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—28no—
756C22×C4—48no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—44no—
761C22×C4—42no—
762C22×C4—44no—
763C22×C4—42no—
764C22×C4—48no—
765C22×C4—48no—
766C22×C4—44no—
767C22×C4—48no—
768C22×C4—44no—
769C22×C4—48no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—816no—
773C22×C4C2×#4114yes—
774C22×C4C2×#4114yes—
775C22×C4C2×#4114yes—
776C22×C4C2×#4114yes—
777C22×C42−1+414yes—
778C22×C4C2512yes—
779C22×C4C2512yes—
780C22×C4C2518yes—
781C22×C4C2514yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C22×C4C2511yescharacteristic
796C22×C4C2512yes—
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—24no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—44no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—48no—
837C4⋊C4—44no—
838C4⋊C4—48no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—216no—
844C22⋊C4—216no—
845C22⋊C4—24no—
846C22⋊C4—24no—
847C22⋊C4—216no—
848C22⋊C4—24no—
849C22⋊C4—28no—
850C22⋊C4—28no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—216no—
854C22⋊C4—28no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—44no—
862C22⋊C4—48no—
863C22⋊C4—44no—
864C22⋊C4—48no—
865C22⋊C4—44no—
866C42—24no—
867C42—24no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—24no—
872C42—24no—
873C42—28no—
874C42—28no—
875C42—24no—
876C42—24no—
877C42—28no—
878C42—48no—
879C42—44no—
880C42—48no—
881C42—44no—
882C42—44no—
883C42—44no—
884C42—44no—
885C42C2×#4114yes—
886C42C2×#4114yes—
887C42C2×#4114yes—
888C42C2×#4114yes—
889C23—22no—
890C23—22no—
891C23—24no—
892C23—24no—
893C23—28no—
894C23—28no—
895C23—216no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—24no—
900C23—24no—
901C23—416no—
902C23—84no—
903C23—84no—
904C23—88no—
905C23C22×#4118yes—
906C23C22×#4112yes—
907C23C22×#4112yes—
908C23C2×2−1+412yes—
909C23C2611yescharacteristic
910Q8—28no—
911Q8—48no—
912Q8—44no—
913Q8—44no—
914D4—216no—
915D4—216no—
916D4—48no—
917D4—44no—
918D4—816no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—28no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—28no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—28no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—28no—
963C2×C4—22no—
964C2×C4—44no—
965C2×C4—44no—
966C2×C4—48no—
967C2×C4—416no—
968C2×C4—48no—
969C2×C4—84no—
970C2×C4—84no—
971C2×C4—88no—
972C2×C4—816no—
973C2×C4—816no—
974C2×C4—84no—
975C2×C4—88no—
976C2×C4—84no—
977C2×C4#552116yes—
978C2×C4C22×#4112yes—
979C2×C4C22×#4112yes—
980C2×C4C22×#4112yes—
981C2×C4C22×#4112yes—
982C2×C4C22×#4112yes—
983C2×C4C22×#4112yes—
984C2×C4C22×#4112yes—
985C2×C4C22×#4112yes—
986C2×C4C2×2−1+412yes—
987C2×C4C2×2−1+412yes—
988C2×C4#58514yes—
989C22—24no—
990C22—22no—
991C22—22no—
992C22—24no—
993C22—216no—
994C22—28no—
995C22—44no—
996C22—44no—
997C22—48no—
998C22—44no—
999C22—42no—
1000C22—42no—
1001C22—42no—
1002C22—44no—
1003C22—816no—
1004C22C2×#55214yes—
1005C22C23×#4111yescharacteristic
1006C22C23×#4111yescharacteristic
1007C22C22×2−1+411yescharacteristic
1008C22C2×#58512yes—
1009C22H(7,𝔽2)12yes—
1010C4—22no—
1011C4—22no—
1012C4—24no—
1013C4—22no—
1014C4—22no—
1015C4—44no—
1016C4—44no—
1017C4—44no—
1018C4—44no—
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—44no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—44no—
1028C4—48no—
1029C4C2×#55214yes—
1030C4C2×#55214yes—
1031C2—24no—
1032C2—48no—
1033C2—82no—
1034C2C22×#55211yescharacteristic
1035C2#6281411yescharacteristic
1036C2#6285511yescharacteristic
1037C2#6296212yes—
1038C2#6299212yes—
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. #59328C2semidirect
2. #59264C2semidirect
3. #59260C2semidirect
4. #45132C2semidirect
5. #44910C2semidirect
6. #43509C2semidirect
7. #43078C2semidirect
8. #38971C2semidirect
9. #38969C2semidirect
10. #38230C2semidirect
11. #38226C2semidirect
12. #36394C2semidirect
13. #36370C2semidirect
14. #35585C2semidirect
16. #35339C2semidirect
17. #35267C2semidirect
18. #34952C2semidirect
19. C2×#2580C2semidirect
20. #34255C2semidirect
21. #34189C2semidirect
22. #34181C2semidirect
23. Q8×#117C2semidirect
30. #2864C22semidirect
31. #2864C22semidirect
32. #2863C22semidirect
33. #2860C22semidirect
34. #2787C22semidirect
35. #2781C22semidirect
36. #2779C22semidirect
37. #2771C22semidirect
38. #2770C22semidirect
39. #2764C22semidirect
40. #2751C22semidirect
41. #2745C22semidirect
42. #2743C22semidirect
43. #2738C22semidirect
44. #2694C22semidirect
45. #2687C22semidirect
46. #2647C22semidirect
47. #2645C22semidirect
48. #2644C22semidirect
49. #2611C22semidirect
50. #2599C22semidirect
51. #2582C22semidirect
52. #2581C22semidirect
53. #2581C22semidirect
60. #2580C22semidirect
61. #2580C22semidirect
63. #2577C22semidirect
64. #2575C22semidirect
65. #2570C22semidirect
66. #2570C22semidirect
70. #2553C22semidirect
71. #2538C22semidirect
72. #2530C22semidirect
73. #2527C22semidirect
75. #2509C22semidirect
76. #2509C22semidirect
77. #2508C22semidirect
78. #2508C22semidirect
79. #2507C22semidirect
80. #2507C22semidirect
81. #2506C22semidirect
82. #2506C22semidirect
83. #2497C22semidirect
84. #2496C22semidirect
85. #2495C22semidirect
86. #2494C22semidirect
87. #2493C22semidirect
89. #2484C22semidirect
91. #2481C22semidirect
92. #2479C22semidirect
93. #2477C22semidirect
94. #2473C22semidirect
95. #2468C22semidirect
96. #2460C22semidirect
97. #2458C22semidirect
107. #2419C22semidirect
108. #2413C22semidirect
112. #2396C22semidirect
113. #2396C22semidirect
116. #2359C22semidirect
119. #2357C22semidirect
120. #2357C22semidirect
121. #2356C22semidirect
122. #2356C22semidirect
123. #2355C22semidirect
124. #2355C22semidirect
125. #2355C22semidirect
130. Q8×C4⋊C4C22semidirect
139. #2343C22semidirect
154. #2314C22semidirect
160. C4×C22⋊Q8C22semidirect
165. #2295C22semidirect
166. #2295C22semidirect
175. #2283C22semidirect
176. #2283C22semidirect
180. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#593282
#592642
#592602
#451322
#449102
#435092
#430782
#389712
#389692
#382302
#382262
#363942
#363702
#355852
#355412
#353392
#352672
#349522
C2×#25802
#342552
#341892
#341812
Q8×#1172
C4×#5352