Finite Group Databasebeta

← #7681489

Subgroups — #7681489

Order 512.

4894 conjugacy classes of subgroups.

The subgroup lattice has 1039 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59250C214yesmaximal, complemented
2#59247C214yesmaximal, complemented
3#59238C218yesmaximal, complemented
4#45256C214yesmaximal, complemented
5#44911C214yesmaximal, complemented
6#44102C214yesmaximal, complemented
7#43965C214yesmaximal, complemented
8#39803C214yesmaximal, complemented
9#39801C214yesmaximal, complemented
10#39758C212yesmaximal, complemented
11#39756C212yesmaximal, complemented
12#36609C212yesmaximal, complemented
13#36601C212yesmaximal, complemented
14#35558C212yesmaximal, complemented
15#35545C212yesmaximal, complemented
16#35330C211yesmaximal, characteristic, complemented
17#35264C212yesmaximal
18#34952C211yesmaximal, characteristic, complemented
19C2×#2580C211yesmaximal, characteristic, complemented
20#34272C212yesmaximal, complemented
21#34189C211yesmaximal, characteristic, complemented
22#34186C211yesmaximal, characteristic, complemented
23Q8×#117C211yesmaximal, characteristic, complemented
24C4×#535C211yesmaximal, characteristic
25C2×#544C2212yes—
26C2×#535C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30#2862C2212yescomplemented
31#2861C2214yes—
32#2859C2212yescomplemented
33#2858C2214yes—
34#2808C2218yescomplemented
35#2798C2218yescomplemented
36#2788C2218yescomplemented
37#2787C2218yescomplemented
38#2786C2218yescomplemented
39#2777C2218yescomplemented
40#2759C2218yescomplemented
41#2759C2218yescomplemented
42#2740C2218yescomplemented
43#2727C2218yescomplemented
44#2715C2218yescomplemented
45#2700C2218yescomplemented
46#2660C2214yescomplemented
47#2641C2214yes—
48#2640C2214yes—
49#2604C2218yescomplemented
50#2601C2218yescomplemented
51#2599C2218yescomplemented
52#2596C2218yescomplemented
53#2592C2218yescomplemented
54#2582C2212yescomplemented
55#2581C2211yescharacteristic, complemented
56#2581C2211yescharacteristic, complemented
57#2580C2212yes—
58#2580C2212yes—
59#2580C2212yes—
60#2580C2214yes—
61#2580C2214yes—
62#2580C2212yes—
63#2580C2211yescharacteristic, complemented
64#2580C2211yescharacteristic, complemented
65#2579C2214yes—
66#2573C2218yescomplemented
67#2560C2218yescomplemented
68#2550C2214yescomplemented
69#2550C2214yescomplemented
70#2549C2214yes—
71#2549C2214yes—
72#2538C2212yescomplemented
73#2532C2218yescomplemented
74#2527C2218yescomplemented
75#2523C2218yescomplemented
76#2521C2218yescomplemented
77#2514C2214yescomplemented
78#2513C2214yes—
79#2513C2214yes—
80#2513C2214yes—
81#2513C2214yes—
82#2513C2214yescomplemented
83#2512C2214yes—
84#2512C2214yes—
85#2512C2214yes—
86#2512C2214yes—
87#2512C2214yescomplemented
88#2511C2214yescomplemented
89#2510C2218yes—
90#2497C2214yescomplemented
91#2496C2214yescomplemented
92#2495C2214yescomplemented
93#2494C2214yescomplemented
94#2491C2214yes—
95#2491C2214yes—
96#2490C2214yes—
97#2490C2214yes—
98#2487C2212yes—
99#2481C2218yes—
100#2480C2218yes—
101#2480C2218yes—
102#2478C2218yescomplemented
103#2474C2218yescomplemented
104#2472C2218yes—
105#2472C2218yes—
106#2469C2218yescomplemented
107#2466C2218yescomplemented
108#2466C2218yescomplemented
109#2448C2218yescomplemented
110#2447C2218yescomplemented
111#2409C2212yes—
112#2396C2212yescomplemented
113#2396C2212yescomplemented
114C2×#399C2212yes—
115C2×#393C2212yes—
116#2373C2218yescomplemented
117#2370C2214yescomplemented
118#2370C2214yescomplemented
119#2369C2214yescomplemented
120#2368C2218yes—
121#2367C2218yescomplemented
122#2365C2214yescomplemented
123#2360C2218yes—
124#2357C2212yes—
125#2357C2212yes—
126#2357C2212yes—
127#2357C2212yes—
128#2357C2212yescomplemented
129#2357C2212yescomplemented
130#2356C2212yescomplemented
131#2356C2212yescomplemented
132#2355C2212yescomplemented
133#2355C2212yescomplemented
134#2355C2212yescomplemented
135#2354C2214yes—
136#2354C2214yes—
137#2353C2214yes—
138#2353C2214yes—
139Q8×C4⋊C4C2212yescomplemented
140#2345C2212yes—
141#2345C2214yes—
142Q8×C22⋊C4C2212yes—
143#2331C2214yescomplemented
144#2330C2214yescomplemented
145#2328C2212yes—
146#2326C2212yes—
147#2324C2214yes—
148#2321C2214yes—
149#2317C2212yes—
150#2317C2211yescharacteristic
151#2314C2214yescomplemented
152#2312C2214yes—
153#2311C2211yescharacteristic
154#2311C2212yes—
155#2309C2211yescharacteristic
156#2309C2212yes—
157C4×C4⋊Q8C2214yescomplemented
158C4×#127C2212yes—
159C4×#125C2214yescomplemented
160C4×#124C2212yes—
161C4×C22⋊Q8C2214yescomplemented
162C4×#121C2214yes—
163C4×#120C2214yes—
164#2297C2212yes—
165#2296C2212yes—
166#2295C2212yescomplemented
167#2295C2214yescomplemented
168C2×#390C2212yes—
169C2×#389C2212yes—
170C2×#385C2214yes—
171#2285C2211yescharacteristic
172#2285C2211yescharacteristic
173#2285C2212yes—
174#2283C2212yescomplemented
175#2283C2212yescomplemented
176C2×#382C2211yescharacteristic
177#2280C2214yes—
178#2274C2212yes—
179#2274C2212yes—
180C42×Q8C2212yescomplemented
181C4×#117C2211yescharacteristic
182C4×#117C2212yes—
183C22×#41C2311yescharacteristic
184C23×Q8C2311yescharacteristic
185C23×D4C2311yescharacteristic
186C24×C4C2312yes—
187#544—216no—
188#535—28no—
189C2×C4⋊Q8C2314yes—
190C2×C4⋊Q8C2314yes—
191C2×#127C2312yes—
192C2×#126C2318yes—
193C2×#126C2318yes—
194C2×#126C2318yes—
195C2×#125C2314yes—
196C2×#125C2314yes—
197C2×#124C2312yes—
198C2×#124C2318yes—
199C2×#124C2318yes—
200C2×C22⋊Q8C2318yes—
201C2×C22⋊Q8C2314yes—
202C2×#121C2314yes—
203C2×#120C2314yes—
204C4×#41—28no—
205C2×C4×Q8—28no—
206C2×C4×Q8C2311yescharacteristic
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2312yes—
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2314yes—
215C2×C4×Q8C2318yes—
216C2×C4×D4—28no—
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2312yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2318yes—
226C2×#117C2311yescharacteristic
227C2×#117C2312yes—
228C2×#117C2311yescharacteristic
229C2×#117C2312yes—
230C2×#117C2312yes—
231C2×#117C2318yes—
232C2×#117C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2314yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2314yes—
240C22×C22⋊C4C2314yes—
241C22×C42C2312yes—
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244#401C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2312yes—
248#400C2312yes—
249#400C2318yes—
250#399C2314yes—
251#399C2318yes—
252#399C2314yes—
253#399C2312yes—
254#399C2312yes—
255#398C2318yes—
256#398C2314yes—
257#398C2314yes—
258#398C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#396C2318yes—
271#396C2314yes—
272#396C2314yes—
273#396C2318yes—
274#396C2318yes—
275#395C2312yes—
276#395C2312yes—
277#395C2318yes—
278#395C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#393C2318yes—
284#393C2314yes—
285#393C2314yes—
286#393C2312yes—
287#393C2312yes—
288#393C2318yes—
289#393C2318yes—
290#391C2314yes—
291#391C2318yes—
292#391C2312yes—
293#391C2314yes—
294#391C2312yes—
295#391C2312yes—
296#391C2314yes—
297#391C2318yes—
298#391C2318yes—
299#391C2318yes—
300#391C2314yes—
301#391C2314yes—
302#391C2318yes—
303#390C2318yes—
304#390C2312yes—
305#390C2312yes—
306#390C2318yes—
307#390C2314yes—
308#390C2312yes—
309#390C2314yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2314yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2312yes—
319#390C2312yes—
320#390C2318yes—
321#389C2312yes—
322#389C2314yes—
323#389C2312yes—
324#389C2318yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2318yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2318yes—
336#389C2318yes—
337#389C2318yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2314yes—
368#387C2314yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2314yes—
374#387C2314yes—
375#387C2314yes—
376#387C2314yes—
377#387C2314yes—
378#387C2314yes—
379#387C2318yes—
380#387C2318yes—
381#386C2318yes—
382#386C2314yes—
383#386C2318yes—
384#386C2314yes—
385#386C2314yes—
386#386C2318yes—
387#385C2314yes—
388#385C2318yes—
389#385C2318yes—
390#385C2314yes—
391#385C2314yes—
392#385C2314yes—
393#385C2314yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#384C2312yes—
399#384C2312yes—
400#384C2314yes—
401#384C2312yes—
402#384C2312yes—
403#384C2312yes—
404#383C2314yes—
405#383C2318yes—
406#383C2314yes—
407#382C2312yes—
408#382C2312yes—
409#382C2314yes—
410#382C2312yes—
411#382C2312yes—
412#382C2312yes—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2312yes—
418#382C2312yes—
419#381C2314yes—
420#381C2314yes—
421#381C2314yes—
422#381C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2312yes—
427#380C2312yes—
428#380C2312yes—
429#380C2314yes—
430#380C2312yes—
431#380C2314yes—
432#380C2318yes—
433#380C2314yes—
434#379C2318yes—
435#379C2314yes—
436C4×C4⋊C4C2318yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2318yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2318yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477#376C2312yes—
478#376C2314yes—
479#376C2314yes—
480#376C2314yes—
481C2×#95C2312yes—
482C2×#95C2312yes—
483C2×#95C2314yes—
484C43C2314yes—
485C43C2312yes—
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×Q8C2418yes—
497C22×D4—24no—
498C22×D4—24no—
499C22×D4—24no—
500C22×D4C2412yes—
501C22×D4C2412yes—
502C22×D4C2412yes—
503C22×D4C2411yescharacteristic
504C22×D4C2418yes—
505C23×C4—28no—
506C23×C4—84no—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2414yes—
511C23×C4C2412yes—
512C23×C4C2414yes—
513C23×C4C2412yes—
514C23×C4C2414yes—
515C23×C4C2412yes—
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C4⋊Q8—216no—
520C4⋊Q8—216no—
521#127—28no—
522#126—416no—
523#126—88no—
524#126—88no—
525#125—216no—
526#125—216no—
527#124—28no—
528#124—416no—
529#124—88no—
530C22⋊Q8—232no—
531C22⋊Q8—48no—
532#121—216no—
533#120—216no—
534C4×Q8—28no—
535C4×Q8—24no—
536C4×Q8—24no—
537C4×Q8—24no—
538C4×Q8—24no—
539C4×Q8—28no—
540C4×Q8—24no—
541C4×Q8—24no—
542C4×Q8—48no—
543C4×Q8—88no—
544C4×D4—28no—
545C4×D4—28no—
546C4×D4—28no—
547C4×D4—28no—
548C4×D4—28no—
549C4×D4—28no—
550C4×D4—24no—
551C4×D4—24no—
552C4×D4—88no—
553#117—24no—
554#117—28no—
555#117—24no—
556#117—28no—
557#117—28no—
558#117—88no—
559#117#4118yes—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—28no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—28no—
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⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2412yes—
606C2×C22⋊C4—28no—
607C2×C22⋊C4—48no—
608C2×C22⋊C4—84no—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2412yes—
636C2×C42—28no—
637C2×C42—28no—
638C2×C42#4118yes—
639C2×C42C2412yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2414yes—
650C2×C42C2418yes—
651C2×C42C2418yes—
652C2×C42C2414yes—
653C2×C42C2414yes—
654C2×C42C2418yes—
655C2×C42C2414yes—
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2418yes—
659C2×C42C2411yescharacteristic
660C2×C42C2412yes—
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664#95C2414yes—
665#95C2414yes—
666#95C2418yes—
667#95C2414yes—
668#95C2414yes—
669#95C2418yes—
670#95C2412yes—
671#95C2412yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2418yes—
679#95C2418yes—
680#95C2412yes—
681#95C2412yes—
682#95C2412yes—
683#95C2412yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
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—24no—
709C24—44no—
710C24—44no—
711C24C2514yes—
712C24C2512yes—
713C24C2511yescharacteristic
714#41—416no—
715C2×Q8—22no—
716C2×Q8—24no—
717C2×Q8—22no—
718C2×Q8—22no—
719C2×Q8—22no—
720C2×Q8—216no—
721C2×Q8—22no—
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—42no—
725C2×Q8—42no—
726C2×Q8—48no—
727C2×Q8—48no—
728C2×Q8—416no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—22no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—22no—
738C2×D4—216no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—22no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—416no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—28no—
749C22×C4—24no—
750C22×C4—28no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—28no—
757C22×C4—48no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—44no—
762C22×C4—42no—
763C22×C4—44no—
764C22×C4—42no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—48no—
768C22×C4—44no—
769C22×C4—816no—
770C22×C4C2×#4114yes—
771C22×C4C2×#4114yes—
772C22×C4C2×#4114yes—
773C22×C4C2×#4114yes—
774C22×C42−1+414yes—
775C22×C4C2512yes—
776C22×C4C2512yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2514yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2518yes—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2514yes—
787C22×C4C2512yes—
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2514yes—
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C22×C4C2512yes—
794C22×C4C2511yescharacteristic
795C22×C4C2511yescharacteristic
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—22no—
802C4⋊C4—22no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—216no—
814C4⋊C4—216no—
815C4⋊C4—216no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—48no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—48no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—48no—
836C4⋊C4C2×#4118yes—
837C22⋊C4—24no—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—24no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—216no—
846C22⋊C4—216no—
847C22⋊C4—28no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—44no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—44no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—44no—
863C22⋊C4C2×#4118yes—
864C42—24no—
865C42—24no—
866C42—24no—
867C42—24no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—28no—
872C42—28no—
873C42—24no—
874C42—28no—
875C42—48no—
876C42—48no—
877C42—44no—
878C42—44no—
879C42—44no—
880C42—44no—
881C42—48no—
882C42—44no—
883C42—48no—
884C42C2×#4114yes—
885C42C2×#4114yes—
886C42C2×#4114yes—
887C42C2×#4114yes—
888C42C2×#4118yes—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—24no—
893C23—24no—
894C23—22no—
895C23—22no—
896C23—24no—
897C23—28no—
898C23—24no—
899C23—24no—
900C23—28no—
901C23—416no—
902C23—48no—
903C23—84no—
904C23—88no—
905C23—84no—
906C23C22×#4112yes—
907C23C22×#4112yes—
908C23C2×2−1+412yes—
909C23C2611yescharacteristic
910Q8—28no—
911Q8—48no—
912Q8—44no—
913Q8—44no—
914Q8—816no—
915D4—48no—
916D4—48no—
917D4—48no—
918D4—44no—
919D4—816no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—28no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—28no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—28no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—28no—
962C2×C4—22no—
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—88no—
973C2×C4—84no—
974C2×C4—84no—
975C2×C4#556116yes—
976C2×C4C22×#4112yes—
977C2×C4C22×#4112yes—
978C2×C4C22×#4112yes—
979C2×C4C22×#4112yes—
980C2×C4C22×#4118yes—
981C2×C4C22×#4112yes—
982C2×C4C22×#4112yes—
983C2×C4C22×#4112yes—
984C2×C4C22×#4112yes—
985C2×C4C2×2−1+412yes—
986C2×C4C2×2−1+412yes—
987C2×C4#58514yes—
988C22—24no—
989C22—22no—
990C22—22no—
991C22—24no—
992C22—44no—
993C22—48no—
994C22—42no—
995C22—44no—
996C22—44no—
997C22—42no—
998C22—44no—
999C22—48no—
1000C22—42no—
1001C22—44no—
1002C22—816no—
1003C22C2×#55614yes—
1004C22C23×#4111yescharacteristic
1005C22C23×#4111yescharacteristic
1006C22C22×2−1+411yescharacteristic
1007C22C2×#58512yes—
1008C22H(7,𝔽2)12yes—
1009C4—28no—
1010C4—22no—
1011C4—22no—
1012C4—24no—
1013C4—22no—
1014C4—22no—
1015C4—44no—
1016C4—48no—
1017C4—44no—
1018C4—42no—
1019C4—42no—
1020C4—44no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—44no—
1025C4—44no—
1026C4—44no—
1027C4—42no—
1028C4C2×#55614yes—
1029C4C2×#55614yes—
1030C2—24no—
1031C2—82no—
1032C2—84no—
1033C2C22×#55611yescharacteristic
1034C2#6281411yescharacteristic
1035C2#6285511yescharacteristic
1036C2#6292612yes—
1037C2#6301012yes—
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. #59250C2semidirect
2. #59247C2semidirect
3. #59238C2semidirect
4. #45256C2semidirect
5. #44911C2semidirect
6. #44102C2semidirect
7. #43965C2semidirect
8. #39803C2semidirect
9. #39801C2semidirect
10. #39758C2semidirect
11. #39756C2semidirect
12. #36609C2semidirect
13. #36601C2semidirect
14. #35558C2semidirect
15. #35545C2semidirect
16. #35330C2semidirect
18. #34952C2semidirect
19. C2×#2580C2semidirect
20. #34272C2semidirect
21. #34189C2semidirect
22. #34186C2semidirect
23. Q8×#117C2semidirect
30. #2862C22semidirect
32. #2859C22semidirect
34. #2808C22semidirect
35. #2798C22semidirect
36. #2788C22semidirect
37. #2787C22semidirect
38. #2786C22semidirect
39. #2777C22semidirect
40. #2759C22semidirect
41. #2759C22semidirect
42. #2740C22semidirect
43. #2727C22semidirect
44. #2715C22semidirect
45. #2700C22semidirect
46. #2660C22semidirect
49. #2604C22semidirect
50. #2601C22semidirect
51. #2599C22semidirect
52. #2596C22semidirect
53. #2592C22semidirect
54. #2582C22semidirect
55. #2581C22semidirect
56. #2581C22semidirect
63. #2580C22semidirect
64. #2580C22semidirect
66. #2573C22semidirect
67. #2560C22semidirect
68. #2550C22semidirect
69. #2550C22semidirect
72. #2538C22semidirect
73. #2532C22semidirect
74. #2527C22semidirect
75. #2523C22semidirect
76. #2521C22semidirect
77. #2514C22semidirect
82. #2513C22semidirect
87. #2512C22semidirect
88. #2511C22semidirect
90. #2497C22semidirect
91. #2496C22semidirect
92. #2495C22semidirect
93. #2494C22semidirect
102. #2478C22semidirect
103. #2474C22semidirect
106. #2469C22semidirect
107. #2466C22semidirect
108. #2466C22semidirect
109. #2448C22semidirect
110. #2447C22semidirect
112. #2396C22semidirect
113. #2396C22semidirect
116. #2373C22semidirect
117. #2370C22semidirect
118. #2370C22semidirect
119. #2369C22semidirect
121. #2367C22semidirect
122. #2365C22semidirect
128. #2357C22semidirect
129. #2357C22semidirect
130. #2356C22semidirect
131. #2356C22semidirect
132. #2355C22semidirect
133. #2355C22semidirect
134. #2355C22semidirect
139. Q8×C4⋊C4C22semidirect
143. #2331C22semidirect
144. #2330C22semidirect
151. #2314C22semidirect
157. C4×C4⋊Q8C22semidirect
159. C4×#125C22semidirect
161. C4×C22⋊Q8C22semidirect
166. #2295C22semidirect
167. #2295C22semidirect
174. #2283C22semidirect
175. #2283C22semidirect
180. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#592502
#592472
#592382
#452562
#449112
#441022
#439652
#398032
#398012
#397582
#397562
#366092
#366012
#355582
#355452
#353302
#352642
#349522
C2×#25802
#342722
#341892
#341862
Q8×#1172
C4×#5352