Finite Group Databasebeta

← #7630891

Subgroups — #7630891

Order 512.

5114 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36037C214yesmaximal, complemented
2#35838C214yesmaximal, complemented
3#35824C218yesmaximal, complemented
4#35765C218yesmaximal, complemented
5#35745C214yesmaximal, complemented
6#35710C214yesmaximal, complemented
7#35338C211yesmaximal, characteristic, complemented
8#35313C211yesmaximal, characteristic, complemented
9#35311C211yesmaximal, characteristic, complemented
10#35300C214yesmaximal, complemented
11#35290C214yesmaximal, complemented
12#35286C211yesmaximal, characteristic, complemented
13#35269C214yesmaximal, complemented
14#35266C211yesmaximal, characteristic, complemented
15#35262C211yesmaximal, characteristic
16#34634C211yesmaximal, characteristic, complemented
17#34619C214yesmaximal, complemented
18C2×#2620C211yesmaximal, characteristic
19#34255C211yesmaximal, characteristic, complemented
20#34254C211yesmaximal, characteristic, complemented
21#34214C211yesmaximal, characteristic, complemented
22#34211C211yesmaximal, characteristic, complemented
23#34204C211yesmaximal, characteristic
24#34203C211yesmaximal, characteristic, complemented
25#33996C211yesmaximal, characteristic, complemented
26C2×#533C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C2×#519C2211yescharacteristic
31C2×#518C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C22×#117C2211yescharacteristic
35#2863C2214yescomplemented
36#2861C2214yescomplemented
37#2860C2214yescomplemented
38#2859C2214yescomplemented
39#2855C2214yescomplemented
40#2854C2214yes—
41#2654C2218yescomplemented
42#2653C2218yescomplemented
43#2650C2218yescomplemented
44#2649C2218yescomplemented
45#2647C2214yescomplemented
46#2645C2214yescomplemented
47#2644C2214yescomplemented
48#2640C2214yescomplemented
49#2629C2212yescomplemented
50#2629C2212yescomplemented
51#2628C2212yescomplemented
52#2628C2212yescomplemented
53#2627C2214yes—
54#2626C2214yes—
55#2625C2214yescomplemented
56#2624C2214yes—
57#2620C2212yes—
58#2620C2214yes—
59#2620C2214yes—
60#2620C2212yes—
61#2620C2212yes—
62#2620C2212yes—
63#2594C2218yescomplemented
64#2592C2214yescomplemented
65#2592C2214yescomplemented
66#2587C2218yescomplemented
67#2576C2218yescomplemented
68#2574C2218yescomplemented
69#2573C2218yescomplemented
70#2572C2218yescomplemented
71#2571C2214yescomplemented
72#2561C2218yes—
73#2558C2218yescomplemented
74#2553C2218yescomplemented
75#2552C2214yescomplemented
76#2529C2218yescomplemented
77#2526C2218yescomplemented
78#2525C2218yescomplemented
79#2525C2218yescomplemented
80#2522C2218yescomplemented
81#2519C2218yescomplemented
82#2518C2218yescomplemented
83#2518C2218yescomplemented
84#2516C2218yescomplemented
85#2515C2218yescomplemented
86#2514C2214yescomplemented
87#2513C2214yescomplemented
88#2512C2214yescomplemented
89#2511C2214yescomplemented
90#2504C2212yes—
91#2503C2212yescomplemented
92#2502C2212yescomplemented
93#2501C2212yes—
94#2500C2212yes—
95#2500C2212yes—
96#2499C2212yescomplemented
97#2499C2212yescomplemented
98#2493C2218yes—
99#2484C2214yes—
100#2483C2214yes—
101#2482C2214yes—
102#2480C2218yes—
103#2475C2218yescomplemented
104#2470C2218yescomplemented
105#2469C2218yescomplemented
106#2466C2218yescomplemented
107#2460C2218yescomplemented
108#2458C2218yescomplemented
109#2442C2218yes—
110#2405C2214yes—
111#2401C2218yescomplemented
112#2398C2218yescomplemented
113#2396C2218yescomplemented
114#2396C2214yescomplemented
115#2396C2214yescomplemented
116#2395C2218yescomplemented
117C2×#396C2214yes—
118C2×#394C2214yes—
119#2367C2214yescomplemented
120#2367C2214yescomplemented
121#2363C2214yes—
122#2362C2214yescomplemented
123#2361C2214yes—
124#2360C2218yes—
125#2360C2214yescomplemented
126#2357C2214yescomplemented
127#2356C2214yescomplemented
128#2355C2214yescomplemented
129#2355C2214yescomplemented
130#2354C2214yescomplemented
131Q8×C4⋊C4C2214yescomplemented
132#2344C2214yes—
133#2343C2218yes—
134#2342C2214yes—
135#2342C2214yes—
136#2342C2218yes—
137#2342C2218yes—
138D4×C22⋊C4C2214yes—
139#2330C2214yescomplemented
140#2326C2214yescomplemented
141#2324C2214yes—
142#2323C2214yescomplemented
143#2320C2214yescomplemented
144#2319C2214yescomplemented
145#2317C2211yescharacteristic
146#2317C2211yescharacteristic
147#2317C2211yescharacteristic
148#2317C2211yescharacteristic
149#2316C2211yescharacteristic
150#2316C2211yescharacteristic
151#2310C2211yescharacteristic
152#2310C2211yescharacteristic
153#2310C2211yescharacteristic
154#2309C2211yescharacteristic
155#2309C2211yescharacteristic
156#2309C2211yescharacteristic
157C4×C4⋊Q8C2214yescomplemented
158C4×#124C2214yescomplemented
159C4×C22⋊Q8C2214yescomplemented
160C4×#121C2214yes—
161#2296C2211yescharacteristic
162#2296C2211yescharacteristic
163#2295C2214yescomplemented
164C2×#391C2211yescharacteristic
165#2293C2214yescomplemented
166C2×#390C2211yescharacteristic
167#2285C2211yescharacteristic
168C2×#384C2211yescharacteristic
169#2280C2211yescharacteristic
170#2280C2211yescharacteristic
171#2274C2211yescharacteristic
172#2274C2211yescharacteristic
173#2274C2214yes—
174#2274C2212yescomplemented
175#2274C2212yescomplemented
176#2274C2212yescomplemented
177#2274C2212yescomplemented
178#2273C2214yes—
179C4×#117C2211yescharacteristic
180C4×#117C2211yescharacteristic
181C4×#117C2211yescharacteristic
182C4×#117C2211yescharacteristic
183C4×#117C2212yescomplemented
184C4×#117C2212yescomplemented
185C4×#117C2212yescomplemented
186C4×#117C2212yescomplemented
187C23×Q8C2311yescharacteristic
188C23×D4C2311yescharacteristic
189C23×D4C2312yes—
190C24×C4C2311yescharacteristic
191#533—28no—
192C2×C4⋊Q8C2312yes—
193C2×#126C2318yes—
194C2×#125C2312yes—
195C2×#125C2318yes—
196C2×#124—28no—
197C2×#124C2312yes—
198C2×#124C2314yes—
199C2×#124C2312yes—
200C2×#123C2318yes—
201C2×C22⋊Q8—28no—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2312yes—
205C2×C22⋊Q8C2312yes—
206C2×C22⋊Q8C2312yes—
207C2×#121—28no—
208C2×#121C2312yes—
209C2×#121C2312yes—
210C2×#121C2312yes—
211C2×#121C2312yes—
212#519—28no—
213#518—28no—
214C2×C4×Q8C2314yes—
215C2×C4×Q8C2314yes—
216C2×C4×Q8C2314yes—
217C2×C4×Q8C2318yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2318yes—
221C2×#117—28no—
222C2×#117—28no—
223C2×#117—28no—
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2312yes—
232C2×#117C2314yes—
233C2×#117C2312yes—
234C2×#117C2312yes—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2312yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2318yes—
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2314yes—
255C22×C22⋊C4C2314yes—
256C22×C22⋊C4C2312yes—
257C22×C22⋊C4C2314yes—
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C2314yes—
263C22×C42C2312yes—
264C22×C42C2311yescharacteristic
265C22×C42C2312yes—
266C22×C42C2311yescharacteristic
267#401C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2314yes—
271#400C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#399C2318yes—
277#399C2314yes—
278#399C2314yes—
279#398C2318yes—
280#398C2314yes—
281#398C2318yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#396C2318yes—
295#396C2314yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2314yes—
301#396C2314yes—
302#396C2314yes—
303#395C2314yes—
304#395C2314yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2314yes—
314#393C2314yes—
315#391C2318yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2314yes—
326#391C2312yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2312yes—
331#390C2312yes—
332#390C2314yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2318yes—
337#390C2314yes—
338#390C2312yes—
339#389C2314yes—
340#389C2314yes—
341#389C2318yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2312yes—
351#389C2318yes—
352#389C2318yes—
353#389C2318yes—
354#389C2318yes—
355#389C2312yes—
356#389C2312yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#385C2314yes—
395#385C2314yes—
396#385C2314yes—
397#385C2314yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2314yes—
402#385C2318yes—
403#385C2314yes—
404#385C2318yes—
405#384C2312yes—
406#384C2314yes—
407#384C2312yes—
408#384C2312yes—
409#384C2312yes—
410#384C2312yes—
411#384C2312yes—
412#384C2312yes—
413#383C2318yes—
414#383C2318yes—
415#382C2312yes—
416#382C2312yes—
417#382C2318yes—
418#382C2312yes—
419#382C2312yes—
420#382C2318yes—
421#382C2312yes—
422#381C2314yes—
423#381C2314yes—
424#381C2314yes—
425#381C2318yes—
426#381C2318yes—
427#381C2312yes—
428#381C2312yes—
429#380C2314yes—
430#380C2314yes—
431#380C2318yes—
432#380C2312yes—
433#380C2312yes—
434#380C2314yes—
435#380C2312yes—
436#380C2312yes—
437#379C2314yes—
438#379C2314yes—
439#379C2314yes—
440#379C2312yes—
441#379C2312yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2318yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2318yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2318yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2312yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491#376C2312yes—
492#376C2312yes—
493#376C2318yes—
494#376C2312yes—
495#376C2312yes—
496C2×#95C2314yes—
497C43C2312yes—
498C43C2312yes—
499C43C2312yes—
500C43C2312yes—
501C25C2412yes—
502C25C2411yescharacteristic
503C22×Q8—24no—
504C22×Q8—24no—
505C22×Q8—24no—
506C22×Q8C2412yes—
507C22×Q8C2412yes—
508C22×Q8C2414yes—
509C22×D4—28no—
510C22×D4—24no—
511C22×D4—24no—
512C22×D4—24no—
513C22×D4—84no—
514C22×D4C2412yes—
515C22×D4C2412yes—
516C22×D4C2414yes—
517C22×D4C2414yes—
518C23×C4—24no—
519C23×C4—24no—
520C23×C4#4118yes—
521C23×C4C2412yes—
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2414yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2418yes—
534C23×C4C2412yes—
535C23×C4C2411yescharacteristic
536C4⋊Q8—28no—
537#126—88no—
538#125—28no—
539#125—88no—
540#124—216no—
541#124—28no—
542#124—28no—
543#123—88no—
544C22⋊Q8—28no—
545C22⋊Q8—28no—
546C22⋊Q8—28no—
547C22⋊Q8—28no—
548C22⋊Q8—216no—
549#121—28no—
550#121—28no—
551#121—28no—
552#121—28no—
553C4×Q8—216no—
554C4×Q8—216no—
555C4×Q8—216no—
556C4×Q8—88no—
557C4×D4—216no—
558C4×D4—216no—
559C4×D4—88no—
560#117—28no—
561#117—28no—
562#117—24no—
563#117—24no—
564#117—24no—
565#117—24no—
566#117—24no—
567#117—24no—
568#117—24no—
569#117—24no—
570#117—24no—
571#117—28no—
572#117—28no—
573#117—216no—
574#117—28no—
575#117—28no—
576#117—28no—
577#117—24no—
578#117—24no—
579#117—24no—
580#117—24no—
581#117—88no—
582#117#4118yes—
583C2×C4⋊C4—28no—
584C2×C4⋊C4—24no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4—24no—
587C2×C4⋊C4—28no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—28no—
590C2×C4⋊C4—84no—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C22⋊C4—28no—
633C2×C22⋊C4—28no—
634C2×C22⋊C4—28no—
635C2×C22⋊C4—28no—
636C2×C22⋊C4—216no—
637C2×C22⋊C4—28no—
638C2×C22⋊C4—216no—
639C2×C22⋊C4—84no—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2412yes—
674C2×C42—28no—
675C2×C42—24no—
676C2×C42—28no—
677C2×C42#4118yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2414yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2418yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2418yes—
694C2×C42C2418yes—
695C2×C42C2414yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#95C2418yes—
707#95C2418yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2418yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2414yes—
725#95C2418yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2414yes—
740C24—22no—
741C24—22no—
742C24—24no—
743C24—24no—
744C24—24no—
745C24—42no—
746C24—42no—
747C24—44no—
748C24—44no—
749C24C2×#4114yes—
750C24C2514yes—
751C24C2511yescharacteristic
752C24C2511yescharacteristic
753C24C2511yescharacteristic
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—28no—
757C2×Q8—24no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—44no—
762C2×Q8—44no—
763C2×Q8—416no—
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—416no—
775C2×D4—816no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—232no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—28no—
796C22×C4—216no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—48no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—48no—
807C22×C4—44no—
808C22×C4—42no—
809C22×C4C2×#4114yes—
810C22×C4C2×#4114yes—
811C22×C4C2×#4114yes—
812C22×C4C2×#4114yes—
813C22×C4C2×#4114yes—
814C22×C4C2×#4118yes—
815C22×C4C2×#4114yes—
816C22×C4C2×#4114yes—
817C22×C4C2×#4114yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2514yes—
832C22×C4C2514yes—
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2512yes—
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C4⋊C4—28no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—216no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—44no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4C2×#4118yes—
880C22⋊C4—24no—
881C22⋊C4—24no—
882C22⋊C4—24no—
883C22⋊C4—24no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—28no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—216no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—216no—
900C22⋊C4—216no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—48no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4C2×#4118yes—
914C42—28no—
915C42—24no—
916C42—24no—
917C42—24no—
918C42—24no—
919C42—24no—
920C42—22no—
921C42—22no—
922C42—24no—
923C42—24no—
924C42—24no—
925C42—216no—
926C42—24no—
927C42—24no—
928C42—44no—
929C42—44no—
930C42—44no—
931C42—44no—
932C42—44no—
933C42—48no—
934C42—48no—
935C42—44no—
936C42—44no—
937C42—44no—
938C42C2×#4118yes—
939C42C2×#4118yes—
940C42C2×#4114yes—
941C42C2×#4114yes—
942C23—22no—
943C23—22no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—28no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—28no—
957C23—28no—
958C23—44no—
959C23—44no—
960C23—48no—
961C23—84no—
962C23—84no—
963C23—84no—
964C23—88no—
965C23—88no—
966C23—84no—
967C23C22×#4112yes—
968C23C22×#4112yes—
969C23C22×#4112yes—
970C23C22×#4112yes—
971C23C22×#4112yes—
972C23C2611yescharacteristic
973Q8—416no—
974Q8—48no—
975Q8—48no—
976D4—416no—
977D4—48no—
978D4—48no—
979D4—88no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—28no—
1019C2×C4—28no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—48no—
1032C2×C4—48no—
1033C2×C4—88no—
1034C2×C4—816no—
1035C2×C4—84no—
1036C2×C4—84no—
1037C2×C4—84no—
1038C2×C4—84no—
1039C2×C4—84no—
1040C2×C4#529116yes—
1041C2×C4C22×#4112yes—
1042C2×C4C22×#4118yes—
1043C2×C4C22×#4114yes—
1044C2×C4C22×#4114yes—
1045C2×C4C22×#4112yes—
1046C2×C4C22×#4112yes—
1047C2×C4C22×#4112yes—
1048C2×C4C22×#4112yes—
1049C2×C4C22×#4112yes—
1050C2×C4C22×#4112yes—
1051C2×C4C22×#4112yes—
1052C22—22no—
1053C22—24no—
1054C22—24no—
1055C22—22no—
1056C22—22no—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—44no—
1067C22—48no—
1068C22—48no—
1069C22—44no—
1070C22—44no—
1071C22—88no—
1072C22—168no—
1073C22C2×#52914yes—
1074C22C23×#4111yescharacteristic
1075C22C23×#4111yescharacteristic
1076C22C23×#4111yescharacteristic
1077C22H(7,𝔽2)12yes—
1078C222−1+612yes—
1079C4—24no—
1080C4—24no—
1081C4—28no—
1082C4—22no—
1083C4—22no—
1084C4—42no—
1085C4—42no—
1086C4—44no—
1087C4—44no—
1088C4—42no—
1089C4—42no—
1090C4—44no—
1091C4—44no—
1092C4—44no—
1093C4—44no—
1094C4—44no—
1095C4—42no—
1096C4—42no—
1097C4—44no—
1098C4C2×#52914yes—
1099C4C2×#52914yes—
1100C2—24no—
1101C2—42no—
1102C2—42no—
1103C2—84no—
1104C2C22×#52911yescharacteristic
1105C2#6285511yescharacteristic
1106C2#6285612yes—
1107C2#6285712yes—
1108C2#6286011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36037C2semidirect
2. #35838C2semidirect
3. #35824C2semidirect
4. #35765C2semidirect
5. #35745C2semidirect
6. #35710C2semidirect
7. #35338C2semidirect
8. #35313C2semidirect
9. #35311C2semidirect
10. #35300C2semidirect
11. #35290C2semidirect
12. #35286C2semidirect
13. #35269C2semidirect
14. #35266C2semidirect
16. #34634C2semidirect
17. #34619C2semidirect
19. #34255C2semidirect
20. #34254C2semidirect
21. #34214C2semidirect
22. #34211C2semidirect
24. #34203C2semidirect
25. #33996C2semidirect
35. #2863C22semidirect
36. #2861C22semidirect
37. #2860C22semidirect
38. #2859C22semidirect
39. #2855C22semidirect
41. #2654C22semidirect
42. #2653C22semidirect
43. #2650C22semidirect
44. #2649C22semidirect
45. #2647C22semidirect
46. #2645C22semidirect
47. #2644C22semidirect
48. #2640C22semidirect
49. #2629C22semidirect
50. #2629C22semidirect
51. #2628C22semidirect
52. #2628C22semidirect
55. #2625C22semidirect
63. #2594C22semidirect
64. #2592C22semidirect
65. #2592C22semidirect
66. #2587C22semidirect
67. #2576C22semidirect
68. #2574C22semidirect
69. #2573C22semidirect
70. #2572C22semidirect
71. #2571C22semidirect
73. #2558C22semidirect
74. #2553C22semidirect
75. #2552C22semidirect
76. #2529C22semidirect
77. #2526C22semidirect
78. #2525C22semidirect
79. #2525C22semidirect
80. #2522C22semidirect
81. #2519C22semidirect
82. #2518C22semidirect
83. #2518C22semidirect
84. #2516C22semidirect
85. #2515C22semidirect
86. #2514C22semidirect
87. #2513C22semidirect
88. #2512C22semidirect
89. #2511C22semidirect
91. #2503C22semidirect
92. #2502C22semidirect
96. #2499C22semidirect
97. #2499C22semidirect
103. #2475C22semidirect
104. #2470C22semidirect
105. #2469C22semidirect
106. #2466C22semidirect
107. #2460C22semidirect
108. #2458C22semidirect
111. #2401C22semidirect
112. #2398C22semidirect
113. #2396C22semidirect
114. #2396C22semidirect
115. #2396C22semidirect
116. #2395C22semidirect
119. #2367C22semidirect
120. #2367C22semidirect
122. #2362C22semidirect
125. #2360C22semidirect
126. #2357C22semidirect
127. #2356C22semidirect
128. #2355C22semidirect
129. #2355C22semidirect
130. #2354C22semidirect
131. Q8×C4⋊C4C22semidirect
139. #2330C22semidirect
140. #2326C22semidirect
142. #2323C22semidirect
143. #2320C22semidirect
144. #2319C22semidirect
157. C4×C4⋊Q8C22semidirect
158. C4×#124C22semidirect
159. C4×C22⋊Q8C22semidirect
163. #2295C22semidirect
165. #2293C22semidirect
174. #2274C22semidirect
175. #2274C22semidirect
176. #2274C22semidirect
177. #2274C22semidirect
183. C4×#117C22semidirect
184. C4×#117C22semidirect
185. C4×#117C22semidirect
186. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#360372
#358382
#358242
#357652
#357452
#357102
#353382
#353132
#353112
#353002
#352902
#352862
#352692
#352662
#352622
#346342
#346192
C2×#26202
#342552
#342542
#342142
#342112
#342042
#342032
#339962