Finite Group Databasebeta

← #7630892

Subgroups — #7630892

Order 512.

5106 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36034C214yesmaximal, complemented
2#35837C214yesmaximal, complemented
3#35833C214yesmaximal, complemented
4#35828C214yesmaximal, complemented
5#35774C214yesmaximal, complemented
6#35770C214yesmaximal, complemented
7#35742C214yesmaximal, complemented
8#35706C214yesmaximal, complemented
9#35339C211yesmaximal, characteristic, complemented
10#35324C212yesmaximal, complemented
11#35314C212yesmaximal, complemented
12#35296C212yesmaximal, complemented
13#35290C214yesmaximal, complemented
14#35289C211yesmaximal, characteristic, complemented
15#35268C212yesmaximal, complemented
16#35267C212yesmaximal, complemented
17#35263C212yesmaximal, complemented
18#34633C211yesmaximal, characteristic
19#34619C214yesmaximal, complemented
20C2×#2628C211yesmaximal, characteristic, complemented
21#34253C212yesmaximal, complemented
22#34216C211yesmaximal, characteristic, complemented
23#34208C211yesmaximal, characteristic, complemented
24#34202C212yesmaximal, complemented
25#33996C211yesmaximal, characteristic, complemented
26C2×#532C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C2×#525C2212yes—
29C2×#520C2212yes—
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C22×#117C2211yescharacteristic
33#2864C2212yescomplemented
34#2864C2212yescomplemented
35#2863C2214yescomplemented
36#2862C2212yescomplemented
37#2860C2214yescomplemented
38#2858C2212yescomplemented
39#2855C2214yes—
40#2854C2214yes—
41#2654C2218yescomplemented
42#2653C2218yes—
43#2650C2218yescomplemented
44#2649C2218yes—
45#2647C2214yescomplemented
46#2645C2214yescomplemented
47#2644C2214yescomplemented
48#2640C2214yescomplemented
49#2628C2212yes—
50#2628C2212yes—
51#2628C2212yes—
52#2628C2212yes—
53#2628C2212yes—
54#2628C2212yes—
55#2628C2212yes—
56#2628C2212yes—
57#2625C2214yes—
58#2624C2214yes—
59#2621C2211yescharacteristic
60#2621C2211yescharacteristic
61#2620C2212yes—
62#2620C2212yes—
63#2619C2211yescharacteristic
64#2619C2211yescharacteristic
65#2618C2212yes—
66#2618C2212yes—
67#2617C2212yes—
68#2617C2212yes—
69#2595C2218yescomplemented
70#2588C2218yescomplemented
71#2575C2218yes—
72#2574C2218yescomplemented
73#2573C2218yescomplemented
74#2572C2218yes—
75#2570C2214yescomplemented
76#2570C2214yescomplemented
77#2569C2214yes—
78#2569C2214yes—
79#2563C2214yescomplemented
80#2557C2218yes—
81#2553C2218yes—
82#2547C2214yescomplemented
83#2528C2218yescomplemented
84#2527C2218yes—
85#2525C2218yescomplemented
86#2524C2218yescomplemented
87#2523C2218yes—
88#2521C2218yescomplemented
89#2520C2218yescomplemented
90#2517C2218yes—
91#2516C2218yes—
92#2516C2218yescomplemented
93#2510C2218yes—
94#2504C2214yes—
95#2498C2218yes—
96#2497C2214yescomplemented
97#2496C2214yescomplemented
98#2495C2214yescomplemented
99#2494C2214yescomplemented
100#2487C2214yes—
101#2486C2214yes—
102#2485C2214yes—
103#2485C2214yes—
104#2481C2218yes—
105#2474C2218yescomplemented
106#2471C2218yes—
107#2469C2218yescomplemented
108#2467C2218yes—
109#2459C2218yes—
110#2458C2218yes—
111#2436C2214yes—
112#2412C2218yes—
113#2401C2218yescomplemented
114#2398C2218yes—
115#2396C2218yescomplemented
116#2395C2218yes—
117C2×#400C2212yes—
118C2×#399C2212yes—
119#2392C2212yes—
120#2392C2212yes—
121#2392C2212yes—
122#2392C2212yes—
123C2×#395C2212yes—
124C2×#393C2212yes—
125#2369C2214yescomplemented
126#2365C2214yescomplemented
127#2364C2214yes—
128#2364C2214yes—
129#2359C2218yes—
130#2358C2218yes—
131#2354C2214yes—
132#2353C2218yes—
133#2352C2214yes—
134#2352C2214yes—
135#2352C2218yes—
136#2352C2214yescomplemented
137#2352C2214yescomplemented
138D4×C4⋊C4C2214yes—
139#2347C2214yescomplemented
140#2346C2214yescomplemented
141#2345C2214yes—
142#2345C2214yescomplemented
143#2344C2214yescomplemented
144Q8×C22⋊C4C2214yes—
145#2331C2212yescomplemented
146#2331C2212yescomplemented
147#2328C2212yescomplemented
148#2327C2212yescomplemented
149#2324C2214yes—
150#2323C2214yes—
151#2320C2214yescomplemented
152#2319C2214yescomplemented
153#2317C2212yes—
154#2316C2212yes—
155#2316C2212yes—
156#2311C2212yes—
157#2311C2212yes—
158#2311C2212yes—
159C4×C4⋊Q8C2214yescomplemented
160C4×#124C2214yescomplemented
161C4×C22⋊Q8C2214yes—
162C4×#121C2214yes—
163#2297C2212yes—
164#2295C2214yescomplemented
165#2293C2214yescomplemented
166C2×#389C2212yes—
167#2285C2211yescharacteristic
168C2×#382C2211yescharacteristic
169C2×#380C2212yes—
170#2274C2212yes—
171#2274C2212yes—
172#2274C2212yes—
173#2274C2212yes—
174#2274C2212yes—
175#2274C2212yes—
176#2274C2212yes—
177#2273C2212yes—
178#2273C2212yes—
179C4×#117C2211yescharacteristic
180C4×#117C2212yes—
181C4×#117C2211yescharacteristic
182C4×#117C2211yescharacteristic
183C4×#117C2212yes—
184C4×#117C2211yescharacteristic
185C4×#117C2212yes—
186C4×#117C2212yes—
187C22×#41C2312yes—
188C23×Q8C2312yes—
189C24×C4C2311yescharacteristic
190#532—28no—
191C2×C4⋊Q8—28no—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2311yescharacteristic
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×#127C2311yescharacteristic
198C2×#126C2318yes—
199C2×#124C2312yes—
200C2×#124C2318yes—
201#525—216no—
202C2×#123C2314yes—
203C2×#123C2318yes—
204C2×C22⋊Q8C2312yes—
205C2×C22⋊Q8C2312yes—
206C2×#121C2312yes—
207C2×#121C2312yes—
208C2×#121C2312yes—
209C2×#121C2312yes—
210C2×#120C2314yes—
211#520—216no—
212C2×C4×Q8C2314yes—
213C2×C4×Q8C2318yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2318yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2318yes—
221C2×#117—28no—
222C2×#117—28no—
223C2×#117—28no—
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2312yes—
228C2×#117C2312yes—
229C2×#117C2314yes—
230C2×#117C2312yes—
231C2×#117C2312yes—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2312yes—
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2318yes—
244C2×#117C2311yescharacteristic
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2314yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2314yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2311yescharacteristic
256C22×C22⋊C4C2311yescharacteristic
257C22×C22⋊C4C2312yes—
258C22×C22⋊C4C2314yes—
259C22×C42C2312yes—
260C22×C42C2311yescharacteristic
261C22×C42C2312yes—
262C22×C42C2311yescharacteristic
263#401C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2314yes—
267#400C2318yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2314yes—
272#400C2314yes—
273#400C2318yes—
274#399C2314yes—
275#399C2318yes—
276#399C2314yes—
277#399C2314yes—
278#399C2314yes—
279#398C2318yes—
280#398C2318yes—
281#398C2312yes—
282#398C2312yes—
283#398C2312yes—
284#398C2312yes—
285#398C2318yes—
286#397C2318yes—
287#397C2312yes—
288#397C2318yes—
289#397C2318yes—
290#397C2312yes—
291#397C2312yes—
292#397C2312yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#396C2314yes—
299#396C2314yes—
300#396C2314yes—
301#396C2314yes—
302#396C2318yes—
303#395C2314yes—
304#395C2314yes—
305#395C2314yes—
306#395C2314yes—
307#394C2314yes—
308#394C2312yes—
309#394C2314yes—
310#394C2314yes—
311#394C2314yes—
312#394C2312yes—
313#394C2312yes—
314#394C2312yes—
315#394C2318yes—
316#394C2318yes—
317#393C2318yes—
318#393C2318yes—
319#393C2314yes—
320#393C2314yes—
321#393C2314yes—
322#393C2314yes—
323#392C2312yes—
324#392C2312yes—
325#392C2312yes—
326#392C2312yes—
327#391C2318yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2312yes—
332#391C2318yes—
333#391C2318yes—
334#391C2318yes—
335#391C2312yes—
336#390C2318yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2312yes—
341#390C2318yes—
342#390C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2318yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
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#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
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#387C2318yes—
392#387C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2314yes—
401#386C2318yes—
402#386C2314yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#384C2312yes—
408#384C2314yes—
409#383C2318yes—
410#383C2318yes—
411#382C2318yes—
412#382C2314yes—
413#382C2312yes—
414#382C2312yes—
415#382C2318yes—
416#382C2312yes—
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2312yes—
420#381C2318yes—
421#381C2318yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2318yes—
429#380C2312yes—
430#380C2312yes—
431#380C2318yes—
432#380C2318yes—
433#380C2314yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2318yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2318yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2312yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2312yes—
475C4×C22⋊C4C2318yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486#376C2312yes—
487#376C2312yes—
488#376C2318yes—
489#376C2312yes—
490#376C2312yes—
491C2×#95C2312yes—
492C2×#95C2312yes—
493C2×#95C2314yes—
494C2×#95C2314yes—
495C43C2312yes—
496C43C2312yes—
497C43C2312yes—
498C43C2312yes—
499C25C2411yescharacteristic
500C2×#41—28no—
501C2×#41—28no—
502C2×#41—28no—
503C22×Q8—28no—
504C22×Q8—84no—
505C22×Q8C2412yes—
506C22×Q8C2414yes—
507C22×Q8C2414yes—
508C22×D4C2414yes—
509C22×D4C2412yes—
510C22×D4C2414yes—
511C22×D4C2414yes—
512C22×D4C2412yes—
513C22×D4C2412yes—
514C23×C4—24no—
515C23×C4—24no—
516C23×C4#4118yes—
517C23×C4C2414yes—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2414yes—
525C23×C4C2414yes—
526C23×C4C2414yes—
527C23×C4C2414yes—
528C23×C4C2411yescharacteristic
529C23×C4C2418yes—
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C4⋊Q8—28no—
534C4⋊Q8—28no—
535C4⋊Q8—28no—
536C4⋊Q8—28no—
537C4⋊Q8—24no—
538#127—24no—
539#126—88no—
540#124—28no—
541#124—88no—
542#123—216no—
543#123—88no—
544C22⋊Q8—28no—
545C22⋊Q8—28no—
546#121—28no—
547#121—28no—
548#121—28no—
549#121—28no—
550#120—216no—
551C4×Q8—216no—
552C4×Q8—88no—
553C4×D4—216no—
554C4×D4—216no—
555C4×D4—232no—
556C4×D4—216no—
557C4×D4—28no—
558C4×D4—28no—
559C4×D4—88no—
560#117—28no—
561#117—28no—
562#117—28no—
563#117—24no—
564#117—24no—
565#117—24no—
566#117—28no—
567#117—28no—
568#117—216no—
569#117—28no—
570#117—28no—
571#117—24no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117—24no—
576#117—24no—
577#117—24no—
578#117—24no—
579#117—88no—
580#117#4118yes—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—24no—
583C2×C4⋊C4—28no—
584C2×C4⋊C4—28no—
585C2×C4⋊C4—28no—
586C2×C4⋊C4—28no—
587C2×C4⋊C4—28no—
588C2×C4⋊C4—216no—
589C2×C4⋊C4—84no—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2412yes—
627C2×C22⋊C4—28no—
628C2×C22⋊C4—24no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4—28no—
631C2×C22⋊C4—84no—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2411yescharacteristic
637C2×C22⋊C4C2411yescharacteristic
638C2×C22⋊C4C2411yescharacteristic
639C2×C22⋊C4C2411yescharacteristic
640C2×C22⋊C4C2411yescharacteristic
641C2×C22⋊C4C2411yescharacteristic
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2411yescharacteristic
644C2×C22⋊C4C2411yescharacteristic
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2412yes—
666C2×C42—28no—
667C2×C42—24no—
668C2×C42—28no—
669C2×C42#4118yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2418yes—
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2418yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2412yes—
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696#95C2418yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2414yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2414yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2412yes—
730#95C2412yes—
731#95C2412yes—
732#95C2412yes—
733#95C2418yes—
734C24—22no—
735C24—22no—
736C24—42no—
737C24—42no—
738C24C2×#4114yes—
739C24C2514yes—
740C24C2511yescharacteristic
741C24C2511yescharacteristic
742C24C2511yescharacteristic
743#41—432no—
744C2×Q8—24no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—28no—
748C2×Q8—28no—
749C2×Q8—48no—
750C2×Q8—48no—
751C2×Q8—816no—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—28no—
756C2×D4—28no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—232no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—28no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—216no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—42no—
794C22×C4—44no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—48no—
800C22×C4—42no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4C2×#4114yes—
804C22×C4C2×#4114yes—
805C22×C4C2×#4114yes—
806C22×C4C2×#4114yes—
807C22×C4C2×#4114yes—
808C22×C4C2×#4114yes—
809C22×C4C2×#4114yes—
810C22×C4C2×#4114yes—
811C22×C4C2×#4114yes—
812C22×C4C2×#4114yes—
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2514yes—
816C22×C4C2518yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2518yes—
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C22×C4C2511yescharacteristic
827C22×C4C2514yes—
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—28no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—216no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4C2×#4118yes—
871C22⋊C4—28no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—22no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—22no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—216no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—48no—
897C22⋊C4—44no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4C2×#4118yes—
905C42—28no—
906C42—28no—
907C42—24no—
908C42—24no—
909C42—22no—
910C42—22no—
911C42—22no—
912C42—22no—
913C42—24no—
914C42—28no—
915C42—216no—
916C42—44no—
917C42—44no—
918C42—44no—
919C42—44no—
920C42—44no—
921C42—48no—
922C42—48no—
923C42—44no—
924C42—44no—
925C42—44no—
926C42C2×#4118yes—
927C42C2×#4114yes—
928C42C2×#4114yes—
929C42C2×#4114yes—
930C42C2×#4114yes—
931C23—22no—
932C23—22no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—28no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—48no—
950C23—82no—
951C23—84no—
952C23—82no—
953C23C22×#4112yes—
954C23C22×#4112yes—
955C23C22×#4112yes—
956C23C22×#4112yes—
957C23C22×#4112yes—
958C23C2611yescharacteristic
959Q8—416no—
960Q8—48no—
961Q8—88no—
962D4—416no—
963D4—416no—
964D4—48no—
965D4—84no—
966D4—84no—
967D4—88no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—24no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—28no—
979C2×C4—28no—
980C2×C4—28no—
981C2×C4—28no—
982C2×C4—28no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—28no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—28no—
1005C2×C4—28no—
1006C2×C4—28no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—28no—
1015C2×C4—44no—
1016C2×C4—44no—
1017C2×C4—416no—
1018C2×C4—88no—
1019C2×C4—816no—
1020C2×C4—82no—
1021C2×C4—88no—
1022C2×C4—88no—
1023C2×C4—82no—
1024C2×C4—88no—
1025C2×C4#529116yes—
1026C2×C4C22×#4112yes—
1027C2×C4C22×#4118yes—
1028C2×C4C22×#4112yes—
1029C2×C4C22×#4112yes—
1030C2×C4C22×#4112yes—
1031C2×C4C22×#4112yes—
1032C2×C4C22×#4112yes—
1033C2×C4C22×#4112yes—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4112yes—
1038C2×C4C22×#4112yes—
1039C22—22no—
1040C22—24no—
1041C22—24no—
1042C22—22no—
1043C22—24no—
1044C22—24no—
1045C22—22no—
1046C22—22no—
1047C22—41no—
1048C22—41no—
1049C22—42no—
1050C22—42no—
1051C22—41no—
1052C22—41no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—44no—
1058C22—44no—
1059C22—44no—
1060C22—88no—
1061C22C2×#52914yes—
1062C22C23×#4111yescharacteristic
1063C22C23×#4111yescharacteristic
1064C22C23×#4111yescharacteristic
1065C22H(7,𝔽2)12yes—
1066C222−1+612yes—
1067C4—22no—
1068C4—22no—
1069C4—28no—
1070C4—22no—
1071C4—22no—
1072C4—22no—
1073C4—22no—
1074C4—41no—
1075C4—41no—
1076C4—48no—
1077C4—44no—
1078C4—44no—
1079C4—44no—
1080C4—44no—
1081C4—44no—
1082C4—48no—
1083C4—41no—
1084C4—41no—
1085C4—44no—
1086C4C2×#52914yes—
1087C4C2×#52914yes—
1088C2—24no—
1089C2—42no—
1090C2—42no—
1091C2—84no—
1092C2C22×#52911yescharacteristic
1093C2#6285511yescharacteristic
1094C2#6285612yes—
1095C2#6285712yes—
1096C2#6286011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34633C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36034C2semidirect
2. #35837C2semidirect
3. #35833C2semidirect
4. #35828C2semidirect
5. #35774C2semidirect
6. #35770C2semidirect
7. #35742C2semidirect
8. #35706C2semidirect
9. #35339C2semidirect
10. #35324C2semidirect
11. #35314C2semidirect
12. #35296C2semidirect
13. #35290C2semidirect
14. #35289C2semidirect
15. #35268C2semidirect
16. #35267C2semidirect
17. #35263C2semidirect
19. #34619C2semidirect
20. C2×#2628C2semidirect
21. #34253C2semidirect
22. #34216C2semidirect
23. #34208C2semidirect
24. #34202C2semidirect
25. #33996C2semidirect
33. #2864C22semidirect
34. #2864C22semidirect
35. #2863C22semidirect
36. #2862C22semidirect
37. #2860C22semidirect
38. #2858C22semidirect
41. #2654C22semidirect
43. #2650C22semidirect
45. #2647C22semidirect
46. #2645C22semidirect
47. #2644C22semidirect
48. #2640C22semidirect
69. #2595C22semidirect
70. #2588C22semidirect
72. #2574C22semidirect
73. #2573C22semidirect
75. #2570C22semidirect
76. #2570C22semidirect
79. #2563C22semidirect
82. #2547C22semidirect
83. #2528C22semidirect
85. #2525C22semidirect
86. #2524C22semidirect
88. #2521C22semidirect
89. #2520C22semidirect
92. #2516C22semidirect
96. #2497C22semidirect
97. #2496C22semidirect
98. #2495C22semidirect
99. #2494C22semidirect
105. #2474C22semidirect
107. #2469C22semidirect
113. #2401C22semidirect
115. #2396C22semidirect
125. #2369C22semidirect
126. #2365C22semidirect
136. #2352C22semidirect
137. #2352C22semidirect
139. #2347C22semidirect
140. #2346C22semidirect
142. #2345C22semidirect
143. #2344C22semidirect
145. #2331C22semidirect
146. #2331C22semidirect
147. #2328C22semidirect
148. #2327C22semidirect
151. #2320C22semidirect
152. #2319C22semidirect
159. C4×C4⋊Q8C22semidirect
160. C4×#124C22semidirect
164. #2295C22semidirect
165. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#360342
#358372
#358332
#358282
#357742
#357702
#357422
#357062
#353392
#353242
#353142
#352962
#352902
#352892
#352682
#352672
#352632
#346332
#346192
C2×#26282
#342532
#342162
#342082
#342022
#339962