Finite Group Databasebeta

← #7643458

Subgroups — #7643458

Order 512.

4432 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39603C214yesmaximal, complemented
2#39475C214yesmaximal, complemented
3#39153C214yesmaximal, complemented
4#38927C214yesmaximal, complemented
5#38075C214yesmaximal, complemented
6#38072C214yesmaximal, complemented
7#37859C214yesmaximal
8#37856C214yesmaximal
9#37383C212yesmaximal, complemented
10#37382C212yesmaximal, complemented
11#37381C212yesmaximal
12#37380C212yesmaximal
13#36625C212yesmaximal
14#35646C214yesmaximal, complemented
15#35645C214yesmaximal, complemented
16#35322C211yesmaximal, characteristic, complemented
17#35294C211yesmaximal, characteristic, complemented
18#35291C212yesmaximal, complemented
19#35291C212yesmaximal, complemented
20#35284C212yesmaximal, complemented
21#35283C212yesmaximal, complemented
22#34225C212yesmaximal, complemented
23#34012C211yesmaximal, characteristic
24C2×#533C2212yes—
25C23×C42C2211yescharacteristic
26#2868C2211yescharacteristic, complemented
27#2868C2211yescharacteristic, complemented
28#2862C2212yescomplemented
29#2862C2211yescharacteristic, complemented
30#2859C2212yescomplemented
31#2859C2211yescharacteristic, complemented
32#2857C2212yes—
33#2857C2212yes—
34#2857C2212yes—
35#2857C2212yes—
36#2855C2214yes—
37#2855C2214yes—
38#2851C2214yes—
39#2851C2214yes—
40#2848C2214yes—
41#2848C2214yes—
42#2794C2214yescomplemented
43#2792C2214yescomplemented
44#2791C2218yescomplemented
45#2789C2214yescomplemented
46#2788C2218yes—
47#2787C2218yes—
48#2771C2214yes—
49#2770C2218yes—
50#2769C2214yescomplemented
51#2768C2218yes—
52#2767C2218yescomplemented
53#2765C2218yes—
54#2764C2214yes—
55#2745C2218yes—
56#2744C2218yes—
57#2739C2218yes—
58#2738C2218yes—
59#2736C2214yes—
60#2735C2218yes—
61#2735C2214yes—
62#2647C2214yescomplemented
63#2647C2214yescomplemented
64#2645C2214yescomplemented
65#2645C2214yescomplemented
66#2629C2212yes—
67#2629C2214yes—
68#2628C2212yes—
69#2628C2214yes—
70#2625C2214yes—
71#2625C2214yes—
72#2621C2212yes—
73#2621C2212yes—
74#2577C2218yes—
75#2575C2218yes—
76#2574C2218yes—
77#2573C2218yes—
78#2570C2214yescomplemented
79#2565C2214yescomplemented
80#2565C2214yescomplemented
81#2550C2214yescomplemented
82#2533C2218yescomplemented
83#2530C2218yes—
84#2528C2218yescomplemented
85#2527C2218yes—
86#2524C2218yescomplemented
87#2524C2218yescomplemented
88#2524C2218yescomplemented
89#2522C2218yes—
90#2520C2218yescomplemented
91#2515C2218yes—
92#2514C2214yescomplemented
93#2514C2214yescomplemented
94#2514C2218yescomplemented
95#2511C2214yescomplemented
96#2511C2214yescomplemented
97#2509C2214yescomplemented
98#2509C2214yescomplemented
99#2508C2214yescomplemented
100#2508C2218yescomplemented
101#2508C2214yescomplemented
102#2507C2214yescomplemented
103#2507C2214yescomplemented
104#2499C2214yes—
105#2499C2214yes—
106#2497C2214yes—
107#2497C2214yes—
108#2495C2214yes—
109#2495C2214yes—
110#2494C2214yes—
111#2494C2214yes—
112#2492C2214yes—
113#2492C2214yes—
114#2489C2214yes—
115#2489C2214yes—
116#2453C2214yescomplemented
117#2453C2214yescomplemented
118#2451C2214yescomplemented
119#2451C2214yescomplemented
120#2446C2214yescomplemented
121#2446C2214yescomplemented
122#2441C2214yes—
123#2439C2214yes—
124#2429C2214yes—
125#2429C2214yes—
126#2423C2214yes—
127#2423C2214yes—
128#2421C2214yes—
129#2421C2214yes—
130#2370C2214yescomplemented
131#2370C2214yescomplemented
132#2362C2214yes—
133#2362C2214yes—
134#2356C2214yescomplemented
135#2351C2214yescomplemented
136#2347C2214yes—
137#2346C2214yes—
138#2331C2212yescomplemented
139#2331C2214yescomplemented
140#2330C2212yescomplemented
141#2330C2214yescomplemented
142#2327C2212yescomplemented
143#2327C2212yescomplemented
144#2323C2214yes—
145#2323C2214yes—
146#2323C2214yes—
147#2323C2214yes—
148#2320C2214yescomplemented
149#2320C2214yescomplemented
150#2320C2214yescomplemented
151#2314C2214yes—
152#2314C2214yes—
153C4×C4⋊Q8C2212yescomplemented
154C4×C4⋊Q8C2212yescomplemented
155C4×C4⋊Q8C2212yescomplemented
156C4×C4⋊Q8C2212yescomplemented
157C4×C22⋊Q8C2214yes—
158C4×C22⋊Q8C2214yes—
159C4×C22⋊Q8C2214yes—
160C4×C22⋊Q8C2214yes—
161#2296C2214yes—
162#2285C2211yescharacteristic
163#2285C2211yescharacteristic
164#2285C2212yes—
165#2285C2212yes—
166#2285C2212yes—
167#2283C2212yes—
168#2283C2212yes—
169#2283C2212yes—
170#2283C2212yes—
171#2283C2212yes—
172#2283C2212yes—
173#2280C2211yescharacteristic
174#2280C2211yescharacteristic
175#2280C2214yes—
176#2280C2212yes—
177#2280C2212yes—
178#2276C2214yescomplemented
179C4×#117C2211yescharacteristic
180C4×#117C2212yes—
181C4×#117C2212yes—
182C4×#117C2211yescharacteristic
183C24×C4C2312yes—
184C24×C4C2311yescharacteristic
185#533—216no—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2312yes—
192C2×#125C2314yes—
193C2×#125C2314yes—
194C2×#125C2312yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2314yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2314yes—
210C2×#117C2311yescharacteristic
211C2×#117C2311yescharacteristic
212C2×#117C2312yes—
213C2×#117C2312yes—
214C2×#117C2314yes—
215C2×#117C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C22×C42—28no—
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225#401C2318yes—
226#401C2318yes—
227#400C2314yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#399C2318yes—
242#399C2314yes—
243#398C2318yes—
244#398C2314yes—
245#398C2314yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2314yes—
260#397C2318yes—
261#397C2314yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#395C2318yes—
266#395C2314yes—
267#393C2318yes—
268#393C2314yes—
269#391C2314yes—
270#391C2314yes—
271#391C2314yes—
272#391C2314yes—
273#391C2314yes—
274#391C2314yes—
275#391C2314yes—
276#391C2314yes—
277#391C2318yes—
278#391C2314yes—
279#391C2314yes—
280#391C2314yes—
281#391C2318yes—
282#391C2318yes—
283#391C2314yes—
284#391C2314yes—
285#391C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2318yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2318yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2314yes—
306#389C2314yes—
307#389C2318yes—
308#389C2318yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#384C2312yes—
362#384C2312yes—
363#384C2314yes—
364#384C2314yes—
365#384C2314yes—
366#384C2312yes—
367#384C2312yes—
368#384C2311yescharacteristic
369#384C2311yescharacteristic
370#383C2318yes—
371#383C2318yes—
372#383C2318yes—
373#383C2312yes—
374#383C2312yes—
375#383C2312yes—
376#383C2312yes—
377#382C2314yes—
378#382C2314yes—
379#382C2314yes—
380#382C2314yes—
381#382C2318yes—
382#382C2318yes—
383#382C2318yes—
384#382C2312yes—
385#382C2312yes—
386#382C2312yes—
387#382C2312yes—
388#382C2312yes—
389#382C2311yescharacteristic
390#382C2312yes—
391#382C2312yes—
392#382C2312yes—
393#382C2311yescharacteristic
394#381C2312yes—
395#381C2312yes—
396#381C2318yes—
397#381C2311yescharacteristic
398#381C2312yes—
399#381C2312yes—
400#381C2311yescharacteristic
401#381C2312yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2312yes—
406#380C2312yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2312yes—
415#380C2312yes—
416#380C2312yes—
417#380C2312yes—
418#380C2312yes—
419#380C2312yes—
420#380C2312yes—
421#380C2312yes—
422#380C2312yes—
423#380C2312yes—
424#379C2318yes—
425#379C2311yescharacteristic
426#379C2312yes—
427#379C2311yescharacteristic
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2318yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2318yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2312yes—
460C4×C22⋊C4C2312yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2312yes—
469#376C2312yes—
470#376C2312yes—
471#376C2312yes—
472#376C2311yescharacteristic
473#376C2311yescharacteristic
474#376C2312yes—
475#376C2312yes—
476#376C2318yes—
477C43C2312yes—
478C43C2311yescharacteristic
479C43C2311yescharacteristic
480C25C2411yescharacteristic
481C22×Q8C2414yes—
482C22×Q8C2414yes—
483C22×Q8C2414yes—
484C23×C4—28no—
485C23×C4—24no—
486C23×C4—28no—
487C23×C4—44no—
488C23×C4—42no—
489C23×C4—42no—
490C23×C4C2412yes—
491C23×C4C2412yes—
492C23×C4C2412yes—
493C23×C4C2412yes—
494C23×C4C2412yes—
495C23×C4C2411yescharacteristic
496C23×C4C2412yes—
497C23×C4C2412yes—
498C23×C4C2412yes—
499C23×C4C2411yescharacteristic
500C4⋊Q8—28no—
501C4⋊Q8—28no—
502C4⋊Q8—48no—
503C4⋊Q8—44no—
504C4⋊Q8—44no—
505C4⋊Q8—44no—
506#125—216no—
507#125—48no—
508#125—44no—
509C22⋊Q8—216no—
510C22⋊Q8—216no—
511C22⋊Q8—216no—
512C22⋊Q8—48no—
513C22⋊Q8—48no—
514C22⋊Q8—48no—
515C4×Q8—216no—
516C4×Q8—216no—
517C4×Q8—48no—
518C4×Q8—48no—
519C4×Q8—48no—
520C4×Q8—48no—
521#117—216no—
522#117—28no—
523#117—28no—
524#117—42no—
525#117—42no—
526#117—44no—
527#117—44no—
528#117—42no—
529#117—42no—
530#117—48no—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2411yescharacteristic
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2411yescharacteristic
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2411yescharacteristic
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2412yes—
580C2×C22⋊C4C2411yescharacteristic
581C2×C22⋊C4C2411yescharacteristic
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2412yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2411yescharacteristic
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2411yescharacteristic
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C42—28no—
594C2×C42—24no—
595C2×C42—28no—
596C2×C42—28no—
597C2×C42—28no—
598C2×C42—28no—
599C2×C42#4118yes—
600C2×C42C2412yes—
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2412yes—
604C2×C42C2418yes—
605C2×C42C2412yes—
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2412yes—
610C2×C42C2411yescharacteristic
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2412yes—
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2418yes—
623C2×C42C2418yes—
624C2×C42C2418yes—
625C2×C42C2418yes—
626C2×C42C2418yes—
627C2×C42C2411yescharacteristic
628C2×C42C2412yes—
629C2×C42C2411yescharacteristic
630#95C2412yes—
631#95C2412yes—
632#95C2412yes—
633#95C2412yes—
634#95C2412yes—
635#95C2412yes—
636#95C2412yes—
637#95C2412yes—
638#95C2412yes—
639#95C2412yes—
640#95C2412yes—
641#95C2412yes—
642#95C2412yes—
643#95C2412yes—
644#95C2412yes—
645#95C2412yes—
646#95C2412yes—
647#95C2412yes—
648#95C2412yes—
649#95C2412yes—
650#95C2412yes—
651#95C2412yes—
652#95C2412yes—
653#95C2412yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2414yes—
675#95C2414yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2414yes—
682#95C2414yes—
683C24—22no—
684C24—24no—
685C24—42no—
686C24—41no—
687C24—41no—
688C24C2511yescharacteristic
689C24C2512yes—
690C2×Q8—28no—
691C2×Q8—28no—
692C2×Q8—28no—
693C2×Q8—28no—
694C2×Q8—28no—
695C2×Q8—28no—
696C2×Q8—48no—
697C2×Q8—44no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—22no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—41no—
724C22×C4—41no—
725C22×C4—432no—
726C22×C4—416no—
727C22×C4C2×#4118yes—
728C22×C4C2×#4114yes—
729C22×C42−1+418yes—
730C22×C4C2512yes—
731C22×C4C2512yes—
732C22×C4C2511yescharacteristic
733C22×C4C2511yescharacteristic
734C22×C4C2511yescharacteristic
735C22×C4C2512yes—
736C22×C4C2518yes—
737C22×C4C2512yes—
738C22×C4C2512yes—
739C22×C4C2512yes—
740C22×C4C2512yes—
741C22×C4C2518yes—
742C22×C4C2518yes—
743C22×C4C2518yes—
744C22×C4C2512yes—
745C22×C4C2511yescharacteristic
746C22×C4C2512yes—
747C22×C4C2511yescharacteristic
748C22×C4C2512yes—
749C22×C4C2512yes—
750C22×C4C2511yescharacteristic
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—216no—
754C4⋊C4—216no—
755C4⋊C4—28no—
756C4⋊C4—28no—
757C4⋊C4—24no—
758C4⋊C4—24no—
759C4⋊C4—24no—
760C4⋊C4—24no—
761C4⋊C4—28no—
762C4⋊C4—216no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—41no—
769C4⋊C4—42no—
770C4⋊C4—42no—
771C4⋊C4—42no—
772C4⋊C4—41no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4—48no—
782C4⋊C4—48no—
783C4⋊C4—48no—
784C4⋊C4—48no—
785C4⋊C4—48no—
786C4⋊C4—48no—
787C4⋊C4—48no—
788C4⋊C4—48no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—48no—
792C4⋊C4—44no—
793C22⋊C4—216no—
794C22⋊C4—24no—
795C22⋊C4—24no—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—216no—
799C22⋊C4—41no—
800C22⋊C4—42no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—41no—
807C22⋊C4—42no—
808C22⋊C4—41no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C42—22no—
814C42—24no—
815C42—24no—
816C42—24no—
817C42—24no—
818C42—22no—
819C42—24no—
820C42—216no—
821C42—24no—
822C42—24no—
823C42—24no—
824C42—24no—
825C42—24no—
826C42—24no—
827C42—24no—
828C42—24no—
829C42—22no—
830C42—24no—
831C42—22no—
832C42—22no—
833C42—22no—
834C42—24no—
835C42—48no—
836C42—48no—
837C42—48no—
838C42—48no—
839C42—48no—
840C42C2×#4114yes—
841C42C2×#4118yes—
842C42C2×#4114yes—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—21no—
852C23—21no—
853C23—48no—
854C23—44no—
855C23—44no—
856C23—48no—
857C23—44no—
858C23C22×#4112yes—
859C23C2×2−1+414yes—
860C23C2611yescharacteristic
861Q8—416no—
862Q8—416no—
863Q8—164no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—28no—
871C2×C4—216no—
872C2×C4—216no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—28no—
876C2×C4—28no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—28no—
886C2×C4—28no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—21no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—28no—
907C2×C4—28no—
908C2×C4—28no—
909C2×C4—28no—
910C2×C4—28no—
911C2×C4—28no—
912C2×C4—28no—
913C2×C4—28no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—48no—
918C2×C4—48no—
919C2×C4—48no—
920C2×C4—48no—
921C2×C4—44no—
922C2×C4—48no—
923C2×C4—48no—
924C2×C4C22×#4114yes—
925C2×C4C22×#4112yes—
926C2×C4C22×#4112yes—
927C2×C4C22×#4114yes—
928C2×C4C2×2−1+414yes—
929C2×C4C2×2−1+414yes—
930C2×C4#58512yes—
931C2×C4#58512yes—
932C2×C4#58514yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—22no—
938C22—416no—
939C22—42no—
940C22—41no—
941C22—42no—
942C22—42no—
943C22—41no—
944C22—42no—
945C22—42no—
946C22C23×#4111yescharacteristic
947C22C22×2−1+412yes—
948C22C2×#58512yes—
949C22C2×#58511yescharacteristic
950C22C2×#58511yescharacteristic
951C4—24no—
952C4—24no—
953C4—22no—
954C4—42no—
955C4—48no—
956C4—42no—
957C4—41no—
958C4—41no—
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—48no—
964C4—42no—
965C4—41no—
966C4—48no—
967C4—41no—
968C4—42no—
969C4—48no—
970C4#345514yes—
971C4#349518yes—
972C2—42no—
973C2—44no—
974C2C2×#345511yescharacteristic
975C2C2×#349512yes—
976C2#6283711yescharacteristic
977C2#6283812yes—
978C2#6283911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39603C2semidirect
2. #39475C2semidirect
3. #39153C2semidirect
4. #38927C2semidirect
5. #38075C2semidirect
6. #38072C2semidirect
9. #37383C2semidirect
10. #37382C2semidirect
14. #35646C2semidirect
15. #35645C2semidirect
16. #35322C2semidirect
17. #35294C2semidirect
18. #35291C2semidirect
19. #35291C2semidirect
20. #35284C2semidirect
21. #35283C2semidirect
22. #34225C2semidirect
26. #2868C22semidirect
27. #2868C22semidirect
28. #2862C22semidirect
29. #2862C22semidirect
30. #2859C22semidirect
31. #2859C22semidirect
42. #2794C22semidirect
43. #2792C22semidirect
44. #2791C22semidirect
45. #2789C22semidirect
50. #2769C22semidirect
52. #2767C22semidirect
62. #2647C22semidirect
63. #2647C22semidirect
64. #2645C22semidirect
65. #2645C22semidirect
78. #2570C22semidirect
79. #2565C22semidirect
80. #2565C22semidirect
81. #2550C22semidirect
82. #2533C22semidirect
84. #2528C22semidirect
86. #2524C22semidirect
87. #2524C22semidirect
88. #2524C22semidirect
90. #2520C22semidirect
92. #2514C22semidirect
93. #2514C22semidirect
94. #2514C22semidirect
95. #2511C22semidirect
96. #2511C22semidirect
97. #2509C22semidirect
98. #2509C22semidirect
99. #2508C22semidirect
100. #2508C22semidirect
101. #2508C22semidirect
102. #2507C22semidirect
103. #2507C22semidirect
116. #2453C22semidirect
117. #2453C22semidirect
118. #2451C22semidirect
119. #2451C22semidirect
120. #2446C22semidirect
121. #2446C22semidirect
130. #2370C22semidirect
131. #2370C22semidirect
134. #2356C22semidirect
135. #2351C22semidirect
138. #2331C22semidirect
139. #2331C22semidirect
140. #2330C22semidirect
141. #2330C22semidirect
142. #2327C22semidirect
143. #2327C22semidirect
148. #2320C22semidirect
149. #2320C22semidirect
150. #2320C22semidirect
153. C4×C4⋊Q8C22semidirect
154. C4×C4⋊Q8C22semidirect
155. C4×C4⋊Q8C22semidirect
156. C4×C4⋊Q8C22semidirect
178. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#396032
#394752
#391532
#389272
#380752
#380722
#378592
#378562
#373832
#373822
#373812
#373802
#366252
#356462
#356452
#353222
#352942
#352912
#352842
#352832
#342252
#340122