Finite Group Databasebeta

← #7643534

Subgroups — #7643534

Order 512.

4430 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39928C214yesmaximal, complemented
2#39927C214yesmaximal, complemented
3#39907C214yesmaximal, complemented
4#39901C214yesmaximal, complemented
5#38395C218yesmaximal, complemented
6#38389C218yesmaximal
7#37295C214yesmaximal, complemented
8#37291C214yesmaximal, complemented
9#36625C211yesmaximal, characteristic
10C2×#2851C211yesmaximal, characteristic
11#35585C212yesmaximal, complemented
12#35544C212yesmaximal
13#35544C212yesmaximal
14#35543C212yesmaximal, complemented
15#35339C211yesmaximal, characteristic, complemented
16#35335C211yesmaximal, characteristic, complemented
17#35142C214yesmaximal, complemented
18#35142C214yesmaximal, complemented
19#34217C211yesmaximal, characteristic, complemented
20#34215C211yesmaximal, characteristic, complemented
21#34012C211yesmaximal, characteristic
22C2×#533C2211yescharacteristic
23C22×#125C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2864C2214yescomplemented
26#2859C2212yescomplemented
27#2859C2212yescomplemented
28#2857C2212yes—
29#2857C2212yes—
30#2855C2214yes—
31#2851C2214yes—
32#2851C2214yes—
33#2851C2214yes—
34#2851C2214yes—
35#2851C2212yes—
36#2851C2212yes—
37#2848C2214yes—
38#2776C2218yescomplemented
39#2769C2218yescomplemented
40#2766C2218yescomplemented
41#2762C2218yescomplemented
42#2762C2218yescomplemented
43#2758C2218yescomplemented
44#2755C2218yescomplemented
45#2747C2218yes—
46#2744C2218yes—
47#2739C2218yes—
48#2722C2218yes—
49#2719C2218yescomplemented
50#2704C2218yes—
51#2698C2218yes—
52#2690C2218yes—
53#2689C2218yes—
54#2660C2214yescomplemented
55#2655C2218yescomplemented
56#2655C2218yescomplemented
57#2652C2218yes—
58#2652C2218yes—
59#2647C2212yescomplemented
60#2647C2212yescomplemented
61#2584C2214yescomplemented
62#2584C2214yescomplemented
63#2583C2218yes—
64#2571C2214yescomplemented
65#2570C2214yescomplemented
66#2570C2214yescomplemented
67#2570C2214yescomplemented
68#2570C2214yescomplemented
69#2569C2218yes—
70#2569C2218yes—
71#2552C2214yescomplemented
72#2533C2218yescomplemented
73#2533C2218yescomplemented
74#2528C2218yescomplemented
75#2528C2218yescomplemented
76#2509C2214yescomplemented
77#2509C2214yescomplemented
78#2509C2214yescomplemented
79#2508C2214yescomplemented
80#2508C2214yescomplemented
81#2508C2214yescomplemented
82#2507C2214yescomplemented
83#2507C2214yescomplemented
84#2507C2214yescomplemented
85#2506C2214yescomplemented
86#2506C2214yescomplemented
87#2506C2214yescomplemented
88#2505C2218yes—
89#2497C2214yes—
90#2497C2214yes—
91#2497C2214yes—
92#2497C2214yes—
93#2496C2214yes—
94#2496C2214yes—
95#2496C2214yes—
96#2496C2214yes—
97#2495C2214yes—
98#2495C2214yes—
99#2495C2214yes—
100#2495C2214yes—
101#2494C2214yes—
102#2494C2214yes—
103#2494C2214yes—
104#2494C2214yes—
105#2493C2218yes—
106#2493C2218yes—
107#2480C2218yes—
108#2480C2218yes—
109#2478C2218yes—
110#2478C2218yes—
111#2475C2218yes—
112#2475C2218yes—
113#2473C2218yes—
114#2442C2218yes—
115#2370C2214yescomplemented
116#2370C2214yescomplemented
117#2368C2218yes—
118#2355C2214yescomplemented
119#2355C2214yescomplemented
120#2345C2218yes—
121#2336C2218yescomplemented
122#2336C2218yescomplemented
123#2334C2218yes—
124#2334C2218yes—
125#2331C2214yescomplemented
126#2330C2212yescomplemented
127#2330C2212yescomplemented
128#2317C2212yes—
129#2317C2212yes—
130#2317C2212yes—
131#2317C2212yes—
132#2316C2212yes—
133#2316C2212yes—
134C4×#125C2212yescomplemented
135C4×#125C2212yescomplemented
136C4×#125C2214yescomplemented
137C4×C22⋊Q8C2214yes—
138C4×C22⋊Q8C2214yes—
139#2296C2212yes—
140C2×#389C2212yes—
141C2×#387C2214yes—
142C2×#385C2214yes—
143#2285C2211yescharacteristic
144#2285C2211yescharacteristic
145#2285C2211yescharacteristic
146#2285C2212yes—
147#2285C2212yes—
148#2283C2214yes—
149#2283C2212yes—
150#2283C2212yes—
151#2283C2214yes—
152C2×#382C2211yescharacteristic
153#2280C2212yes—
154#2280C2211yescharacteristic
155#2280C2211yescharacteristic
156#2280C2214yes—
157C2×#380C2212yes—
158#2274C2212yes—
159#2274C2212yes—
160C4×#117C2211yescharacteristic
161C4×#117C2214yes—
162C4×#117C2211yescharacteristic
163C24×C4C2311yescharacteristic
164C24×C4C2312yes—
165#533—28no—
166C2×C4⋊Q8C2312yes—
167C2×#126C2318yes—
168C2×#126C2318yes—
169C2×#125—28no—
170C2×#125C2312yes—
171C2×#125C2311yescharacteristic
172C2×#125C2311yescharacteristic
173C2×#125C2314yes—
174C2×#125C2312yes—
175C2×#125C2318yes—
176C2×#125C2318yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×C4×Q8C2314yes—
181C2×#117C2311yescharacteristic
182C2×#117C2312yes—
183C2×#117C2311yescharacteristic
184C2×#117C2311yescharacteristic
185C2×#117C2312yes—
186C2×#117C2311yescharacteristic
187C2×#117C2314yes—
188C2×#117C2314yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2314yes—
192C22×C4⋊C4C2314yes—
193C22×C22⋊C4C2314yes—
194C22×C42—28no—
195C22×C42C2312yes—
196C22×C42C2312yes—
197C22×C42C2312yes—
198C22×C42C2312yes—
199C22×C42C2312yes—
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202#401C2318yes—
203#401C2318yes—
204#400C2318yes—
205#400C2318yes—
206#400C2318yes—
207#400C2318yes—
208#400C2318yes—
209#400C2318yes—
210#400C2318yes—
211#400C2318yes—
212#400C2318yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#398C2318yes—
221#398C2318yes—
222#398C2318yes—
223#398C2318yes—
224#398C2318yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#397C2318yes—
233#397C2318yes—
234#397C2318yes—
235#397C2318yes—
236#397C2318yes—
237#397C2318yes—
238#396C2318yes—
239#396C2318yes—
240#395C2318yes—
241#395C2318yes—
242#391C2318yes—
243#391C2318yes—
244#391C2314yes—
245#391C2314yes—
246#389C2314yes—
247#389C2314yes—
248#389C2314yes—
249#389C2314yes—
250#389C2314yes—
251#389C2314yes—
252#389C2314yes—
253#389C2314yes—
254#389C2314yes—
255#389C2314yes—
256#389C2318yes—
257#389C2314yes—
258#389C2314yes—
259#389C2314yes—
260#389C2314yes—
261#389C2314yes—
262#389C2314yes—
263#389C2314yes—
264#389C2314yes—
265#389C2318yes—
266#389C2318yes—
267#389C2318yes—
268#389C2318yes—
269#389C2318yes—
270#389C2318yes—
271#389C2318yes—
272#389C2318yes—
273#389C2318yes—
274#389C2314yes—
275#389C2314yes—
276#389C2312yes—
277#389C2312yes—
278#389C2312yes—
279#389C2312yes—
280#389C2314yes—
281#389C2314yes—
282#388C2318yes—
283#388C2318yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#388C2318yes—
288#387C2318yes—
289#387C2318yes—
290#387C2318yes—
291#387C2318yes—
292#387C2318yes—
293#387C2318yes—
294#387C2318yes—
295#387C2318yes—
296#387C2318yes—
297#387C2318yes—
298#387C2318yes—
299#387C2318yes—
300#387C2318yes—
301#387C2318yes—
302#387C2318yes—
303#387C2318yes—
304#387C2318yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2314yes—
310#387C2314yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2314yes—
321#387C2314yes—
322#385C2318yes—
323#385C2314yes—
324#385C2318yes—
325#385C2318yes—
326#385C2318yes—
327#385C2314yes—
328#385C2314yes—
329#385C2318yes—
330#385C2314yes—
331#385C2314yes—
332#385C2314yes—
333#385C2318yes—
334#385C2318yes—
335#385C2318yes—
336#384C2314yes—
337#384C2312yes—
338#384C2314yes—
339#384C2314yes—
340#384C2314yes—
341#384C2311yescharacteristic
342#384C2311yescharacteristic
343#384C2311yescharacteristic
344#384C2311yescharacteristic
345#383C2318yes—
346#383C2318yes—
347#383C2314yes—
348#383C2314yes—
349#382C2312yes—
350#382C2312yes—
351#382C2314yes—
352#382C2312yes—
353#382C2314yes—
354#382C2314yes—
355#382C2318yes—
356#382C2314yes—
357#382C2314yes—
358#382C2312yes—
359#382C2318yes—
360#382C2314yes—
361#382C2314yes—
362#382C2311yescharacteristic
363#382C2311yescharacteristic
364#381C2314yes—
365#381C2314yes—
366#381C2314yes—
367#381C2312yes—
368#381C2312yes—
369#380C2318yes—
370#380C2314yes—
371#380C2314yes—
372#380C2318yes—
373#380C2314yes—
374#380C2314yes—
375#380C2314yes—
376#380C2314yes—
377#380C2314yes—
378#380C2314yes—
379#380C2312yes—
380#380C2312yes—
381#380C2312yes—
382#380C2312yes—
383#380C2314yes—
384#380C2314yes—
385#380C2314yes—
386#380C2312yes—
387#380C2312yes—
388#380C2312yes—
389#380C2312yes—
390#379C2314yes—
391#379C2312yes—
392#379C2312yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2318yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2318yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426#376C2312yes—
427#376C2312yes—
428#376C2314yes—
429#376C2314yes—
430C2×#95C2314yes—
431C2×#95C2314yes—
432C2×#95C2314yes—
433C43C2312yes—
434C43C2312yes—
435C25C2411yescharacteristic
436C22×Q8C2414yes—
437C23×C4—28no—
438C23×C4—24no—
439C23×C4—24no—
440C23×C4—24no—
441C23×C4—44no—
442C23×C4—44no—
443C23×C4C2412yes—
444C23×C4C2411yescharacteristic
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2414yes—
451C23×C4C2414yes—
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C4⋊Q8—28no—
456#126—416no—
457#126—416no—
458#125—216no—
459#125—28no—
460#125—28no—
461#125—24no—
462#125—24no—
463#125—416no—
464#125—416no—
465C22⋊Q8—216no—
466C22⋊Q8—48no—
467C22⋊Q8—48no—
468C4×Q8—216no—
469#117—28no—
470#117—24no—
471#117—24no—
472#117—24no—
473#117—28no—
474#117—24no—
475#117—48no—
476#117—48no—
477C2×C4⋊C4—216no—
478C2×C4⋊C4—28no—
479C2×C4⋊C4—28no—
480C2×C4⋊C4—48no—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C2418yes—
484C2×C4⋊C4C2418yes—
485C2×C4⋊C4C2418yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2414yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2411yescharacteristic
494C2×C4⋊C4C2411yescharacteristic
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2411yescharacteristic
497C2×C4⋊C4C2411yescharacteristic
498C2×C4⋊C4C2412yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C22⋊C4—48no—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C2414yes—
528C2×C22⋊C4C2414yes—
529C2×C22⋊C4C2412yes—
530C2×C22⋊C4C2412yes—
531C2×C22⋊C4C2412yes—
532C2×C22⋊C4C2414yes—
533C2×C22⋊C4C2412yes—
534C2×C22⋊C4C2414yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2414yes—
541C2×C42—28no—
542C2×C42—24no—
543C2×C42—28no—
544C2×C42—28no—
545C2×C42—28no—
546C2×C42—28no—
547C2×C42#4118yes—
548C2×C42C2414yes—
549C2×C42C2412yes—
550C2×C42C2412yes—
551C2×C42C2412yes—
552C2×C42C2412yes—
553C2×C42C2414yes—
554C2×C42C2412yes—
555C2×C42C2411yescharacteristic
556C2×C42C2411yescharacteristic
557C2×C42C2412yes—
558C2×C42C2412yes—
559C2×C42C2412yes—
560C2×C42C2412yes—
561C2×C42C2414yes—
562C2×C42C2414yes—
563C2×C42C2414yes—
564C2×C42C2414yes—
565C2×C42C2418yes—
566C2×C42C2418yes—
567C2×C42C2418yes—
568C2×C42C2418yes—
569C2×C42C2412yes—
570C2×C42C2411yescharacteristic
571C2×C42C2411yescharacteristic
572#95C2418yes—
573#95C2418yes—
574#95C2418yes—
575#95C2418yes—
576#95C2418yes—
577#95C2418yes—
578#95C2414yes—
579#95C2414yes—
580#95C2414yes—
581#95C2414yes—
582#95C2414yes—
583#95C2414yes—
584#95C2414yes—
585#95C2414yes—
586#95C2414yes—
587#95C2414yes—
588#95C2414yes—
589#95C2414yes—
590#95C2418yes—
591#95C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2418yes—
602#95C2418yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616C24—22no—
617C24—24no—
618C24—22no—
619C24—22no—
620C24—42no—
621C24C2512yes—
622C24C2511yescharacteristic
623C2×Q8—28no—
624C2×Q8—44no—
625C2×Q8—44no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—28no—
635C22×C4—28no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—432no—
659C22×C4—416no—
660C22×C4C2×#4118yes—
661C22×C4C2×#4114yes—
662C22×C42−1+414yes—
663C22×C42−1+414yes—
664C22×C4C2512yes—
665C22×C4C2512yes—
666C22×C4C2518yes—
667C22×C4C2512yes—
668C22×C4C2514yes—
669C22×C4C2512yes—
670C22×C4C2514yes—
671C22×C4C2514yes—
672C22×C4C2512yes—
673C22×C4C2514yes—
674C22×C4C2512yes—
675C22×C4C2514yes—
676C22×C4C2514yes—
677C22×C4C2518yes—
678C22×C4C2512yes—
679C22×C4C2512yes—
680C22×C4C2512yes—
681C22×C4C2511yescharacteristic
682C22×C4C2511yescharacteristic
683C4⋊C4—216no—
684C4⋊C4—216no—
685C4⋊C4—28no—
686C4⋊C4—28no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—28no—
690C4⋊C4—28no—
691C4⋊C4—28no—
692C4⋊C4—28no—
693C4⋊C4—28no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—24no—
698C4⋊C4—22no—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—24no—
702C4⋊C4—216no—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—28no—
706C4⋊C4—28no—
707C4⋊C4—48no—
708C4⋊C4—44no—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—44no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C4⋊C4—48no—
715C4⋊C4—48no—
716C4⋊C4—48no—
717C4⋊C4—48no—
718C4⋊C4—48no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—48no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—48no—
726C22⋊C4—28no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—28no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—216no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—28no—
736C22⋊C4—28no—
737C22⋊C4—48no—
738C22⋊C4—44no—
739C22⋊C4—44no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C42—22no—
743C42—24no—
744C42—24no—
745C42—24no—
746C42—24no—
747C42—24no—
748C42—22no—
749C42—28no—
750C42—24no—
751C42—24no—
752C42—24no—
753C42—24no—
754C42—28no—
755C42—44no—
756C42—44no—
757C42—44no—
758C42—44no—
759C42—48no—
760C42—48no—
761C42—48no—
762C42—48no—
763C42C2×#4118yes—
764C42C2×#4114yes—
765C42C2×#4114yes—
766C23—22no—
767C23—22no—
768C23—28no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—48no—
776C23—48no—
777C23—44no—
778C23—44no—
779C23C22×#4112yes—
780C23C2×2−1+412yes—
781C23C2×2−1+412yes—
782C23#58514yes—
783C23C2611yescharacteristic
784Q8—88no—
785C2×C4—216no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—28no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—28no—
817C2×C4—28no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—28no—
823C2×C4—28no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—48no—
831C2×C4—48no—
832C2×C4—48no—
833C2×C4—48no—
834C2×C4—48no—
835C2×C4—44no—
836C2×C4—48no—
837C2×C4—48no—
838C2×C4—88no—
839C2×C4—88no—
840C2×C4#541116yes—
841C2×C4C22×#4114yes—
842C2×C4C22×#4114yes—
843C2×C4C22×#4112yes—
844C2×C4C22×#4112yes—
845C2×C4C2×2−1+412yes—
846C2×C4C2×2−1+412yes—
847C2×C4C2×2−1+412yes—
848C2×C4C2×2−1+412yes—
849C2×C4#58514yes—
850C22—24no—
851C22—22no—
852C22—24no—
853C22—22no—
854C22—24no—
855C22—24no—
856C22—24no—
857C22—416no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22C2×#54114yes—
863C22C23×#4111yescharacteristic
864C22C22×2−1+411yescharacteristic
865C22C22×2−1+411yescharacteristic
866C22C2×#58512yes—
867C22C2×#58512yes—
868C4—24no—
869C4—24no—
870C4—24no—
871C4—42no—
872C4—48no—
873C4—44no—
874C4—44no—
875C4—42no—
876C4—44no—
877C4—42no—
878C4—44no—
879C4—44no—
880C4—48no—
881C4—42no—
882C4—44no—
883C4—42no—
884C4—42no—
885C4C2×#54114yes—
886C4C2×#54114yes—
887C2—24no—
888C2—44no—
889C2C22×#54111yescharacteristic
890C2#6281412yes—
891C2#6282511yescharacteristic
892C2#6283112yes—
893C2#6283811yescharacteristic
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. #39928C2semidirect
2. #39927C2semidirect
3. #39907C2semidirect
4. #39901C2semidirect
5. #38395C2semidirect
7. #37295C2semidirect
8. #37291C2semidirect
11. #35585C2semidirect
14. #35543C2semidirect
15. #35339C2semidirect
16. #35335C2semidirect
17. #35142C2semidirect
18. #35142C2semidirect
19. #34217C2semidirect
20. #34215C2semidirect
25. #2864C22semidirect
26. #2859C22semidirect
27. #2859C22semidirect
38. #2776C22semidirect
39. #2769C22semidirect
40. #2766C22semidirect
41. #2762C22semidirect
42. #2762C22semidirect
43. #2758C22semidirect
44. #2755C22semidirect
49. #2719C22semidirect
54. #2660C22semidirect
55. #2655C22semidirect
56. #2655C22semidirect
59. #2647C22semidirect
60. #2647C22semidirect
61. #2584C22semidirect
62. #2584C22semidirect
64. #2571C22semidirect
65. #2570C22semidirect
66. #2570C22semidirect
67. #2570C22semidirect
68. #2570C22semidirect
71. #2552C22semidirect
72. #2533C22semidirect
73. #2533C22semidirect
74. #2528C22semidirect
75. #2528C22semidirect
76. #2509C22semidirect
77. #2509C22semidirect
78. #2509C22semidirect
79. #2508C22semidirect
80. #2508C22semidirect
81. #2508C22semidirect
82. #2507C22semidirect
83. #2507C22semidirect
84. #2507C22semidirect
85. #2506C22semidirect
86. #2506C22semidirect
87. #2506C22semidirect
115. #2370C22semidirect
116. #2370C22semidirect
118. #2355C22semidirect
119. #2355C22semidirect
121. #2336C22semidirect
122. #2336C22semidirect
125. #2331C22semidirect
126. #2330C22semidirect
127. #2330C22semidirect
134. C4×#125C22semidirect
135. C4×#125C22semidirect
136. C4×#125C22semidirect

Maximal subgroups

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

subgroupindex
#399282
#399272
#399072
#399012
#383952
#383892
#372952
#372912
#366252
C2×#28512
#355852
#355442
#355432
#353392
#353352
#351422
#342172
#342152
#340122