Finite Group Databasebeta

← #7649967

Subgroups — #7649967

Order 512.

5344 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42718C214yesmaximal, complemented
2#42615C214yesmaximal, complemented
3#42601C214yesmaximal, complemented
4#42577C214yesmaximal, complemented
5#40639C218yesmaximal, complemented
6#40144C214yesmaximal, complemented
7#40077C214yesmaximal, complemented
8#39400C214yesmaximal, complemented
9#39021C214yesmaximal, complemented
10#37880C214yesmaximal, complemented
11#37692C214yesmaximal, complemented
12#35555C212yesmaximal, complemented
13#35544C212yesmaximal, complemented
14#35540C212yesmaximal, complemented
15#35253C212yesmaximal, complemented
16#35174C211yesmaximal, characteristic, complemented
17C2×#2537C211yesmaximal, characteristic
18#34809C212yesmaximal, complemented
19#34248C211yesmaximal, characteristic, complemented
20#34204C212yesmaximal, complemented
21C2×#544C2211yescharacteristic
22C2×#539C2214yescomplemented
23C22×#121C2212yes—
24C22×#121C2212yes—
25C2×#518C2211yescharacteristic
26C2×#518C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×#117C2212yes—
30#2857C2214yescomplemented
31#2851C2214yescomplemented
32#2848C2214yes—
33#2827C2218yescomplemented
34#2827C2218yescomplemented
35#2787C2218yescomplemented
36#2770C2218yescomplemented
37#2747C2218yescomplemented
38#2746C2218yescomplemented
39#2743C2218yescomplemented
40#2740C2218yescomplemented
41#2737C2218yescomplemented
42#2711C2218yescomplemented
43#2708C2218yescomplemented
44#2707C2218yescomplemented
45#2695C2218yescomplemented
46#2694C2218yescomplemented
47#2691C2218yescomplemented
48#2690C2218yescomplemented
49#2687C2218yescomplemented
50#2681C2218yescomplemented
51#2653C2218yescomplemented
52#2649C2218yescomplemented
53#2646C2214yescomplemented
54#2639C2214yescomplemented
55#2638C2218yescomplemented
56#2633C2218yescomplemented
57#2629C2214yescomplemented
58#2628C2214yescomplemented
59#2627C2214yescomplemented
60#2626C2214yes—
61#2618C2214yescomplemented
62#2570C2214yescomplemented
63#2570C2214yescomplemented
64#2552C2214yescomplemented
65#2552C2214yescomplemented
66#2537C2214yes—
67#2537C2214yes—
68#2537C2214yes—
69#2537C2214yes—
70#2507C2214yescomplemented
71#2507C2214yescomplemented
72#2506C2214yescomplemented
73#2506C2214yescomplemented
74#2497C2214yescomplemented
75#2497C2214yescomplemented
76#2496C2214yescomplemented
77#2496C2214yescomplemented
78#2495C2214yescomplemented
79#2495C2214yescomplemented
80#2494C2214yescomplemented
81#2494C2214yescomplemented
82#2493C2218yes—
83#2493C2218yescomplemented
84#2487C2212yescomplemented
85#2487C2212yescomplemented
86#2486C2212yescomplemented
87#2486C2212yescomplemented
88#2485C2212yescomplemented
89#2485C2212yescomplemented
90#2485C2212yescomplemented
91#2485C2212yescomplemented
92#2484C2214yes—
93#2483C2214yes—
94#2483C2218yes—
95#2482C2214yes—
96#2480C2218yes—
97#2473C2218yes—
98#2473C2218yes—
99#2473C2218yescomplemented
100#2466C2218yescomplemented
101#2460C2218yescomplemented
102#2454C2214yescomplemented
103#2454C2214yescomplemented
104#2452C2214yescomplemented
105#2452C2214yescomplemented
106#2443C2218yescomplemented
107#2442C2214yescomplemented
108#2441C2214yescomplemented
109#2440C2214yescomplemented
110#2439C2214yescomplemented
111#2438C2218yes—
112#2437C2218yes—
113#2425C2218yescomplemented
114#2422C2214yescomplemented
115#2422C2214yescomplemented
116#2422C2214yescomplemented
117#2422C2214yescomplemented
118#2420C2214yescomplemented
119#2420C2214yescomplemented
120#2420C2214yescomplemented
121#2420C2214yescomplemented
122#2405C2214yes—
123#2405C2218yes—
124#2395C2214yescomplemented
125#2395C2214yescomplemented
126C2×#394C2214yes—
127#2363C2214yescomplemented
128#2363C2214yescomplemented
129#2361C2214yescomplemented
130#2361C2214yescomplemented
131#2349C2214yescomplemented
132#2349C2214yescomplemented
133D4×C4⋊C4C2214yescomplemented
134D4×C4⋊C4C2214yescomplemented
135#2342C2218yes—
136D4×C22⋊C4C2218yes—
137#2329C2214yescomplemented
138#2325C2214yescomplemented
139#2324C2214yescomplemented
140#2324C2214yescomplemented
141#2317C2212yes—
142#2317C2212yes—
143#2317C2212yes—
144#2316C2211yescharacteristic
145#2316C2212yes—
146#2315C2214yes—
147#2313C2214yescomplemented
148#2309C2212yes—
149C4×#123C2214yescomplemented
150C4×#123C2214yescomplemented
151C4×#121C2214yescomplemented
152C4×#121C2214yescomplemented
153#2296C2212yes—
154#2296C2212yes—
155C2×#385C2214yes—
156C2×#384C2211yescharacteristic
157#2280C2212yes—
158#2280C2212yes—
159#2280C2212yes—
160C2×#380C2212yes—
161C2×#380C2212yes—
162#2274C2212yes—
163C23×D4C2311yescharacteristic
164C23×D4C2311yescharacteristic
165C23×D4C2314yes—
166C24×C4C2312yes—
167C24×C4C2312yes—
168#544—44no—
169#539—416no—
170C2×C4⋊Q8C2314yes—
171C2×#126C2318yes—
172C2×#125C2314yes—
173C2×#125C2318yes—
174C2×#125C2318yes—
175C2×#123C2314yes—
176C2×#123C2318yes—
177C2×#123C2314yes—
178C2×#123C2318yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2318yes—
183C2×#121—216no—
184C2×#121—48no—
185C2×#121C2314yes—
186C2×#121C2314yes—
187C2×#121C2314yes—
188C2×#121C2314yes—
189C2×#121C2314yes—
190C2×#121C2314yes—
191C2×#121C2318yes—
192#518—28no—
193#518—44no—
194C2×C4×D4—44no—
195C2×C4×D4—44no—
196C2×C4×D4C2314yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2318yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2312yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2318yes—
208C2×#117—48no—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2314yes—
214C2×#117C2314yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2312yes—
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2314yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C22⋊C4C2314yes—
227C22×C22⋊C4C2314yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2314yes—
230C22×C22⋊C4C2314yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2314yes—
233C22×C42C2311yescharacteristic
234C22×C42C2314yes—
235#401C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2314yes—
242#400C2318yes—
243#400C2314yes—
244#399C2314yes—
245#399C2318yes—
246#399C2318yes—
247#399C2314yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2314yes—
255#398C2318yes—
256#398C2318yes—
257#398C2314yes—
258#397C2314yes—
259#397C2314yes—
260#397C2314yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2314yes—
266#397C2318yes—
267#397C2314yes—
268#397C2318yes—
269#397C2314yes—
270#397C2318yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#396C2318yes—
276#395C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2314yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2314yes—
285#394C2318yes—
286#394C2318yes—
287#394C2314yes—
288#394C2314yes—
289#393C2318yes—
290#393C2318yes—
291#391C2318yes—
292#390C2314yes—
293#390C2314yes—
294#390C2314yes—
295#390C2314yes—
296#390C2318yes—
297#390C2318yes—
298#389C2312yes—
299#389C2312yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2318yes—
313#389C2318yes—
314#389C2312yes—
315#389C2312yes—
316#389C2318yes—
317#389C2312yes—
318#389C2312yes—
319#389C2312yes—
320#389C2312yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2314yes—
327#388C2318yes—
328#388C2314yes—
329#388C2318yes—
330#388C2314yes—
331#388C2314yes—
332#387C2314yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2314yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2314yes—
344#387C2314yes—
345#386C2318yes—
346#386C2318yes—
347#386C2314yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2314yes—
353#385C2314yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2314yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2314yes—
370#385C2314yes—
371#385C2318yes—
372#385C2314yes—
373#385C2314yes—
374#384C2314yes—
375#384C2314yes—
376#384C2314yes—
377#384C2314yes—
378#384C2314yes—
379#383C2318yes—
380#382C2314yes—
381#382C2314yes—
382#382C2314yes—
383#381C2318yes—
384#381C2314yes—
385#381C2318yes—
386#381C2314yes—
387#381C2314yes—
388#381C2314yes—
389#381C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2318yes—
393#380C2318yes—
394#380C2314yes—
395#380C2318yes—
396#380C2312yes—
397#380C2312yes—
398#380C2314yes—
399#380C2312yes—
400#380C2314yes—
401#380C2312yes—
402#380C2318yes—
403#380C2314yes—
404#380C2312yes—
405#380C2314yes—
406#380C2312yes—
407#380C2312yes—
408#380C2312yes—
409#380C2312yes—
410#380C2312yes—
411#380C2318yes—
412#380C2314yes—
413#380C2314yes—
414#380C2312yes—
415#380C2312yes—
416#379C2318yes—
417#379C2314yes—
418#379C2314yes—
419#379C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C2×#95C2314yes—
438C2×#95C2314yes—
439C2×#95C2314yes—
440C25C2412yes—
441C25C2412yes—
442C22×Q8C2414yes—
443C22×D4—216no—
444C22×D4—24no—
445C22×D4—24no—
446C22×D4—24no—
447C22×D4—42no—
448C22×D4—42no—
449C22×D4—48no—
450C22×D4—84no—
451C22×D4#4118yes—
452C22×D4C2412yes—
453C22×D4C2418yes—
454C22×D4C2414yes—
455C22×D4C2411yescharacteristic
456C22×D4C2418yes—
457C22×D4C2411yescharacteristic
458C23×C4—28no—
459C23×C4—28no—
460C23×C4—28no—
461C23×C4—44no—
462C23×C4—44no—
463C23×C4—44no—
464C23×C4C2412yes—
465C23×C4C2411yescharacteristic
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C23×C4C2412yes—
472C23×C4C2414yes—
473C23×C4C2414yes—
474C23×C4C2414yes—
475C23×C4C2414yes—
476C23×C4C2414yes—
477C23×C4C2414yes—
478C23×C4C2414yes—
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2411yescharacteristic
482C4⋊Q8—48no—
483#126—416no—
484#125—48no—
485#125—416no—
486#125—88no—
487#123—216no—
488#123—416no—
489#123—48no—
490#123—88no—
491C22⋊Q8—416no—
492C22⋊Q8—48no—
493C22⋊Q8—48no—
494C22⋊Q8—48no—
495#121—216no—
496#121—216no—
497#121—216no—
498#121—216no—
499#121—216no—
500#121—416no—
501#121—48no—
502C4×D4—216no—
503C4×D4—216no—
504C4×D4—48no—
505C4×D4—48no—
506C4×D4—48no—
507C4×D4—48no—
508C4×D4—44no—
509C4×D4—44no—
510C4×D4—44no—
511C4×D4—44no—
512C4×D4—416no—
513C4×D4—88no—
514#117—28no—
515#117—28no—
516#117—28no—
517#117—28no—
518#117—48no—
519#117—48no—
520#117—44no—
521#117—44no—
522C2×C4⋊C4—28no—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—48no—
525C2×C4⋊C4—44no—
526C2×C4⋊C4—44no—
527C2×C4⋊C4—44no—
528C2×C4⋊C4—48no—
529C2×C4⋊C4—42no—
530C2×C4⋊C4—82no—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2411yescharacteristic
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2411yescharacteristic
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C22⋊C4—216no—
571C2×C22⋊C4—216no—
572C2×C22⋊C4—48no—
573C2×C22⋊C4—48no—
574C2×C22⋊C4—48no—
575C2×C22⋊C4—44no—
576C2×C22⋊C4—44no—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2412yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C42—24no—
611C2×C42—48no—
612C2×C42C2414yes—
613C2×C42C2414yes—
614C2×C42C2414yes—
615C2×C42C2414yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2418yes—
621C2×C42C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2414yes—
629#95C2414yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2418yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655C24—24no—
656C24—24no—
657C24—24no—
658C24—24no—
659C24—24no—
660C24—24no—
661C24—42no—
662C24—42no—
663C24—42no—
664C24—42no—
665C24—42no—
666C24—42no—
667C24—42no—
668C24C2×#4118yes—
669C24C2512yes—
670C24C2514yes—
671C24C2512yes—
672C24C2511yescharacteristic
673C2×Q8—44no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×D4—216no—
677C2×D4—216no—
678C2×D4—24no—
679C2×D4—216no—
680C2×D4—232no—
681C2×D4—28no—
682C2×D4—22no—
683C2×D4—28no—
684C2×D4—24no—
685C2×D4—41no—
686C2×D4—42no—
687C2×D4—41no—
688C2×D4—48no—
689C2×D4—41no—
690C2×D4—41no—
691C2×D4—416no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—832no—
695C2×D4C2×#41116yes—
696C2×D4H(5,𝔽2)14yes—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—24no—
701C22×C4—22no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—24no—
708C22×C4—28no—
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—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—41no—
724C22×C4—41no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—42no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—432no—
749C22×C4—816no—
750C22×C4C2×#4114yes—
751C22×C4H(5,𝔽2)14yes—
752C22×C42−1+414yes—
753C22×C4C2512yes—
754C22×C4C2514yes—
755C22×C4C2512yes—
756C22×C4C2514yes—
757C22×C4C2514yes—
758C22×C4C2514yes—
759C22×C4C2518yes—
760C22×C4C2514yes—
761C22×C4C2514yes—
762C22×C4C2512yes—
763C22×C4C2514yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2511yescharacteristic
767C22×C4C2511yescharacteristic
768C22×C4C2512yes—
769C4⋊C4—28no—
770C4⋊C4—28no—
771C4⋊C4—24no—
772C4⋊C4—24no—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—48no—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C4⋊C4—41no—
789C4⋊C4—42no—
790C4⋊C4—41no—
791C4⋊C4—44no—
792C4⋊C4—48no—
793C4⋊C4—48no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—48no—
797C4⋊C4—48no—
798C4⋊C4—44no—
799C4⋊C4—48no—
800C4⋊C4—44no—
801C4⋊C4—48no—
802C4⋊C4—44no—
803C4⋊C4—48no—
804C4⋊C4—48no—
805C4⋊C4—48no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C22⋊C4—28no—
809C22⋊C4—216no—
810C22⋊C4—216no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—216no—
815C22⋊C4—28no—
816C22⋊C4—28no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—44no—
820C22⋊C4—44no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—48no—
824C22⋊C4—42no—
825C22⋊C4—42no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—48no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—48no—
833C22⋊C4—44no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C42—28no—
842C42—24no—
843C42—24no—
844C42—28no—
845C42—28no—
846C42—28no—
847C42—44no—
848C42—44no—
849C42—48no—
850C42—48no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—21no—
855C23—22no—
856C23—24no—
857C23—22no—
858C23—24no—
859C23—22no—
860C23—24no—
861C23—24no—
862C23—22no—
863C23—24no—
864C23—22no—
865C23—24no—
866C23—22no—
867C23—216no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—48no—
876C23—48no—
877C23—48no—
878C23—48no—
879C23—48no—
880C23—48no—
881C23—84no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23—84no—
886C23—84no—
887C23—84no—
888C23C22×#4118yes—
889C23C22×#4112yes—
890C23C2×H(5,𝔽2)14yes—
891C23C2×H(5,𝔽2)12yes—
892C23C2×2−1+412yes—
893C23C2611yescharacteristic
894Q8—164no—
895D4—232no—
896D4—44no—
897D4—48no—
898D4—44no—
899D4—432no—
900D4—816no—
901C2×C4—28no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—28no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—28no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—28no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—44no—
946C2×C4—48no—
947C2×C4—48no—
948C2×C4—48no—
949C2×C4—48no—
950C2×C4—48no—
951C2×C4—88no—
952C2×C4—88no—
953C2×C4—88no—
954C2×C4—88no—
955C2×C4—88no—
956C2×C4—84no—
957C2×C4—88no—
958C2×C4—88no—
959C2×C4—164no—
960C2×C4—164no—
961C2×C4#539116yescomplemented
962C2×C4C22×#4114yes—
963C2×C4C2×H(5,𝔽2)12yes—
964C2×C4C2×H(5,𝔽2)14yes—
965C2×C4C2×2−1+414yes—
966C2×C4#58512yes—
967C22—22no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—28no—
974C22—24no—
975C22—28no—
976C22—24no—
977C22—24no—
978C22—28no—
979C22—42no—
980C22—44no—
981C22—42no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—44no—
987C22—42no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—816no—
995C22—816no—
996C22C2×#53914yes—
997C22C23×#4111yescharacteristic
998C22C22×H(5,𝔽2)11yescharacteristic
999C22C22×H(5,𝔽2)11yescharacteristic
1000C22C22×2−1+411yescharacteristic
1001C22C2×#58511yescharacteristic
1002C22H(7,𝔽2)11yescharacteristic
1003C222−1+611yescharacteristic
1004C4—22no—
1005C4—22no—
1006C4—44no—
1007C4—48no—
1008C4—44no—
1009C4—44no—
1010C4—44no—
1011C4—44no—
1012C4—42no—
1013C4—44no—
1014C4—44no—
1015C4—44no—
1016C4—42no—
1017C4—42no—
1018C4—44no—
1019C4C2×#53918yes—
1020C2—24no—
1021C2—48no—
1022C2—44no—
1023C2—82no—
1024C2C22×#53911yescharacteristic
1025C2#6281811yescharacteristic
1026C2#6287511yescharacteristic
1027C2#6291511yescharacteristic
1028C2#6292911yescharacteristic
1029C2#6298311yescharacteristic
1030C2#6299111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#2537C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42718C2semidirect
2. #42615C2semidirect
3. #42601C2semidirect
4. #42577C2semidirect
5. #40639C2semidirect
6. #40144C2semidirect
7. #40077C2semidirect
8. #39400C2semidirect
9. #39021C2semidirect
10. #37880C2semidirect
11. #37692C2semidirect
12. #35555C2semidirect
13. #35544C2semidirect
14. #35540C2semidirect
15. #35253C2semidirect
16. #35174C2semidirect
18. #34809C2semidirect
19. #34248C2semidirect
20. #34204C2semidirect
22. C2×#539C22semidirect
30. #2857C22semidirect
31. #2851C22semidirect
33. #2827C22semidirect
34. #2827C22semidirect
35. #2787C22semidirect
36. #2770C22semidirect
37. #2747C22semidirect
38. #2746C22semidirect
39. #2743C22semidirect
40. #2740C22semidirect
41. #2737C22semidirect
42. #2711C22semidirect
43. #2708C22semidirect
44. #2707C22semidirect
45. #2695C22semidirect
46. #2694C22semidirect
47. #2691C22semidirect
48. #2690C22semidirect
49. #2687C22semidirect
50. #2681C22semidirect
51. #2653C22semidirect
52. #2649C22semidirect
53. #2646C22semidirect
54. #2639C22semidirect
55. #2638C22semidirect
56. #2633C22semidirect
57. #2629C22semidirect
58. #2628C22semidirect
59. #2627C22semidirect
61. #2618C22semidirect
62. #2570C22semidirect
63. #2570C22semidirect
64. #2552C22semidirect
65. #2552C22semidirect
70. #2507C22semidirect
71. #2507C22semidirect
72. #2506C22semidirect
73. #2506C22semidirect
74. #2497C22semidirect
75. #2497C22semidirect
76. #2496C22semidirect
77. #2496C22semidirect
78. #2495C22semidirect
79. #2495C22semidirect
80. #2494C22semidirect
81. #2494C22semidirect
83. #2493C22semidirect
84. #2487C22semidirect
85. #2487C22semidirect
86. #2486C22semidirect
87. #2486C22semidirect
88. #2485C22semidirect
89. #2485C22semidirect
90. #2485C22semidirect
91. #2485C22semidirect
99. #2473C22semidirect
100. #2466C22semidirect
101. #2460C22semidirect
102. #2454C22semidirect
103. #2454C22semidirect
104. #2452C22semidirect
105. #2452C22semidirect
106. #2443C22semidirect
107. #2442C22semidirect
108. #2441C22semidirect
109. #2440C22semidirect
110. #2439C22semidirect
113. #2425C22semidirect
114. #2422C22semidirect
115. #2422C22semidirect
116. #2422C22semidirect
117. #2422C22semidirect
118. #2420C22semidirect
119. #2420C22semidirect
120. #2420C22semidirect
121. #2420C22semidirect
124. #2395C22semidirect
125. #2395C22semidirect
127. #2363C22semidirect
128. #2363C22semidirect
129. #2361C22semidirect
130. #2361C22semidirect
131. #2349C22semidirect
132. #2349C22semidirect
133. D4×C4⋊C4C22semidirect
134. D4×C4⋊C4C22semidirect
137. #2329C22semidirect
138. #2325C22semidirect
139. #2324C22semidirect
140. #2324C22semidirect
147. #2313C22semidirect
149. C4×#123C22semidirect
150. C4×#123C22semidirect
151. C4×#121C22semidirect
152. C4×#121C22semidirect
961. C2×C4#539semidirect

Maximal subgroups

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

subgroupindex
#427182
#426152
#426012
#425772
#406392
#401442
#400772
#394002
#390212
#378802
#376922
#355552
#355442
#355402
#352532
#351742
C2×#25372
#348092
#342482
#342042