Finite Group Databasebeta

← #8108340

Subgroups — #8108340

Order 512.

6486 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59006C214yesmaximal, complemented
2#53178C218yesmaximal, complemented
3#45745C218yesmaximal, complemented
4#45728C214yesmaximal, complemented
5#37881C214yesmaximal, complemented
6#37873C214yesmaximal, complemented
7#37861C214yesmaximal, complemented
8#37702C214yesmaximal, complemented
9#37692C214yesmaximal, complemented
10#37684C214yesmaximal, complemented
11#36729C214yesmaximal, complemented
12#36728C212yesmaximal, complemented
13#36719C214yesmaximal, complemented
14#36718C212yesmaximal, complemented
15C2×#2848C212yesmaximal, complemented
16C2×#2847C211yesmaximal, characteristic
17C25×C4C2211yescharacteristic
18C2×#551C2214yescomplemented
19C2×#543C2212yescomplemented
20C2×#539C2214yescomplemented
21C22×C22⋊Q8C2212yes—
22C22×C22⋊Q8C2212yescomplemented
23C22×C22⋊Q8C2212yescomplemented
24C22×#121C2212yes—
25C22×#121C2211yescharacteristic
26C22×#120C2212yes—
27#2848C2214yes—
28#2848C2214yes—
29#2848C2214yes—
30#2848C2214yes—
31#2848C2214yescomplemented
32#2848C2214yescomplemented
33#2848C2214yescomplemented
34#2848C2214yescomplemented
35#2847C2214yes—
36#2847C2214yes—
37#2847C2214yes—
38#2847C2214yes—
39#2827C2218yescomplemented
40#2788C2218yescomplemented
41#2781C2218yescomplemented
42#2779C2218yescomplemented
43#2768C2218yescomplemented
44#2747C2218yescomplemented
45#2742C2218yescomplemented
46#2741C2218yescomplemented
47#2732C2218yescomplemented
48#2728C2218yescomplemented
49#2723C2218yescomplemented
50#2722C2218yescomplemented
51#2717C2214yescomplemented
52#2715C2218yescomplemented
53#2711C2218yescomplemented
54#2708C2218yescomplemented
55#2704C2218yescomplemented
56#2704C2218yescomplemented
57#2702C2218yescomplemented
58#2702C2218yescomplemented
59#2697C2214yescomplemented
60#2695C2218yescomplemented
61#2692C2218yescomplemented
62#2692C2218yescomplemented
63#2691C2218yescomplemented
64#2690C2218yescomplemented
65#2685C2218yescomplemented
66#2684C2214yescomplemented
67#2683C2218yescomplemented
68#2683C2214yescomplemented
69#2681C2218yescomplemented
70#2681C2218yescomplemented
71#2681C2218yescomplemented
72#2672C2218yescomplemented
73#2672C2218yescomplemented
74#2659C2212yescomplemented
75#2659C2214yescomplemented
76#2646C2212yescomplemented
77#2639C2214yescomplemented
78#2627C2214yescomplemented
79#2626C2214yescomplemented
80#2618C2214yescomplemented
81#2583C2214yescomplemented
82#2549C2218yescomplemented
83#2534C2218yescomplemented
84#2505C2218yescomplemented
85#2498C2218yescomplemented
86#2488C2218yescomplemented
87#2481C2218yescomplemented
88#2480C2218yes—
89#2480C2218yescomplemented
90#2473C2218yescomplemented
91#2472C2218yescomplemented
92#2449C2218yescomplemented
93#2449C2218yescomplemented
94#2443C2218yescomplemented
95#2442C2218yescomplemented
96#2438C2218yescomplemented
97#2437C2218yes—
98#2437C2218yescomplemented
99#2435C2214yes—
100#2425C2218yescomplemented
101#2418C2218yescomplemented
102#2417C2218yescomplemented
103#2413C2218yescomplemented
104#2412C2218yescomplemented
105#2411C2218yescomplemented
106#2409C2218yescomplemented
107#2405C2218yes—
108#2405C2214yes—
109#2405C2214yescomplemented
110#2379C2214yescomplemented
111#2376C2214yescomplemented
112#2358C2214yescomplemented
113#2342C2218yes—
114D4×C22⋊C4C2218yes—
115#2329C2214yescomplemented
116#2329C2214yescomplemented
117#2325C2214yescomplemented
118#2316C2214yescomplemented
119#2312C2212yescomplemented
120C2×#386C2214yes—
121C2×#386C2212yes—
122C2×#385C2214yes—
123C2×#385C2214yescomplemented
124C2×#385C2214yescomplemented
125C2×#380C2211yescharacteristic
126C2×#380C2212yes—
127C2×#380C2212yes—
128C2×#380C2212yescomplemented
129C2×#380C2212yescomplemented
130C2×#379C2214yes—
131C26C2311yescharacteristic
132C23×Q8C2312yes—
133C23×D4C2314yes—
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C24×C4—44no—
137C24×C4—48no—
138C24×C4C2312yes—
139C24×C4C2312yes—
140C24×C4C2311yescharacteristic
141C24×C4C2312yes—
142C24×C4C2312yes—
143C24×C4C2312yes—
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146#551—416no—
147#543—48no—
148#539—416no—
149C2×#126C2318yes—
150C2×#126C2318yescomplemented
151C2×#125C2318yescomplemented
152C2×#124C2314yes—
153C2×#124C2314yes—
154C2×#123C2318yes—
155C2×#123C2314yes—
156C2×#123C2318yes—
157C2×#123C2314yes—
158C2×#123C2318yescomplemented
159C2×C22⋊Q8—48no—
160C2×C22⋊Q8—48no—
161C2×C22⋊Q8—48no—
162C2×C22⋊Q8C2314yes—
163C2×C22⋊Q8C2314yes—
164C2×C22⋊Q8C2314yes—
165C2×C22⋊Q8C2314yes—
166C2×C22⋊Q8C2314yes—
167C2×C22⋊Q8C2314yes—
168C2×C22⋊Q8C2314yes—
169C2×C22⋊Q8C2314yes—
170C2×C22⋊Q8C2314yes—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2314yes—
173C2×C22⋊Q8C2314yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2318yes—
176C2×C22⋊Q8C2318yescomplemented
177C2×C22⋊Q8C2318yescomplemented
178C2×C22⋊Q8C2318yescomplemented
179C2×#121—44no—
180C2×#121—48no—
181C2×#121C2314yes—
182C2×#121C2314yes—
183C2×#121C2314yes—
184C2×#121C2314yes—
185C2×#121C2314yes—
186C2×#121C2314yes—
187C2×#120—48no—
188C2×#120C2314yes—
189C2×#120C2318yes—
190C2×#120C2314yes—
191C2×C4×D4C2318yes—
192C2×C4×D4C2318yes—
193C2×#117C2318yes—
194C22×C4⋊C4C2314yes—
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2314yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2314yes—
201C22×C4⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2314yes—
204C22×C22⋊C4C2314yes—
205C22×C22⋊C4C2314yes—
206C22×C22⋊C4C2314yes—
207C22×C22⋊C4C2314yes—
208C22×C22⋊C4C2314yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2314yes—
211C22×C22⋊C4C2314yes—
212C22×C22⋊C4C2314yes—
213#400C2318yescomplemented
214#400C2318yescomplemented
215#400C2318yescomplemented
216#400C2318yescomplemented
217#400C2318yescomplemented
218#399C2318yes—
219#399C2318yescomplemented
220#399C2318yescomplemented
221#398C2318yescomplemented
222#398C2318yescomplemented
223#398C2318yescomplemented
224#398C2318yescomplemented
225#398C2318yescomplemented
226#398C2318yescomplemented
227#398C2318yescomplemented
228#398C2318yescomplemented
229#398C2318yescomplemented
230#397C2318yes—
231#397C2318yes—
232#397C2318yes—
233#397C2318yescomplemented
234#397C2318yescomplemented
235#397C2318yescomplemented
236#396C2318yes—
237#396C2318yes—
238#396C2318yes—
239#396C2318yescomplemented
240#396C2318yescomplemented
241#396C2318yescomplemented
242#396C2318yescomplemented
243#396C2318yescomplemented
244#395C2318yescomplemented
245#395C2318yescomplemented
246#395C2318yescomplemented
247#395C2318yescomplemented
248#394C2318yes—
249#394C2318yes—
250#394C2318yes—
251#394C2318yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yescomplemented
257#394C2318yescomplemented
258#393C2318yes—
259#393C2318yescomplemented
260#393C2318yescomplemented
261#391C2318yescomplemented
262#391C2318yescomplemented
263#391C2318yescomplemented
264#390C2318yes—
265#390C2318yes—
266#390C2314yes—
267#390C2314yes—
268#389C2318yescomplemented
269#389C2318yescomplemented
270#389C2318yescomplemented
271#389C2318yescomplemented
272#389C2318yescomplemented
273#389C2318yescomplemented
274#389C2318yescomplemented
275#388C2318yes—
276#388C2318yes—
277#388C2318yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#388C2318yes—
282#388C2318yescomplemented
283#388C2318yescomplemented
284#388C2318yescomplemented
285#388C2318yescomplemented
286#388C2318yescomplemented
287#387C2318yescomplemented
288#387C2318yescomplemented
289#387C2318yescomplemented
290#387C2318yescomplemented
291#387C2318yescomplemented
292#387C2318yescomplemented
293#386C2314yes—
294#386C2318yes—
295#386C2318yes—
296#386C2318yes—
297#386C2318yes—
298#386C2314yes—
299#386C2318yes—
300#386C2318yes—
301#386C2318yes—
302#386C2318yes—
303#386C2318yes—
304#386C2318yes—
305#386C2318yes—
306#386C2314yes—
307#386C2314yes—
308#386C2318yescomplemented
309#385C2318yes—
310#385C2318yes—
311#385C2318yes—
312#385C2318yes—
313#385C2318yes—
314#385C2318yes—
315#385C2318yes—
316#385C2318yes—
317#385C2318yes—
318#385C2318yes—
319#385C2318yes—
320#385C2318yes—
321#385C2318yes—
322#385C2318yes—
323#385C2318yes—
324#385C2318yes—
325#385C2318yes—
326#385C2318yescomplemented
327#385C2318yescomplemented
328#382C2318yescomplemented
329#381C2318yes—
330#380C2314yes—
331#380C2314yes—
332#380C2314yes—
333#380C2318yes—
334#380C2314yes—
335#380C2314yes—
336#380C2314yes—
337#380C2314yes—
338#380C2314yes—
339#380C2314yes—
340#380C2314yes—
341#380C2314yes—
342#380C2314yes—
343#380C2314yes—
344#380C2314yes—
345#380C2314yes—
346#380C2314yes—
347#380C2314yes—
348#380C2314yes—
349#380C2318yes—
350#380C2318yes—
351#380C2318yescomplemented
352#379C2314yes—
353#379C2318yes—
354#379C2318yes—
355#379C2318yes—
356#379C2318yes—
357#379C2318yes—
358C4×C22⋊C4C2314yes—
359C4×C22⋊C4C2318yes—
360C4×C22⋊C4C2318yes—
361C2×#95C2314yes—
362C2×#95C2312yes—
363C2×#95C2314yes—
364C2×#95C2314yes—
365C2×#95C2314yes—
366C25—24no—
367C25—28no—
368C25—44no—
369C25—42no—
370C25—42no—
371C25C2412yes—
372C25C2411yescharacteristic
373C25C2411yescharacteristic
374C25C2412yes—
375C25C2412yes—
376C25C2411yescharacteristic
377C22×Q8—44no—
378C22×Q8—44no—
379C22×Q8—44no—
380C22×Q8C2414yes—
381C22×Q8C2414yes—
382C22×Q8C2414yes—
383C22×D4—216no—
384C22×D4—44no—
385C22×D4—42no—
386C22×D4—44no—
387C22×D4—48no—
388C22×D4—44no—
389C22×D4—48no—
390C22×D4—44no—
391C22×D4C2418yes—
392C22×D4C2414yes—
393C22×D4C2414yes—
394C22×D4C2418yes—
395C22×D4C2414yes—
396C23×C4—24no—
397C23×C4—28no—
398C23×C4—28no—
399C23×C4—28no—
400C23×C4—28no—
401C23×C4—44no—
402C23×C4—44no—
403C23×C4—44no—
404C23×C4—44no—
405C23×C4—44no—
406C23×C4—44no—
407C23×C4—44no—
408C23×C4—44no—
409C23×C4—44no—
410C23×C4—44no—
411C23×C4—44no—
412C23×C4—44no—
413C23×C4—44no—
414C23×C4—44no—
415C23×C4—44no—
416C23×C4—44no—
417C23×C4—42no—
418C23×C4—464no—
419C23×C4C2414yes—
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2414yes—
431C23×C4C2414yes—
432C23×C4C2414yes—
433C23×C4C2412yes—
434C23×C4C2414yes—
435C23×C4C2412yes—
436C23×C4C2412yes—
437C23×C4C2412yes—
438C23×C4C2414yes—
439C23×C4C2414yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2412yes—
443#126—416no—
444#126—416no—
445#125—416no—
446#124—48no—
447#124—48no—
448#123—48no—
449#123—48no—
450#123—416no—
451#123—416no—
452#123—416no—
453C22⋊Q8—216no—
454C22⋊Q8—216no—
455C22⋊Q8—48no—
456C22⋊Q8—48no—
457C22⋊Q8—48no—
458C22⋊Q8—416no—
459C22⋊Q8—416no—
460C22⋊Q8—416no—
461C22⋊Q8—416no—
462C22⋊Q8—48no—
463C22⋊Q8—48no—
464C22⋊Q8—48no—
465C22⋊Q8—48no—
466C22⋊Q8—48no—
467C22⋊Q8—48no—
468C22⋊Q8—48no—
469C22⋊Q8—48no—
470#121—216no—
471#121—48no—
472#121—48no—
473#121—48no—
474#121—48no—
475#121—48no—
476#120—216no—
477#120—416no—
478#120—48no—
479C4×D4—416no—
480C4×D4—416no—
481#117—416no—
482C2×C4⋊C4—216no—
483C2×C4⋊C4—44no—
484C2×C4⋊C4—44no—
485C2×C4⋊C4—48no—
486C2×C4⋊C4—48no—
487C2×C4⋊C4—44no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—44no—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2418yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C22⋊C4—216no—
516C2×C22⋊C4—216no—
517C2×C22⋊C4—28no—
518C2×C22⋊C4—48no—
519C2×C22⋊C4—48no—
520C2×C22⋊C4—48no—
521C2×C22⋊C4—44no—
522C2×C22⋊C4—48no—
523C2×C22⋊C4—48no—
524C2×C22⋊C4—48no—
525C2×C22⋊C4—48no—
526C2×C22⋊C4C2418yes—
527C2×C22⋊C4C2418yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2414yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2418yes—
540C2×C22⋊C4C2418yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2418yes—
553C2×C42C2414yes—
554C2×C42C2418yes—
555C2×C42C2418yes—
556C2×C42C2414yes—
557#95C2418yes—
558#95C2418yes—
559#95C2418yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C2418yes—
566#95C2418yes—
567#95C2418yes—
568#95C2418yes—
569#95C2418yes—
570#95C2418yes—
571#95C2418yes—
572#95C2418yes—
573#95C2418yes—
574#95C2418yes—
575#95C2418yes—
576#95C2418yes—
577C24—24no—
578C24—24no—
579C24—24no—
580C24—22no—
581C24—24no—
582C24—24no—
583C24—22no—
584C24—24no—
585C24—24no—
586C24—24no—
587C24—24no—
588C24—22no—
589C24—22no—
590C24—24no—
591C24—24no—
592C24—24no—
593C24—24no—
594C24—24no—
595C24—28no—
596C24—41no—
597C24—42no—
598C24—42no—
599C24—42no—
600C24—42no—
601C24—42no—
602C24—41no—
603C24—41no—
604C24—42no—
605C24—41no—
606C24—44no—
607C24—42no—
608C24—42no—
609C24—432no—
610C24—416no—
611C24—416no—
612C24—432no—
613C24—416no—
614C24H(5,𝔽2)14yes—
615C242−1+418yes—
616C24C2514yes—
617C24C2511yescharacteristic
618C24C2512yes—
619C24C2511yescharacteristic
620C24C2512yes—
621C24C2511yescharacteristic
622C2×Q8—28no—
623C2×Q8—28no—
624C2×Q8—44no—
625C2×Q8—44no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—44no—
631C2×Q8—816no—
632C2×D4—216no—
633C2×D4—216no—
634C2×D4—216no—
635C2×D4—28no—
636C2×D4—216no—
637C2×D4—28no—
638C2×D4—28no—
639C2×D4—48no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—48no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—88no—
648C2×D4—832no—
649C2×D4—816no—
650C22×C4—22no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—28no—
656C22×C4—28no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—28no—
661C22×C4—24no—
662C22×C4—28no—
663C22×C4—28no—
664C22×C4—28no—
665C22×C4—28no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—41no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—44no—
701C22×C4—42no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—42no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—48no—
714C22×C4—44no—
715C22×C4—416no—
716C22×C4—432no—
717C22×C4—432no—
718C22×C4—432no—
719C22×C4—432no—
720C22×C4—432no—
721C22×C4—432no—
722C22×C4—416no—
723C22×C4H(5,𝔽2)14yes—
724C22×C4H(5,𝔽2)18yes—
725C22×C4C2518yes—
726C22×C4C2518yes—
727C22×C4C2512yes—
728C22×C4C2514yes—
729C22×C4C2518yes—
730C22×C4C2518yes—
731C22×C4C2518yes—
732C22×C4C2512yes—
733C22×C4C2512yes—
734C22×C4C2512yes—
735C4⋊C4—216no—
736C4⋊C4—216no—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—216no—
740C4⋊C4—216no—
741C4⋊C4—28no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C4⋊C4—44no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—44no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C22⋊C4—216no—
761C22⋊C4—216no—
762C22⋊C4—216no—
763C22⋊C4—216no—
764C22⋊C4—216no—
765C22⋊C4—28no—
766C22⋊C4—216no—
767C22⋊C4—216no—
768C22⋊C4—216no—
769C22⋊C4—216no—
770C22⋊C4—216no—
771C22⋊C4—48no—
772C22⋊C4—44no—
773C22⋊C4—48no—
774C22⋊C4—48no—
775C22⋊C4—48no—
776C22⋊C4—48no—
777C22⋊C4—48no—
778C22⋊C4—48no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—48no—
786C22⋊C4—48no—
787C42—44no—
788C42—48no—
789C42—48no—
790C42—44no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—22no—
797C23—21no—
798C23—28no—
799C23—216no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—21no—
806C23—22no—
807C23—21no—
808C23—21no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—21no—
814C23—216no—
815C23—216no—
816C23—216no—
817C23—24no—
818C23—28no—
819C23—24no—
820C23—28no—
821C23—24no—
822C23—44no—
823C23—48no—
824C23—44no—
825C23—48no—
826C23—48no—
827C23—48no—
828C23—48no—
829C23—44no—
830C23—48no—
831C23—48no—
832C23—48no—
833C23—48no—
834C23—48no—
835C23—48no—
836C23—48no—
837C23—48no—
838C23—44no—
839C23—48no—
840C23—44no—
841C23—44no—
842C23—48no—
843C23—44no—
844C23—4128no—
845C23—48no—
846C23—44no—
847C23—48no—
848C23—88no—
849C23—84no—
850C23—84no—
851C23—88no—
852C23C2×H(5,𝔽2)12yes—
853C23C2×H(5,𝔽2)14yes—
854C23C2×H(5,𝔽2)14yes—
855C23C2×H(5,𝔽2)12yes—
856C23C2×2−1+414yes—
857C23C2×2−1+414yes—
858C23C2×2−1+414yes—
859C23#58512yes—
860C23C2611yescharacteristic
861Q8—88no—
862Q8—88no—
863Q8—164no—
864D4—432no—
865D4—88no—
866D4—816no—
867D4—88no—
868D4—88no—
869C2×C4—28no—
870C2×C4—216no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—28no—
878C2×C4—28no—
879C2×C4—24no—
880C2×C4—28no—
881C2×C4—28no—
882C2×C4—28no—
883C2×C4—28no—
884C2×C4—24no—
885C2×C4—28no—
886C2×C4—28no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—24no—
897C2×C4—28no—
898C2×C4—48no—
899C2×C4—44no—
900C2×C4—48no—
901C2×C4—48no—
902C2×C4—48no—
903C2×C4—44no—
904C2×C4—48no—
905C2×C4—48no—
906C2×C4—48no—
907C2×C4—48no—
908C2×C4—48no—
909C2×C4—48no—
910C2×C4—48no—
911C2×C4—44no—
912C2×C4—416no—
913C2×C4—88no—
914C2×C4—88no—
915C2×C4—88no—
916C2×C4—84no—
917C2×C4—88no—
918C2×C4—164no—
919C2×C4—164no—
920C2×C4C2×H(5,𝔽2)14yes—
921C2×C4C2×H(5,𝔽2)14yes—
922C2×C4C2×H(5,𝔽2)14yes—
923C22—24no—
924C22—24no—
925C22—24no—
926C22—24no—
927C22—22no—
928C22—22no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—22no—
937C22—22no—
938C22—24no—
939C22—24no—
940C22—432no—
941C22—416no—
942C22—416no—
943C22—432no—
944C22—416no—
945C22—42no—
946C22—42no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—42no—
951C22—41no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—48no—
956C22—44no—
957C22—44no—
958C22—44no—
959C22—48no—
960C22—168no—
961C22#353618yes—
962C22#353814yes—
963C22C22×H(5,𝔽2)11yescharacteristic
964C22C22×H(5,𝔽2)12yes—
965C22C22×H(5,𝔽2)11yescharacteristic
966C22C22×2−1+412yes—
967C22C2×#58511yescharacteristic
968C4—24no—
969C4—24no—
970C4—24no—
971C4—48no—
972C4—48no—
973C4—42no—
974C4—48no—
975C4—48no—
976C4—44no—
977C4—48no—
978C2—24no—
979C2—28no—
980C2—44no—
981C2—42no—
982C2—42no—
983C2—84no—
984C2C2×#353612yes—
985C2C2×#353811yescharacteristic
986C2#6281711yescharacteristic
987C2#6281811yescharacteristic
988C2#6281912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#2847C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59006C2semidirect
2. #53178C2semidirect
3. #45745C2semidirect
4. #45728C2semidirect
5. #37881C2semidirect
6. #37873C2semidirect
7. #37861C2semidirect
8. #37702C2semidirect
9. #37692C2semidirect
10. #37684C2semidirect
11. #36729C2semidirect
12. #36728C2semidirect
13. #36719C2semidirect
14. #36718C2semidirect
15. C2×#2848C2semidirect
18. C2×#551C22semidirect
19. C2×#543C22semidirect
20. C2×#539C22semidirect
22. C22×C22⋊Q8C22semidirect
23. C22×C22⋊Q8C22semidirect
31. #2848C22semidirect
32. #2848C22semidirect
33. #2848C22semidirect
34. #2848C22semidirect
39. #2827C22semidirect
40. #2788C22semidirect
41. #2781C22semidirect
42. #2779C22semidirect
43. #2768C22semidirect
44. #2747C22semidirect
45. #2742C22semidirect
46. #2741C22semidirect
47. #2732C22semidirect
48. #2728C22semidirect
49. #2723C22semidirect
50. #2722C22semidirect
51. #2717C22semidirect
52. #2715C22semidirect
53. #2711C22semidirect
54. #2708C22semidirect
55. #2704C22semidirect
56. #2704C22semidirect
57. #2702C22semidirect
58. #2702C22semidirect
59. #2697C22semidirect
60. #2695C22semidirect
61. #2692C22semidirect
62. #2692C22semidirect
63. #2691C22semidirect
64. #2690C22semidirect
65. #2685C22semidirect
66. #2684C22semidirect
67. #2683C22semidirect
68. #2683C22semidirect
69. #2681C22semidirect
70. #2681C22semidirect
71. #2681C22semidirect
72. #2672C22semidirect
73. #2672C22semidirect
74. #2659C22semidirect
75. #2659C22semidirect
76. #2646C22semidirect
77. #2639C22semidirect
78. #2627C22semidirect
79. #2626C22semidirect
80. #2618C22semidirect
81. #2583C22semidirect
82. #2549C22semidirect
83. #2534C22semidirect
84. #2505C22semidirect
85. #2498C22semidirect
86. #2488C22semidirect
87. #2481C22semidirect
89. #2480C22semidirect
90. #2473C22semidirect
91. #2472C22semidirect
92. #2449C22semidirect
93. #2449C22semidirect
94. #2443C22semidirect
95. #2442C22semidirect
96. #2438C22semidirect
98. #2437C22semidirect
100. #2425C22semidirect
101. #2418C22semidirect
102. #2417C22semidirect
103. #2413C22semidirect
104. #2412C22semidirect
105. #2411C22semidirect
106. #2409C22semidirect
109. #2405C22semidirect
110. #2379C22semidirect
111. #2376C22semidirect
112. #2358C22semidirect
115. #2329C22semidirect
116. #2329C22semidirect
117. #2325C22semidirect
118. #2316C22semidirect
119. #2312C22semidirect
123. C2×#385C22semidirect
124. C2×#385C22semidirect
128. C2×#380C22semidirect
129. C2×#380C22semidirect
150. C2×#126C23semidirect
151. C2×#125C23semidirect
158. C2×#123C23semidirect
176. C2×C22⋊Q8C23semidirect
177. C2×C22⋊Q8C23semidirect
178. C2×C22⋊Q8C23semidirect
213. #400C23semidirect
214. #400C23semidirect
215. #400C23semidirect
216. #400C23semidirect
217. #400C23semidirect
219. #399C23semidirect
220. #399C23semidirect
221. #398C23semidirect
222. #398C23semidirect
223. #398C23semidirect
224. #398C23semidirect
225. #398C23semidirect
226. #398C23semidirect
227. #398C23semidirect
228. #398C23semidirect
229. #398C23semidirect
233. #397C23semidirect
234. #397C23semidirect
235. #397C23semidirect
239. #396C23semidirect
240. #396C23semidirect
241. #396C23semidirect
242. #396C23semidirect
243. #396C23semidirect
244. #395C23semidirect
245. #395C23semidirect
246. #395C23semidirect
247. #395C23semidirect
256. #394C23semidirect
257. #394C23semidirect
259. #393C23semidirect
260. #393C23semidirect
261. #391C23semidirect
262. #391C23semidirect
263. #391C23semidirect
268. #389C23semidirect
269. #389C23semidirect
270. #389C23semidirect
271. #389C23semidirect
272. #389C23semidirect
273. #389C23semidirect
274. #389C23semidirect
282. #388C23semidirect
283. #388C23semidirect
284. #388C23semidirect
285. #388C23semidirect
286. #388C23semidirect
287. #387C23semidirect
288. #387C23semidirect
289. #387C23semidirect
290. #387C23semidirect
291. #387C23semidirect
292. #387C23semidirect
308. #386C23semidirect
326. #385C23semidirect
327. #385C23semidirect
328. #382C23semidirect
351. #380C23semidirect

Maximal subgroups

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

subgroupindex
#590062
#531782
#457452
#457282
#378812
#378732
#378612
#377022
#376922
#376842
#367292
#367282
#367192
#367182
C2×#28482
C2×#28472