Subgroups — #31771516

Order 17216.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22575514	C₂	1	2	yes	maximal
2	#22575453	C₂	1	1	yes	maximal, characteristic
3	#16864411	—	2	2	no	—
4	C₂×Dic₅₃₈	C₄	1	1	yes	characteristic
5	C₂×Dic₅₃₈	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₂₆₉	—	2	2	no	—
7	C₄²×C₂₆₉	C₄	1	1	yes	characteristic
8	#14524137	—	4	2	no	—
9	Dic₅₃₈	—	4	1	no	—
10	Dic₅₃₈	—	4	1	no	—
11	C₂×Dic₂₆₉	—	2	1	no	—
12	C₂×Dic₂₆₉	D₄	1	2	yes	—
13	C₂×C₄×C₂₆₉	—	2	1	no	—
14	C₂×C₄×C₂₆₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₂₆₉	—	2	2	no	—
17	C₄×C₂₆₉	—	2	1	no	—
18	Dic₂₆₉	—	2	2	no	—
19	Dic₂₆₉	—	4	1	no	—
20	C₂×C₂₆₉	—	2	1	no	—
21	C₂×C₂₆₉	#99	1	1	yes	characteristic
22	C₂₆₉	#356	1	1	yes	characteristic, complemented, Sylow
23	#356	—	269	1	no	maximal, Sylow
24	C₄⋊Q₈	—	269	1	no	—
25	#101	—	269	2	no	—
26	C₂×Q₈	—	269	1	no	—
27	C₂×Q₈	—	269	1	no	—
28	M₁₆	—	538	2	no	—
29	C₄⋊C₄	—	538	2	no	—
30	C₄²	#11761640	1	1	yes	characteristic
31	Q₈	—	1076	1	no	—
32	Q₈	—	1076	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	269	2	no	—
35	C₂×C₄	—	538	1	no	—
36	C₂×C₄	C₂×#11761640	1	1	yes	characteristic
37	C₈	—	1076	2	no	—
38	C₂²	C₂²⋊#11761640	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	2	1	no	—
41	C₄	—	538	2	no	—
42	C₄	—	1076	1	no	—
43	C₂	—	2	1	no	—
44	C₂	#22575512	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₂₆₉	#356	semidirect

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