Subgroups — #28412391

Order 14656.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301049	C₂	1	2	yes	maximal
2	#20300986	C₂	1	1	yes	maximal, characteristic
3	#16814675	—	2	2	no	—
4	C₂×Dic₄₅₈	C₂²	1	1	yes	characteristic
5	#16814645	—	2	2	no	—
6	C₄×Dic₂₂₉	C₄	1	1	yes	characteristic
7	C₂×Q₈×C₂₂₉	C₄	1	1	yes	characteristic
8	#14270087	—	4	2	no	—
9	Dic₄₅₈	—	4	1	no	—
10	C₂×Dic₂₂₉	—	2	1	no	—
11	C₂×Dic₂₂₉	D₄	1	2	yes	—
12	Q₈×C₂₂₉	—	4	1	no	—
13	C₂×C₄×C₂₂₉	—	2	1	no	—
14	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₂₂₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₂₂₉	—	2	1	no	—
17	C₄×C₂₂₉	—	4	1	no	—
18	Dic₂₂₉	—	2	2	no	—
19	Dic₂₂₉	—	2	2	no	—
20	C₂×C₂₂₉	—	2	1	no	—
21	C₂×C₂₂₉	#99	1	1	yes	characteristic
22	C₂₂₉	#356	1	1	yes	characteristic, complemented, Sylow
23	#356	—	229	1	no	maximal, Sylow
24	C₄⋊Q₈	—	229	1	no	—
25	#101	—	229	2	no	—
26	C₂×Q₈	—	229	1	no	—
27	C₂×Q₈	#11745021	1	1	yes	characteristic
28	M₁₆	—	458	2	no	—
29	C₄⋊C₄	—	458	2	no	—
30	C₄²	—	229	1	no	—
31	Q₈	—	4	1	no	—
32	Q₈	—	916	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	458	1	no	—
35	C₂×C₄	—	229	2	no	—
36	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
37	C₈	—	916	2	no	—
38	C₂²	C₂²⋊#11745021	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	4	1	no	—
41	C₄	—	458	2	no	—
42	C₄	—	458	2	no	—
43	C₂	—	2	1	no	—
44	C₂	#20301046	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₂₂₉	#356	semidirect

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