Subgroups — #7096

Order 256.

93 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1712	C₂	1	1	yes	maximal, characteristic
2	#1370	C₂	1	2	yes	maximal, complemented
3	#493	—	2	2	no	—
4	#493	C₄	1	2	yes	—
5	C₄⋊C₁₆	—	2	2	no	—
6	C₈²	C₂²	1	1	yes	characteristic
7	C₂×D₈	—	4	2	no	—
8	C₂×D₈	—	4	2	no	—
9	C₂×D₈	—	4	2	no	—
10	#127	—	2	2	no	—
11	C₂×C₁₆	—	4	2	no	—
12	C₄×C₈	C₂×C₄	1	1	yes	characteristic
13	C₄×C₈	D₄	1	2	yes	—
14	C₂×D₄	—	4	2	no	—
15	C₂×D₄	—	4	4	no	—
16	D₈	—	8	4	no	—
17	D₈	—	8	4	no	—
18	D₈	—	8	2	no	—
19	D₈	—	8	2	no	—
20	C₂×C₈	—	2	1	no	—
21	C₂×C₈	D₈	1	2	yes	—
22	C₂×C₈	SD₁₆	1	2	yes	—
23	C₄²	C₂²⋊C₄	1	1	yes	characteristic
24	C₁₆	—	8	2	no	—
25	C₂³	—	8	2	no	—
26	D₄	—	8	4	no	—
27	D₄	—	8	4	no	—
28	D₄	—	8	4	no	—
29	C₂×C₄	#100	1	1	yes	characteristic
30	C₂×C₄	#102	1	2	yes	—
31	C₈	—	2	2	no	—
32	C₈	—	2	2	no	—
33	C₈	D₁₆	1	2	yes	—
34	C₈	SD₃₂	1	2	yes	—
35	C₂²	—	16	2	no	—
36	C₂²	—	16	4	no	—
37	C₂²	#331	1	1	yes	characteristic
38	C₄	—	2	1	no	—
39	C₄	#357	1	2	yes	—
40	C₄	#361	1	2	yes	—
41	C₂	—	32	2	no	—
42	C₂	#1357	1	1	yes	characteristic
43	C₂	#1361	1	2	yes	—

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

N	H ≅ G/N	type
2. #1370	C₂	semidirect

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

subgroup	index
#1712	2
#1370	2