Subgroups — #7092

Order 256.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1709	C₂	1	1	yes	maximal, characteristic
2	#1367	C₂	1	2	yes	maximal, complemented
3	#494	C₄	1	1	yes	characteristic
4	#493	C₄	1	1	yes	characteristic
5	#486	—	2	2	no	—
6	C₄⋊C₁₆	—	2	2	no	—
7	C₈²	C₂²	1	1	yes	characteristic
8	C₂×Q₁₆	—	4	1	no	—
9	C₂×D₈	—	4	1	no	—
10	C₄⋊Q₈	—	2	1	no	—
11	#127	—	2	1	no	—
12	C₂×C₁₆	—	4	2	no	—
13	#102	—	4	2	no	—
14	#102	—	4	2	no	—
15	C₄×C₈	C₂×C₄	1	1	yes	characteristic
16	C₄×C₈	D₄	1	2	yes	—
17	C₂×Q₈	—	4	1	no	—
18	C₂×D₄	—	4	1	no	—
19	C₂×D₄	—	4	2	no	—
20	Q₁₆	—	8	2	no	—
21	D₈	—	8	2	no	—
22	C₂×C₈	—	2	1	no	—
23	C₂×C₈	D₈	1	2	yes	—
24	C₂×C₈	SD₁₆	1	2	yes	—
25	C₄⋊C₄	—	4	2	no	—
26	C₄²	C₂²⋊C₄	1	1	yes	characteristic
27	C₁₆	—	8	2	no	—
28	C₂³	—	8	1	no	—
29	Q₈	—	8	2	no	—
30	D₄	—	8	2	no	—
31	D₄	—	8	2	no	—
32	D₄	—	8	2	no	—
33	C₂×C₄	—	8	1	no	—
34	C₂×C₄	#100	1	1	yes	characteristic
35	C₂×C₄	#102	1	2	yes	—
36	C₈	—	2	2	no	—
37	C₈	—	2	2	no	—
38	C₈	—	2	2	no	—
39	C₂²	—	16	1	no	—
40	C₂²	—	16	2	no	—
41	C₂²	#331	1	1	yes	characteristic
42	C₄	—	2	1	no	—
43	C₄	—	16	1	no	—
44	C₄	#359	1	2	yes	—
45	C₄	#360	1	2	yes	—
46	C₂	—	32	1	no	—
47	C₂	#1357	1	1	yes	characteristic
48	C₂	#1360	1	2	yes	—

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

N	H ≅ G/N	type
2. #1367	C₂	semidirect

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

subgroup	index
#1709	2
#1367	2