Subgroups — #7448

Order 256.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2246	C₂	1	1	yes	maximal, characteristic
2	#1422	C₂	1	1	yes	maximal, characteristic, complemented
3	#1373	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆	—	2	1	no	—
5	C₂×D₁₆	C₄	1	2	yes	—
6	#493	—	2	1	no	—
7	M₆₄	—	2	1	no	—
8	#364	—	2	1	no	—
9	C₄×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×D₈	—	2	2	no	—
11	C₂×D₈	—	4	1	no	—
12	#127	—	4	1	no	—
13	D₁₆	—	4	2	no	—
14	D₁₆	—	4	1	no	—
15	D₁₆	—	4	1	no	—
16	M₃₂	—	4	1	no	—
17	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆	D₄	1	1	yes	characteristic
19	C₄×C₈	D₄	1	1	yes	characteristic
20	C₃₂	—	4	1	no	—
21	C₂×D₄	—	4	2	no	—
22	C₂×D₄	—	8	2	no	—
23	D₈	—	4	2	no	—
24	D₈	—	4	2	no	—
25	D₈	—	8	1	no	—
26	D₈	—	8	1	no	—
27	C₂×C₈	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈	D₈	1	1	yes	characteristic
29	C₄²	SD₁₆	1	1	yes	characteristic
30	C₁₆	—	2	1	no	—
31	C₁₆	—	8	1	no	—
32	C₁₆	D₈	1	1	yes	characteristic
33	C₁₆	SD₁₆	1	1	yes	characteristic
34	C₂³	—	8	2	no	—
35	D₄	—	8	2	no	—
36	D₄	—	8	2	no	—
37	D₄	—	16	4	no	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	#102	1	1	yes	characteristic
40	C₈	#100	1	1	yes	characteristic
41	C₈	#102	1	1	yes	characteristic
42	C₈	D₁₆	1	1	yes	characteristic
43	C₈	SD₃₂	1	1	yes	characteristic
44	C₂²	—	16	4	no	—
45	C₂²	—	16	2	no	—
46	C₂²	#361	1	1	yes	characteristic
47	C₄	—	2	2	no	—
48	C₄	#331	1	1	yes	characteristic
49	C₄	#357	1	1	yes	characteristic
50	C₂	—	2	1	no	—
51	C₂	—	32	2	no	—
52	C₂	#1361	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #1422	C₂	semidirect
3. #1373	C₂	semidirect

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