Subgroups — #7390

Order 256.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2177	C₂	1	1	yes	maximal, characteristic
2	#1398	C₂	1	1	yes	maximal, characteristic, complemented
3	#1369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆	C₄	1	1	yes	characteristic
5	C₄×D₈	—	2	1	no	—
6	M₆₄	—	2	1	no	—
7	#367	C₄	1	1	yes	characteristic
8	#364	—	2	1	no	—
9	#357	—	2	1	no	—
10	#346	C₂²	1	1	yes	characteristic
11	C₂×D₈	—	2	1	no	—
12	C₄×D₄	—	4	1	no	—
13	D₁₆	—	2	1	no	—
14	D₁₆	C₈	1	2	yes	—
15	M₃₂	—	4	1	no	—
16	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₆	D₄	1	1	yes	characteristic
18	#107	—	2	1	no	—
19	#102	—	4	1	no	—
20	C₄×C₈	D₄	1	1	yes	characteristic
21	C₃₂	—	2	2	no	—
22	C₂×D₄	—	4	1	no	—
23	C₂²×C₄	—	8	1	no	—
24	D₈	—	2	2	no	—
25	D₈	—	4	1	no	—
26	C₂×C₈	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈	D₈	1	1	yes	characteristic
28	C₄⋊C₄	—	4	1	no	—
29	C₂²⋊C₄	—	8	1	no	—
30	C₄²	SD₁₆	1	1	yes	characteristic
31	C₁₆	—	2	1	no	—
32	C₁₆	—	8	1	no	—
33	C₁₆	C₂×C₈	1	1	yes	characteristic
34	C₁₆	M₁₆	1	1	yes	characteristic
35	C₂³	—	8	1	no	—
36	D₄	—	4	2	no	—
37	D₄	—	8	1	no	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	—	8	1	no	—
40	C₂×C₄	—	16	2	no	—
41	C₂×C₄	#102	1	1	yes	characteristic
42	C₈	—	2	1	no	—
43	C₈	C₂²⋊C₈	1	1	yes	characteristic
44	C₈	#104	1	1	yes	characteristic
45	C₂²	—	8	2	no	—
46	C₂²	—	16	1	no	—
47	C₂²	—	16	1	no	—
48	C₂²	#361	1	1	yes	characteristic
49	C₄	—	4	1	no	—
50	C₄	—	16	1	no	—
51	C₄	D₄⋊C₈	1	1	yes	characteristic
52	C₄	#360	1	1	yes	characteristic
53	C₂	—	2	1	no	—
54	C₂	—	16	2	no	—
55	C₂	#1333	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #1398	C₂	semidirect
3. #1369	C₂	semidirect

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