Subgroups — #1330

Order 128.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#436	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#346	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×M₁₆	—	2	1	no	—
5	C₄×D₄	C₄	1	1	yes	characteristic
6	C₂×C₁₆	—	2	1	no	—
7	C₂×C₁₆	—	2	1	no	—
8	C₄⋊C₈	C₄	1	1	yes	characteristic
9	C₂²⋊C₈	—	2	1	no	—
10	C₄×C₈	C₂²	1	1	yes	characteristic
11	C₂×D₄	C₈	1	1	yes	characteristic
12	C₂²×C₄	—	2	1	no	—
13	M₁₆	—	4	1	no	—
14	M₁₆	—	4	1	no	—
15	C₂×C₈	—	2	1	no	—
16	C₂×C₈	D₄	1	1	yes	characteristic
17	C₂×C₈	D₄	1	1	yes	characteristic
18	C₄⋊C₄	C₈	1	1	yes	characteristic
19	C₂²⋊C₄	—	2	1	no	—
20	C₄²	C₂×C₄	1	1	yes	characteristic
21	C₁₆	—	2	2	no	—
22	C₁₆	—	4	1	no	—
23	C₂³	—	2	1	no	—
24	D₄	—	4	1	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	—	4	1	no	—
27	C₂×C₄	—	4	1	no	—
28	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄	M₁₆	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₈	—	4	1	no	—
33	C₈	D₈	1	1	yes	characteristic
34	C₈	SD₁₆	1	1	yes	characteristic
35	C₂²	—	4	1	no	—
36	C₂²	—	4	1	no	—
37	C₂²	—	4	1	no	—
38	C₂²	C₂²⋊C₈	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	2	1	no	—
41	C₄	—	4	1	no	—
42	C₄	#102	1	1	yes	characteristic
43	C₄	#104	1	1	yes	characteristic
44	C₂	—	8	1	no	—
45	C₂	D₄⋊C₈	1	1	yes	characteristic
46	C₂	#349	1	1	yes	characteristic
47	C₂	#350	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₄⋊C₁₆	C₂	semidirect
3. #346	C₂	semidirect

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