Subgroups — #1361

Order 128.

59 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#493	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#335	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈	—	2	1	no	—
5	C₂×D₈	C₄	1	2	yes	—
6	#127	—	2	1	no	—
7	C₂×C₁₆	—	2	1	no	—
8	C₄⋊C₈	—	2	1	no	—
9	C₄×C₈	C₂²	1	1	yes	characteristic
10	C₂×D₄	—	2	2	no	—
11	C₂×D₄	—	4	1	no	—
12	C₂×D₄	—	4	1	no	—
13	D₈	—	4	2	no	—
14	D₈	—	4	1	no	—
15	D₈	—	4	1	no	—
16	C₂×C₈	—	4	1	no	—
17	C₂×C₈	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈	D₄	1	1	yes	characteristic
19	C₄²	D₄	1	1	yes	characteristic
20	C₁₆	—	4	1	no	—
21	C₂³	—	4	2	no	—
22	D₄	—	4	2	no	—
23	D₄	—	4	2	no	—
24	D₄	—	8	2	no	—
25	D₄	—	8	1	no	—
26	D₄	—	8	1	no	—
27	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄	D₈	1	1	yes	characteristic
29	C₂×C₄	SD₁₆	1	1	yes	characteristic
30	C₈	—	2	1	no	—
31	C₈	—	8	1	no	—
32	C₈	D₈	1	1	yes	characteristic
33	C₈	SD₁₆	1	1	yes	characteristic
34	C₂²	—	8	2	no	—
35	C₂²	—	8	2	no	—
36	C₂²	—	8	2	no	—
37	C₂²	#102	1	1	yes	characteristic
38	C₄	—	2	1	no	—
39	C₄	#100	1	1	yes	characteristic
40	C₄	#102	1	1	yes	characteristic
41	C₄	D₁₆	1	1	yes	characteristic
42	C₄	SD₃₂	1	1	yes	characteristic
43	C₂	—	16	2	no	—
44	C₂	#331	1	1	yes	characteristic
45	C₂	#357	1	1	yes	characteristic
46	C₂	#361	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. #335	C₂	semidirect

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