Subgroups — #1319

Order 128.

67 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#391	C₂	1	1	yes	maximal, characteristic
2	#324	C₂	1	2	yes	maximal
3	C₂²×Q₈	C₄	1	1	yes	characteristic
4	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
5	C₂×C₄²	C₄	1	1	yes	characteristic
6	C₂²⋊C₈	—	2	2	no	—
7	#95	—	2	2	no	—
8	C₂×Q₈	—	2	1	no	—
9	C₂×Q₈	—	4	1	no	—
10	C₂×Q₈	—	4	1	no	—
11	C₂×Q₈	C₈	1	2	yes	complemented
12	C₂²×C₄	—	2	1	no	—
13	C₂²×C₄	—	2	1	no	—
14	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄	D₄	1	2	yes	—
16	C₂×C₈	—	4	2	no	—
17	C₄⋊C₄	—	4	1	no	—
18	C₄²	—	4	1	no	—
19	C₂³	C₂²⋊C₄	1	1	yes	characteristic
20	Q₈	—	4	2	no	—
21	Q₈	—	4	2	no	—
22	C₂×C₄	—	2	1	no	—
23	C₂×C₄	—	2	1	no	—
24	C₂×C₄	—	2	2	no	—
25	C₂×C₄	—	2	2	no	—
26	C₂×C₄	—	2	2	no	—
27	C₂×C₄	—	4	1	no	—
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	—	4	1	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	4	2	no	—
32	C₂×C₄	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄	M₁₆	1	1	yes	characteristic
34	C₈	—	8	2	no	—
35	C₂²	—	2	1	no	—
36	C₂²	—	2	1	no	—
37	C₂²	C₂²⋊C₈	1	1	yes	characteristic
38	C₂²	#99	1	1	yes	characteristic
39	C₂²	#100	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	2	1	no	—
42	C₄	—	4	2	no	—
43	C₄	—	4	2	no	—
44	C₄	—	4	2	no	—
45	C₂	—	2	1	no	—
46	C₂	—	2	1	no	—
47	C₂	#323	1	1	yes	characteristic
48	C₂	#354	1	1	yes	characteristic
49	C₂	#356	1	1	yes	characteristic

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

N	H ≅ G/N	type
11. C₂×Q₈	C₈	semidirect

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

subgroup	index
#391	2
#324	2