Subgroups — #1272

Order 128.

83 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	#336	C₂	1	2	yes	maximal
3	C₂²×Q₈	C₄	1	1	yes	characteristic
4	C₂²×C₈	—	2	2	no	—
5	C₂×C₄⋊C₄	C₄	1	1	yes	characteristic
6	C₂×C₄²	C₂²	1	1	yes	characteristic
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	—	2	4	no	—
17	C₂×C₈	—	4	2	no	—
18	C₂×C₈	—	4	2	no	—
19	C₄⋊C₄	—	4	1	no	—
20	C₄²	—	4	1	no	—
21	C₂³	C₂²⋊C₄	1	1	yes	characteristic
22	Q₈	—	4	2	no	—
23	Q₈	—	4	2	no	—
24	C₂×C₄	—	2	2	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	—	2	2	no	—
28	C₂×C₄	—	2	2	no	—
29	C₂×C₄	—	4	1	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	4	1	no	—
32	C₂×C₄	—	4	2	no	—
33	C₂×C₄	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄	M₁₆	1	1	yes	characteristic
35	C₂×C₄	SD₁₆	1	2	yes	—
36	C₂×C₄	Q₁₆	1	2	yes	—
37	C₈	—	4	4	no	—
38	C₂²	C₂²⋊C₈	1	1	yes	characteristic
39	C₂²	#99	1	1	yes	characteristic
40	C₂²	#100	1	1	yes	characteristic
41	C₂²	#103	1	2	yes	—
42	C₂²	#104	1	2	yes	—
43	C₄	—	2	1	no	—
44	C₄	—	2	1	no	—
45	C₄	—	2	2	no	—
46	C₄	—	2	2	no	—
47	C₄	—	4	2	no	—
48	C₄	—	8	1	no	—
49	C₂	#323	1	1	yes	characteristic
50	C₂	Q₈⋊C₈	1	2	yes	—
51	C₂	#328	1	2	yes	—
52	C₂	#329	1	1	yes	characteristic
53	C₂	#333	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
#336	2