Subgroups — #2986

Order 128.

165 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#533	C₂	1	1	yes	maximal, characteristic
2	#446	C₂	1	4	yes	maximal, complemented
3	C₈×Q₈	C₂	1	4	yes	maximal, complemented
4	#433	C₂	1	4	yes	maximal
5	#431	C₂	1	2	yes	maximal
6	C₄⋊Q₈	C₄	1	2	yes	—
7	#125	C₄	1	2	yes	—
8	C₂²⋊Q₈	C₄	1	4	yes	—
9	C₄×Q₈	C₂²	1	4	yes	—
10	#117	C₂²	1	2	yes	—
11	C₂×C₄²	C₂²	1	1	yes	characteristic
12	C₄⋊C₈	C₂²	1	2	yes	—
13	C₄⋊C₈	C₂²	1	2	yes	—
14	C₄⋊C₈	C₂²	1	8	yes	—
15	C₂²⋊C₈	C₂²	1	4	yes	—
16	#97	C₂²	1	4	yes	—
17	C₄×C₈	C₂²	1	4	yes	—
18	C₄×C₈	C₂²	1	4	yes	—
19	C₂×Q₈	C₂×C₄	1	4	yes	—
20	C₂²×C₄	C₂×C₄	1	2	yes	—
21	C₂²×C₄	C₂³	1	1	yes	characteristic
22	C₂×C₈	C₂³	1	4	yes	—
23	C₂×C₈	C₂³	1	4	yes	—
24	C₄⋊C₄	C₂×C₄	1	4	yes	—
25	C₄⋊C₄	C₂×C₄	1	8	yes	—
26	C₄⋊C₄	C₂×C₄	1	4	yes	—
27	C₂²⋊C₄	C₂×C₄	1	4	yes	—
28	C₄²	C₂×C₄	1	1	yes	characteristic
29	C₄²	C₂×C₄	1	1	yes	characteristic
30	C₄²	C₂³	1	2	yes	—
31	C₄²	C₂³	1	4	yes	—
32	C₂³	C₂²×C₄	1	1	yes	characteristic
33	Q₈	—	2	8	no	—
34	C₂×C₄	—	2	4	no	—
35	C₂×C₄	—	2	2	no	—
36	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄	C₂²×C₄	1	2	yes	—
38	C₂×C₄	C₂²×C₄	1	8	yes	—
39	C₂×C₄	C₂²×C₄	1	2	yes	—
40	C₂×C₄	C₂⁴	1	1	yes	characteristic
41	C₈	—	2	4	no	—
42	C₈	—	2	4	no	—
43	C₂²	—	2	1	no	—
44	C₂²	—	2	2	no	—
45	C₂²	C₂³×C₄	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	2	2	no	—
48	C₄	—	2	8	no	—
49	C₄	#131	1	4	yes	—
50	C₄	2₋¹⁺⁴	1	2	yes	—
51	C₂	—	4	1	no	—
52	C₂	#519	1	1	yes	characteristic
53	C₂	C₂×#131	1	2	yes	—

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

N	H ≅ G/N	type
2. #446	C₂	semidirect
3. C₈×Q₈	C₂	semidirect

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