Subgroups — #2987

Order 128.

157 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	8	yes	maximal, complemented
3	#433	C₂	1	4	yes	maximal
4	#432	C₂	1	2	yes	maximal
5	C₄⋊Q₈	C₄	1	2	yes	—
6	#125	C₄	1	2	yes	—
7	C₂²⋊Q₈	C₄	1	4	yes	—
8	C₄×Q₈	C₂²	1	4	yes	—
9	#117	C₂²	1	2	yes	—
10	C₂×C₄²	C₂²	1	1	yes	characteristic
11	C₄⋊C₈	C₂²	1	4	yes	—
12	C₄⋊C₈	C₂²	1	8	yes	—
13	C₂²⋊C₈	C₂²	1	4	yes	—
14	#97	C₂²	1	4	yes	—
15	#97	C₂²	1	4	yes	—
16	C₄×C₈	C₂²	1	4	yes	—
17	C₂×Q₈	C₂×C₄	1	4	yes	—
18	C₂²×C₄	C₂×C₄	1	2	yes	—
19	C₂²×C₄	C₂³	1	1	yes	characteristic
20	C₂×C₈	C₂³	1	8	yes	—
21	C₄⋊C₄	C₂×C₄	1	4	yes	—
22	C₄⋊C₄	C₂×C₄	1	8	yes	—
23	C₄⋊C₄	C₂×C₄	1	4	yes	—
24	C₂²⋊C₄	C₂×C₄	1	4	yes	—
25	C₄²	C₂×C₄	1	1	yes	characteristic
26	C₄²	C₂×C₄	1	1	yes	characteristic
27	C₄²	C₂³	1	4	yes	—
28	C₄²	C₂³	1	2	yes	—
29	C₂³	C₂²×C₄	1	1	yes	characteristic
30	Q₈	—	4	4	no	—
31	C₂×C₄	—	2	2	no	—
32	C₂×C₄	—	4	2	no	—
33	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄	C₂²×C₄	1	2	yes	—
35	C₂×C₄	C₂²×C₄	1	2	yes	—
36	C₂×C₄	C₂²×C₄	1	8	yes	—
37	C₂×C₄	C₂⁴	1	1	yes	characteristic
38	C₈	—	2	8	no	—
39	C₂²	—	2	1	no	—
40	C₂²	—	2	2	no	—
41	C₂²	C₂³×C₄	1	1	yes	characteristic
42	C₄	—	2	1	no	—
43	C₄	—	2	2	no	—
44	C₄	—	2	2	no	—
45	C₄	—	2	8	no	—
46	C₄	2₋¹⁺⁴	1	2	yes	—
47	C₂	—	4	1	no	—
48	C₂	#519	1	1	yes	characteristic
49	C₂	#568	1	2	yes	—

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

N	H ≅ G/N	type
2. #446	C₂	semidirect

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