Subgroups — #1544

Order 128.

101 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	#431	C₂	1	2	yes	maximal
3	#332	C₂	1	4	yes	maximal, complemented
4	C₄⋊Q₈	C₂²	1	2	yes	—
5	#125	C₄	1	2	yes	—
6	C₂²⋊Q₈	—	2	2	no	—
7	C₄×Q₈	—	2	2	no	—
8	#117	C₄	1	2	yes	—
9	C₂×C₄²	C₂²	1	1	yes	characteristic
10	C₄⋊C₈	C₂²	1	4	yes	—
11	C₂²⋊C₈	—	2	2	no	—
12	C₄×C₈	—	2	2	no	—
13	C₂×Q₈	—	2	2	no	—
14	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄	D₄	1	2	yes	—
16	C₂×C₈	—	2	4	no	—
17	C₄⋊C₄	—	2	4	no	—
18	C₄⋊C₄	—	2	2	no	—
19	C₄⋊C₄	C₂×C₄	1	4	yes	—
20	C₂²⋊C₄	—	2	2	no	—
21	C₄²	—	2	2	no	—
22	C₄²	C₂×C₄	1	1	yes	characteristic
23	C₄²	D₄	1	2	yes	—
24	C₄²	C₂³	1	1	yes	characteristic
25	C₂³	C₂²⋊C₄	1	1	yes	characteristic
26	Q₈	—	4	4	no	—
27	C₂×C₄	—	2	2	no	—
28	C₂×C₄	—	2	4	no	—
29	C₂×C₄	—	2	4	no	—
30	C₂×C₄	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄	C₂×D₄	1	2	yes	—
34	C₈	—	4	4	no	—
35	C₂²	—	2	1	no	—
36	C₂²	—	2	2	no	—
37	C₂²	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₄	—	2	1	no	—
39	C₄	—	2	2	no	—
40	C₄	—	4	4	no	—
41	C₄	#101	1	2	yes	—
42	C₄	#135	1	4	yes	—
43	C₂	—	4	1	no	—
44	C₂	C₂×#101	1	1	yes	characteristic
45	C₂	#416	1	2	yes	—

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

N	H ≅ G/N	type
3. #332	C₂	semidirect

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