Subgroups — #1960

Order 128.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#103	C₂	1	4	yes	maximal
3	C₂×#97	C₂	1	1	yes	maximal, characteristic
4	#382	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈	C₂²	1	2	yes	—
6	C₂²×C₈	C₂²	1	2	yes	—
7	C₄⋊Q₈	—	2	2	no	—
8	C₄⋊Q₈	C₄	1	4	yes	complemented
9	C₂×C₄⋊C₄	—	2	2	no	—
10	C₂×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₄²	C₂²	1	1	yes	characteristic
12	#103	—	2	8	no	—
13	#97	—	2	2	no	—
14	#95	—	2	2	no	—
15	C₂×Q₈	—	2	2	no	—
16	C₂×Q₈	—	2	4	no	—
17	C₂×Q₈	—	2	4	no	—
18	C₂×Q₈	C₂×C₄	1	4	yes	—
19	C₂²×C₄	—	2	2	no	—
20	C₂²×C₄	—	2	2	no	—
21	C₂²×C₄	D₄	1	2	yes	—
22	C₂²×C₄	C₂³	1	1	yes	characteristic
23	C₂×C₈	—	2	2	no	—
24	C₂×C₈	—	2	2	no	—
25	C₂×C₈	D₄	1	4	yes	—
26	C₄⋊C₄	—	2	8	no	—
27	C₄⋊C₄	—	2	4	no	—
28	C₄²	C₂×C₄	1	2	yes	—
29	C₄²	D₄	1	2	yes	—
30	C₂³	C₂×D₄	1	1	yes	characteristic
31	Q₈	—	2	8	no	—
32	Q₈	—	4	4	no	—
33	C₂×C₄	—	2	4	no	—
34	C₂×C₄	—	2	4	no	—
35	C₂×C₄	—	4	2	no	—
36	C₂×C₄	—	4	2	no	—
37	C₂×C₄	—	4	2	no	—
38	C₂×C₄	—	4	4	no	—
39	C₂×C₄	C₂²⋊C₄	1	4	yes	—
40	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄	C₂×D₄	1	2	yes	—
42	C₂×C₄	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄	#41	1	2	yes	—
44	C₈	—	2	4	no	—
45	C₂²	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂²	#124	1	1	yes	characteristic
47	C₂²	#127	1	1	yes	characteristic
48	C₂²	#137	1	4	yes	—
49	C₄	—	2	4	no	—
50	C₄	—	4	4	no	—
51	C₄	—	8	2	no	—
52	C₄	C₄×D₄	1	2	yes	—
53	C₄	#121	1	2	yes	—
54	C₂	#390	1	1	yes	characteristic
55	C₂	#419	1	2	yes	—
56	C₂	#491	1	2	yes	—
57	C₂	#497	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³	C₂×D₄
commutator	C₂×C₄	C₂²×C₄
Frattini, cosocle	C₂²×C₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
8. C₄⋊Q₈	C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Q₈	2
C₂×#103	2
C₂×#97	2
#382	2