Subgroups — C₄×#101 #1756

Order 128.

148 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×#101	C₂	1	2	yes	maximal
3	C₄×M₁₆	C₂	1	2	yes	maximal
4	#343	C₂	1	2	yes	maximal
5	C₂²×Q₈	C₂²	1	1	yes	characteristic
6	C₂×M₁₆	C₂²	1	4	yes	—
7	C₄×Q₈	—	2	2	no	—
8	C₄×Q₈	—	2	2	no	—
9	C₂×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
11	C₂×C₄²	C₄	1	2	yes	—
12	C₂×C₄²	C₂²	1	1	yes	characteristic
13	#101	C₄	1	8	yes	direct product factor
14	#97	—	2	2	no	—
15	C₄×C₈	—	2	2	no	—
16	C₂×Q₈	—	2	2	no	—
17	C₂×Q₈	—	2	2	no	—
18	C₂×Q₈	C₂×C₄	1	4	yes	—
19	C₂²×C₄	C₂×C₄	1	2	yes	—
20	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄	C₂×C₄	1	2	yes	—
22	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄	C₂³	1	1	yes	characteristic
24	M₁₆	—	2	4	no	—
25	M₁₆	C₂×C₄	1	8	yes	—
26	C₂×C₈	—	2	4	no	—
27	C₄⋊C₄	—	2	4	no	—
28	C₄⋊C₄	—	2	2	no	—
29	C₄²	—	2	2	no	—
30	C₄²	—	2	2	no	—
31	C₄²	D₄	1	2	yes	—
32	C₄²	D₄	1	2	yes	—
33	C₂³	C₂²×C₄	1	1	yes	characteristic
34	Q₈	—	2	8	no	—
35	C₂×C₄	—	2	2	no	—
36	C₂×C₄	—	2	2	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	2	2	no	—
39	C₂×C₄	—	4	1	no	—
40	C₂×C₄	—	4	2	no	—
41	C₂×C₄	C₄²	1	4	yes	—
42	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₄	C₂²⋊C₄	1	2	yes	—
44	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₄	C₂²×C₄	1	2	yes	—
46	C₂×C₄	C₂×D₄	1	2	yes	—
47	C₂×C₄	#41	1	2	yes	—
48	C₈	—	2	8	no	—
49	C₂²	—	2	1	no	—
50	C₂²	—	2	1	no	—
51	C₂²	C₂×C₄²	1	1	yes	characteristic
52	C₂²	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂²	#117	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	2	1	no	—
56	C₄	—	2	2	no	—
57	C₄	—	4	2	no	—
58	C₄	#101	1	2	yes	direct product factor
59	C₄	C₄×D₄	1	4	yes	—
60	C₂	—	2	1	no	—
61	C₂	—	2	1	no	—
62	C₂	C₄×C₂²⋊C₄	1	1	yes	characteristic
63	C₂	C₂×#101	1	1	yes	characteristic
64	C₂	#413	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄
commutator	C₂²	C₂×C₄²
Frattini, cosocle	C₂²×C₄	C₂³
socle	C₂²	C₂×C₂²⋊C₄
prime radical	C₂³	C₂²×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ 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
13. #101	C₄	direct (N × H)
58. C₄	#101	direct (N × H)

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×#101	2
C₄×M₁₆	2
#343	2

Subgroups — C4×#101 #1756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#101 #1756