Subgroups — C₄×SD₃₂ #2173

Order 128.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₃₂	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₈	C₂	1	1	yes	maximal, characteristic
4	#367	C₂	1	1	yes	maximal, characteristic, complemented
5	#358	C₂	1	1	yes	maximal, characteristic, complemented
6	#357	C₂	1	1	yes	maximal, characteristic
7	C₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₁₆	C₂²	1	1	yes	characteristic
9	C₂×D₈	C₂²	1	1	yes	characteristic
10	C₄×Q₈	—	2	1	no	—
11	C₄×D₄	—	2	1	no	—
12	SD₃₂	C₄	1	4	yes	direct product factor
13	C₂×C₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₆	C₂²	1	1	yes	characteristic
15	#107	C₂²	1	1	yes	characteristic
16	#107	C₂²	1	1	yes	characteristic
17	#103	—	2	1	no	—
18	#102	—	2	1	no	—
19	C₄×C₈	C₂²	1	1	yes	characteristic
20	C₂×Q₈	—	2	1	no	—
21	C₂×D₄	—	2	1	no	—
22	C₂²×C₄	—	4	1	no	—
23	Q₁₆	—	2	1	no	—
24	Q₁₆	C₂×C₄	1	2	yes	complemented
25	D₈	—	2	1	no	—
26	D₈	C₂×C₄	1	2	yes	—
27	C₂×C₈	D₄	1	1	yes	characteristic
28	C₂×C₈	C₂³	1	1	yes	characteristic
29	C₄⋊C₄	—	2	1	no	—
30	C₄⋊C₄	—	2	1	no	—
31	C₄⋊C₄	—	4	1	no	—
32	C₂²⋊C₄	—	4	1	no	—
33	C₄²	—	4	1	no	—
34	C₄²	D₄	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	C₂×C₄	1	2	yes	complemented
37	C₂³	—	4	1	no	—
38	Q₈	—	2	2	no	—
39	Q₈	—	4	1	no	—
40	D₄	—	2	2	no	—
41	D₄	—	4	1	no	—
42	C₂×C₄	—	4	1	no	—
43	C₂×C₄	—	4	1	no	—
44	C₂×C₄	—	4	1	no	—
45	C₂×C₄	—	8	2	no	—
46	C₂×C₄	D₈	1	1	yes	characteristic
47	C₂×C₄	D₈	1	1	yes	characteristic
48	C₂×C₄	C₂×D₄	1	1	yes	characteristic
49	C₈	—	2	1	no	—
50	C₈	C₂²×C₄	1	1	yes	characteristic
51	C₈	#41	1	1	yes	characteristic
52	C₂²	—	4	2	no	—
53	C₂²	—	8	1	no	—
54	C₂²	—	8	1	no	—
55	C₂²	C₂×D₈	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	4	2	no	—
58	C₄	—	8	1	no	—
59	C₄	—	8	1	no	—
60	C₄	SD₃₂	1	2	yes	direct product factor
61	C₄	C₄×D₄	1	1	yes	characteristic
62	C₄	#135	1	1	yes	characteristic
63	C₂	—	8	2	no	—
64	C₂	C₄×D₈	1	1	yes	characteristic
65	C₂	C₂×SD₃₂	1	1	yes	characteristic
66	C₂	#508	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈
commutator	C₈	C₂²×C₄
Frattini, cosocle	C₂×C₈	C₂³
socle	C₂²	C₂×D₈
prime radical	C₂×D₈	C₂²
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₄×Q₁₆	C₂	semidirect
4. #367	C₂	semidirect
5. #358	C₂	semidirect
7. C₄×C₁₆	C₂	semidirect
12. SD₃₂	C₄	direct (N × H)
24. Q₁₆	C₂×C₄	semidirect
36. C₁₆	C₂×C₄	semidirect
60. C₄	SD₃₂	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×SD₃₂	2
C₄×Q₁₆	2
C₄×D₈	2
#367	2
#358	2
#357	2
C₄×C₁₆	2

Subgroups — C4×SD32 #2173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×SD₃₂ #2173