Subgroups — C₂×#357 #2136

Order 128.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	#357	C₂	1	4	yes	maximal, direct product factor
5	C₂²×D₄	—	2	1	no	—
6	C₂×D₈	—	2	1	no	—
7	C₂×D₈	—	2	2	no	—
8	C₂×D₈	C₄	1	4	yes	complemented
9	C₂×D₈	C₂²	1	2	yes	—
10	C₂²×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄	—	2	1	no	—
12	C₂×C₁₆	—	2	2	no	—
13	C₂×C₁₆	C₂²	1	2	yes	complemented
14	#107	—	2	1	no	—
15	#107	C₂²	1	2	yes	complemented
16	C₂⁴	—	4	1	no	—
17	C₂×D₄	—	2	4	no	—
18	C₂×D₄	—	2	2	no	—
19	C₂×D₄	—	4	1	no	—
20	C₂×D₄	—	4	2	no	—
21	C₂²×C₄	—	4	1	no	—
22	C₂²×C₄	D₄	1	1	yes	characteristic
23	D₈	—	2	4	no	—
24	D₈	—	2	2	no	—
25	D₈	C₂×C₄	1	4	yes	complemented
26	C₂×C₈	C₂×C₄	1	2	yes	—
27	C₂×C₈	D₄	1	1	yes	characteristic
28	C₂×C₈	D₄	1	2	yes	—
29	C₂×C₈	C₂³	1	1	yes	characteristic
30	C₄⋊C₄	—	2	2	no	—
31	C₄⋊C₄	—	4	1	no	—
32	C₁₆	—	2	2	no	—
33	C₂³	—	4	4	no	—
34	C₂³	—	4	2	no	—
35	C₂³	—	8	2	no	—
36	C₂³	—	8	2	no	—
37	C₂³	D₈	1	1	yes	characteristic
38	D₄	—	2	4	no	—
39	D₄	—	4	4	no	—
40	D₄	—	4	2	no	—
41	C₂×C₄	—	4	2	no	—
42	C₂×C₄	—	8	2	no	—
43	C₂×C₄	C₂²⋊C₄	1	2	yes	—
44	C₂×C₄	D₈	1	1	yes	characteristic
45	C₂×C₄	SD₁₆	1	2	yes	—
46	C₂×C₄	C₂×D₄	1	1	yes	characteristic
47	C₈	C₂²⋊C₄	1	2	yes	—
48	C₈	C₂²×C₄	1	1	yes	characteristic
49	C₈	C₂×D₄	1	1	yes	characteristic
50	C₂²	—	4	4	no	—
51	C₂²	—	8	8	no	—
52	C₂²	—	8	2	no	—
53	C₂²	—	8	2	no	—
54	C₂²	#102	1	2	yes	—
55	C₂²	D₁₆	1	2	yes	—
56	C₂²	SD₃₂	1	2	yes	—
57	C₂²	C₂×D₈	1	1	yes	characteristic
58	C₄	—	8	2	no	—
59	C₄	#102	1	2	yes	—
60	C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₄	C₂×SD₁₆	1	1	yes	characteristic
62	C₂	—	8	4	no	—
63	C₂	#357	1	4	yes	direct product factor
64	C₂	C₂×#102	1	1	yes	characteristic
65	C₂	C₂×D₁₆	1	1	yes	characteristic
66	C₂	C₂×SD₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	D₈
commutator	C₈	C₂²×C₄
Frattini, cosocle	C₂×C₈	C₂³
prime radical	C₂²×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×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. C₂²×C₁₆	C₂	semidirect
3. C₂×#107	C₂	semidirect
4. #357	C₂	direct (N × H)
8. C₂×D₈	C₄	semidirect
13. C₂×C₁₆	C₂²	semidirect
15. #107	C₂²	semidirect
25. D₈	C₂×C₄	semidirect
63. C₂	#357	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₈	2
C₂²×C₁₆	2
C₂×#107	2
#357	2

Subgroups — C2×#357 #2136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#357 #2136