Subgroups — C₂×#364 #2152

Order 128.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#364	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈	C₄	1	1	yes	characteristic
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₄²	C₄	1	1	yes	characteristic
7	M₃₂	—	2	2	no	—
8	M₃₂	C₂²	1	4	yes	—
9	C₂×C₁₆	—	2	2	no	—
10	C₄×C₈	C₄	1	2	yes	—
11	C₄×C₈	C₂²	1	2	yes	—
12	C₂²×C₄	—	2	1	no	—
13	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈	C₈	1	2	yes	—
15	C₂×C₈	C₈	1	2	yes	—
16	C₂×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈	C₂×C₄	1	2	yes	—
18	C₂×C₈	D₄	1	1	yes	characteristic
19	C₂×C₈	D₄	1	1	yes	characteristic
20	C₂×C₈	Q₈	1	1	yes	characteristic
21	C₂×C₈	Q₈	1	1	yes	characteristic
22	C₂×C₈	C₂³	1	1	yes	characteristic
23	C₄²	—	2	1	no	—
24	C₄²	C₂×C₄	1	2	yes	—
25	C₁₆	—	2	4	no	—
26	C₂³	M₁₆	1	1	yes	characteristic
27	C₂×C₄	—	2	4	no	—
28	C₂×C₄	—	2	2	no	—
29	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄	M₁₆	1	1	yes	characteristic
34	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
35	C₈	C₄⋊C₄	1	1	yes	characteristic
36	C₈	C₄⋊C₄	1	1	yes	characteristic
37	C₈	C₂×C₈	1	4	yes	—
38	C₈	C₂×D₄	1	1	yes	characteristic
39	C₈	C₂×Q₈	1	1	yes	characteristic
40	C₂²	—	2	2	no	—
41	C₂²	C₄⋊C₈	1	1	yes	characteristic
42	C₂²	C₄⋊C₈	1	1	yes	characteristic
43	C₂²	C₂×M₁₆	1	1	yes	characteristic
44	C₄	—	2	4	no	—
45	C₄	C₄⋊C₈	1	1	yes	characteristic
46	C₄	C₄⋊C₈	1	1	yes	characteristic
47	C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄	C₂²×C₈	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	—	2	1	no	—
51	C₂	#364	1	2	yes	direct product factor
52	C₂	C₂×C₄⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄
commutator	C₄	C₂²×C₈
Frattini, cosocle	C₂×C₈	C₂³
socle	C₂²	C₄⋊C₈
prime radical	C₂³	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈ ◁ 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
3. #364	C₂	direct (N × H)
51. C₂	#364	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×M₃₂	2
C₂×C₄×C₈	2
#364	2

Subgroups — C2×#364 #2152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#364 #2152