Subgroups — C₂×#433 #2919

Order 128.

206 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#117	C₂	1	1	yes	maximal, characteristic
2	#433	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₂²⋊C₈	C₂	1	2	yes	maximal
5	C₂×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×C₄	C₂²	1	1	yes	characteristic
8	C₂²×C₈	C₂²	1	2	yes	—
9	C₂²×C₈	C₂²	1	2	yes	—
10	#117	C₄	1	4	yes	—
11	#117	C₂²	1	4	yes	—
12	C₂×C₄⋊C₄	C₄	1	2	yes	—
13	C₂×C₂²⋊C₄	C₄	1	2	yes	—
14	C₂×C₄²	C₂²	1	1	yes	characteristic
15	C₂×C₄²	C₂²	1	1	yes	characteristic
16	C₄⋊C₈	C₂²	1	8	yes	complemented
17	C₂²⋊C₈	C₂²	1	8	yes	—
18	#97	C₂²	1	4	yes	complemented
19	C₄×C₈	C₂²	1	4	yes	complemented
20	C₂⁴	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄	—	2	4	no	—
22	C₂²×C₄	C₂×C₄	1	2	yes	—
23	C₂²×C₄	C₂×C₄	1	2	yes	—
24	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄	C₂×C₄	1	2	yes	—
26	C₂²×C₄	C₂³	1	2	yes	—
27	C₂²×C₄	C₂³	1	1	yes	characteristic
28	C₂×C₈	—	2	4	no	—
29	C₂×C₈	—	2	4	no	—
30	C₂×C₈	C₂³	1	4	yes	—
31	C₂×C₈	C₂³	1	4	yes	—
32	C₄⋊C₄	C₂×C₄	1	8	yes	—
33	C₂²⋊C₄	C₂×C₄	1	8	yes	—
34	C₄²	C₂×C₄	1	2	yes	—
35	C₄²	C₂×C₄	1	2	yes	—
36	C₄²	C₂³	1	2	yes	—
37	C₄²	C₂³	1	2	yes	—
38	C₂³	—	2	2	no	—
39	C₂³	—	2	4	no	—
40	C₂³	C₂²×C₄	1	2	yes	—
41	C₂³	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	—	2	4	no	—
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	—	2	4	no	—
46	C₂×C₄	—	2	4	no	—
47	C₂×C₄	C₂²×C₄	1	4	yes	—
48	C₂×C₄	C₂²×C₄	1	4	yes	—
49	C₂×C₄	C₂²×C₄	1	2	yes	—
50	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄	#41	1	4	yes	—
52	C₂×C₄	C₂⁴	1	1	yes	characteristic
53	C₈	—	2	4	no	—
54	C₈	—	2	4	no	—
55	C₂²	—	2	2	no	—
56	C₂²	—	2	4	no	—
57	C₂²	—	4	4	no	—
58	C₂²	#117	1	2	yes	—
59	C₂²	#131	1	4	yes	—
60	C₂²	C₂³×C₄	1	1	yes	characteristic
61	C₄	—	2	2	no	—
62	C₄	—	2	4	no	—
63	C₄	—	2	4	no	—
64	C₄	#117	1	2	yes	—
65	C₄	C₂×#41	1	2	yes	—
66	C₂	—	4	2	no	—
67	C₂	#433	1	4	yes	direct product factor
68	C₂	C₂×#117	1	1	yes	characteristic
69	C₂	C₂×#131	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³
commutator	C₂²	C₂³×C₄
Frattini, cosocle	C₂×C₄	C₂⁴
socle	C₂³	C₂²×C₄
prime radical	C₂⁴	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #433	C₂	direct (N × H)
3. C₂×C₄⋊C₈	C₂	semidirect
5. C₂×#97	C₂	semidirect
6. C₂×C₄×C₈	C₂	semidirect
16. C₄⋊C₈	C₂²	semidirect
18. #97	C₂²	semidirect
19. C₄×C₈	C₂²	semidirect
67. C₂	#433	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×#117	2
#433	2
C₂×C₄⋊C₈	2
C₂×C₂²⋊C₈	2
C₂×#97	2
C₂×C₄×C₈	2

Subgroups — C2×#433 #2919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#433 #2919