Subgroups — C₂×#392 #2384

Order 128.

906 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄	C₂	1	3	yes	maximal, complemented
2	C₂²×C₂²⋊C₄	C₂	1	3	yes	maximal, complemented
3	#392	C₂	1	8	yes	maximal, direct product factor
4	C₂×#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵	C₂²	1	3	yes	—
6	C₂²×D₄	—	2	24	no	—
7	C₂²×D₄	—	2	12	no	—
8	C₂²×D₄	C₂²	1	12	yes	complemented
9	C₂³×C₄	C₂²	1	1	yes	characteristic
10	C₂³×C₄	C₂²	1	3	yes	—
11	C₂×C₂²⋊C₄	—	2	12	no	—
12	C₂×C₂²⋊C₄	C₂²	1	12	yes	complemented
13	#95	C₂²	1	4	yes	complemented
14	C₂⁴	—	2	6	no	—
15	C₂⁴	—	2	12	no	—
16	C₂⁴	—	2	12	no	—
17	C₂⁴	—	2	6	no	—
18	C₂⁴	D₄	1	12	yes	complemented
19	C₂⁴	C₂³	1	6	yes	—
20	C₂⁴	C₂³	1	1	yes	characteristic
21	C₂×D₄	—	2	96	no	—
22	C₂×D₄	—	2	48	no	—
23	C₂×D₄	—	2	24	no	—
24	C₂²×C₄	—	2	12	no	—
25	C₂²×C₄	—	2	6	no	—
26	C₂²×C₄	D₄	1	12	yes	complemented
27	C₂²×C₄	C₂³	1	2	yes	—
28	C₂²×C₄	C₂³	1	6	yes	—
29	C₂²⋊C₄	—	2	24	no	—
30	C₂³	—	2	48	no	—
31	C₂³	—	2	24	no	—
32	C₂³	—	2	6	no	—
33	C₂³	—	2	12	no	—
34	C₂³	—	2	12	no	—
35	C₂³	—	2	6	no	—
36	C₂³	—	4	12	no	—
37	C₂³	—	4	24	no	—
38	C₂³	—	4	12	no	—
39	C₂³	C₂×D₄	1	6	yes	—
40	C₂³	C₂×D₄	1	6	yes	—
41	C₂³	C₂×D₄	1	12	yes	complemented
42	C₂³	#41	1	2	yes	—
43	C₂³	C₂⁴	1	1	yes	characteristic
44	D₄	—	2	96	no	—
45	C₂×C₄	—	2	24	no	—
46	C₂×C₄	—	2	12	no	—
47	C₂×C₄	—	2	6	no	—
48	C₂×C₄	—	4	4	no	—
49	C₂×C₄	C₂×D₄	1	12	yes	complemented
50	C₂²	—	2	24	no	—
51	C₂²	—	2	12	no	—
52	C₂²	—	4	6	no	—
53	C₂²	—	4	12	no	—
54	C₂²	—	4	6	no	—
55	C₂²	—	4	48	no	—
56	C₂²	#120	1	12	yes	—
57	C₂²	#121	1	12	yes	—
58	C₂²	#127	1	4	yes	—
59	C₂²	C₂²×D₄	1	3	yes	—
60	C₂²	C₂²×D₄	1	3	yes	—
61	C₂²	C₂×#41	1	1	yes	characteristic
62	C₄	—	2	12	no	—
63	C₄	—	4	2	no	—
64	C₂	—	4	12	no	—
65	C₂	#392	1	8	yes	direct product factor
66	C₂	C₂×#120	1	3	yes	—
67	C₂	C₂×#121	1	3	yes	—
68	C₂	C₂×#127	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄	C₂	semidirect
2. C₂²×C₂²⋊C₄	C₂	semidirect
3. #392	C₂	direct (N × H)
4. C₂×#95	C₂	semidirect
8. C₂²×D₄	C₂²	semidirect
12. C₂×C₂²⋊C₄	C₂²	semidirect
13. #95	C₂²	semidirect
18. C₂⁴	D₄	semidirect
26. C₂²×C₄	D₄	semidirect
41. C₂³	C₂×D₄	semidirect
49. C₂×C₄	C₂×D₄	semidirect
65. C₂	#392	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄	2
C₂²×C₂²⋊C₄	2
#392	2
C₂×#95	2

Subgroups — C2×#392 #2384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#392 #2384