Subgroups — C₂×#381 #2279

Order 128.

572 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₄	C₂	1	2	yes	maximal
3	#381	C₂	1	8	yes	maximal, direct product factor
4	C₂×#95	C₂	1	4	yes	maximal, complemented
5	C₂⁵	C₂²	1	1	yes	characteristic
6	C₂³×C₄	—	2	8	no	—
7	C₂³×C₄	C₄	1	8	yes	complemented
8	C₂³×C₄	C₂²	1	4	yes	—
9	C₂³×C₄	C₂²	1	2	yes	—
10	C₂³×C₄	C₂²	1	4	yes	—
11	C₂×C₂²⋊C₄	—	2	8	no	—
12	C₂×C₂²⋊C₄	C₂²	1	8	yes	—
13	#95	C₂²	1	16	yes	complemented
14	C₂⁴	—	2	8	no	—
15	C₂⁴	C₂×C₄	1	4	yes	—
16	C₂⁴	D₄	1	8	yes	—
17	C₂⁴	C₂³	1	2	yes	—
18	C₂⁴	C₂³	1	1	yes	characteristic
19	C₂²×C₄	—	2	32	no	—
20	C₂²×C₄	—	2	8	no	—
21	C₂²×C₄	—	2	16	no	—
22	C₂²×C₄	—	2	8	no	—
23	C₂²×C₄	—	2	16	no	—
24	C₂²×C₄	C₂×C₄	1	8	yes	—
25	C₂²×C₄	C₂×C₄	1	16	yes	complemented
26	C₂²×C₄	C₂³	1	8	yes	—
27	C₂²×C₄	C₂³	1	4	yes	—
28	C₂²⋊C₄	—	2	16	no	—
29	C₂³	—	2	16	no	—
30	C₂³	—	2	32	no	—
31	C₂³	—	2	8	no	—
32	C₂³	C₂²⋊C₄	1	16	yes	—
33	C₂³	C₂²×C₄	1	4	yes	—
34	C₂³	C₂²×C₄	1	2	yes	—
35	C₂³	C₂×D₄	1	8	yes	—
36	C₂³	C₂×D₄	1	4	yes	—
37	C₂³	#41	1	8	yes	—
38	C₂³	C₂⁴	1	1	yes	characteristic
39	C₂×C₄	—	2	16	no	—
40	C₂×C₄	—	2	32	no	—
41	C₂×C₄	—	2	8	no	—
42	C₂×C₄	—	2	8	no	—
43	C₂×C₄	—	2	16	no	—
44	C₂×C₄	—	4	16	no	—
45	C₂×C₄	C₂²×C₄	1	8	yes	—
46	C₂²	—	2	8	no	—
47	C₂²	—	2	16	no	—
48	C₂²	—	2	32	no	—
49	C₂²	C₂×C₂²⋊C₄	1	8	yes	—
50	C₂²	C₂×C₂²⋊C₄	1	4	yes	—
51	C₂²	#117	1	8	yes	—
52	C₂²	#123	1	16	yes	—
53	C₂²	C₂³×C₄	1	1	yes	characteristic
54	C₂²	C₂²×D₄	1	2	yes	—
55	C₂²	C₂×#41	1	4	yes	—
56	C₄	—	2	8	no	—
57	C₄	—	4	8	no	—
58	C₂	—	2	8	no	—
59	C₂	#381	1	8	yes	direct product factor
60	C₂	C₂²×C₂²⋊C₄	1	1	yes	characteristic
61	C₂	C₂×#117	1	2	yes	—
62	C₂	C₂×#123	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴	C₂³
commutator	C₂²	C₂³×C₄
Frattini, cosocle	C₂³	C₂⁴
prime radical	C₂⁵	C₂²
LCS	G ▷ C₂² ▷ 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
3. #381	C₂	direct (N × H)
4. C₂×#95	C₂	semidirect
7. C₂³×C₄	C₄	semidirect
13. #95	C₂²	semidirect
25. C₂²×C₄	C₂×C₄	semidirect
59. C₂	#381	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄	2
C₂²×C₂²⋊C₄	2
#381	2
C₂×#95	2

Subgroups — C2×#381 #2279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#381 #2279