Subgroups — C₂×#382 #2281

Order 128.

356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₄	C₂	1	2	yes	maximal
2	C₂²×C₄²	C₂	1	1	yes	maximal, characteristic
3	#382	C₂	1	8	yes	maximal, direct product factor
4	C₂×#95	C₂	1	4	yes	maximal
5	C₂³×C₄	C₂²	1	4	yes	—
6	C₂³×C₄	C₂²	1	2	yes	—
7	C₂³×C₄	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄	—	2	8	no	—
9	C₂×C₄⋊C₄	C₂²	1	8	yes	—
10	C₂×C₄²	C₄	1	8	yes	complemented
11	C₂×C₄²	C₂²	1	4	yes	—
12	#95	C₂²	1	16	yes	—
13	C₂⁴	C₂³	1	1	yes	characteristic
14	C₂²×C₄	—	2	8	no	—
15	C₂²×C₄	—	2	8	no	—
16	C₂²×C₄	—	2	16	no	—
17	C₂²×C₄	C₂×C₄	1	8	yes	—
18	C₂²×C₄	C₂×C₄	1	4	yes	—
19	C₂²×C₄	D₄	1	4	yes	—
20	C₂²×C₄	Q₈	1	4	yes	—
21	C₂²×C₄	C₂³	1	8	yes	—
22	C₂²×C₄	C₂³	1	4	yes	—
23	C₂²×C₄	C₂³	1	2	yes	—
24	C₄⋊C₄	—	2	16	no	—
25	C₄²	C₂×C₄	1	16	yes	complemented
26	C₂³	C₂²×C₄	1	2	yes	—
27	C₂³	C₂×D₄	1	2	yes	—
28	C₂³	C₂×Q₈	1	2	yes	—
29	C₂³	#41	1	8	yes	—
30	C₂³	C₂⁴	1	1	yes	characteristic
31	C₂×C₄	—	2	16	no	—
32	C₂×C₄	—	2	8	no	—
33	C₂×C₄	—	2	8	no	—
34	C₂×C₄	—	2	16	no	—
35	C₂×C₄	—	4	16	no	—
36	C₂×C₄	C₄⋊C₄	1	16	yes	—
37	C₂×C₄	C₂²×C₄	1	8	yes	—
38	C₂×C₄	C₂²×C₄	1	4	yes	—
39	C₂×C₄	C₂×D₄	1	4	yes	—
40	C₂×C₄	C₂×Q₈	1	4	yes	—
41	C₂²	C₂×C₄⋊C₄	1	4	yes	—
42	C₂²	#117	1	8	yes	—
43	C₂²	#124	1	8	yes	—
44	C₂²	#125	1	8	yes	—
45	C₂²	C₂³×C₄	1	1	yes	characteristic
46	C₂²	C₂²×D₄	1	1	yes	characteristic
47	C₂²	C₂²×Q₈	1	1	yes	characteristic
48	C₂²	C₂×#41	1	4	yes	—
49	C₄	—	2	8	no	—
50	C₄	—	4	8	no	—
51	C₄	C₂×C₄⋊C₄	1	8	yes	—
52	C₂	#382	1	8	yes	direct product factor
53	C₂	C₂²×C₄⋊C₄	1	1	yes	characteristic
54	C₂	C₂×#117	1	2	yes	—
55	C₂	C₂×#124	1	2	yes	—
56	C₂	C₂×#125	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴	C₂³
commutator	C₂²	C₂³×C₄
Frattini, cosocle	C₂³	C₂⁴
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. #382	C₂	direct (N × H)
10. C₂×C₄²	C₄	semidirect
25. C₄²	C₂×C₄	semidirect
52. C₂	#382	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×C₄⋊C₄	2
C₂²×C₄²	2
#382	2
C₂×#95	2

Subgroups — C2×#382 #2281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#382 #2281