Subgroups — C₂×#423 #2903

Order 128.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₁₆	C₂	1	2	yes	maximal
2	C₂²×C₄²	C₂	1	1	yes	maximal, characteristic
3	#423	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄⋊C₈	C₂	1	4	yes	maximal, complemented
5	C₂³×C₄	C₄	1	2	yes	—
6	C₂³×C₄	C₂²	1	1	yes	characteristic
7	C₂×M₁₆	—	2	8	no	—
8	C₂×M₁₆	C₂²	1	8	yes	—
9	C₂²×C₈	C₂²	1	4	yes	—
10	C₂×C₄²	C₄	1	1	yes	characteristic
11	C₂×C₄²	C₄	1	4	yes	—
12	C₂×C₄²	C₄	1	1	yes	characteristic
13	C₂×C₄²	C₂²	1	4	yes	—
14	C₂×C₄²	C₂²	1	2	yes	—
15	C₄⋊C₈	C₂²	1	16	yes	complemented
16	C₂⁴	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄	—	2	8	no	—
18	C₂²×C₄	C₂×C₄	1	2	yes	—
19	C₂²×C₄	C₂×C₄	1	8	yes	—
20	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄	C₂×C₄	1	2	yes	—
22	C₂²×C₄	C₂×C₄	1	2	yes	—
23	C₂²×C₄	D₄	1	4	yes	—
24	C₂²×C₄	Q₈	1	4	yes	—
25	C₂²×C₄	C₂³	1	2	yes	—
26	C₂²×C₄	C₂³	1	1	yes	characteristic
27	M₁₆	—	2	16	no	—
28	C₂×C₈	—	2	8	no	—
29	C₂×C₈	C₂³	1	8	yes	—
30	C₄²	C₂×C₄	1	4	yes	—
31	C₄²	C₂×C₄	1	4	yes	—
32	C₄²	C₂×C₄	1	4	yes	—
33	C₄²	C₂³	1	4	yes	—
34	C₂³	—	2	4	no	—
35	C₂³	C₄⋊C₄	1	4	yes	—
36	C₂³	C₂²×C₄	1	2	yes	—
37	C₂³	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄	—	2	4	no	—
39	C₂×C₄	—	2	16	no	—
40	C₂×C₄	C₄⋊C₄	1	8	yes	—
41	C₂×C₄	C₄⋊C₄	1	4	yes	—
42	C₂×C₄	M₁₆	1	8	yes	complemented
43	C₂×C₄	C₂²×C₄	1	4	yes	—
44	C₂×C₄	C₂²×C₄	1	2	yes	—
45	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄	C₂²×C₄	1	4	yes	—
47	C₂×C₄	C₂×D₄	1	2	yes	—
48	C₂×C₄	C₂×D₄	1	4	yes	—
49	C₂×C₄	C₂×Q₈	1	4	yes	—
50	C₂×C₄	C₂×Q₈	1	2	yes	—
51	C₂×C₄	C₂⁴	1	1	yes	characteristic
52	C₈	—	2	8	no	—
53	C₂²	—	2	4	no	—
54	C₂²	—	2	8	no	—
55	C₂²	C₂×C₄⋊C₄	1	4	yes	—
56	C₂²	C₂×C₄⋊C₄	1	2	yes	—
57	C₂²	C₂×M₁₆	1	4	yes	—
58	C₂²	C₂³×C₄	1	1	yes	characteristic
59	C₄	—	2	4	no	—
60	C₄	C₂×C₄⋊C₄	1	4	yes	—
61	C₄	C₂×C₄⋊C₄	1	2	yes	—
62	C₄	C₂×M₁₆	1	8	yes	complemented
63	C₄	C₂²×D₄	1	1	yes	characteristic
64	C₄	C₂²×Q₈	1	1	yes	characteristic
65	C₂	—	2	4	no	—
66	C₂	#423	1	4	yes	direct product factor
67	C₂	C₂²×C₄⋊C₄	1	1	yes	characteristic
68	C₂	C₂²×M₁₆	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
3. #423	C₂	direct (N × H)
4. C₂×C₄⋊C₈	C₂	semidirect
15. C₄⋊C₈	C₂²	semidirect
42. C₂×C₄	M₁₆	semidirect
62. C₄	C₂×M₁₆	semidirect
66. C₂	#423	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×M₁₆	2
C₂²×C₄²	2
#423	2
C₂×C₄⋊C₈	2

Subgroups — C2×#423 #2903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#423 #2903