Subgroups — C₂×#432 #2918

Order 128.

244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²	C₂	1	1	yes	maximal, characteristic
2	#432	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	2	yes	maximal, complemented
6	C₂³×C₄	C₄	1	1	yes	characteristic
7	C₂³×C₄	C₄	1	1	yes	characteristic
8	C₂³×C₄	C₂²	1	1	yes	characteristic
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	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	8	yes	complemented
19	C₂⁴	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄	—	2	4	no	—
21	C₂²×C₄	—	2	4	no	—
22	C₂²×C₄	—	2	4	no	—
23	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄	C₂×C₄	1	2	yes	—
25	C₂²×C₄	C₂×C₄	1	4	yes	—
26	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄	C₂×C₄	1	4	yes	—
30	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄	C₂³	1	2	yes	—
32	C₂²×C₄	C₂³	1	1	yes	characteristic
33	C₂×C₈	—	2	8	no	—
34	C₂×C₈	C₂³	1	8	yes	—
35	C₄²	C₂×C₄	1	4	yes	—
36	C₄²	C₂×C₄	1	4	yes	—
37	C₄²	C₂×C₄	1	2	yes	—
38	C₄²	C₂×C₄	1	2	yes	—
39	C₄²	C₂³	1	2	yes	—
40	C₄²	C₂³	1	2	yes	—
41	C₂³	—	2	2	no	—
42	C₂³	—	2	2	no	—
43	C₂³	M₁₆	1	4	yes	—
44	C₂³	C₂²×C₄	1	2	yes	—
45	C₂³	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	2	8	no	—
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	2	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	2	4	no	—
52	C₂×C₄	—	2	8	no	—
53	C₂×C₄	—	2	4	no	—
54	C₂×C₄	M₁₆	1	4	yes	—
55	C₂×C₄	C₂²×C₄	1	2	yes	—
56	C₂×C₄	C₂²×C₄	1	2	yes	—
57	C₂×C₄	C₂²×C₄	1	2	yes	—
58	C₂×C₄	C₂²×C₄	1	2	yes	—
59	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₄	C₂²×C₄	1	2	yes	—
61	C₂×C₄	#41	1	4	yes	—
62	C₂×C₄	C₂⁴	1	1	yes	characteristic
63	C₈	—	2	8	no	—
64	C₂²	—	2	2	no	—
65	C₂²	—	2	2	no	—
66	C₂²	—	2	8	no	—
67	C₂²	#117	1	2	yes	—
68	C₂²	C₂×M₁₆	1	4	yes	—
69	C₂²	C₂×M₁₆	1	2	yes	—
70	C₂²	C₂×M₁₆	1	2	yes	—
71	C₂²	C₂³×C₄	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	2	2	no	—
74	C₄	—	2	2	no	—
75	C₄	—	2	2	no	—
76	C₄	#117	1	2	yes	—
77	C₄	C₂×M₁₆	1	4	yes	—
78	C₄	C₂×#41	1	2	yes	—
79	C₂	—	2	4	no	—
80	C₂	#432	1	4	yes	direct product factor
81	C₂	C₂×#117	1	1	yes	characteristic
82	C₂	C₂²×M₁₆	1	1	yes	characteristic
83	C₂	C₂²×M₁₆	1	1	yes	characteristic

	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. #432	C₂	direct (N × H)
3. C₂×C₄⋊C₈	C₂	semidirect
5. C₂×#97	C₂	semidirect
16. C₄⋊C₈	C₂²	semidirect
18. #97	C₂²	semidirect
80. C₂	#432	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×C₄²	2
#432	2
C₂×C₄⋊C₈	2
C₂×C₂²⋊C₈	2
C₂×#97	2

Subgroups — C2×#432 #2918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#432 #2918