Subgroups — C₂×C₄×#95 #13745

Order 256.

2231 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²	C₂	1	3	yes	maximal
2	C₂²×#95	C₂	1	4	yes	maximal
3	C₄×#95	C₂	1	8	yes	maximal, direct product factor
4	C₂⁴×C₄	C₂²	1	6	yes	—
5	C₂⁴×C₄	C₂²	1	1	yes	characteristic
6	C₂²×C₄²	—	2	24	no	—
7	C₂²×C₄²	C₄	1	24	yes	complemented
8	C₂²×C₄²	C₂²	1	12	yes	—
9	C₂×#95	C₄	1	32	yes	direct product factor
10	C₂×#95	C₂²	1	16	yes	—
11	C₂⁵	C₂³	1	1	yes	characteristic
12	C₂³×C₄	—	2	24	no	—
13	C₂³×C₄	—	2	24	no	—
14	C₂³×C₄	C₂×C₄	1	48	yes	—
15	C₂³×C₄	C₂×C₄	1	24	yes	—
16	C₂³×C₄	C₂×C₄	1	12	yes	—
17	C₂³×C₄	D₄	1	12	yes	—
18	C₂³×C₄	Q₈	1	4	yes	—
19	C₂³×C₄	C₂³	1	12	yes	—
20	C₂³×C₄	C₂³	1	2	yes	—
21	C₂×C₄²	—	2	96	no	—
22	C₂×C₄²	—	2	48	no	—
23	C₂×C₄²	C₂×C₄	1	48	yes	complemented
24	#95	C₂×C₄	1	64	yes	direct product factor
25	C₂⁴	C₂²×C₄	1	6	yes	—
26	C₂⁴	C₂²×C₄	1	8	yes	—
27	C₂⁴	C₂×D₄	1	6	yes	—
28	C₂⁴	C₂×Q₈	1	2	yes	—
29	C₂⁴	#41	1	8	yes	—
30	C₂⁴	C₂⁴	1	1	yes	characteristic
31	C₂²×C₄	—	2	48	no	—
32	C₂²×C₄	—	2	48	no	—
33	C₂²×C₄	—	2	192	no	—
34	C₂²×C₄	—	2	24	no	—
35	C₂²×C₄	—	2	24	no	—
36	C₂²×C₄	C₄²	1	16	yes	—
37	C₂²×C₄	C₄²	1	96	yes	complemented
38	C₂²×C₄	C₂²⋊C₄	1	48	yes	—
39	C₂²×C₄	C₄⋊C₄	1	48	yes	—
40	C₂²×C₄	C₂²×C₄	1	48	yes	—
41	C₂²×C₄	C₂²×C₄	1	24	yes	—
42	C₂²×C₄	C₂²×C₄	1	12	yes	—
43	C₂²×C₄	C₂×D₄	1	12	yes	—
44	C₂²×C₄	C₂×Q₈	1	4	yes	—
45	C₄²	—	2	96	no	—
46	C₂³	C₂×C₄²	1	4	yes	—
47	C₂³	C₂×C₄²	1	24	yes	—
48	C₂³	C₂×C₂²⋊C₄	1	12	yes	—
49	C₂³	C₂×C₄⋊C₄	1	12	yes	—
50	C₂³	#117	1	24	yes	—
51	C₂³	C₄×D₄	1	48	yes	—
52	C₂³	C₄×Q₈	1	16	yes	—
53	C₂³	C₂³×C₄	1	3	yes	—
54	C₂³	C₂³×C₄	1	4	yes	—
55	C₂³	C₂²×D₄	1	3	yes	—
56	C₂³	C₂²×Q₈	1	1	yes	characteristic
57	C₂³	C₂×#41	1	4	yes	—
58	C₂×C₄	—	2	24	no	—
59	C₂×C₄	—	2	24	no	—
60	C₂×C₄	—	2	96	no	—
61	C₂×C₄	—	2	192	no	—
62	C₂×C₄	#95	1	64	yes	direct product factor
63	C₂×C₄	C₂×C₄²	1	8	yes	—
64	C₂×C₄	C₂×C₄²	1	48	yes	complemented
65	C₂×C₄	C₂×C₂²⋊C₄	1	24	yes	—
66	C₂×C₄	C₂×C₄⋊C₄	1	24	yes	—
67	C₂²	C₄³	1	8	yes	—
68	C₂²	C₂×#95	1	8	yes	—
69	C₂²	#376	1	8	yes	—
70	C₂²	C₄×C₂²⋊C₄	1	48	yes	—
71	C₂²	C₄×C₄⋊C₄	1	48	yes	—
72	C₂²	C₂²×C₄²	1	1	yes	characteristic
73	C₂²	C₂²×C₄²	1	6	yes	—
74	C₂²	C₂²×C₂²⋊C₄	1	3	yes	—
75	C₂²	C₂²×C₄⋊C₄	1	3	yes	—
76	C₂²	C₂×#117	1	6	yes	—
77	C₂²	C₂×C₄×D₄	1	12	yes	—
78	C₂²	C₂×C₄×Q₈	1	4	yes	—
79	C₄	—	2	48	no	—
80	C₄	C₂×#95	1	16	yes	direct product factor
81	C₂	C₄×#95	1	16	yes	direct product factor
82	C₂	C₂×C₄³	1	1	yes	characteristic
83	C₂	C₂²×#95	1	1	yes	characteristic
84	C₂	C₂×#376	1	1	yes	characteristic
85	C₂	C₂×C₄×C₂²⋊C₄	1	6	yes	—
86	C₂	C₂×C₄×C₄⋊C₄	1	6	yes	—

	subgroup	G/H
center	C₂⁴×C₄	C₂²
commutator	C₂	C₂×C₄³
Frattini, cosocle	C₂⁴	C₂⁴
socle, prime radical	C₂⁵	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂⁴ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. C₄×#95	C₂	direct (N × H)
7. C₂²×C₄²	C₄	semidirect
9. C₂×#95	C₄	direct (N × H)
23. C₂×C₄²	C₂×C₄	semidirect
24. #95	C₂×C₄	direct (N × H)
37. C₂²×C₄	C₄²	semidirect
62. C₂×C₄	#95	direct (N × H)
64. C₂×C₄	C₂×C₄²	semidirect
80. C₄	C₂×#95	direct (N × H)
81. C₂	C₄×#95	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×C₄²	2
C₂²×#95	2
C₄×#95	2

Subgroups — C2×C4×#95 #13745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#95 #13745