Subgroups — C₂×#3407 #62623

Order 256.

1037 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131	C₂	1	1	yes	maximal, characteristic
2	#3407	C₂	1	16	yes	maximal, direct product factor
3	C₂×#504	C₂	1	8	yes	maximal, complemented
4	C₂²×M₃₂	C₂	1	6	yes	maximal, complemented
5	C₂²×#41	C₄	1	1	yes	characteristic
6	C₂×#131	C₄	1	4	yes	—
7	C₂×#131	C₄	1	8	yes	—
8	C₂×#131	C₂²	1	4	yes	—
9	C₂×#131	C₂²	1	8	yes	—
10	C₂²×M₁₆	C₄	1	3	yes	—
11	C₂³×C₈	C₂²	1	3	yes	—
12	#504	C₂²	1	64	yes	complemented
13	C₂×M₃₂	C₂²	1	4	yes	—
14	C₂×M₃₂	C₂²	1	12	yes	complemented
15	C₂×M₃₂	C₂²	1	48	yes	complemented
16	C₂²×C₁₆	C₂²	1	12	yes	complemented
17	C₂×#41	C₈	1	4	yes	—
18	C₂×#41	C₈	1	8	yes	—
19	C₂×#41	C₂×C₄	1	4	yes	—
20	C₂×#41	C₂×C₄	1	8	yes	—
21	C₂²×Q₈	C₈	1	1	yes	characteristic
22	C₂²×D₄	C₈	1	3	yes	—
23	C₂³×C₄	C₂×C₄	1	3	yes	—
24	#131	C₂×C₄	1	16	yes	—
25	#131	C₂×C₄	1	32	yes	—
26	#131	C₂³	1	16	yes	—
27	C₂×M₁₆	C₂×C₄	1	12	yes	—
28	C₂×M₁₆	C₂×C₄	1	24	yes	—
29	C₂²×C₈	C₂×C₄	1	3	yes	—
30	C₂²×C₈	C₂×C₄	1	6	yes	—
31	C₂²×C₈	C₂×C₄	1	12	yes	—
32	C₂²×C₈	C₂³	1	12	yes	—
33	C₂²×C₈	C₂³	1	1	yes	characteristic
34	C₂²×C₈	C₂³	1	6	yes	—
35	M₃₂	C₂³	1	16	yes	—
36	M₃₂	C₂³	1	48	yes	complemented
37	C₂×C₁₆	C₂³	1	8	yes	—
38	C₂×C₁₆	C₂³	1	48	yes	complemented
39	C₂⁴	C₂×C₈	1	3	yes	—
40	#41	C₂×C₈	1	16	yes	—
41	#41	C₂×C₈	1	32	yes	—
42	#41	C₂²×C₄	1	16	yes	—
43	C₂×Q₈	C₂×C₈	1	8	yes	—
44	C₂×Q₈	C₂×C₈	1	4	yes	—
45	C₂×D₄	C₂×C₈	1	12	yes	—
46	C₂×D₄	C₂×C₈	1	24	yes	—
47	C₂²×C₄	C₂×C₈	1	3	yes	—
48	C₂²×C₄	C₂×C₈	1	6	yes	—
49	C₂²×C₄	C₂×C₈	1	12	yes	—
50	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄	C₂²×C₄	1	12	yes	—
52	C₂²×C₄	C₂²×C₄	1	6	yes	—
53	M₁₆	C₂²×C₄	1	48	yes	—
54	C₂×C₈	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₈	C₂²×C₄	1	2	yes	—
56	C₂×C₈	C₂²×C₄	1	12	yes	—
57	C₂×C₈	C₂²×C₄	1	6	yes	—
58	C₂×C₈	C₂²×C₄	1	24	yes	—
59	C₂×C₈	C₂²×C₄	1	12	yes	—
60	C₂×C₈	C₂⁴	1	12	yes	—
61	C₂×C₈	C₂⁴	1	2	yes	—
62	C₂×C₈	C₂⁴	1	1	yes	characteristic
63	C₁₆	C₂⁴	1	16	yes	—
64	C₂³	—	4	6	no	—
65	C₂³	C₂²×C₈	1	1	yes	characteristic
66	C₂³	C₂²×C₈	1	6	yes	—
67	C₂³	C₂²×C₈	1	12	yes	—
68	Q₈	C₂²×C₈	1	16	yes	—
69	D₄	C₂²×C₈	1	48	yes	—
70	C₂×C₄	C₂²×C₈	1	2	yes	—
71	C₂×C₄	C₂²×C₈	1	1	yes	characteristic
72	C₂×C₄	C₂²×C₈	1	12	yes	—
73	C₂×C₄	C₂²×C₈	1	6	yes	—
74	C₂×C₄	C₂²×C₈	1	24	yes	—
75	C₂×C₄	C₂²×C₈	1	12	yes	—
76	C₂×C₄	C₂³×C₄	1	2	yes	—
77	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
78	C₂×C₄	C₂³×C₄	1	12	yes	—
79	C₈	C₂³×C₄	1	2	yes	—
80	C₈	C₂³×C₄	1	1	yes	characteristic
81	C₈	C₂³×C₄	1	12	yes	—
82	C₈	C₂⁵	1	1	yes	characteristic
83	C₂²	—	2	2	no	—
84	C₂²	—	2	12	no	—
85	C₂²	—	4	12	no	—
86	C₂²	C₂³×C₈	1	2	yes	—
87	C₂²	C₂³×C₈	1	12	yes	—
88	C₂²	C₂³×C₈	1	1	yes	characteristic
89	C₄	C₂³×C₈	1	2	yes	—
90	C₄	C₂³×C₈	1	1	yes	characteristic
91	C₄	C₂³×C₈	1	12	yes	—
92	C₄	C₂⁴×C₄	1	1	yes	characteristic
93	C₂	—	2	2	no	—
94	C₂	—	2	12	no	—
95	C₂	#3407	1	2	yes	direct product factor
96	C₂	C₂⁴×C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂⁴
commutator	C₂	C₂⁴×C₈
Frattini, cosocle	C₈	C₂⁵
socle	C₂²	C₂³×C₈
prime radical	C₂²×#41	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈ ◁ G
LECS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #3407	C₂	direct (N × H)
3. C₂×#504	C₂	semidirect
4. C₂²×M₃₂	C₂	semidirect
12. #504	C₂²	semidirect
14. C₂×M₃₂	C₂²	semidirect
15. C₂×M₃₂	C₂²	semidirect
16. C₂²×C₁₆	C₂²	semidirect
36. M₃₂	C₂³	semidirect
38. C₂×C₁₆	C₂³	semidirect
95. C₂	#3407	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×#131	2
#3407	2
C₂×#504	2
C₂²×M₃₂	2

Subgroups — C2×#3407 #62623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3407 #62623