Subgroups — C₄×#347 #12540

Order 256.

209 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#347	C₂	1	4	yes	maximal
2	C₄×M₃₂	C₂	1	2	yes	maximal
3	C₄×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×M₃₂	C₂²	1	4	yes	—
5	C₂×#97	C₄	1	2	yes	—
6	C₂×#97	C₂²	1	2	yes	—
7	C₂×C₄×C₈	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
9	C₄³	C₄	1	1	yes	characteristic
10	#347	C₄	1	16	yes	direct product factor
11	#346	C₄	1	4	yes	complemented
12	C₄×C₁₆	C₄	1	4	yes	complemented
13	C₂²×C₈	C₂×C₄	1	2	yes	—
14	C₂²×C₈	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈	C₂³	1	1	yes	characteristic
16	C₂×C₄²	—	2	2	no	—
17	C₂×C₄²	C₂×C₄	1	2	yes	—
18	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
19	M₃₂	C₂×C₄	1	16	yes	—
20	C₂×C₁₆	C₂×C₄	1	8	yes	—
21	#97	—	2	4	no	—
22	#97	C₂×C₄	1	8	yes	—
23	C₄×C₈	—	2	2	no	—
24	C₄×C₈	C₂×C₄	1	2	yes	—
25	C₄×C₈	C₂×C₄	1	2	yes	—
26	C₂²×C₄	—	2	2	no	—
27	C₂²×C₄	M₁₆	1	2	yes	—
28	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₈	—	2	2	no	—
30	C₂×C₈	—	2	2	no	—
31	C₂×C₈	C₄²	1	4	yes	—
32	C₂×C₈	C₄²	1	2	yes	—
33	C₂×C₈	M₁₆	1	4	yes	—
34	C₂×C₈	C₂²×C₄	1	2	yes	—
35	C₂×C₈	C₂²×C₄	1	4	yes	—
36	C₄²	—	2	2	no	—
37	C₄²	—	4	4	no	—
38	C₄²	C₄²	1	4	yes	—
39	C₄²	C₄²	1	1	yes	characteristic
40	C₄²	C₄²	1	1	yes	characteristic
41	C₄²	M₁₆	1	2	yes	—
42	C₁₆	C₄²	1	16	yes	complemented
43	C₂³	C₂×M₁₆	1	1	yes	characteristic
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	—	2	4	no	—
46	C₂×C₄	—	4	4	no	—
47	C₂×C₄	#97	1	2	yes	—
48	C₂×C₄	#97	1	2	yes	—
49	C₂×C₄	C₂×C₄²	1	1	yes	characteristic
50	C₂×C₄	C₂×C₄²	1	2	yes	—
51	C₂×C₄	C₂×M₁₆	1	2	yes	—
52	C₂×C₄	C₂×M₁₆	1	1	yes	characteristic
53	C₈	—	2	4	no	—
54	C₈	#97	1	4	yes	—
55	C₈	C₂×C₄²	1	4	yes	—
56	C₂²	—	2	2	no	—
57	C₂²	C₂×#97	1	1	yes	characteristic
58	C₂²	C₄×M₁₆	1	2	yes	—
59	C₄	—	2	2	no	—
60	C₄	—	4	4	no	—
61	C₄	#347	1	4	yes	direct product factor
62	C₄	C₄³	1	1	yes	characteristic
63	C₄	C₂×#97	1	1	yes	characteristic
64	C₄	C₄×M₁₆	1	2	yes	—
65	C₂	—	2	2	no	—
66	C₂	C₄×#97	1	1	yes	characteristic
67	C₂	C₂×#347	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄²
commutator	C₄	C₄³
Frattini, cosocle	C₂²×C₈	C₂³
socle	C₂²	C₂×#97
prime radical	C₂³	C₂×M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄² ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
10. #347	C₄	direct (N × H)
11. #346	C₄	semidirect
12. C₄×C₁₆	C₄	semidirect
42. C₁₆	C₄²	semidirect
61. C₄	#347	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#347	2
C₄×M₃₂	2
C₄×#97	2

Subgroups — C4×#347 #12540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#347 #12540