Subgroups — C₄×#106 #1774

Order 128.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#106	C₂	1	2	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄	C₂	1	2	yes	maximal
4	#340	C₂	1	2	yes	maximal
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	C₂²×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂×C₄²	—	2	2	no	—
9	C₂×C₄²	C₂²	1	1	yes	characteristic
10	#106	C₄	1	8	yes	direct product factor
11	C₄×C₈	C₄	1	4	yes	complemented
12	#95	—	2	2	no	—
13	C₂²×C₄	—	2	4	no	—
14	C₂²×C₄	D₄	1	1	yes	characteristic
15	C₂²×C₄	D₄	1	1	yes	characteristic
16	C₂²×C₄	C₂³	1	1	yes	characteristic
17	C₂×C₈	—	2	2	no	—
18	C₂×C₈	C₂×C₄	1	2	yes	—
19	C₂×C₈	C₂×C₄	1	2	yes	—
20	C₂×C₈	C₂×C₄	1	4	yes	—
21	C₄⋊C₄	—	2	4	no	—
22	C₄⋊C₄	C₂×C₄	1	8	yes	—
23	C₄²	—	4	4	no	—
24	C₄²	C₂×C₄	1	2	yes	—
25	C₄²	Q₈	1	2	yes	—
26	C₂³	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄	—	2	2	no	—
28	C₂×C₄	—	2	8	no	—
29	C₂×C₄	—	4	4	no	—
30	C₂×C₄	—	4	4	no	—
31	C₂×C₄	C₄⋊C₄	1	2	yes	—
32	C₂×C₄	C₄⋊C₄	1	2	yes	—
33	C₂×C₄	SD₁₆	1	4	yes	—
34	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄	C₂²×C₄	1	2	yes	—
36	C₂×C₄	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄	#41	1	2	yes	—
38	C₈	—	2	2	no	—
39	C₈	C₄²	1	4	yes	complemented
40	C₂²	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂²	C₄×D₄	1	2	yes	—
42	C₂²	C₂×SD₁₆	1	2	yes	—
43	C₂²	#135	1	2	yes	—
44	C₄	—	2	2	no	—
45	C₄	—	4	8	no	—
46	C₄	#106	1	4	yes	direct product factor
47	C₄	C₂×C₄²	1	1	yes	characteristic
48	C₄	#117	1	1	yes	characteristic
49	C₄	C₄×Q₈	1	2	yes	—
50	C₂	C₄×C₄⋊C₄	1	1	yes	characteristic
51	C₂	C₂×#106	1	1	yes	characteristic
52	C₂	#427	1	1	yes	characteristic
53	C₂	C₄×SD₁₆	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄
commutator	C₄	C₂×C₄²
Frattini, cosocle	C₂²×C₄	C₂³
socle, prime radical	C₂³	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
10. #106	C₄	direct (N × H)
11. C₄×C₈	C₄	semidirect
39. C₈	C₄²	semidirect
46. C₄	#106	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×#106	2
C₂×C₄×C₈	2
C₄×C₄⋊C₄	2
#340	2

Subgroups — C4×#106 #1774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#106 #1774