Subgroups — C₄×#103 #1761

Order 128.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#103	C₂	1	2	yes	maximal
3	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	#340	C₂	1	2	yes	maximal
6	C₂²×Q₈	C₂²	1	1	yes	characteristic
7	C₂²×C₈	C₂²	1	2	yes	—
8	C₄×Q₈	—	2	2	no	—
9	C₄×Q₈	C₄	1	4	yes	complemented
10	C₂×C₄⋊C₄	—	2	1	no	—
11	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₄²	—	2	1	no	—
14	C₂×C₄²	—	2	1	no	—
15	C₂×C₄²	C₂²	1	1	yes	characteristic
16	#103	C₄	1	8	yes	direct product factor
17	C₄×C₈	—	2	2	no	—
18	#95	—	2	1	no	—
19	C₂×Q₈	—	2	1	no	—
20	C₂×Q₈	—	2	2	no	—
21	C₂×Q₈	C₂×C₄	1	4	yes	—
22	C₂×Q₈	C₂×C₄	1	2	yes	—
23	C₂²×C₄	—	2	1	no	—
24	C₂²×C₄	—	2	2	no	—
25	C₂²×C₄	—	2	1	no	—
26	C₂²×C₄	D₄	1	1	yes	characteristic
27	C₂²×C₄	D₄	1	1	yes	characteristic
28	C₂²×C₄	C₂³	1	1	yes	characteristic
29	C₂×C₈	—	2	2	no	—
30	C₂×C₈	—	2	2	no	—
31	C₂×C₈	C₂×C₄	1	4	yes	—
32	C₄⋊C₄	—	2	4	no	—
33	C₄⋊C₄	—	2	1	no	—
34	C₄⋊C₄	—	2	2	no	—
35	C₄⋊C₄	C₂×C₄	1	4	yes	—
36	C₄⋊C₄	C₂×C₄	1	2	yes	—
37	C₄²	—	2	4	no	—
38	C₄²	—	4	2	no	—
39	C₄²	C₂×C₄	1	2	yes	—
40	C₄²	D₄	1	2	yes	—
41	C₂³	C₂×D₄	1	1	yes	characteristic
42	Q₈	—	2	2	no	—
43	Q₈	—	2	4	no	—
44	Q₈	C₄²	1	4	yes	complemented
45	C₂×C₄	—	2	2	no	—
46	C₂×C₄	—	2	4	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	2	4	no	—
50	C₂×C₄	—	4	2	no	—
51	C₂×C₄	—	4	2	no	—
52	C₂×C₄	—	4	2	no	—
53	C₂×C₄	C₂²⋊C₄	1	2	yes	—
54	C₂×C₄	C₂²⋊C₄	1	2	yes	—
55	C₂×C₄	SD₁₆	1	2	yes	—
56	C₂×C₄	Q₁₆	1	2	yes	—
57	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄	C₂²×C₄	1	2	yes	—
59	C₂×C₄	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄	#41	1	2	yes	—
61	C₈	—	2	4	no	—
62	C₂²	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂²	C₄×D₄	1	2	yes	—
64	C₂²	C₂×SD₁₆	1	1	yes	characteristic
65	C₂²	C₂×Q₁₆	1	1	yes	characteristic
66	C₂²	#135	1	2	yes	—
67	C₄	—	2	4	no	—
68	C₄	—	2	2	no	—
69	C₄	—	4	2	no	—
70	C₄	—	4	4	no	—
71	C₄	#103	1	4	yes	direct product factor
72	C₄	C₂×C₄²	1	1	yes	characteristic
73	C₄	#117	1	1	yes	characteristic
74	C₄	C₄×D₄	1	2	yes	—
75	C₂	C₄×C₂²⋊C₄	1	1	yes	characteristic
76	C₂	C₂×#103	1	1	yes	characteristic
77	C₂	#416	1	1	yes	characteristic
78	C₂	C₄×SD₁₆	1	2	yes	—
79	C₂	C₄×Q₁₆	1	2	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
9. C₄×Q₈	C₄	semidirect
16. #103	C₄	direct (N × H)
44. Q₈	C₄²	semidirect
71. C₄	#103	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×C₄×Q₈	2
C₂×#103	2
C₂×C₄×C₈	2
C₄×C₄⋊C₄	2
#340	2

Subgroups — C4×#103 #1761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#103 #1761