Subgroups — C₄×#117 #2270

Order 128.

376 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#117	C₂	1	2	yes	maximal
2	C₂²×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄	C₂	1	4	yes	maximal, complemented
4	C₄×C₂²⋊C₄	C₂	1	4	yes	maximal
5	#376	C₂	1	2	yes	maximal, complemented
6	C₄³	C₂	1	2	yes	maximal, complemented
7	C₂³×C₄	C₂²	1	2	yes	—
8	C₂³×C₄	C₂²	1	1	yes	characteristic
9	#117	C₄	1	16	yes	direct product factor
10	C₂×C₄⋊C₄	C₂²	1	4	yes	—
11	C₂×C₂²⋊C₄	C₂²	1	4	yes	—
12	C₂×C₄²	C₄	1	8	yes	complemented
13	C₂×C₄²	C₂²	1	8	yes	—
14	C₂×C₄²	C₂²	1	1	yes	characteristic
15	C₂×C₄²	C₂²	1	2	yes	—
16	C₂×C₄²	C₂²	1	4	yes	—
17	C₂×C₄²	C₂²	1	1	yes	characteristic
18	#95	C₂²	1	8	yes	—
19	C₂⁴	C₂³	1	1	yes	characteristic
20	C₂²×C₄	—	2	8	no	—
21	C₂²×C₄	C₂×C₄	1	8	yes	—
22	C₂²×C₄	C₂×C₄	1	4	yes	—
23	C₂²×C₄	C₂×C₄	1	8	yes	—
24	C₂²×C₄	C₂³	1	2	yes	—
25	C₂²×C₄	C₂³	1	8	yes	—
26	C₂²×C₄	C₂³	1	1	yes	characteristic
27	C₂²×C₄	C₂³	1	1	yes	characteristic
28	C₂²×C₄	C₂³	1	2	yes	—
29	C₄⋊C₄	C₂×C₄	1	16	yes	complemented
30	C₂²⋊C₄	C₂×C₄	1	16	yes	—
31	C₄²	—	2	16	no	—
32	C₄²	C₂×C₄	1	4	yes	—
33	C₄²	C₂×C₄	1	8	yes	—
34	C₄²	C₂×C₄	1	4	yes	—
35	C₄²	C₂×C₄	1	16	yes	complemented
36	C₂³	—	2	4	no	—
37	C₂³	C₂²×C₄	1	4	yes	—
38	C₂³	C₂²×C₄	1	2	yes	—
39	C₂³	C₂⁴	1	1	yes	characteristic
40	C₂×C₄	—	2	16	no	—
41	C₂×C₄	—	2	4	no	—
42	C₂×C₄	—	2	16	no	—
43	C₂×C₄	C₄²	1	16	yes	complemented
44	C₂×C₄	C₂²×C₄	1	4	yes	—
45	C₂×C₄	C₂²×C₄	1	16	yes	—
46	C₂×C₄	C₂²×C₄	1	2	yes	—
47	C₂×C₄	C₂²×C₄	1	2	yes	—
48	C₂×C₄	C₂²×C₄	1	4	yes	—
49	C₂×C₄	C₂²×C₄	1	4	yes	—
50	C₂×C₄	C₂²×C₄	1	4	yes	—
51	C₂×C₄	#41	1	8	yes	—
52	C₂²	—	2	4	no	—
53	C₂²	—	2	8	no	—
54	C₂²	C₂×C₄²	1	4	yes	—
55	C₂²	C₂³×C₄	1	1	yes	characteristic
56	C₂²	C₂³×C₄	1	2	yes	—
57	C₂²	C₂×#41	1	4	yes	—
58	C₄	—	2	4	no	—
59	C₄	—	2	16	no	—
60	C₄	C₂×C₄²	1	4	yes	—
61	C₄	C₂×C₄²	1	4	yes	—
62	C₄	#117	1	8	yes	direct product factor
63	C₂	—	2	4	no	—
64	C₂	C₂²×C₄²	1	1	yes	characteristic
65	C₂	C₂×#117	1	2	yes	—
66	C₂	C₄×#41	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²
commutator	C₂	C₂²×C₄²
Frattini, socle, cosocle	C₂³	C₂⁴
prime radical	C₂⁴	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. C₄×C₄⋊C₄	C₂	semidirect
5. #376	C₂	semidirect
6. C₄³	C₂	semidirect
9. #117	C₄	direct (N × H)
12. C₂×C₄²	C₄	semidirect
29. C₄⋊C₄	C₂×C₄	semidirect
35. C₄²	C₂×C₄	semidirect
43. C₂×C₄	C₄²	semidirect
62. C₄	#117	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×#117	2
C₂²×C₄²	2
C₄×C₄⋊C₄	2
C₄×C₂²⋊C₄	2
#376	2
C₄³	2

Subgroups — C4×#117 #2270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#117 #2270