Subgroups — C₂×#474 #3070

Order 128.

240 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, complemented
2	C₂×C₄×D₄	C₂	1	1	yes	maximal, characteristic
3	#474	C₂	1	8	yes	maximal, direct product factor
4	C₂×#107	C₂	1	2	yes	maximal, complemented
5	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#102	C₂	1	2	yes	maximal
7	C₂²×Q₈	—	2	1	no	—
8	C₂²×D₄	C₂²	1	1	yes	characteristic
9	C₂³×C₄	—	2	1	no	—
10	C₂²×C₈	C₂²	1	2	yes	—
11	C₄⋊Q₈	—	2	2	no	—
12	C₄⋊Q₈	C₂²	1	4	yes	complemented
13	C₄×D₄	—	2	2	no	—
14	C₄×D₄	C₂²	1	4	yes	—
15	C₂×C₄⋊C₄	—	2	1	no	—
16	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₄	—	2	1	no	—
19	C₂×C₄²	C₂²	1	1	yes	characteristic
20	#107	C₂²	1	8	yes	complemented
21	C₄⋊C₈	C₂²	1	4	yes	complemented
22	#102	C₂²	1	8	yes	—
23	C₂⁴	—	2	1	no	—
24	C₂×Q₈	—	2	4	no	—
25	C₂×Q₈	—	4	4	no	—
26	C₂×D₄	—	2	1	no	—
27	C₂×D₄	—	2	2	no	—
28	C₂×D₄	Q₈	1	4	yes	complemented
29	C₂×D₄	C₂³	1	2	yes	—
30	C₂²×C₄	—	2	1	no	—
31	C₂²×C₄	—	2	2	no	—
32	C₂²×C₄	—	2	4	no	—
33	C₂²×C₄	—	4	4	no	—
34	C₂²×C₄	D₄	1	1	yes	characteristic
35	C₂²×C₄	D₄	1	1	yes	characteristic
36	C₂²×C₄	C₂³	1	1	yes	characteristic
37	C₂×C₈	—	2	4	no	—
38	C₂×C₈	C₂³	1	4	yes	—
39	C₄⋊C₄	—	2	4	no	—
40	C₄⋊C₄	—	2	1	no	—
41	C₄⋊C₄	—	2	2	no	—
42	C₄⋊C₄	C₂³	1	4	yes	—
43	C₄⋊C₄	C₂³	1	2	yes	—
44	C₂²⋊C₄	—	2	4	no	—
45	C₄²	D₄	1	2	yes	—
46	C₄²	C₂³	1	2	yes	—
47	C₂³	—	2	4	no	—
48	C₂³	—	2	2	no	—
49	C₂³	—	4	2	no	—
50	C₂³	—	4	2	no	—
51	C₂³	C₂×D₄	1	1	yes	characteristic
52	Q₈	—	4	8	no	—
53	D₄	—	2	4	no	—
54	D₄	—	2	2	no	—
55	D₄	C₂×Q₈	1	4	yes	complemented
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	4	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	—	4	4	no	—
61	C₂×C₄	—	4	8	no	—
62	C₂×C₄	D₈	1	4	yes	—
63	C₂×C₄	C₂×D₄	1	2	yes	—
64	C₂×C₄	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄	C₂×D₄	1	2	yes	—
66	C₂×C₄	C₂×Q₈	1	2	yes	—
67	C₂×C₄	#41	1	2	yes	—
68	C₂×C₄	C₂⁴	1	1	yes	characteristic
69	C₈	—	2	4	no	—
70	C₂²	—	2	4	no	—
71	C₂²	—	4	2	no	—
72	C₂²	—	4	2	no	—
73	C₂²	—	4	8	no	—
74	C₂²	C₂²⋊Q₈	1	2	yes	—
75	C₂²	C₂×D₈	1	2	yes	—
76	C₂²	#137	1	2	yes	—
77	C₂²	C₂²×D₄	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	4	2	no	—
80	C₄	—	4	4	no	—
81	C₄	C₂²⋊Q₈	1	2	yes	—
82	C₄	C₂×D₈	1	4	yes	—
83	C₄	C₂²×Q₈	1	1	yes	characteristic
84	C₄	C₂×#41	1	1	yes	characteristic
85	C₂	—	4	4	no	—
86	C₂	#474	1	4	yes	direct product factor
87	C₂	C₂×C₂²⋊Q₈	1	1	yes	characteristic
88	C₂	C₂²×D₈	1	1	yes	characteristic
89	C₂	C₂×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴
prime radical	C₂²×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₄⋊Q₈	C₂	semidirect
3. #474	C₂	direct (N × H)
4. C₂×#107	C₂	semidirect
5. C₂×C₄⋊C₈	C₂	semidirect
12. C₄⋊Q₈	C₂²	semidirect
20. #107	C₂²	semidirect
21. C₄⋊C₈	C₂²	semidirect
28. C₂×D₄	Q₈	semidirect
55. D₄	C₂×Q₈	semidirect
86. C₂	#474	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×C₄×D₄	2
#474	2
C₂×#107	2
C₂×C₄⋊C₈	2
C₂×#102	2

Subgroups — C2×#474 #3070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#474 #3070