Subgroups — C₂×#497 #3149

Order 128.

282 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₁₆	C₂	1	2	yes	maximal, complemented
2	C₂²×SD₁₆	C₂	1	2	yes	maximal
3	C₂×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#124	C₂	1	1	yes	maximal, characteristic
5	#497	C₂	1	8	yes	maximal, direct product factor
6	C₂×#97	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Q₈	C₂²	1	1	yes	characteristic
8	C₂²×Q₈	C₂²	1	2	yes	—
9	C₂²×D₄	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆	—	2	8	no	—
11	C₂×Q₁₆	C₂²	1	8	yes	complemented
12	C₂×SD₁₆	—	2	8	no	—
13	C₂×SD₁₆	C₂²	1	8	yes	—
14	C₂²×C₈	C₂²	1	2	yes	—
15	C₄⋊Q₈	—	2	2	no	—
16	C₄⋊Q₈	C₂²	1	4	yes	complemented
17	#124	—	2	2	no	—
18	#124	C₂²	1	4	yes	—
19	C₂×C₄⋊C₄	—	2	2	no	—
20	C₂×C₂²⋊C₄	—	2	2	no	—
21	C₂×C₄²	C₂²	1	1	yes	characteristic
22	#97	C₂²	1	4	yes	complemented
23	C₂⁴	—	2	1	no	—
24	C₂×Q₈	—	2	1	no	—
25	C₂×Q₈	—	2	2	no	—
26	C₂×Q₈	—	2	4	no	—
27	C₂×Q₈	—	2	4	no	—
28	C₂×Q₈	—	2	4	no	—
29	C₂×Q₈	C₂³	1	2	yes	—
30	C₂×Q₈	C₂³	1	4	yes	—
31	C₂×D₄	—	2	4	no	—
32	C₂×D₄	—	2	1	no	—
33	C₂×D₄	C₂³	1	2	yes	—
34	C₂²×C₄	—	2	1	no	—
35	C₂²×C₄	—	2	2	no	—
36	C₂²×C₄	D₄	1	2	yes	—
37	C₂²×C₄	C₂³	1	1	yes	characteristic
38	Q₁₆	—	2	16	no	—
39	SD₁₆	—	2	16	no	—
40	C₂×C₈	D₄	1	8	yes	—
41	C₂×C₈	C₂³	1	4	yes	—
42	C₄⋊C₄	—	2	8	no	—
43	C₂²⋊C₄	—	2	8	no	—
44	C₄²	D₄	1	2	yes	—
45	C₄²	C₂³	1	2	yes	—
46	C₂³	—	2	2	no	—
47	C₂³	—	4	2	no	—
48	C₂³	—	4	4	no	—
49	C₂³	C₂×D₄	1	1	yes	characteristic
50	Q₈	—	2	4	no	—
51	Q₈	—	2	4	no	—
52	Q₈	—	2	4	no	—
53	Q₈	—	4	2	no	—
54	Q₈	—	4	4	no	—
55	D₄	—	2	4	no	—
56	D₄	—	4	2	no	—
57	C₂×C₄	—	2	4	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	—	4	4	no	—
62	C₂×C₄	C₂×D₄	1	4	yes	—
63	C₂×C₄	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄	C₂×D₄	1	4	yes	—
65	C₂×C₄	C₂⁴	1	1	yes	characteristic
66	C₈	C₂×D₄	1	8	yes	—
67	C₂²	—	4	2	no	—
68	C₂²	—	4	4	no	—
69	C₂²	—	8	4	no	—
70	C₂²	#127	1	2	yes	—
71	C₂²	#137	1	4	yes	—
72	C₂²	C₂²×D₄	1	1	yes	characteristic
73	C₄	—	2	4	no	—
74	C₄	—	4	2	no	—
75	C₄	—	4	4	no	—
76	C₄	#127	1	2	yes	—
77	C₄	C₂²×D₄	1	2	yes	—
78	C₂	—	8	2	no	—
79	C₂	#497	1	4	yes	direct product factor
80	C₂	C₂×#127	1	1	yes	characteristic
81	C₂	C₂×#137	1	2	yes	—

	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. C₂²×Q₁₆	C₂	semidirect
3. C₂×C₄⋊Q₈	C₂	semidirect
5. #497	C₂	direct (N × H)
6. C₂×#97	C₂	semidirect
11. C₂×Q₁₆	C₂²	semidirect
16. C₄⋊Q₈	C₂²	semidirect
22. #97	C₂²	semidirect
79. C₂	#497	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Q₁₆	2
C₂²×SD₁₆	2
C₂×C₄⋊Q₈	2
C₂×#124	2
#497	2
C₂×#97	2

Subgroups — C2×#497 #3149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#497 #3149