Subgroups — C₂×#534 #3445

Order 128.

992 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄	C₂	1	2	yes	maximal, complemented
2	#534	C₂	1	16	yes	maximal, direct product factor
3	C₂×#123	C₂	1	4	yes	maximal, complemented
4	C₂×#121	C₂	1	4	yes	maximal, complemented
5	C₂×#120	C₂	1	4	yes	maximal, complemented
6	C₂²×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁵	C₂²	1	1	yes	characteristic
8	C₂⁵	C₂²	1	2	yes	complemented
9	C₂²×D₄	—	2	16	no	—
10	C₂²×D₄	C₂²	1	4	yes	—
11	C₂²×D₄	C₂²	1	4	yes	complemented
12	C₂²×D₄	C₂²	1	4	yes	complemented
13	C₂²×D₄	C₂²	1	16	yes	complemented
14	C₂³×C₄	C₂²	1	2	yes	complemented
15	C₂³×C₄	C₂²	1	2	yes	complemented
16	#123	C₂²	1	32	yes	complemented
17	#121	C₂²	1	32	yes	complemented
18	#120	C₂²	1	32	yes	complemented
19	C₂×C₄⋊C₄	C₂²	1	4	yes	complemented
20	C₂×C₂²⋊C₄	C₂²	1	4	yes	complemented
21	C₂×C₂²⋊C₄	C₂²	1	8	yes	complemented
22	C₂×C₂²⋊C₄	C₂²	1	8	yes	complemented
23	C₂⁴	—	2	8	no	—
24	C₂⁴	—	4	4	no	—
25	C₂⁴	—	4	8	no	—
26	C₂⁴	D₄	1	8	yes	complemented
27	C₂⁴	C₂³	1	4	yes	—
28	C₂⁴	C₂³	1	2	yes	—
29	C₂⁴	C₂³	1	1	yes	characteristic
30	C₂⁴	C₂³	1	4	yes	—
31	C₂⁴	C₂³	1	8	yes	complemented
32	C₂×D₄	—	2	16	no	—
33	C₂×D₄	—	2	16	no	—
34	C₂×D₄	—	2	64	no	—
35	C₂×D₄	—	4	8	no	—
36	C₂×D₄	C₂³	1	16	yes	—
37	C₂×D₄	C₂³	1	16	yes	complemented
38	C₂×D₄	C₂³	1	16	yes	complemented
39	C₂²×C₄	—	2	8	no	—
40	C₂²×C₄	—	4	4	no	—
41	C₂²×C₄	C₂³	1	4	yes	—
42	C₂²×C₄	C₂³	1	4	yes	—
43	C₂²×C₄	C₂³	1	8	yes	complemented
44	C₂²×C₄	C₂³	1	8	yes	complemented
45	C₄⋊C₄	C₂³	1	16	yes	complemented
46	C₂²⋊C₄	C₂³	1	16	yes	complemented
47	C₂²⋊C₄	C₂³	1	32	yes	complemented
48	C₂³	—	2	4	no	—
49	C₂³	—	2	8	no	—
50	C₂³	—	2	8	no	—
51	C₂³	—	2	16	no	—
52	C₂³	—	2	16	no	—
53	C₂³	—	4	16	no	—
54	C₂³	—	4	8	no	—
55	C₂³	—	4	16	no	—
56	C₂³	—	4	32	no	—
57	C₂³	C₂×D₄	1	8	yes	—
58	C₂³	C₂×D₄	1	4	yes	—
59	C₂³	C₂×D₄	1	16	yes	complemented
60	C₂³	C₂⁴	1	8	yes	—
61	C₂³	C₂⁴	1	4	yes	—
62	C₂³	C₂⁴	1	2	yes	—
63	C₂³	C₂⁴	1	1	yes	characteristic
64	D₄	—	2	32	no	—
65	D₄	—	2	32	no	—
66	D₄	—	4	16	no	—
67	C₂×C₄	—	2	8	no	—
68	C₂×C₄	—	2	16	no	—
69	C₂×C₄	—	2	8	no	—
70	C₂×C₄	—	4	8	no	—
71	C₂×C₄	C₂⁴	1	8	yes	—
72	C₂×C₄	C₂⁴	1	8	yes	—
73	C₂²	—	2	16	no	—
74	C₂²	—	2	8	no	—
75	C₂²	—	2	4	no	—
76	C₂²	—	2	8	no	—
77	C₂²	—	2	8	no	—
78	C₂²	—	2	16	no	—
79	C₂²	—	4	16	no	—
80	C₂²	—	4	32	no	—
81	C₂²	—	4	16	no	—
82	C₂²	C₂²×D₄	1	8	yes	—
83	C₂²	C₂²×D₄	1	4	yes	—
84	C₂²	C₂²×D₄	1	2	yes	—
85	C₂²	H(5,𝔽₂)	1	4	yes	—
86	C₂²	C₂⁵	1	1	yes	characteristic
87	C₄	—	2	8	no	—
88	C₄	—	2	8	no	—
89	C₂	—	2	8	no	—
90	C₂	—	2	4	no	—
91	C₂	—	4	8	no	—
92	C₂	#534	1	4	yes	direct product factor
93	C₂	C₂³×D₄	1	1	yes	characteristic
94	C₂	C₂×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄	C₂	semidirect
2. #534	C₂	direct (N × H)
3. C₂×#123	C₂	semidirect
4. C₂×#121	C₂	semidirect
5. C₂×#120	C₂	semidirect
6. C₂²×C₂²⋊C₄	C₂	semidirect
8. C₂⁵	C₂²	semidirect
11. C₂²×D₄	C₂²	semidirect
12. C₂²×D₄	C₂²	semidirect
13. C₂²×D₄	C₂²	semidirect
14. C₂³×C₄	C₂²	semidirect
15. C₂³×C₄	C₂²	semidirect
16. #123	C₂²	semidirect
17. #121	C₂²	semidirect
18. #120	C₂²	semidirect
19. C₂×C₄⋊C₄	C₂²	semidirect
20. C₂×C₂²⋊C₄	C₂²	semidirect
21. C₂×C₂²⋊C₄	C₂²	semidirect
22. C₂×C₂²⋊C₄	C₂²	semidirect
26. C₂⁴	D₄	semidirect
31. C₂⁴	C₂³	semidirect
37. C₂×D₄	C₂³	semidirect
38. C₂×D₄	C₂³	semidirect
43. C₂²×C₄	C₂³	semidirect
44. C₂²×C₄	C₂³	semidirect
45. C₄⋊C₄	C₂³	semidirect
46. C₂²⋊C₄	C₂³	semidirect
47. C₂²⋊C₄	C₂³	semidirect
59. C₂³	C₂×D₄	semidirect
92. C₂	#534	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄	2
#534	2
C₂×#123	2
C₂×#121	2
C₂×#120	2
C₂²×C₂²⋊C₄	2

Subgroups — C2×#534 #3445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#534 #3445