Subgroups — C₂²×#103 #2891

Order 128.

408 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×#103	C₂	1	12	yes	maximal, direct product factor
5	C₂²×Q₈	—	2	4	no	—
6	C₂²×Q₈	—	2	3	no	—
7	C₂²×Q₈	C₄	1	8	yes	complemented
8	C₂²×Q₈	C₂²	1	6	yes	—
9	C₂³×C₄	—	2	1	no	—
10	C₂³×C₄	—	2	1	no	—
11	C₂³×C₄	C₂²	1	1	yes	characteristic
12	C₂²×C₈	—	2	4	no	—
13	C₂²×C₈	C₂²	1	6	yes	—
14	C₂×C₄⋊C₄	—	2	3	no	—
15	C₂×C₄⋊C₄	C₂²	1	6	yes	—
16	#103	C₂²	1	16	yes	direct product factor
17	C₂⁴	D₄	1	1	yes	characteristic
18	C₂×Q₈	—	2	24	no	—
19	C₂×Q₈	—	2	12	no	—
20	C₂×Q₈	—	2	6	no	—
21	C₂×Q₈	C₂×C₄	1	24	yes	complemented
22	C₂×Q₈	C₂³	1	4	yes	—
23	C₂²×C₄	—	2	8	no	—
24	C₂²×C₄	—	2	6	no	—
25	C₂²×C₄	—	2	6	no	—
26	C₂²×C₄	—	4	4	no	—
27	C₂²×C₄	C₂×C₄	1	4	yes	—
28	C₂²×C₄	D₄	1	3	yes	—
29	C₂²×C₄	D₄	1	4	yes	—
30	C₂²×C₄	C₂³	1	3	yes	—
31	C₂×C₈	—	2	12	no	—
32	C₂×C₈	C₂³	1	4	yes	—
33	C₄⋊C₄	—	2	6	no	—
34	C₄⋊C₄	C₂³	1	4	yes	—
35	C₂³	C₂²⋊C₄	1	4	yes	—
36	C₂³	SD₁₆	1	4	yes	—
37	C₂³	Q₁₆	1	4	yes	—
38	C₂³	C₂×D₄	1	3	yes	—
39	Q₈	—	2	24	no	—
40	Q₈	—	2	4	no	—
41	Q₈	C₂²×C₄	1	8	yes	complemented
42	C₂×C₄	—	2	24	no	—
43	C₂×C₄	—	2	4	no	—
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	—	4	12	no	—
46	C₂×C₄	C₂²⋊C₄	1	12	yes	—
47	C₂×C₄	C₂²×C₄	1	6	yes	—
48	C₂×C₄	C₂×D₄	1	3	yes	—
49	C₂×C₄	C₂×D₄	1	6	yes	—
50	C₂×C₄	C₂⁴	1	1	yes	characteristic
51	C₈	—	2	4	no	—
52	C₂²	#103	1	16	yes	direct product factor
53	C₂²	C₂×C₂²⋊C₄	1	6	yes	—
54	C₂²	C₂×SD₁₆	1	6	yes	—
55	C₂²	C₂×Q₁₆	1	6	yes	—
56	C₂²	C₂²×D₄	1	1	yes	characteristic
57	C₄	—	2	8	no	—
58	C₄	—	4	4	no	—
59	C₄	C₂×C₂²⋊C₄	1	6	yes	—
60	C₄	C₂³×C₄	1	1	yes	characteristic
61	C₄	C₂²×D₄	1	1	yes	characteristic
62	C₂	C₂×#103	1	12	yes	direct product factor
63	C₂	C₂²×C₂²⋊C₄	1	1	yes	characteristic
64	C₂	C₂²×SD₁₆	1	1	yes	characteristic
65	C₂	C₂²×Q₁₆	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₂×#103	C₂	direct (N × H)
7. C₂²×Q₈	C₄	semidirect
16. #103	C₂²	direct (N × H)
21. C₂×Q₈	C₂×C₄	semidirect
41. Q₈	C₂²×C₄	semidirect
52. C₂²	#103	direct (N × H)
62. C₂	C₂×#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
C₂³×Q₈	2
C₂³×C₈	2
C₂²×C₄⋊C₄	2
C₂×#103	2

Subgroups — C22×#103 #2891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#103 #2891