Subgroups — C₂×#441 #2941

Order 128.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈	C₂	1	2	yes	maximal
3	#441	C₂	1	8	yes	maximal, direct product factor
4	C₂×#106	C₂	1	1	yes	maximal, characteristic
5	C₂×#103	C₂	1	2	yes	maximal
6	C₂×#97	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈	C₂²	1	2	yes	—
8	C₂×Q₁₆	C₄	1	8	yes	complemented
9	C₂×Q₁₆	C₂²	1	4	yes	—
10	C₂²×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₈	C₂²	1	1	yes	characteristic
12	C₄×Q₈	—	2	4	no	—
13	C₄×Q₈	C₂²	1	8	yes	—
14	C₂×C₄⋊C₄	—	2	2	no	—
15	C₂×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₄²	—	2	2	no	—
17	C₂×C₄²	C₂²	1	1	yes	characteristic
18	#106	C₂²	1	4	yes	—
19	#103	C₂²	1	8	yes	—
20	#97	C₂²	1	4	yes	—
21	C₂×Q₈	—	2	2	no	—
22	C₂×Q₈	—	2	4	no	—
23	C₂×Q₈	C₂×C₄	1	8	yes	—
24	C₂×Q₈	C₂³	1	4	yes	—
25	C₂²×C₄	—	2	2	no	—
26	C₂²×C₄	—	2	2	no	—
27	C₂²×C₄	D₄	1	2	yes	—
28	C₂²×C₄	C₂³	1	1	yes	characteristic
29	Q₁₆	C₂×C₄	1	16	yes	complemented
30	C₂×C₈	—	2	2	no	—
31	C₂×C₈	C₂×C₄	1	4	yes	—
32	C₂×C₈	C₂³	1	2	yes	—
33	C₂×C₈	C₂³	1	2	yes	—
34	C₄⋊C₄	—	2	8	no	—
35	C₄⋊C₄	—	2	2	no	—
36	C₄⋊C₄	C₂³	1	4	yes	—
37	C₄²	—	2	8	no	—
38	C₄²	D₄	1	2	yes	—
39	C₄²	C₂³	1	2	yes	—
40	C₂³	C₂×D₄	1	1	yes	characteristic
41	Q₈	—	2	8	no	—
42	Q₈	—	2	4	no	—
43	Q₈	C₂²×C₄	1	8	yes	—
44	C₂×C₄	—	2	8	no	—
45	C₂×C₄	—	2	4	no	—
46	C₂×C₄	—	2	4	no	—
47	C₂×C₄	—	2	4	no	—
48	C₂×C₄	—	4	4	no	—
49	C₂×C₄	C₂²×C₄	1	2	yes	—
50	C₂×C₄	C₂×D₄	1	4	yes	—
51	C₂×C₄	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄	#41	1	2	yes	—
53	C₂×C₄	C₂⁴	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	C₂²×C₄	1	4	yes	—
56	C₂²	C₄×D₄	1	2	yes	—
57	C₂²	#137	1	4	yes	—
58	C₂²	C₂²×D₄	1	1	yes	characteristic
59	C₄	—	2	8	no	—
60	C₄	—	2	4	no	—
61	C₄	—	4	4	no	—
62	C₄	C₄×D₄	1	2	yes	—
63	C₄	C₂³×C₄	1	1	yes	characteristic
64	C₄	C₂×#41	1	1	yes	characteristic
65	C₂	#441	1	4	yes	direct product factor
66	C₂	C₂×C₄×D₄	1	1	yes	characteristic
67	C₂	C₂×#137	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³	C₂×D₄
commutator	C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄	C₂⁴
LCS	G ▷ 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
3. #441	C₂	direct (N × H)
8. C₂×Q₁₆	C₄	semidirect
29. Q₁₆	C₂×C₄	semidirect
65. C₂	#441	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
C₂×C₄×Q₈	2
#441	2
C₂×#106	2
C₂×#103	2
C₂×#97	2

Subgroups — C2×#441 #2941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#441 #2941