Subgroups — C₂×#499 #3158

Order 128.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#125	C₂	1	2	yes	maximal
2	#499	C₂	1	8	yes	maximal, direct product factor
3	C₂×#107	C₂	1	2	yes	maximal
4	C₂×#106	C₂	1	2	yes	maximal
5	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₈	C₂²	1	1	yes	characteristic
8	#125	—	2	4	no	—
9	#125	C₂²	1	8	yes	—
10	C₂×C₄⋊C₄	—	2	4	no	—
11	C₂×C₄⋊C₄	C₂²	1	4	yes	—
12	C₂×C₄²	C₂²	1	1	yes	characteristic
13	#107	C₂²	1	8	yes	—
14	#106	C₂²	1	8	yes	—
15	C₄×C₈	C₂²	1	4	yes	—
16	C₂²×C₄	—	2	4	no	—
17	C₂²×C₄	D₄	1	2	yes	—
18	C₂²×C₄	C₂³	1	1	yes	characteristic
19	C₂×C₈	Q₈	1	4	yes	—
20	C₂×C₈	Q₈	1	4	yes	—
21	C₂×C₈	C₂³	1	2	yes	—
22	C₂×C₈	C₂³	1	2	yes	—
23	C₄⋊C₄	—	2	16	no	—
24	C₄⋊C₄	—	2	4	no	—
25	C₄⋊C₄	C₂³	1	8	yes	—
26	C₄²	D₄	1	2	yes	—
27	C₄²	C₂³	1	2	yes	—
28	C₂³	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄	—	2	4	no	—
30	C₂×C₄	—	2	8	no	—
31	C₂×C₄	—	4	8	no	—
32	C₂×C₄	C₂×D₄	1	4	yes	—
33	C₂×C₄	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄	C₂×Q₈	1	2	yes	—
35	C₂×C₄	C₂×Q₈	1	2	yes	—
36	C₂×C₄	C₂⁴	1	1	yes	characteristic
37	C₈	C₂×Q₈	1	4	yes	—
38	C₈	C₂×Q₈	1	4	yes	—
39	C₂²	C₄⋊Q₈	1	2	yes	—
40	C₂²	#135	1	4	yes	—
41	C₂²	C₂²×D₄	1	1	yes	characteristic
42	C₄	—	2	4	no	—
43	C₄	—	4	8	no	—
44	C₄	C₄⋊Q₈	1	2	yes	—
45	C₄	C₂²×Q₈	1	1	yes	characteristic
46	C₄	C₂²×Q₈	1	1	yes	characteristic
47	C₂	#499	1	4	yes	direct product factor
48	C₂	C₂×C₄⋊Q₈	1	1	yes	characteristic
49	C₂	C₂×#135	1	2	yes	—

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

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

N	H ≅ G/N	type
2. #499	C₂	direct (N × H)
47. C₂	#499	direct (N × H)

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