Subgroups — #2248

Order 128.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₃₂	C₂	1	4	yes	maximal, complemented
2	#494	C₂	1	1	yes	maximal, characteristic, complemented
3	#493	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₁₆	—	2	1	no	—
6	C₂×Q₁₆	C₂²	1	2	yes	—
7	C₂×D₈	—	2	1	no	—
8	C₂×D₈	C₂²	1	2	yes	—
9	C₄⋊Q₈	—	2	1	no	—
10	#127	—	2	1	no	—
11	SD₃₂	—	2	8	no	—
12	C₂×C₁₆	C₂²	1	2	yes	—
13	C₄×C₈	C₂²	1	1	yes	characteristic
14	C₂×Q₈	—	2	2	no	—
15	C₂×D₄	—	2	2	no	—
16	C₂×D₄	—	4	2	no	—
17	Q₁₆	—	2	4	no	—
18	Q₁₆	—	4	2	no	—
19	D₈	—	2	4	no	—
20	D₈	—	4	2	no	—
21	C₂×C₈	D₄	1	1	yes	characteristic
22	C₂×C₈	C₂³	1	1	yes	characteristic
23	C₄⋊C₄	—	4	2	no	—
24	C₄²	D₄	1	1	yes	characteristic
25	C₁₆	D₄	1	4	yes	complemented
26	C₂³	—	4	2	no	—
27	Q₈	—	4	2	no	—
28	Q₈	—	4	2	no	—
29	D₄	—	4	2	no	—
30	D₄	—	4	2	no	—
31	D₄	—	8	4	no	—
32	C₂×C₄	—	4	2	no	—
33	C₂×C₄	D₈	1	2	yes	—
34	C₂×C₄	C₂×D₄	1	1	yes	characteristic
35	C₈	D₈	1	2	yes	—
36	C₈	C₂×D₄	1	2	yes	—
37	C₂²	—	8	2	no	—
38	C₂²	—	8	4	no	—
39	C₂²	C₂×D₈	1	1	yes	characteristic
40	C₄	—	8	2	no	—
41	C₄	SD₃₂	1	4	yes	complemented
42	C₄	#127	1	1	yes	characteristic
43	C₄	C₂×D₈	1	1	yes	characteristic
44	C₂	—	16	2	no	—
45	C₂	#493	1	1	yes	characteristic
46	C₂	C₂×SD₃₂	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³
prime radical	#493	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

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

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