Subgroups — #2251

Order 128.

89 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂	C₂	1	2	yes	maximal, complemented
2	C₂×SD₃₂	C₂	1	2	yes	maximal
3	#495	C₂	1	1	yes	maximal, characteristic
4	#494	C₂	1	1	yes	maximal, characteristic, complemented
5	#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₁₆	—	2	1	no	—
7	C₂×Q₁₆	C₂²	1	2	yes	—
8	C₂×Q₁₆	C₂²	1	1	yes	characteristic
9	C₂×SD₁₆	—	2	1	no	—
10	C₂×D₈	C₂²	1	1	yes	characteristic
11	C₄⋊Q₈	—	2	1	no	—
12	#124	—	2	1	no	—
13	Q₃₂	—	2	4	no	—
14	SD₃₂	—	2	4	no	—
15	C₂×C₁₆	C₂²	1	2	yes	—
16	C₄×C₈	C₂²	1	1	yes	characteristic
17	C₂×Q₈	—	2	1	no	—
18	C₂×Q₈	—	2	2	no	—
19	C₂×D₄	—	2	1	no	—
20	Q₁₆	—	2	2	no	—
21	Q₁₆	—	2	2	no	—
22	Q₁₆	—	2	2	no	—
23	Q₁₆	—	4	2	no	—
24	SD₁₆	—	4	2	no	—
25	D₈	—	2	2	no	—
26	C₂×C₈	D₄	1	1	yes	characteristic
27	C₂×C₈	C₂³	1	1	yes	characteristic
28	C₄⋊C₄	—	4	2	no	—
29	C₂²⋊C₄	—	4	2	no	—
30	C₄²	D₄	1	1	yes	characteristic
31	C₁₆	D₄	1	4	yes	—
32	C₂³	—	4	1	no	—
33	Q₈	—	4	2	no	—
34	Q₈	—	4	1	no	—
35	Q₈	—	4	1	no	—
36	Q₈	—	4	2	no	—
37	D₄	—	4	1	no	—
38	D₄	—	4	1	no	—
39	C₂×C₄	—	4	1	no	—
40	C₂×C₄	—	4	2	no	—
41	C₂×C₄	D₈	1	2	yes	—
42	C₂×C₄	C₂×D₄	1	1	yes	characteristic
43	C₈	D₈	1	2	yes	—
44	C₈	C₂×D₄	1	2	yes	—
45	C₂²	—	8	1	no	—
46	C₂²	—	8	2	no	—
47	C₂²	C₂×D₈	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	8	1	no	—
50	C₄	—	8	2	no	—
51	C₄	#127	1	1	yes	characteristic
52	C₄	C₂×D₈	1	1	yes	characteristic
53	C₂	—	16	1	no	—
54	C₂	#493	1	1	yes	characteristic
55	C₂	#510	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³
prime radical	C₂×D₈	C₂²
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.