Subgroups — #2183

Order 128.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆	C₂	1	2	yes	maximal
4	#346	C₂	1	2	yes	maximal
5	C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₄×Q₈	C₄	1	1	yes	characteristic
7	C₂×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₁₆	C₂²	1	2	yes	—
9	C₂×C₁₆	C₂²	1	1	yes	characteristic
10	C₄⋊C₈	C₄	1	2	yes	—
11	C₄⋊C₈	C₄	1	1	yes	characteristic
12	C₄×C₈	C₂²	1	1	yes	characteristic
13	C₄×C₈	C₂²	1	2	yes	—
14	C₂×Q₈	C₈	1	1	yes	characteristic
15	C₂×C₈	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈	C₂×C₄	1	2	yes	—
17	C₂×C₈	C₂³	1	1	yes	characteristic
18	C₄⋊C₄	C₈	1	2	yes	—
19	C₄⋊C₄	C₈	1	1	yes	characteristic
20	C₄²	C₂×C₄	1	2	yes	—
21	C₄²	C₂×C₄	1	1	yes	characteristic
22	C₁₆	—	2	1	no	—
23	C₁₆	—	2	2	no	—
24	C₁₆	Q₈	1	2	yes	complemented
25	Q₈	—	2	2	no	—
26	C₂×C₄	C₂×C₈	1	2	yes	—
27	C₂×C₄	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄	C₂×C₈	1	2	yes	—
29	C₂×C₄	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₈	—	2	2	no	—
33	C₈	C₂×Q₈	1	1	yes	characteristic
34	C₈	#41	1	1	yes	characteristic
35	C₂²	C₂²×C₈	1	1	yes	characteristic
36	C₄	—	2	2	no	—
37	C₄	—	2	2	no	—
38	C₄	—	2	1	no	—
39	C₄	M₃₂	1	2	yes	—
40	C₄	C₄×Q₈	1	1	yes	characteristic
41	C₄	#131	1	1	yes	characteristic
42	C₂	C₈×Q₈	1	1	yes	characteristic
43	C₂	C₂×M₃₂	1	1	yes	characteristic
44	C₂	#504	1	1	yes	characteristic

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

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

N	H ≅ G/N	type
24. C₁₆	Q₈	semidirect

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