Subgroups — #2859

Order 128.

236 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	#389	C₂	1	8	yes	maximal
3	#384	C₂	1	2	yes	maximal
4	#382	C₂	1	2	yes	maximal
5	C₄³	C₂	1	1	yes	maximal, characteristic
6	#125	—	2	8	no	—
7	C₂×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂×C₄⋊C₄	C₂²	1	8	yes	—
9	C₂×C₄⋊C₄	C₂²	1	8	yes	—
10	C₂×C₄²	C₂²	1	4	yes	—
11	C₂×C₄²	C₂²	1	1	yes	characteristic
12	C₂×C₄²	C₂²	1	1	yes	characteristic
13	C₂×C₄²	C₂²	1	1	yes	characteristic
14	#95	C₂²	1	8	yes	—
15	C₂²×C₄	C₂³	1	8	yes	—
16	C₂²×C₄	C₂³	1	2	yes	—
17	C₂²×C₄	C₂³	1	2	yes	—
18	C₂²×C₄	C₂³	1	1	yes	characteristic
19	C₂²×C₄	C₂³	1	2	yes	—
20	C₄⋊C₄	—	2	16	no	—
21	C₄⋊C₄	—	2	8	no	—
22	C₄⋊C₄	—	2	16	no	—
23	C₄²	—	2	8	no	—
24	C₄²	D₄	1	4	yes	—
25	C₄²	Q₈	1	4	yes	—
26	C₄²	Q₈	1	4	yes	—
27	C₂³	C₂⁴	1	1	yes	characteristic
28	C₂×C₄	—	2	4	no	—
29	C₂×C₄	—	2	4	no	—
30	C₂×C₄	—	2	8	no	—
31	C₂×C₄	—	2	16	no	—
32	C₂×C₄	C₂×D₄	1	4	yes	—
33	C₂×C₄	C₂×D₄	1	2	yes	—
34	C₂×C₄	C₂×Q₈	1	4	yes	—
35	C₂×C₄	C₂×Q₈	1	4	yes	—
36	C₂×C₄	C₂×Q₈	1	2	yes	—
37	C₂×C₄	C₂×Q₈	1	2	yes	—
38	C₂×C₄	#41	1	8	yes	—
39	C₂²	C₂²×D₄	1	1	yes	characteristic
40	C₂²	C₂²×Q₈	1	1	yes	characteristic
41	C₂²	C₂²×Q₈	1	1	yes	characteristic
42	C₂²	C₂×#41	1	4	yes	—
43	C₄	—	2	4	no	—
44	C₄	—	2	4	no	—
45	C₄	—	4	8	no	—
46	C₄	#125	1	8	yes	complemented
47	C₄	C₄⋊Q₈	1	4	yes	—
48	C₂	C₂×#125	1	2	yes	—
49	C₂	C₂×C₄⋊Q₈	1	1	yes	characteristic
50	C₂	#532	1	2	yes	—
51	C₂	#533	1	2	yes	—

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

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

N	H ≅ G/N	type
46. C₄	#125	semidirect

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