Subgroups — #2658

Order 128.

306 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Q₈	C₂	1	3	yes	maximal, complemented
2	C₂×#124	C₂	1	3	yes	maximal
3	#399	C₂	1	8	yes	maximal, complemented
4	#376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₈	C₂²	1	3	yes	—
6	C₂²×D₄	C₂²	1	1	yes	characteristic
7	C₄⋊Q₈	—	2	12	no	—
8	#124	—	2	12	no	—
9	C₂×C₄⋊C₄	C₂²	1	12	yes	—
10	C₂×C₂²⋊C₄	C₂²	1	12	yes	—
11	C₂×C₄²	C₂²	1	3	yes	—
12	#95	C₂²	1	4	yes	—
13	C₂⁴	C₂³	1	2	yes	—
14	C₂×Q₈	—	2	6	no	—
15	C₂×Q₈	—	2	12	no	—
16	C₂×D₄	—	2	6	no	—
17	C₂²×C₄	C₂³	1	6	yes	—
18	C₂²×C₄	C₂³	1	6	yes	—
19	C₂²×C₄	C₂³	1	1	yes	characteristic
20	C₄⋊C₄	—	2	24	no	—
21	C₂²⋊C₄	—	2	24	no	—
22	C₄²	D₄	1	12	yes	—
23	C₂³	—	2	6	no	—
24	C₂³	—	2	8	no	—
25	C₂³	C₂⁴	1	1	yes	characteristic
26	Q₈	—	4	12	no	—
27	D₄	—	4	4	no	—
28	C₂×C₄	—	2	12	no	—
29	C₂×C₄	—	2	6	no	—
30	C₂×C₄	—	2	12	no	—
31	C₂×C₄	C₂×D₄	1	12	yes	—
32	C₂×C₄	C₂×D₄	1	6	yes	—
33	C₂²	—	4	2	no	—
34	C₂²	—	4	12	no	—
35	C₂²	C₂²×D₄	1	3	yes	—
36	C₂²	2₋¹⁺⁴	1	4	yes	—
37	C₄	—	2	12	no	—
38	C₄	—	4	6	no	—
39	C₄	#127	1	4	yes	—
40	C₂	—	8	2	no	—
41	C₂	C₂×#127	1	1	yes	characteristic
42	C₂	#536	1	6	yes	—

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁴
prime radical	C₂²×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ 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.