Subgroups — #2862

Order 128.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Q₈	C₂	1	2	yes	maximal
2	#391	C₂	1	8	yes	maximal
3	#382	C₂	1	4	yes	maximal
4	C₄³	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈	C₂²	1	4	yes	—
6	C₄⋊Q₈	—	2	8	no	—
7	C₂×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂×C₄⋊C₄	C₂²	1	4	yes	—
9	C₂×C₄²	C₂²	1	4	yes	—
10	C₂×C₄²	C₂²	1	1	yes	characteristic
11	C₂×C₄²	C₂²	1	2	yes	—
12	#95	C₂²	1	16	yes	—
13	C₂×Q₈	—	2	8	no	—
14	C₂×Q₈	—	2	16	no	—
15	C₂²×C₄	C₂³	1	8	yes	—
16	C₂²×C₄	C₂³	1	4	yes	—
17	C₂²×C₄	C₂³	1	1	yes	characteristic
18	C₂²×C₄	C₂³	1	2	yes	—
19	C₄⋊C₄	—	2	8	no	—
20	C₄⋊C₄	—	2	8	no	—
21	C₄²	—	2	8	no	—
22	C₄²	D₄	1	4	yes	—
23	C₄²	Q₈	1	8	yes	complemented
24	C₂³	C₂⁴	1	1	yes	characteristic
25	Q₈	—	4	16	no	—
26	C₂×C₄	—	2	8	no	—
27	C₂×C₄	—	2	8	no	—
28	C₂×C₄	—	2	16	no	—
29	C₂×C₄	C₂×D₄	1	4	yes	—
30	C₂×C₄	C₂×D₄	1	2	yes	—
31	C₂×C₄	C₂×Q₈	1	8	yes	—
32	C₂×C₄	C₂×Q₈	1	4	yes	—
33	C₂×C₄	#41	1	8	yes	—
34	C₂²	C₂²×D₄	1	1	yes	characteristic
35	C₂²	C₂²×Q₈	1	2	yes	—
36	C₂²	C₂×#41	1	4	yes	—
37	C₄	—	2	8	no	—
38	C₄	—	4	8	no	—
39	C₄	#124	1	8	yes	—
40	C₄	C₄⋊Q₈	1	4	yes	—
41	C₂	C₂×#124	1	2	yes	—
42	C₂	C₂×C₄⋊Q₈	1	1	yes	characteristic
43	C₂	#533	1	4	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
23. C₄²	Q₈	semidirect

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