Subgroups — #2863

Order 128.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#391	C₂	1	3	yes	maximal
2	#389	C₂	1	3	yes	maximal
3	#387	C₂	1	6	yes	maximal
4	#383	C₂	1	2	yes	maximal
5	C₄³	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄	C₂²	1	6	yes	—
8	C₂×C₄⋊C₄	C₂²	1	3	yes	—
9	C₂×C₄²	C₂²	1	3	yes	—
10	C₂×C₄²	C₂²	1	3	yes	—
11	C₂×C₄²	C₂²	1	1	yes	characteristic
12	#95	C₂²	1	6	yes	—
13	#95	C₂²	1	6	yes	—
14	#95	C₂²	1	6	yes	—
15	C₂×Q₈	—	2	6	no	—
16	C₂²×C₄	C₂³	1	2	yes	—
17	C₂²×C₄	C₂³	1	6	yes	—
18	C₂²×C₄	C₂³	1	3	yes	—
19	C₂²×C₄	C₂³	1	3	yes	—
20	C₂²×C₄	C₂³	1	1	yes	characteristic
21	C₄⋊C₄	—	2	12	no	—
22	C₄⋊C₄	—	2	6	no	—
23	C₄²	—	2	6	no	—
24	C₄²	—	2	6	no	—
25	C₄²	Q₈	1	4	yes	complemented
26	C₂³	C₂⁴	1	1	yes	characteristic
27	Q₈	—	4	4	no	—
28	C₂×C₄	—	2	3	no	—
29	C₂×C₄	—	2	3	no	—
30	C₂×C₄	—	2	3	no	—
31	C₂×C₄	—	2	3	no	—
32	C₂×C₄	—	2	6	no	—
33	C₂×C₄	—	2	12	no	—
34	C₂×C₄	—	2	6	no	—
35	C₂×C₄	C₂×Q₈	1	6	yes	—
36	C₂×C₄	#41	1	6	yes	—
37	C₂×C₄	#41	1	6	yes	—
38	C₂²	C₂²×Q₈	1	1	yes	characteristic
39	C₂²	C₂×#41	1	3	yes	—
40	C₂²	C₂×#41	1	3	yes	—
41	C₄	—	2	6	no	—
42	C₄	—	2	6	no	—
43	C₄	—	4	2	no	—
44	C₄	—	4	6	no	—
45	C₄	#126	1	4	yes	—
46	C₂	C₂×#126	1	1	yes	characteristic
47	C₂	#529	1	3	yes	—
48	C₂	#533	1	3	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
25. C₄²	Q₈	semidirect

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