Subgroups — C₂×#395 #2387

Order 128.

454 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₄	C₂	1	3	yes	maximal
3	#395	C₂	1	8	yes	maximal, direct product factor
4	C₂×#95	C₂	1	3	yes	maximal
5	C₂²×Q₈	—	2	12	no	—
6	C₂²×Q₈	C₂²	1	4	yes	—
7	C₂³×C₄	C₂²	1	1	yes	characteristic
8	C₂³×C₄	C₂²	1	3	yes	—
9	C₂³×C₄	C₂²	1	3	yes	—
10	C₂×C₄⋊C₄	—	2	12	no	—
11	C₂×C₄⋊C₄	C₂²	1	12	yes	—
12	#95	C₂²	1	12	yes	—
13	C₂⁴	C₂³	1	1	yes	characteristic
14	C₂×Q₈	—	2	32	no	—
15	C₂×Q₈	—	2	24	no	—
16	C₂²×C₄	—	2	6	no	—
17	C₂²×C₄	—	2	12	no	—
18	C₂²×C₄	—	2	6	no	—
19	C₂²×C₄	—	2	6	no	—
20	C₂²×C₄	D₄	1	12	yes	—
21	C₂²×C₄	Q₈	1	12	yes	complemented
22	C₂²×C₄	C₂³	1	2	yes	—
23	C₂²×C₄	C₂³	1	6	yes	—
24	C₂²×C₄	C₂³	1	6	yes	—
25	C₄⋊C₄	—	2	24	no	—
26	C₂³	C₂×D₄	1	6	yes	—
27	C₂³	C₂×Q₈	1	6	yes	—
28	C₂³	#41	1	2	yes	—
29	C₂³	C₂⁴	1	1	yes	characteristic
30	Q₈	—	2	32	no	—
31	C₂×C₄	—	2	24	no	—
32	C₂×C₄	—	2	24	no	—
33	C₂×C₄	—	2	6	no	—
34	C₂×C₄	—	2	12	no	—
35	C₂×C₄	—	2	6	no	—
36	C₂×C₄	—	2	6	no	—
37	C₂×C₄	—	4	4	no	—
38	C₂×C₄	C₂×D₄	1	12	yes	—
39	C₂×C₄	C₂×Q₈	1	12	yes	complemented
40	C₂²	#120	1	4	yes	—
41	C₂²	C₂²⋊Q₈	1	12	yes	—
42	C₂²	C₄⋊Q₈	1	12	yes	—
43	C₂²	C₂²×D₄	1	3	yes	—
44	C₂²	C₂²×Q₈	1	3	yes	—
45	C₂²	C₂×#41	1	1	yes	characteristic
46	C₄	—	2	12	no	—
47	C₄	—	2	12	no	—
48	C₄	—	4	2	no	—
49	C₂	#395	1	8	yes	direct product factor
50	C₂	C₂×#120	1	1	yes	characteristic
51	C₂	C₂×C₂²⋊Q₈	1	3	yes	—
52	C₂	C₂×C₄⋊Q₈	1	3	yes	—

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