Subgroups — #2086

Order 128.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#107	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#389	C₂	1	2	yes	maximal
4	#340	C₂	1	2	yes	maximal
5	#340	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄	—	2	2	no	—
9	C₂×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₄²	C₂²	1	1	yes	characteristic
12	#107	—	2	2	no	—
13	C₄⋊C₈	—	2	2	no	—
14	#95	—	2	2	no	—
15	C₂²×C₄	—	2	2	no	—
16	C₂²×C₄	—	2	2	no	—
17	C₂²×C₄	D₄	1	1	yes	characteristic
18	C₂²×C₄	D₄	1	1	yes	characteristic
19	C₂²×C₄	C₂³	1	1	yes	characteristic
20	C₂×C₈	—	2	2	no	—
21	C₂×C₈	—	2	1	no	—
22	C₂×C₈	—	2	2	no	—
23	C₂×C₈	D₄	1	2	yes	—
24	C₄⋊C₄	—	2	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄⋊C₄	—	2	2	no	—
27	C₄⋊C₄	—	4	4	no	—
28	C₄⋊C₄	Q₈	1	4	yes	—
29	C₄²	—	2	1	no	—
30	C₄²	—	2	1	no	—
31	C₂³	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	4	no	—
36	C₂×C₄	—	2	2	no	—
37	C₂×C₄	—	4	2	no	—
38	C₂×C₄	—	4	2	no	—
39	C₂×C₄	—	4	2	no	—
40	C₂×C₄	—	4	2	no	—
41	C₂×C₄	—	4	2	no	—
42	C₂×C₄	D₈	1	2	yes	—
43	C₂×C₄	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄	C₂×Q₈	1	2	yes	—
45	C₂×C₄	#41	1	2	yes	—
46	C₂×C₄	#41	1	1	yes	characteristic
47	C₈	—	2	2	no	—
48	C₈	—	4	1	no	—
49	C₂²	#121	1	1	yes	characteristic
50	C₂²	C₂²⋊Q₈	1	2	yes	—
51	C₂²	C₂×D₈	1	1	yes	characteristic
52	C₂²	#135	1	1	yes	characteristic
53	C₂²	#137	1	2	yes	—
54	C₄	—	2	2	no	—
55	C₄	—	4	1	no	—
56	C₄	—	4	4	no	—
57	C₄	—	8	2	no	—
58	C₄	#123	1	1	yes	characteristic
59	C₄	#125	1	2	yes	—
60	C₄	C₄⋊Q₈	1	1	yes	characteristic
61	C₂	#398	1	1	yes	characteristic
62	C₂	#466	1	1	yes	characteristic
63	C₂	#470	1	1	yes	characteristic
64	C₂	#474	1	2	yes	—
65	C₂	#479	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Maximal subgroups

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

subgroup	index
C₂×#107	2
C₂×C₄⋊C₈	2
#389	2
#340	2