Subgroups — #2100

Order 128.

107 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#389	C₂	1	1	yes	maximal, characteristic
2	#384	C₂	1	1	yes	maximal, characteristic
3	#340	C₂	1	2	yes	maximal
4	#340	C₂	1	2	yes	maximal
5	#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊C₄	—	2	1	no	—
8	C₂×C₄⋊C₄	—	2	1	no	—
9	C₂×C₄⋊C₄	—	2	1	no	—
10	C₂×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₄²	C₂²	1	1	yes	characteristic
14	#95	—	2	1	no	—
15	C₂²×C₄	—	2	1	no	—
16	C₂²×C₄	—	2	1	no	—
17	C₂²×C₄	—	2	2	no	—
18	C₂²×C₄	D₄	1	1	yes	characteristic
19	C₂²×C₄	D₄	1	1	yes	characteristic
20	C₂²×C₄	C₂³	1	1	yes	characteristic
21	C₂×C₈	—	2	2	no	—
22	C₂×C₈	—	2	2	no	—
23	C₂×C₈	—	2	2	no	—
24	C₄⋊C₄	—	2	1	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄⋊C₄	—	2	4	no	—
27	C₄⋊C₄	—	4	2	no	—
28	C₄⋊C₄	—	4	2	no	—
29	C₄⋊C₄	—	4	2	no	—
30	C₄⋊C₄	Q₈	1	2	yes	—
31	C₄²	—	2	2	no	—
32	C₂³	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	4	1	no	—
39	C₂×C₄	—	4	1	no	—
40	C₂×C₄	—	4	1	no	—
41	C₂×C₄	—	4	2	no	—
42	C₂×C₄	—	4	1	no	—
43	C₂×C₄	—	4	2	no	—
44	C₂×C₄	—	4	2	no	—
45	C₂×C₄	—	4	1	no	—
46	C₂×C₄	SD₁₆	1	2	yes	—
47	C₂×C₄	Q₁₆	1	2	yes	—
48	C₂×C₄	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₄	#41	1	2	yes	—
50	C₂×C₄	#41	1	2	yes	—
51	C₂×C₄	#41	1	1	yes	characteristic
52	C₈	—	4	2	no	—
53	C₂²	C₂²⋊Q₈	1	1	yes	characteristic
54	C₂²	#123	1	1	yes	characteristic
55	C₂²	#124	1	1	yes	characteristic
56	C₂²	C₂×SD₁₆	1	1	yes	characteristic
57	C₂²	C₂×Q₁₆	1	1	yes	characteristic
58	C₂²	AGL(1,ℤ/8)	1	1	yes	characteristic
59	C₂²	AGL(1,ℤ/8)	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	—	2	2	no	—
62	C₄	—	4	2	no	—
63	C₄	—	8	1	no	—
64	C₄	—	8	2	no	—
65	C₄	#125	1	2	yes	—
66	C₄	#126	1	2	yes	—
67	C₂	#400	1	1	yes	characteristic
68	C₂	#476	1	1	yes	characteristic
69	C₂	#477	1	1	yes	characteristic
70	C₂	#481	1	1	yes	characteristic
71	C₂	#484	1	1	yes	characteristic
72	C₂	#487	1	1	yes	characteristic
73	C₂	#490	1	1	yes	characteristic

	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
#389	2
#384	2
#340	2
#336	2