Subgroups — #1940

Order 128.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#97	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	#336	C₂	1	2	yes	maximal
6	C₂²×C₈	C₂²	1	2	yes	—
7	C₂²×C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₄²	C₂²	1	2	yes	—
11	C₂×C₄²	C₂²	1	1	yes	characteristic
12	C₄⋊C₈	—	2	4	no	—
13	C₄⋊C₈	—	2	2	no	—
14	#97	—	2	2	no	—
15	#95	C₄	1	1	yes	characteristic
16	#95	C₄	1	1	yes	characteristic
17	C₂²×C₄	C₂×C₄	1	2	yes	—
18	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄	C₂×C₄	1	2	yes	—
21	C₂²×C₄	C₂³	1	1	yes	characteristic
22	C₂×C₈	—	2	1	no	—
23	C₂×C₈	—	2	1	no	—
24	C₂×C₈	—	2	1	no	—
25	C₂×C₈	—	2	1	no	—
26	C₂×C₈	—	2	2	no	—
27	C₂×C₈	—	2	2	no	—
28	C₂×C₈	—	2	2	no	—
29	C₂×C₈	D₄	1	2	yes	—
30	C₂×C₈	Q₈	1	2	yes	—
31	C₄⋊C₄	—	2	4	no	—
32	C₄²	—	2	2	no	—
33	C₄²	—	2	2	no	—
34	C₄²	D₄	1	2	yes	—
35	C₄²	Q₈	1	2	yes	—
36	C₂³	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	2	2	no	—
39	C₂×C₄	—	2	2	no	—
40	C₂×C₄	—	2	2	no	—
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	C₄⋊C₄	1	2	yes	—
45	C₂×C₄	C₄⋊C₄	1	2	yes	—
46	C₂×C₄	M₁₆	1	4	yes	—
47	C₂×C₄	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₄	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₄	#41	1	1	yes	characteristic
52	C₂×C₄	#41	1	1	yes	characteristic
53	C₈	—	2	2	no	—
54	C₈	—	2	2	no	—
55	C₈	—	4	2	no	—
56	C₂²	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂²	C₄×D₄	1	1	yes	characteristic
58	C₂²	C₄×Q₈	1	1	yes	characteristic
59	C₂²	C₂×M₁₆	1	2	yes	—
60	C₂²	#131	1	2	yes	—
61	C₄	—	2	2	no	—
62	C₄	—	2	2	no	—
63	C₄	—	2	4	no	—
64	C₄	—	4	2	no	—
65	C₄	#121	1	1	yes	characteristic
66	C₄	C₂²⋊Q₈	1	1	yes	characteristic
67	C₄	#125	1	1	yes	characteristic
68	C₄	C₄⋊Q₈	1	1	yes	characteristic
69	C₂	#389	1	1	yes	characteristic
70	C₂	#423	1	1	yes	characteristic
71	C₂	#424	1	1	yes	characteristic
72	C₂	#435	1	2	yes	—
73	C₂	#446	1	2	yes	—

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₄	C₂³
commutator, socle, prime radical	C₂³	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ 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×C₄⋊C₈	2
C₂×#97	2
C₄×C₄⋊C₄	2
#336	2