Group #1917 — subgroups

Subgroups — #1917

Order 128.

114 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#97	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	#336	C₂	1	1	yes	maximal, characteristic
5	#336	C₂	1	1	yes	maximal, characteristic
6	#336	C₂	1	1	yes	maximal, characteristic
7	#336	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₂×C₄²	C₂²	1	1	yes	characteristic
15	C₂×C₄²	C₂²	1	1	yes	characteristic
16	C₂×C₄²	C₂²	1	1	yes	characteristic
17	C₄⋊C₈	—	2	2	no	—
18	#97	—	2	2	no	—
19	#95	C₄	1	1	yes	characteristic
20	#95	C₄	1	1	yes	characteristic
21	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄	C₂³	1	1	yes	characteristic
28	C₂×C₈	—	2	1	no	—
29	C₂×C₈	—	2	1	no	—
30	C₂×C₈	—	2	1	no	—
31	C₂×C₈	—	2	1	no	—
32	C₂×C₈	—	2	1	no	—
33	C₂×C₈	—	2	1	no	—
34	C₂×C₈	—	2	1	no	—
35	C₂×C₈	—	2	1	no	—
36	C₂×C₈	—	2	1	no	—
37	C₂×C₈	—	2	1	no	—
38	C₂×C₈	D₄	1	2	yes	—
39	C₂×C₈	Q₈	1	2	yes	—
40	C₄⋊C₄	—	2	2	no	—
41	C₄⋊C₄	—	2	2	no	—
42	C₄²	—	2	1	no	—
43	C₄²	—	2	1	no	—
44	C₄²	—	2	1	no	—
45	C₄²	—	2	1	no	—
46	C₄²	—	2	1	no	—
47	C₄²	—	2	1	no	—
48	C₂³	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	M₁₆	1	2	yes	—
66	C₂×C₄	M₁₆	1	2	yes	—
67	C₂×C₄	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄	C₂×Q₈	1	1	yes	characteristic
69	C₂×C₄	#41	1	1	yes	characteristic
70	C₂×C₄	#41	1	1	yes	characteristic
71	C₂×C₄	#41	1	1	yes	characteristic
72	C₂×C₄	#41	1	1	yes	characteristic
73	C₈	—	2	2	no	—
74	C₈	—	2	2	no	—
75	C₈	—	4	1	no	—
76	C₈	—	4	1	no	—
77	C₂²	#117	1	1	yes	characteristic
78	C₂²	C₄×D₄	1	1	yes	characteristic
79	C₂²	C₄×Q₈	1	1	yes	characteristic
80	C₂²	C₂×M₁₆	1	1	yes	characteristic
81	C₂²	C₂×M₁₆	1	1	yes	characteristic
82	C₂²	#131	1	1	yes	characteristic
83	C₂²	#131	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	—	2	2	no	—
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	4	1	no	—
89	C₄	—	4	1	no	—
90	C₄	C₂²⋊Q₈	1	1	yes	characteristic
91	C₄	#123	1	1	yes	characteristic
92	C₄	#125	1	1	yes	characteristic
93	C₄	#126	1	1	yes	characteristic
94	C₂	#387	1	1	yes	characteristic
95	C₂	#432	1	1	yes	characteristic
96	C₂	#433	1	1	yes	characteristic
97	C₂	#435	1	1	yes	characteristic
98	C₂	#436	1	1	yes	characteristic
99	C₂	#446	1	1	yes	characteristic
100	C₂	#446	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×#97

C₂

yes

maximal, characteristic

C₄×C₄⋊C₄

C₂

yes

maximal, characteristic

#336

C₂

yes

maximal, characteristic

#336

C₂

yes

maximal, characteristic

#336

C₂

yes

maximal, characteristic

#336

C₂

yes

maximal, characteristic

C₂²×C₈

C₂²

yes

characteristic

C₂²×C₈

C₂²

yes

characteristic

C₂²×C₈

C₂²

yes

characteristic

C₂²×C₈

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₄

yes

characteristic

C₂×C₄⋊C₄

C₄

yes

characteristic

C₂×C₄²

C₂²

yes

characteristic

C₂×C₄²

C₂²

yes

characteristic

C₂×C₄²

C₂²

yes

characteristic

C₄⋊C₈

—

#97

—

#95

C₄

yes

characteristic

#95

C₄

yes

characteristic

C₂²×C₄

C₂×C₄

yes

characteristic

C₂²×C₄

C₂×C₄

yes

characteristic

C₂²×C₄

C₂×C₄

yes

characteristic

C₂²×C₄

C₂×C₄

yes

characteristic

C₂²×C₄

C₂×C₄

yes

characteristic

C₂²×C₄

C₂×C₄

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄

yes

—

C₂×C₈

Q₈

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²×C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

M₁₆

yes

—

C₂×C₄

M₁₆

yes

—

C₂×C₄

C₂×D₄

yes

characteristic

C₂×C₄

C₂×Q₈

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

#117

yes

characteristic

C₂²

C₄×D₄

yes

characteristic

C₂²

C₄×Q₈

yes

characteristic

C₂²

C₂×M₁₆

yes

characteristic

C₂²

C₂×M₁₆

yes

C₂²

yes

C₂²

yes

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

C₂²⋊Q₈

yes

C₄

yes

C₄

yes

C₄

yes

C₂

yes

C₂

yes

C₂

yes

C₂

yes

C₂

yes

C₂

yes

100

C₂

#446

yes

characteristic

	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

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

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

subgroup

index

C₂×C₄⋊C₈

C₂×#97

C₄×C₄⋊C₄

#336

Subgroups — #1917

Conjugacy classes of subgroups

Maximal subgroups