Group #10632 — subgroups

Subgroups — #10632

Order 256.

155 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 155 conjugacy classes of subgroups — too many to draw. Only its 53 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	#1960	C₂	1	1	yes	maximal, characteristic
2	#1849	C₂	1	1	yes	maximal, characteristic
3	#1546	C₂	1	2	yes	maximal
4	#1286	C₂	1	2	yes	maximal
5	#1281	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	#431	C₂²	1	2	yes	—
8	C₂×#108	—	2	1	no	—
9	C₂×#108	—	2	1	no	—
10	#423	C₂²	1	2	yes	—
11	C₂×#103	—	2	1	no	—
12	C₂×#103	—	2	1	no	—
13	C₂×#97	C₂²	1	1	yes	characteristic
14	#382	C₂²	1	1	yes	characteristic
15	#332	—	2	4	no	—
16	C₂²×Q₈	—	2	1	no	—
17	C₂×M₁₆	—	2	2	no	—
18	C₂²×C₈	D₄	1	1	yes	characteristic
19	C₂²×C₈	D₄	1	1	yes	characteristic
20	C₄⋊Q₈	—	2	2	no	—
21	C₄⋊Q₈	—	2	1	no	—
22	C₄⋊Q₈	D₄	1	2	yes	—
23	C₂×C₄⋊C₄	—	2	2	no	—
24	C₂×C₄⋊C₄	—	2	1	no	—
25	C₂×C₄²	C₂³	1	1	yes	characteristic
26	#108	—	4	2	no	—
27	#108	—	4	2	no	—
28	C₄⋊C₈	—	2	2	no	—
29	C₄⋊C₈	—	2	2	no	—
30	C₄⋊C₈	—	2	2	no	—
31	#103	—	4	2	no	—
32	#103	—	4	2	no	—
33	C₂²⋊C₈	—	2	2	no	—
34	#97	—	2	2	no	—
35	C₄×C₈	—	2	2	no	—
36	#95	—	2	2	no	—
37	C₂×Q₈	—	2	2	no	—
38	C₂×Q₈	—	4	1	no	—
39	C₂×Q₈	—	4	1	no	—
40	C₂×Q₈	—	4	1	no	—
41	C₂×Q₈	—	4	1	no	—
42	C₂×Q₈	—	4	1	no	—
43	C₂²×C₄	—	4	1	no	—
44	C₂²×C₄	—	4	1	no	—
45	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄	#41	1	2	yes	—
47	M₁₆	—	4	2	no	—
48	M₁₆	—	4	2	no	—
49	C₂×C₈	—	2	1	no	—
50	C₂×C₈	—	2	1	no	—
51	C₂×C₈	—	2	1	no	—
52	C₂×C₈	—	2	1	no	—
53	C₂×C₈	—	4	2	no	—
54	C₂×C₈	—	4	2	no	—
55	C₂×C₈	D₈	1	2	yes	—
56	C₂×C₈	SD₁₆	1	2	yes	—
57	C₄⋊C₄	—	2	4	no	—
58	C₄⋊C₄	—	4	2	no	—
59	C₄⋊C₄	—	4	1	no	—
60	C₄⋊C₄	—	4	1	no	—
61	C₄²	C₂×D₄	1	1	yes	characteristic
62	C₄²	#41	1	1	yes	characteristic
63	C₄²	#41	1	2	yes	—
64	C₂³	#124	1	1	yes	characteristic
65	Q₈	—	4	2	no	—
66	Q₈	—	4	2	no	—
67	Q₈	—	8	1	no	—
68	Q₈	—	8	1	no	—
69	C₂×C₄	—	4	2	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	8	1	no	—
72	C₂×C₄	—	8	1	no	—
73	C₂×C₄	—	8	2	no	—
74	C₂×C₄	—	8	1	no	—
75	C₂×C₄	#121	1	1	yes	characteristic
76	C₂×C₄	#123	1	2	yes	—
77	C₂×C₄	#123	1	1	yes	characteristic
78	C₂×C₄	#126	1	2	yes	—
79	C₂×C₄	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄	C₂×SD₁₆	1	1	yes	characteristic
81	C₂×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
82	C₂×C₄	#137	1	1	yes	characteristic
83	C₈	—	2	2	no	—
84	C₈	—	2	2	no	—
85	C₈	—	8	2	no	—
86	C₈	—	8	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	#397	1	1	yes	characteristic
89	C₂²	#486	1	1	yes	characteristic
90	C₂²	#489	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	2	2	no	—
93	C₄	—	8	2	no	—
94	C₄	—	16	1	no	—
95	C₄	#459	1	1	yes	characteristic
96	C₄	#461	1	1	yes	characteristic
97	C₄	#480	1	1	yes	characteristic
98	C₄	#481	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	2	1	no	—
101	C₂	#2071	1	1	yes	characteristic
102	C₂	#2082	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#1960

C₂

yes

maximal, characteristic

#1849

C₂

yes

maximal, characteristic

#1546

C₂

yes

maximal

#1286

C₂

yes

maximal

#1281

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈

C₂²

yes

characteristic

#431

C₂²

yes

—

C₂×#108

—

C₂×#108

—

#423

C₂²

yes

—

C₂×#103

—

C₂×#103

—

C₂×#97

C₂²

yes

characteristic

#382

C₂²

yes

characteristic

#332

—

C₂²×Q₈

—

C₂×M₁₆

—

C₂²×C₈

D₄

yes

characteristic

C₂²×C₈

D₄

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂³

yes

characteristic

#108

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#103

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄

yes

characteristic

C₂²×C₄

#41

yes

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₈

yes

—

C₂×C₈

SD₁₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×D₄

yes

C₄²

yes

C₄²

yes

—

C₂³

#124

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#121

yes

characteristic

C₂×C₄

#123

yes

—

C₂×C₄

#123

yes

characteristic

C₂×C₄

#126

yes

—

C₂×C₄

C₂×D₈

yes

characteristic

C₂×C₄

C₂×SD₁₆

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

—

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₄

yes

C₄

yes

C₂

—

100

C₂

—

101

C₂

#2071

yes

characteristic

102

C₂

#2082

yes

—

	subgroup	G/H
center, socle	C₂²	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³
prime radical	C₂³	#124
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

subgroup

G/H

center, socle

C₂²

#397

commutator, Frattini, cosocle

C₂×C₄²

C₂³

prime radical

C₂³

#124

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ G

LECS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

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

subgroup	index
#1960	2
#1849	2
#1546	2
#1286	2
#1281	2

subgroup

index

Subgroups — #10632

Conjugacy classes of subgroups

Maximal subgroups