Group #21446813 — subgroups

Subgroups — #21446813

Order 7808.

228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 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	#16839786	C₂	1	1	yes	maximal, characteristic
2	C₄×#11758194	C₂	1	1	yes	maximal, characteristic
3	#16839531	C₂	1	4	yes	maximal
4	C₂×#125×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758194	C₂²	1	2	yes	—
6	C₂×#11758194	C₂²	1	2	yes	—
7	C₄⋊#92418	—	2	2	no	—
8	#14519688	—	2	1	no	—
9	C₄×#92418	—	2	1	no	—
10	#125×C₆₁	—	2	1	no	—
11	#125×C₆₁	—	2	1	no	—
12	#125×C₆₁	—	2	2	no	—
13	C₂×C₄⋊C₄×C₆₁	C₄	1	4	yes	—
14	C₂×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₆₁	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₆₁	—	2	4	no	—
20	C₄⋊C₄×C₆₁	—	2	4	no	—
21	C₄⋊C₄×C₆₁	—	2	2	no	—
22	C₄⋊C₄×C₆₁	—	2	2	no	—
23	C₄²×C₆₁	D₄	1	1	yes	characteristic
24	C₄²×C₆₁	D₄	1	1	yes	characteristic
25	C₄²×C₆₁	D₄	1	2	yes	—
26	#11758194	—	2	2	no	—
27	#11758194	—	2	4	no	—
28	#11758194	Q₈	1	4	yes	—
29	C₂×#92418	—	2	2	no	—
30	C₂×#92418	—	2	2	no	—
31	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	—	2	4	no	—
33	C₂×C₄×C₆₁	—	4	2	no	—
34	C₂×C₄×C₆₁	—	4	4	no	—
35	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
36	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₆₁	C₂×Q₈	1	2	yes	—
40	C₂×C₄×C₆₁	#41	1	2	yes	—
41	#92418	—	2	4	no	—
42	#92418	—	4	2	no	—
43	C₂²×C₆₁	—	2	2	no	—
44	C₂²×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₆₁	C₄×Q₈	1	2	yes	—
46	C₄×C₆₁	—	2	2	no	—
47	C₄×C₆₁	—	2	2	no	—
48	C₄×C₆₁	—	4	4	no	—
49	C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
50	C₄×C₆₁	#124	1	1	yes	characteristic
51	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
52	#1998	—	61	1	no	maximal, Sylow
53	C₂×C₆₁	—	2	2	no	—
54	C₂×C₆₁	#391	1	1	yes	characteristic
55	C₂×C₆₁	#413	1	2	yes	—
56	C₂×#125	D₆₁	1	1	yes	characteristic
57	#423	—	61	1	no	—
58	C₄×M₁₆	—	61	1	no	—
59	#343	—	61	4	no	—
60	C₆₁	#1998	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	61	2	no	—
62	C₂×M₁₆	—	61	2	no	—
63	#125	—	2	1	no	—
64	#125	—	2	1	no	—
65	#125	—	2	2	no	—
66	C₂×C₄⋊C₄	Dic₆₁	1	4	yes	—
67	C₂×C₄⋊C₄	C₂×D₆₁	1	2	yes	—
68	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
69	C₄⋊C₈	—	122	2	no	—
70	#97	—	122	1	no	—
71	C₄×C₈	—	122	1	no	—
72	C₂²×C₄	C₂×Dic₆₁	1	4	yes	—
73	C₂²×C₄	C₂×Dic₆₁	1	2	yes	—
74	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
75	M₁₆	—	61	4	no	—
76	M₁₆	—	122	2	no	—
77	M₁₆	—	122	4	no	—
78	C₂×C₈	—	122	2	no	—
79	C₂×C₈	—	122	2	no	—
80	C₄⋊C₄	—	2	4	no	—
81	C₄⋊C₄	—	2	4	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	2	2	no	—
84	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
85	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
86	C₄²	C₂²⋊D₆₁	1	2	yes	—
87	C₂³	C₂²×Dic₆₁	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	4	4	no	—
91	C₂×C₄	C₂²⋊Dic₆₁	1	2	yes	—
92	C₂×C₄	C₂²⋊Dic₆₁	1	2	yes	—
93	C₂×C₄	Q₈×D₆₁	1	2	yes	—
94	C₂×C₄	#11758226	1	2	yes	—
95	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
96	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
97	C₈	—	122	4	no	—
98	C₈	—	244	2	no	—
99	C₂²	—	2	2	no	—
100	C₂²	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
101	C₂²	Q₈×Dic₆₁	1	2	yes	—
102	C₄	—	2	2	no	—
103	C₄	—	2	2	no	—
104	C₄	—	4	4	no	—
105	C₄	#14519753	1	2	yes	—
106	C₄	#14519766	1	1	yes	characteristic
107	C₄	#14519775	1	1	yes	characteristic
108	C₂	—	2	2	no	—
109	C₂	#16839669	1	1	yes	characteristic
110	C₂	#16839746	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16839786

C₂

yes

maximal, characteristic

C₄×#11758194

C₂

yes

maximal, characteristic

#16839531

C₂

yes

maximal

C₂×#125×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

—

C₂×#11758194

C₂²

yes

—

C₄⋊#92418

—

#14519688

—

C₄×#92418

—

#125×C₆₁

—

#125×C₆₁

—

#125×C₆₁

—

C₂×C₄⋊C₄×C₆₁

C₄

yes

—

C₂×C₄⋊C₄×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

D₄

yes

characteristic

C₄²×C₆₁

D₄

yes

characteristic

C₄²×C₆₁

D₄

yes

—

#11758194

—

#11758194

—

#11758194

Q₈

yes

—

C₂×#92418

—

C₂×#92418

—

C₂³×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

—

C₂×C₄×C₆₁

#41

yes

—

#92418

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₆₁

C₄×Q₈

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂²⋊Q₈

yes

—

C₄×C₆₁

#124

yes

characteristic

C₄×C₆₁

C₄⋊Q₈

yes

characteristic

#1998

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#391

yes

characteristic

C₂×C₆₁

#413

yes

—

C₂×#125

D₆₁

yes

characteristic

#423

—

C₄×M₁₆

—

#343

—

C₆₁

#1998

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

#125

—

#125

—

#125

—

C₂×C₄⋊C₄

Dic₆₁

yes

—

C₂×C₄⋊C₄

C₂×D₆₁

yes

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

C₄⋊C₈

—

122

—

#97

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

C₂×Dic₆₁

yes

—

C₂²×C₄

C₂×Dic₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₆₁

yes

characteristic

C₄²

C₂²⋊D₆₁

yes

characteristic

C₄²

C₂²⋊D₆₁

yes

—

C₂³

C₂²×Dic₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₆₁

yes

—

C₂×C₄

C₂²⋊Dic₆₁

yes

—

C₂×C₄

Q₈×D₆₁

yes

—

C₂×C₄

#11758226

yes

—

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

122

—

C₈

—

244

—

C₂²

—

100

C₂²

C₂×C₂²⋊Dic₆₁

yes

characteristic

101

C₂²

Q₈×Dic₆₁

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

#14519753

yes

—

106

C₄

#14519766

yes

characteristic

107

C₄

#14519775

yes

characteristic

108

C₂

—

109

C₂

#16839669

yes

characteristic

110

C₂

#16839746

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₆₁
commutator	C₂³×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#125×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₂²⋊C₄
hypercenter	C₂×#125	D₆₁
hypocenter	C₆₁	#1998
LCS	G ▷ C₂³×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₆₁

commutator

C₂³×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×#125×C₆₁

C₂

socle

C₂²×C₆₁

C₂×C₂²⋊C₄

D₆₁

C₆₁

G ▷ C₂³×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
60. C₆₁	#1998	semidirect

H ≅ G/N

type

60. C₆₁

#1998

semidirect

Subgroups — #21446813

Conjugacy classes of subgroups

Complements