Group #21460703 — subgroups

Subgroups — #21460703

Order 7808.

150 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 48 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	#16840779	C₂	1	1	yes	maximal, characteristic
2	C₄×#11758217	C₂	1	1	yes	maximal, characteristic
3	#16839785	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758217	—	2	1	no	—
5	#14519844	C₄	1	2	yes	—
6	C₂²⋊#92420	—	2	1	no	—
7	#14519832	C₄	1	2	yes	—
8	C₄×#92420	—	2	1	no	—
9	C₄×#92420	—	2	1	no	—
10	C₂×#11758194	C₄	1	1	yes	characteristic
11	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
12	#14519706	—	2	1	no	—
13	#14519706	—	2	1	no	—
14	C₂×M₁₆×C₆₁	C₄	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
17	C₂²×Dic₆₁	Q₈	1	1	yes	characteristic
18	#11758217	—	2	4	no	—
19	C₂×#92420	—	2	2	no	—
20	C₂×#92420	—	2	2	no	—
21	M₁₆×C₆₁	—	4	1	no	—
22	C₂×C₈×C₆₁	—	2	1	no	—
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₆₁	D₄	1	1	yes	characteristic
26	C₄×Dic₆₁	D₄	1	1	yes	characteristic
27	#11758194	—	4	1	no	—
28	C₂×#92418	—	2	1	no	—
29	C₂³×C₆₁	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	—	2	1	no	—
31	C₂×C₄×C₆₁	—	2	1	no	—
32	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	—	2	2	no	—
35	C₂×Dic₆₁	—	2	2	no	—
36	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
39	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
40	#92420	—	2	4	no	—
41	#92420	—	4	2	no	—
42	C₈×C₆₁	—	4	1	no	—
43	#92418	—	4	1	no	—
44	C₂²×C₆₁	—	2	1	no	—
45	C₂²×C₆₁	—	2	1	no	—
46	C₂²×C₆₁	—	2	1	no	—
47	C₂²×C₆₁	#95	1	1	yes	characteristic
48	C₄×C₆₁	—	2	1	no	—
49	C₄×C₆₁	#100	1	1	yes	characteristic
50	C₄×C₆₁	#101	1	1	yes	characteristic
51	Dic₆₁	—	2	1	no	—
52	Dic₆₁	—	2	1	no	—
53	Dic₆₁	#104	1	2	yes	—
54	Dic₆₁	#108	1	2	yes	—
55	#1299	—	61	1	no	maximal, Sylow
56	C₂×C₆₁	—	4	1	no	—
57	C₂×C₆₁	#339	1	1	yes	characteristic
58	C₂×C₆₁	#341	1	1	yes	characteristic
59	C₂×C₆₁	#343	1	1	yes	characteristic
60	#431	—	61	1	no	—
61	#423	—	61	1	no	—
62	C₄×M₁₆	—	61	1	no	—
63	C₆₁	#1299	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₁₆	—	61	1	no	—
65	C₂×M₁₆	—	122	1	no	—
66	C₂×M₁₆	#6923	1	1	yes	characteristic
67	C₂×C₄²	—	61	1	no	—
68	C₄⋊C₈	—	61	2	no	—
69	C₄⋊C₈	—	122	1	no	—
70	C₄⋊C₈	—	122	1	no	—
71	C₂²⋊C₈	—	122	1	no	—
72	#97	—	61	2	no	—
73	C₄×C₈	—	122	1	no	—
74	C₄×C₈	—	122	1	no	—
75	C₂²×C₄	—	61	1	no	—
76	C₂²×C₄	—	61	1	no	—
77	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
78	M₁₆	—	4	1	no	—
79	M₁₆	—	122	4	no	—
80	M₁₆	—	244	1	no	—
81	C₂×C₈	—	2	1	no	—
82	C₂×C₈	—	122	2	no	—
83	C₂×C₈	—	122	2	no	—
84	C₂×C₈	—	122	1	no	—
85	C₄²	—	61	1	no	—
86	C₄²	—	61	1	no	—
87	C₄²	—	61	1	no	—
88	C₄²	—	61	1	no	—
89	C₂³	C₄⋊#6923	1	1	yes	characteristic
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	61	1	no	—
94	C₂×C₄	—	61	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	122	2	no	—
97	C₂×C₄	—	122	2	no	—
98	C₂×C₄	C₄×#6923	1	1	yes	characteristic
99	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
100	C₈	—	4	1	no	—
101	C₈	—	122	4	no	—
102	C₈	—	244	2	no	—
103	C₈	—	244	1	no	—
104	C₂²	—	2	1	no	—
105	C₂²	—	2	1	no	—
106	C₂²	—	2	1	no	—
107	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	61	2	no	—
110	C₄	—	61	2	no	—
111	C₄	—	122	1	no	—
112	C₄	—	122	1	no	—
113	C₄	#14519837	1	1	yes	characteristic
114	C₄	#14519838	1	1	yes	characteristic
115	C₂	—	4	1	no	—
116	C₂	#16840634	1	1	yes	characteristic
117	C₂	#16840637	1	1	yes	characteristic
118	C₂	#16840642	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840779

C₂

yes

maximal, characteristic

C₄×#11758217

C₂

yes

maximal, characteristic

#16839785

C₂

yes

maximal, characteristic

C₂×#11758217

—

#14519844

C₄

yes

—

C₂²⋊#92420

—

#14519832

C₄

yes

—

C₄×#92420

—

C₄×#92420

—

C₂×#11758194

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519706

—

#14519706

—

C₂×M₁₆×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

D₄

yes

characteristic

C₂²×Dic₆₁

Q₈

yes

—

—

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

#11758194

—

C₂×#92418

—

C₂³×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

#92420

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#95

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

—

Dic₆₁

#104

yes

—

Dic₆₁

#108

yes

—

#1299

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

C₄×M₁₆

—

C₆₁

#1299

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

122

—

C₂×M₁₆

#6923

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

#97

—

C₄×C₈

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄⋊#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₄×#6923

yes

characteristic

C₂×C₄

C₂²⋊#6923

yes

characteristic

100

C₈

—

101

C₈

—

122

—

102

C₈

—

244

—

103

C₈

—

244

—

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

122

—

112

C₄

—

122

—

113

C₄

#14519837

yes

characteristic

114

C₄

#14519838

yes

characteristic

115

C₂

—

116

C₂

#16840634

yes

characteristic

117

C₂

#16840637

yes

characteristic

118

C₂

#16840642

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×M₁₆×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₂×M₁₆	#6923
hypocenter	C₆₁	#1299
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

subgroup

G/H

center

C₂×C₄

C₂²⋊#6923

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂×M₁₆×C₆₁

C₄

C₂²×C₆₁

C₂×M₁₆

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
63. C₆₁	#1299	semidirect

H ≅ G/N

type

63. C₆₁

#1299

semidirect

Subgroups — #21460703

Conjugacy classes of subgroups

Complements