Group #21461737 — subgroups

Subgroups — #21461737

Order 7808.

216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 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×#14519844	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#92420	C₂	1	1	yes	maximal, characteristic
3	#16840628	C₂	1	4	yes	maximal
4	#16839607	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92420	C₂²	1	2	yes	—
6	C₂²×#92420	C₂²	1	2	yes	—
7	#14519844	—	2	2	no	—
8	C₄⋊#92420	—	2	2	no	—
9	C₂×C₄×Dic₆₁	C₂²	1	2	yes	—
10	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
11	#14519684	C₄	1	1	yes	characteristic
12	#14519684	C₄	1	2	yes	—
13	#95×C₆₁	C₄	1	1	yes	characteristic
14	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
17	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
19	C₂×#92420	—	2	2	no	—
20	C₂×#92420	—	2	2	no	—
21	C₂×#92420	—	2	4	no	—
22	C₂×#92420	—	2	4	no	—
23	C₄×Dic₆₁	—	2	2	no	—
24	C₄×Dic₆₁	—	2	2	no	—
25	C₄×Dic₆₁	D₄	1	2	yes	—
26	C₄×Dic₆₁	Q₈	1	2	yes	—
27	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₆₁	—	2	2	no	—
29	C₂×C₄×C₆₁	—	2	2	no	—
30	C₂×C₄×C₆₁	—	2	2	no	—
31	C₂×C₄×C₆₁	—	2	2	no	—
32	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
33	C₂×Dic₆₁	—	2	1	no	—
34	C₂×Dic₆₁	—	2	1	no	—
35	C₂×Dic₆₁	—	2	2	no	—
36	C₂×Dic₆₁	—	2	2	no	—
37	C₂×Dic₆₁	—	2	2	no	—
38	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
39	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
41	C₂×Dic₆₁	#41	1	2	yes	—
42	C₂×Dic₆₁	#41	1	2	yes	—
43	#92420	—	4	2	no	—
44	#92420	—	4	2	no	—
45	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₆₁	#117	1	2	yes	—
47	C₂²×C₆₁	#131	1	2	yes	—
48	C₂²×C₆₁	#131	1	1	yes	characteristic
49	C₂²×C₆₁	#131	1	1	yes	characteristic
50	C₄×C₆₁	—	2	2	no	—
51	C₄×C₆₁	—	4	2	no	—
52	Dic₆₁	—	2	2	no	—
53	Dic₆₁	—	4	2	no	—
54	Dic₆₁	#124	1	1	yes	characteristic
55	Dic₆₁	#124	1	1	yes	characteristic
56	Dic₆₁	#125	1	2	yes	—
57	#1832	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	#382	1	1	yes	characteristic
59	C₂×C₆₁	#424	1	1	yes	characteristic
60	C₂×C₆₁	#424	1	1	yes	characteristic
61	C₂×C₆₁	#433	1	2	yes	—
62	C₂×C₆₁	#433	1	2	yes	—
63	C₂×C₄⋊C₈	—	61	1	no	—
64	C₂×C₄⋊C₈	—	61	1	no	—
65	#376	—	61	1	no	—
66	#336	—	61	4	no	—
67	C₆₁	#1832	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₈	—	61	2	no	—
69	C₂²×C₈	—	61	2	no	—
70	C₂×C₄²	—	61	1	no	—
71	C₂×C₄²	—	61	2	no	—
72	C₄⋊C₈	—	122	2	no	—
73	C₄⋊C₈	—	122	2	no	—
74	#95	—	61	2	no	—
75	#95	—	61	1	no	—
76	#95	#6923	1	1	yes	characteristic
77	C₂²×C₄	—	61	1	no	—
78	C₂²×C₄	—	61	1	no	—
79	C₂²×C₄	—	61	2	no	—
80	C₂²×C₄	C₂×#6923	1	2	yes	—
81	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
82	C₂×C₈	—	122	2	no	—
83	C₂×C₈	—	122	2	no	—
84	C₂×C₈	—	122	4	no	—
85	C₂×C₈	—	122	4	no	—
86	C₄²	—	61	2	no	—
87	C₄²	—	61	2	no	—
88	C₄²	—	122	2	no	—
89	C₄²	—	122	2	no	—
90	C₂³	C₂²×#6923	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	2	no	—
98	C₂×C₄	—	61	2	no	—
99	C₂×C₄	—	61	2	no	—
100	C₂×C₄	—	122	1	no	—
101	C₂×C₄	—	122	1	no	—
102	C₂×C₄	—	122	2	no	—
103	C₂×C₄	—	122	2	no	—
104	C₂×C₄	—	122	2	no	—
105	C₂×C₄	C₄⋊#6923	1	2	yes	—
106	C₈	—	244	2	no	—
107	C₈	—	244	2	no	—
108	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
109	C₂²	#14519856	1	2	yes	—
110	C₂²	#14519864	1	2	yes	—
111	C₂²	#14519864	1	1	yes	characteristic
112	C₂²	#14519865	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	4	2	no	—
115	C₄	—	61	1	no	—
116	C₄	—	61	1	no	—
117	C₄	—	61	2	no	—
118	C₄	—	122	2	no	—
119	C₄	—	244	2	no	—
120	C₂	#16840706	1	1	yes	characteristic
121	C₂	#16840768	1	1	yes	characteristic
122	C₂	#16840769	1	1	yes	characteristic
123	C₂	#16840786	1	2	yes	—
124	C₂	#16840787	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519844

C₂

yes

maximal, characteristic

C₂×C₄⋊#92420

C₂

yes

maximal, characteristic

#16840628

C₂

yes

maximal

#16839607

C₂

yes

maximal, characteristic

C₂²×#92420

C₂²

yes

—

C₂²×#92420

C₂²

yes

—

#14519844

—

C₄⋊#92420

—

C₂×C₄×Dic₆₁

C₂²

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519684

C₄

yes

characteristic

#14519684

C₄

yes

—

#95×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

—

C₂²×Dic₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂³

yes

—

—

—

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

D₄

yes

—

C₄×Dic₆₁

Q₈

yes

—

C₂³×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

C₂×Q₈

yes

characteristic

C₂×Dic₆₁

#41

yes

—

C₂×Dic₆₁

#41

yes

—

#92420

—

#92420

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#117

yes

—

C₂²×C₆₁

#131

yes

—

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

yes

Dic₆₁

yes

Dic₆₁

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

#433

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

#376

—

#336

—

C₆₁

#1832

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

—

C₄²

—

C₄²

—

122

—

C₄²

—

122

—

C₂³

C₂²×#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

122

—

101

C₂×C₄

—

122

—

102

C₂×C₄

—

122

—

103

C₂×C₄

—

122

—

104

C₂×C₄

—

122

—

105

C₂×C₄

C₄⋊#6923

yes

—

106

C₈

—

244

—

107

C₈

—

244

—

108

C₂²

C₂×C₄⋊#6923

yes

characteristic

109

C₂²

#14519856

yes

—

110

C₂²

#14519864

yes

—

111

C₂²

#14519864

yes

characteristic

112

C₂²

#14519865

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

122

—

119

C₄

—

244

—

120

C₂

#16840706

yes

characteristic

121

C₂

#16840768

yes

characteristic

122

C₂

#16840769

yes

characteristic

123

C₂

#16840786

yes

—

124

C₂

#16840787

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#6923
commutator, socle	C₂³×C₆₁	C₂²×C₄
Fitting	#95×C₆₁	C₄
hypercenter	#95	#6923
hypocenter	C₆₁	#1832
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#6923

commutator, socle

C₂³×C₆₁

C₂²×C₄

Fitting

#95×C₆₁

C₄

C₆₁

G ▷ C₂³×C₆₁ ▷ C₆₁

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
67. C₆₁	#1832	semidirect

H ≅ G/N

type

67. C₆₁

#1832

semidirect

Subgroups — #21461737

Conjugacy classes of subgroups

Complements