Group #22626163 — subgroups

Subgroups — #22626163

Order 9344.

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

normal subgroups only

This group has 228 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×#14556665	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#11924031	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989482	C₂	1	4	yes	maximal, complemented
4	C₂×#14556599	C₂	1	1	yes	maximal, characteristic
5	#14556665	—	2	2	no	—
6	C₂×#11924031	—	2	2	no	—
7	C₂×#11924031	C₂²	1	2	yes	—
8	C₂×#11924031	C₂²	1	2	yes	—
9	C₂×#11924028	C₄	1	1	yes	characteristic
10	#14556599	—	2	2	no	—
11	#14556599	—	2	2	no	—
12	C₂×#11924011	C₄	1	2	yes	—
13	C₂²×#10596831	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₇₃	C₂²	1	2	yes	—
15	C₂×M₁₆×C₇₃	C₄	1	1	yes	characteristic
16	#11924031	—	2	2	no	—
17	#11924031	—	2	2	no	—
18	#11924028	—	2	2	no	—
19	#11924028	—	2	2	no	—
20	C₂×Dic₁₄₆	C₈	1	1	yes	characteristic
21	C₂×D₂₉₂	C₈	1	1	yes	characteristic
22	C₂×C₂²⋊D₇₃	C₈	1	2	yes	—
23	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
24	#11924011	—	2	4	no	—
25	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
26	C₂×#10596831	D₄	1	2	yes	—
27	C₂×#10596831	D₄	1	2	yes	—
28	C₂×#10596831	C₂³	1	1	yes	characteristic
29	C₈×D₇₃	—	2	2	no	—
30	C₈×D₇₃	—	2	2	no	—
31	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
32	M₁₆×C₇₃	—	2	2	no	—
33	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
34	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
35	C₂²×D₇₃	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₇₃	M₁₆	1	2	yes	—
39	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
40	C₂²⋊D₇₃	—	2	4	no	—
41	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
42	D₂₉₂	—	2	2	no	—
43	C₄×D₇₃	—	2	2	no	—
44	C₄×D₇₃	—	2	2	no	—
45	Dic₁₄₆	—	2	2	no	—
46	C₈×C₇₃	—	2	2	no	—
47	#10596831	C₂²⋊C₄	1	2	yes	—
48	#10596831	C₂×D₄	1	1	yes	characteristic
49	#10596831	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₇₃	—	2	2	no	—
51	C₂²×C₇₃	C₂²⋊C₈	1	2	yes	—
52	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
53	C₂×D₇₃	—	2	2	no	—
54	C₂×D₇₃	—	2	4	no	—
55	C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
56	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
58	Dic₇₃	—	2	2	no	—
59	C₂×C₇₃	—	2	2	no	—
60	C₂×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
61	C₂×C₇₃	#504	1	2	yes	—
62	D₇₃	—	4	2	no	—
63	#2113	—	73	1	no	maximal, Sylow
64	C₇₃	#2113	1	1	yes	characteristic, complemented, Sylow
65	C₂×#131	—	73	1	no	—
66	C₂×M₃₂	—	73	1	no	—
67	C₂²×C₁₆	—	73	1	no	—
68	C₂²⋊C₁₆	—	73	4	no	—
69	C₂×#41	—	73	1	no	—
70	#131	—	146	2	no	—
71	#131	—	146	2	no	—
72	C₂×M₁₆	—	73	2	no	—
73	C₂×M₁₆	#64408	1	1	yes	characteristic
74	C₂²×C₈	—	73	1	no	—
75	C₂²×C₈	—	73	2	no	—
76	M₃₂	—	146	2	no	—
77	C₂×C₁₆	—	73	2	no	—
78	C₂×C₁₆	—	73	2	no	—
79	C₂×C₁₆	—	146	2	no	—
80	#41	—	146	2	no	—
81	#41	—	146	2	no	—
82	C₂×Q₈	—	73	1	no	—
83	C₂×D₄	—	73	2	no	—
84	C₂×D₄	—	73	1	no	—
85	C₂²×C₄	—	73	2	no	—
86	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
87	M₁₆	—	2	2	no	—
88	M₁₆	—	146	4	no	—
89	C₂×C₈	—	73	2	no	—
90	C₂×C₈	—	73	2	no	—
91	C₂×C₈	—	73	1	no	—
92	C₂×C₈	—	73	1	no	—
93	C₂×C₈	—	146	2	no	—
94	C₂×C₈	—	146	2	no	—
95	C₂×C₈	C₂×#64408	1	2	yes	—
96	C₁₆	—	146	2	no	—
97	C₁₆	—	146	2	no	—
98	C₂³	—	73	2	no	—
99	C₂³	#11924036	1	1	yes	characteristic
100	Q₈	—	146	2	no	—
101	D₄	—	146	4	no	—
102	D₄	—	146	2	no	—
103	C₂×C₄	—	73	2	no	—
104	C₂×C₄	—	146	2	no	—
105	C₂×C₄	—	146	2	no	—
106	C₂×C₄	C₂²⋊#64408	1	2	yes	—
107	C₂×C₄	#11924036	1	1	yes	characteristic
108	C₂×C₄	#11924038	1	2	yes	—
109	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
110	C₈	—	2	2	no	—
111	C₈	—	73	1	no	—
112	C₈	—	73	1	no	—
113	C₈	—	73	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	146	4	no	—
116	C₂²	—	146	2	no	—
117	C₂²	#14556648	1	2	yes	—
118	C₂²	C₂×#11924036	1	1	yes	characteristic
119	C₄	—	146	2	no	—
120	C₄	#14556648	1	2	yes	—
121	C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
122	C₄	C₂×#11924038	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	292	2	no	—
125	C₂	C₂×#14556648	1	1	yes	characteristic
126	C₂	#17989646	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556665

C₂

yes

maximal, characteristic, complemented

C₂²×#11924031

C₂

yes

maximal, characteristic, complemented

#17989482

C₂

yes

maximal, complemented

C₂×#14556599

C₂

yes

maximal, characteristic

#14556665

—

C₂×#11924031

—

C₂×#11924031

C₂²

yes

—

C₂×#11924031

C₂²

yes

—

C₂×#11924028

C₄

yes

—

—

C₄

yes

—

C₂²×#10596831

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

—

C₂×M₁₆×C₇₃

C₄

yes

—

—

—

—

C₂×Dic₁₄₆

C₈

yes

characteristic

C₂×D₂₉₂

C₈

yes

characteristic

C₂×C₂²⋊D₇₃

C₈

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

#11924011

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

D₄

yes

—

C₂×#10596831

D₄

yes

—

C₂×#10596831

C₂³

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

C₂×C₈

yes

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

C₂²⋊C₄

yes

—

#10596831

C₂×D₄

yes

characteristic

#10596831

C₂×D₄

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

C₂²⋊C₈

yes

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

C₂²⋊C₈

yes

—

C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₇₃

#504

yes

—

D₇₃

—

#2113

—

maximal, Sylow

C₇₃

#2113

yes

characteristic, complemented, Sylow

C₂×#131

—

C₂×M₃₂

—

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₂×#41

—

#131

—

146

—

#131

—

146

—

C₂×M₁₆

—

C₂×M₁₆

#64408

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

#41

—

146

—

#41

—

146

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

—

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

—

C₂³

#11924036

yes

characteristic

100

Q₈

—

146

—

101

D₄

—

146

—

102

D₄

—

146

—

103

C₂×C₄

—

104

C₂×C₄

—

146

—

105

C₂×C₄

—

146

—

106

C₂×C₄

C₂²⋊#64408

yes

—

107

C₂×C₄

#11924036

yes

characteristic

108

C₂×C₄

#11924038

yes

—

109

C₂×C₄

C₂²×#64408

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

—

115

C₂²

—

146

—

116

C₂²

—

146

—

117

C₂²

#14556648

yes

—

118

C₂²

C₂×#11924036

yes

characteristic

119

C₄

—

146

—

120

C₄

#14556648

yes

—

121

C₄

C₂×C₂²⋊#64408

yes

characteristic

122

C₄

C₂×#11924038

yes

characteristic

123

C₂

—

124

C₂

—

292

—

125

C₂

C₂×#14556648

yes

characteristic

126

C₂

#17989646

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	C₂×M₁₆×C₇₃	C₄
hypercenter	C₂×M₁₆	#64408
hypocenter	C₇₃	#2113
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#64408

commutator, socle

C₂²×C₇₃

C₂²×C₈

Fitting

C₂×M₁₆×C₇₃

C₄

C₂×M₁₆

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. C₂×#14556665	C₂	semidirect
2. C₂²×#11924031	C₂	semidirect
3. #17989482	C₂	semidirect
64. C₇₃	#2113	semidirect

H ≅ G/N

type

1. C₂×#14556665

C₂

semidirect

2. C₂²×#11924031

C₂

semidirect

3. #17989482

C₂

semidirect

64. C₇₃

#2113

semidirect

Subgroups — #22626163

Conjugacy classes of subgroups

Complements