Group #22625751 — subgroups

Subgroups — #22625751

Order 9344.

220 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 92 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×#14556662	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556661	C₂	1	1	yes	maximal, characteristic
3	C₄×#11924038	C₂	1	2	yes	maximal
4	#17989463	C₂	1	2	yes	maximal
5	#97×D₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924038	C₂²	1	2	yes	—
7	C₂×#11924038	C₂²	1	2	yes	—
8	#14556662	C₄	1	4	yes	complemented
9	#14556661	C₄	1	4	yes	complemented
10	#14556646	—	2	2	no	—
11	C₄×#10596833	—	2	2	no	—
12	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
14	C₄²×D₇₃	C₂²	1	1	yes	characteristic
15	#14556502	C₄	1	1	yes	characteristic
16	#14556501	C₄	1	1	yes	characteristic
17	#14556501	C₄	1	1	yes	characteristic
18	#97×C₇₃	C₄	1	1	yes	characteristic
19	#11924038	—	2	2	no	—
20	#11924038	—	2	2	no	—
21	#11924038	C₂×C₄	1	4	yes	—
22	#11924038	C₂×C₄	1	4	yes	—
23	C₂×#10596833	—	2	2	no	—
24	C₂×#10596833	—	2	2	no	—
25	C₂×C₄×D₇₃	Q₈	1	2	yes	—
26	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
27	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
28	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
29	C₈×D₇₃	—	2	1	no	—
30	C₈×D₇₃	—	2	1	no	—
31	C₈×D₇₃	C₂×C₄	1	2	yes	—
32	C₈×D₇₃	C₂×C₄	1	2	yes	—
33	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
34	C₄×Dic₇₃	D₄	1	2	yes	—
35	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
37	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₇₃	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
42	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
43	C₄×D₇₃	—	4	2	no	—
44	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
45	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
46	C₄×D₇₃	#41	1	1	yes	characteristic
47	C₄×D₇₃	#41	1	1	yes	characteristic
48	#10596833	—	2	4	no	—
49	#10596833	—	2	4	no	—
50	C₈×C₇₃	—	2	1	no	—
51	C₈×C₇₃	C₄²	1	2	yes	—
52	#10596831	—	2	1	no	—
53	#10596831	C₄²	1	2	yes	—
54	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₂×D₇₃	—	2	2	no	—
56	C₂×D₇₃	C₄×Q₈	1	1	yes	characteristic
57	C₂×D₇₃	C₄×Q₈	1	1	yes	characteristic
58	C₄×C₇₃	—	2	2	no	—
59	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
60	C₄×C₇₃	#117	1	1	yes	characteristic
61	Dic₇₃	—	2	2	no	—
62	Dic₇₃	C₄×D₄	1	1	yes	characteristic
63	Dic₇₃	C₄×D₄	1	1	yes	characteristic
64	C₂×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₇₃	#430	1	2	yes	—
66	D₇₃	—	2	1	no	—
67	D₇₃	—	2	1	no	—
68	#1778	—	73	1	no	maximal, Sylow
69	C₇₃	#1778	1	1	yes	characteristic, complemented, Sylow
70	C₂×#108	—	73	1	no	—
71	C₂×#108	—	73	1	no	—
72	C₄×M₁₆	—	73	2	no	—
73	C₂×#97	—	73	1	no	—
74	#341	—	73	2	no	—
75	C₂×M₁₆	—	73	2	no	—
76	C₂×M₁₆	—	73	2	no	—
77	C₂²×C₈	—	73	1	no	—
78	C₂²×C₈	—	73	1	no	—
79	C₂×C₄²	—	73	1	no	—
80	#108	—	73	4	no	—
81	#108	—	73	4	no	—
82	#97	—	73	1	no	—
83	#97	—	73	1	no	—
84	#97	—	73	1	no	—
85	#97	—	146	2	no	—
86	#97	#64408	1	1	yes	characteristic
87	C₄×C₈	—	146	2	no	—
88	C₂²×C₄	—	73	2	no	—
89	C₂²×C₄	—	73	1	no	—
90	M₁₆	—	73	4	no	—
91	M₁₆	—	73	4	no	—
92	M₁₆	—	146	2	no	—
93	M₁₆	—	146	2	no	—
94	C₂×C₈	—	73	1	no	—
95	C₂×C₈	—	73	2	no	—
96	C₂×C₈	—	73	2	no	—
97	C₂×C₈	—	73	1	no	—
98	C₂×C₈	—	146	1	no	—
99	C₂×C₈	—	146	1	no	—
100	C₂×C₈	—	146	2	no	—
101	C₂×C₈	—	146	2	no	—
102	C₂×C₈	C₂×#64408	1	1	yes	characteristic
103	C₂×C₈	C₂×#64408	1	1	yes	characteristic
104	C₄²	—	73	2	no	—
105	C₄²	—	73	1	no	—
106	C₄²	C₂×#64408	1	1	yes	characteristic
107	C₂³	—	73	1	no	—
108	C₂×C₄	—	292	2	no	—
109	C₂×C₄	—	73	1	no	—
110	C₂×C₄	—	73	1	no	—
111	C₂×C₄	—	73	1	no	—
112	C₂×C₄	—	73	1	no	—
113	C₂×C₄	—	73	1	no	—
114	C₂×C₄	—	73	2	no	—
115	C₂×C₄	C₄⋊#64408	1	2	yes	—
116	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
117	C₈	—	2	1	no	—
118	C₈	—	73	2	no	—
119	C₈	—	146	4	no	—
120	C₈	—	146	4	no	—
121	C₈	—	146	1	no	—
122	C₈	C₄×#64408	1	2	yes	—
123	C₂²	—	73	1	no	—
124	C₂²	—	73	1	no	—
125	C₂²	—	146	2	no	—
126	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	73	1	no	—
129	C₄	—	73	1	no	—
130	C₄	—	146	2	no	—
131	C₄	C₂×C₄×#64408	1	1	yes	characteristic
132	C₄	#14556670	1	1	yes	characteristic
133	C₂	—	146	1	no	—
134	C₂	—	146	1	no	—
135	C₂	C₄×C₄⋊#64408	1	1	yes	characteristic
136	C₂	#17989602	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556662

C₂

yes

maximal, characteristic

C₂×#14556661

C₂

yes

maximal, characteristic

C₄×#11924038

C₂

yes

maximal

#17989463

C₂

yes

maximal

#97×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924038

C₂²

yes

—

C₂×#11924038

C₂²

yes

—

#14556662

C₄

yes

complemented

#14556661

C₄

yes

complemented

#14556646

—

C₄×#10596833

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

C₄²×D₇₃

C₂²

yes

characteristic

#14556502

C₄

yes

characteristic

#14556501

C₄

yes

characteristic

#14556501

C₄

yes

characteristic

#97×C₇₃

C₄

yes

—

—

C₂×C₄

yes

—

#11924038

C₂×C₄

yes

—

C₂×#10596833

—

C₂×#10596833

—

C₂×C₄×D₇₃

Q₈

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

—

C₈×D₇₃

C₂×C₄

yes

—

C₈×D₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

C₂²×C₄

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

C₄×D₇₃

yes

C₄×D₇₃

yes

—

—

C₈×C₇₃

—

C₈×C₇₃

C₄²

yes

—

#10596831

—

#10596831

C₄²

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄×Q₈

yes

characteristic

C₂×D₇₃

C₄×Q₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

#117

yes

characteristic

Dic₇₃

—

Dic₇₃

C₄×D₄

yes

characteristic

Dic₇₃

C₄×D₄

yes

characteristic

C₂×C₇₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₇₃

#430

yes

—

D₇₃

—

D₇₃

—

#1778

—

maximal, Sylow

C₇₃

#1778

yes

characteristic, complemented, Sylow

C₂×#108

—

C₂×#108

—

C₄×M₁₆

—

C₂×#97

—

#341

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

—

—

—

—

—

—

146

—

#97

#64408

yes

characteristic

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

100

C₂×C₈

—

146

—

101

C₂×C₈

—

146

—

102

C₂×C₈

C₂×#64408

yes

characteristic

103

C₂×C₈

C₂×#64408

yes

characteristic

104

C₄²

—

105

C₄²

—

106

C₄²

C₂×#64408

yes

characteristic

107

C₂³

—

108

C₂×C₄

—

292

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

C₄⋊#64408

yes

—

116

C₂×C₄

C₂²×#64408

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

146

—

120

C₈

—

146

—

121

C₈

—

146

—

122

C₈

C₄×#64408

yes

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

146

—

126

C₂²

C₂×C₄⋊#64408

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

146

—

131

C₄

C₂×C₄×#64408

yes

characteristic

132

C₄

#14556670

yes

characteristic

133

C₂

—

146

—

134

C₂

—

146

—

135

C₂

C₄×C₄⋊#64408

yes

characteristic

136

C₂

#17989602

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#64408
commutator	C₄×C₇₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×#64408
Fitting	#97×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	#97	#64408
hypocenter	C₇₃	#1778
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#64408

commutator

C₄×C₇₃

C₂×C₄²

Frattini

C₂×C₄

C₂²×#64408

Fitting

#97×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄⋊C₄

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
8. #14556662	C₄	semidirect
9. #14556661	C₄	semidirect
69. C₇₃	#1778	semidirect

H ≅ G/N

type

8. #14556662

C₄

semidirect

9. #14556661

C₄

semidirect

69. C₇₃

#1778

semidirect

Subgroups — #22625751

Conjugacy classes of subgroups

Complements