Group #22609979 — subgroups

Subgroups — #22609979

Order 9344.

252 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556598	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556526	C₂	1	2	yes	maximal, complemented
3	#17988571	C₂	1	1	yes	maximal, characteristic
4	#17988345	C₂	1	2	yes	maximal, complemented
5	#413×C₇₃	C₂	1	1	yes	maximal, characteristic
6	#14556598	—	2	4	no	—
7	C₂×#11924012	C₄	1	2	yes	—
8	C₂×#11924012	C₂²	1	2	yes	—
9	C₂×#11924012	C₂²	1	1	yes	characteristic
10	C₂²×#10596831	C₄	1	2	yes	—
11	C₂²×#10596831	C₂²	1	1	yes	characteristic
12	#14556526	—	2	4	no	—
13	#14556510	—	2	1	no	—
14	#14556508	—	2	1	no	—
15	C₂×#41×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
17	#101×C₇₃	—	2	1	no	—
18	#100×C₇₃	—	2	1	no	—
19	#11924012	—	2	2	no	—
20	#11924012	—	2	4	no	—
21	#11924012	—	2	2	no	—
22	#11924012	—	2	2	no	—
23	C₂×#10596831	—	2	4	no	—
24	C₂×#10596831	—	2	2	no	—
25	C₂×#10596831	C₂×C₄	1	2	yes	—
26	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
27	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
28	C₂×#10596831	D₄	1	4	yes	—
29	#41×C₇₃	—	2	2	no	—
30	#41×C₇₃	—	2	2	no	—
31	C₂×Q₈×C₇₃	D₄	1	1	yes	characteristic
32	C₂×D₄×C₇₃	D₄	1	1	yes	characteristic
33	C₂×D₄×C₇₃	Q₈	1	2	yes	—
34	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
35	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
36	M₁₆×C₇₃	—	2	2	no	—
37	M₁₆×C₇₃	—	2	2	no	—
38	C₂×C₈×C₇₃	—	2	2	no	—
39	C₂³×C₇₃	C₄⋊C₄	1	2	yes	—
40	C₂³×C₇₃	C₂×Q₈	1	1	yes	characteristic
41	Q₈×C₇₃	—	2	2	no	—
42	D₄×C₇₃	—	2	4	no	—
43	D₄×C₇₃	—	2	2	no	—
44	C₂×C₄×C₇₃	—	2	2	no	—
45	C₂×C₄×C₇₃	—	2	2	no	—
46	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
47	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₇₃	#41	1	2	yes	—
51	C₈×C₇₃	—	4	2	no	—
52	#10596831	—	2	2	no	—
53	#10596831	—	4	2	no	—
54	#10596831	C₂²⋊C₄	1	2	yes	—
55	#10596831	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₇₃	—	2	2	no	—
57	C₂²×C₇₃	—	4	1	no	—
58	C₂²×C₇₃	—	4	2	no	—
59	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₇₃	C₂²⋊Q₈	1	2	yes	—
61	C₄×C₇₃	—	2	2	no	—
62	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₄×C₇₃	#117	1	1	yes	characteristic
64	C₄×C₇₃	#121	1	2	yes	—
65	C₂×C₇₃	—	2	1	no	—
66	C₂×C₇₃	—	2	2	no	—
67	C₂×C₇₃	—	4	2	no	—
68	C₂×C₇₃	#380	1	1	yes	characteristic
69	#1813	—	73	1	no	maximal, Sylow
70	C₇₃	#1813	1	1	yes	characteristic, complemented, Sylow
71	C₂×#131	—	73	1	no	—
72	C₂×#108	—	73	2	no	—
73	#413	—	73	1	no	—
74	#413	D₇₃	1	1	yes	characteristic
75	#338	—	73	2	no	—
76	C₂×#41	C₂×D₇₃	1	1	yes	characteristic
77	#131	—	146	4	no	—
78	C₂×M₁₆	—	73	2	no	—
79	C₂×M₁₆	—	73	1	no	—
80	C₂×M₁₆	—	73	2	no	—
81	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
82	C₂²×C₈	—	73	1	no	—
83	C₂²×C₈	—	73	2	no	—
84	#108	—	146	4	no	—
85	#101	—	2	1	no	—
86	#101	—	146	1	no	—
87	#100	—	2	1	no	—
88	#100	—	146	1	no	—
89	#41	—	2	2	no	—
90	#41	—	2	2	no	—
91	C₂×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
92	C₂×D₄	Dic₁₄₆	1	2	yes	—
93	C₂×D₄	C₂²⋊D₇₃	1	1	yes	characteristic
94	C₂²×C₄	C₄×D₇₃	1	2	yes	—
95	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
96	M₁₆	—	2	2	no	—
97	M₁₆	—	2	2	no	—
98	M₁₆	—	146	2	no	—
99	M₁₆	—	146	2	no	—
100	M₁₆	—	146	4	no	—
101	M₁₆	—	146	2	no	—
102	C₂×C₈	—	2	2	no	—
103	C₂×C₈	—	73	1	no	—
104	C₂×C₈	—	73	1	no	—
105	C₂×C₈	—	73	4	no	—
106	C₂×C₈	—	73	2	no	—
107	C₂×C₈	—	146	2	no	—
108	C₂×C₈	—	146	4	no	—
109	C₂³	#11924007	1	2	yes	—
110	C₂³	C₂×Dic₁₄₆	1	1	yes	characteristic
111	Q₈	—	2	2	no	—
112	D₄	—	2	4	no	—
113	D₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	#11924007	1	2	yes	—
117	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
118	C₂×C₄	D₄×D₇₃	1	2	yes	—
119	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
120	C₂×C₄	#11924027	1	2	yes	—
121	C₈	—	4	2	no	—
122	C₈	—	292	2	no	—
123	C₈	—	73	2	no	—
124	C₈	—	73	2	no	—
125	C₈	—	146	2	no	—
126	C₂²	—	2	2	no	—
127	C₂²	—	4	1	no	—
128	C₂²	—	4	2	no	—
129	C₂²	C₂×#11924007	1	1	yes	characteristic
130	C₂²	#14556568	1	2	yes	—
131	C₄	—	2	2	no	—
132	C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
133	C₄	#14556547	1	1	yes	characteristic
134	C₄	#14556563	1	2	yes	—
135	C₂	—	2	1	no	—
136	C₂	—	2	2	no	—
137	C₂	—	4	2	no	—
138	C₂	#17988445	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556598

C₂

yes

maximal, characteristic

C₂×#14556526

C₂

yes

maximal, complemented

#17988571

C₂

yes

maximal, characteristic

#17988345

C₂

yes

maximal, complemented

#413×C₇₃

C₂

yes

maximal, characteristic

#14556598

—

C₂×#11924012

C₄

yes

—

C₂×#11924012

C₂²

yes

—

C₂×#11924012

C₂²

yes

characteristic

C₂²×#10596831

C₄

yes

—

C₂²×#10596831

C₂²

yes

—

—

—

C₂×#41×C₇₃

C₂²

yes

characteristic

C₂×M₁₆×C₇₃

C₂²

yes

—

#101×C₇₃

—

#100×C₇₃

—

—

—

—

—

—

—

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

D₄

yes

—

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

D₄

yes

characteristic

C₂×D₄×C₇₃

D₄

yes

characteristic

C₂×D₄×C₇₃

Q₈

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂³×C₇₃

C₄⋊C₄

yes

—

C₂³×C₇₃

C₂×Q₈

yes

characteristic

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₈×C₇₃

—

#10596831

—

#10596831

—

#10596831

C₂²⋊C₄

yes

—

#10596831

C₂²⋊C₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₂²⋊C₄

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic

#338

—

C₂×#41

C₂×D₇₃

yes

characteristic

#131

—

146

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₂²×C₈

—

C₂²×C₈

—

#108

—

146

—

#101

—

#101

—

146

—

#100

—

#100

—

146

—

#41

—

#41

—

C₂×Q₈

C₂²⋊D₇₃

yes

characteristic

C₂×D₄

Dic₁₄₆

yes

—

C₂×D₄

C₂²⋊D₇₃

yes

characteristic

C₂²×C₄

C₄×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

100

M₁₆

—

146

—

101

M₁₆

—

146

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

146

—

108

C₂×C₈

—

146

—

109

C₂³

#11924007

yes

—

110

C₂³

C₂×Dic₁₄₆

yes

characteristic

111

Q₈

—

112

D₄

—

113

D₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

#11924007

yes

—

117

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

118

C₂×C₄

D₄×D₇₃

yes

—

119

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

120

C₂×C₄

#11924027

yes

—

121

C₈

—

122

C₈

—

292

—

123

C₈

—

124

C₈

—

125

C₈

—

146

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

C₂×#11924007

yes

characteristic

130

C₂²

#14556568

yes

—

131

C₄

—

132

C₄

C₂²⋊C₄×D₇₃

yes

characteristic

133

C₄

#14556547

yes

characteristic

134

C₄

#14556563

yes

—

135

C₂

—

136

C₂

—

137

C₂

—

138

C₂

#17988445

yes

characteristic

	subgroup	G/H
center	C₄	#14556547
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#413×C₇₃	C₂
socle	C₂×C₇₃	#380
hypercenter	#413	D₇₃
hypocenter	C₇₃	#1813
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #413

subgroup

G/H

center

C₄

#14556547

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#413×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #413

N	H ≅ G/N	type
2. C₂×#14556526	C₂	semidirect
4. #17988345	C₂	semidirect
70. C₇₃	#1813	semidirect

H ≅ G/N

type

2. C₂×#14556526

C₂

semidirect

4. #17988345

C₂

semidirect

70. C₇₃

#1813

semidirect

Subgroups — #22609979

Conjugacy classes of subgroups

Complements