Group #22610150 — subgroups

Subgroups — #22610150

Order 9344.

252 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 85 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	#17989354	C₂	1	1	yes	maximal, characteristic
2	#17988635	C₂	1	2	yes	maximal, complemented
3	#17988571	C₂	1	1	yes	maximal, characteristic
4	#17988352	C₂	1	2	yes	maximal, complemented
5	#408×C₇₃	C₂	1	1	yes	maximal, characteristic
6	#14556598	—	2	4	no	—
7	C₂×#11924012	—	2	2	no	—
8	C₂×#11924012	C₂²	1	2	yes	—
9	C₂×#11924012	C₂²	1	2	yes	—
10	#14556526	—	2	4	no	—
11	#14556510	C₄	1	2	yes	—
12	#14556508	C₄	1	2	yes	—
13	C₂×#41×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂²⋊C₈×C₇₃	—	2	2	no	—
17	#11924012	—	2	4	no	—
18	#11924012	—	2	2	no	—
19	#11924012	—	2	2	no	—
20	#11924012	C₂×C₄	1	4	yes	—
21	#11924012	D₄	1	4	yes	—
22	C₂×#10596831	—	2	4	no	—
23	C₂×#10596831	—	2	2	no	—
24	C₂×#10596831	—	2	2	no	—
25	#41×C₇₃	—	2	2	no	—
26	#41×C₇₃	—	2	2	no	—
27	C₂×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×D₄×C₇₃	Q₈	1	2	yes	—
30	C₂²×C₄×C₇₃	D₄	1	2	yes	—
31	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
32	M₁₆×C₇₃	—	2	2	no	—
33	C₂×C₈×C₇₃	—	2	1	no	—
34	C₂×C₈×C₇₃	—	2	1	no	—
35	C₂×C₈×C₇₃	—	2	2	no	—
36	C₂³×C₇₃	C₄⋊C₄	1	2	yes	—
37	C₂³×C₇₃	C₂×Q₈	1	1	yes	characteristic
38	Q₈×C₇₃	—	2	2	no	—
39	D₄×C₇₃	—	2	4	no	—
40	D₄×C₇₃	—	2	2	no	—
41	C₂×C₄×C₇₃	—	2	2	no	—
42	C₂×C₄×C₇₃	—	2	2	no	—
43	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₇₃	#41	1	2	yes	—
48	C₈×C₇₃	—	4	1	no	—
49	C₈×C₇₃	—	4	1	no	—
50	#10596831	—	2	4	no	—
51	#10596831	—	2	4	no	—
52	C₂²×C₇₃	—	2	2	no	—
53	C₂²×C₇₃	—	4	1	no	—
54	C₂²×C₇₃	—	4	2	no	—
55	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₇₃	C₂²⋊Q₈	1	2	yes	—
57	C₄×C₇₃	—	2	2	no	—
58	C₄×C₇₃	C₄×D₄	1	2	yes	—
59	C₄×C₇₃	#120	1	1	yes	characteristic
60	C₄×C₇₃	#123	1	1	yes	characteristic
61	C₂×C₇₃	—	2	1	no	—
62	C₂×C₇₃	—	2	2	no	—
63	C₂×C₇₃	—	4	2	no	—
64	C₂×C₇₃	#385	1	1	yes	characteristic
65	#1858	—	73	1	no	maximal, Sylow
66	C₇₃	#1858	1	1	yes	characteristic, complemented, Sylow
67	#568	—	73	1	no	—
68	#430	—	73	2	no	—
69	#413	—	73	1	no	—
70	#408	D₇₃	1	1	yes	characteristic
71	#341	—	73	2	no	—
72	C₂×#41	C₂×D₇₃	1	1	yes	characteristic
73	#131	—	146	4	no	—
74	C₂×M₁₆	—	73	2	no	—
75	C₂×M₁₆	—	73	2	no	—
76	C₂×M₁₆	—	146	2	no	—
77	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
78	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
79	#108	—	146	4	no	—
80	#101	—	73	2	no	—
81	#100	—	73	2	no	—
82	C₂²⋊C₈	—	2	2	no	—
83	#41	—	2	2	no	—
84	#41	—	2	2	no	—
85	C₂×Q₈	C₄×D₇₃	1	1	yes	characteristic
86	C₂×D₄	Dic₁₄₆	1	2	yes	—
87	C₂×D₄	C₄×D₇₃	1	1	yes	characteristic
88	C₂²×C₄	C₂²⋊D₇₃	1	2	yes	—
89	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
90	M₁₆	—	2	2	no	—
91	M₁₆	—	73	4	no	—
92	M₁₆	—	73	4	no	—
93	M₁₆	—	146	4	no	—
94	M₁₆	—	146	2	no	—
95	M₁₆	—	146	2	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	146	4	no	—
100	C₂×C₈	—	146	2	no	—
101	C₂×C₈	—	146	2	no	—
102	C₂³	#11924007	1	2	yes	—
103	C₂³	C₂×Dic₁₄₆	1	1	yes	characteristic
104	Q₈	—	2	2	no	—
105	D₄	—	2	4	no	—
106	D₄	—	2	2	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	#11924007	1	2	yes	—
110	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
111	C₂×C₄	D₄×D₇₃	1	2	yes	—
112	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
113	C₂×C₄	#11924027	1	2	yes	—
114	C₈	—	4	1	no	—
115	C₈	—	4	1	no	—
116	C₈	—	146	4	no	—
117	C₈	—	146	4	no	—
118	C₂²	—	2	2	no	—
119	C₂²	—	4	1	no	—
120	C₂²	—	4	2	no	—
121	C₂²	C₂×#11924007	1	1	yes	characteristic
122	C₂²	#14556568	1	2	yes	—
123	C₄	—	2	2	no	—
124	C₄	#14556551	1	2	yes	—
125	C₄	#14556559	1	1	yes	characteristic
126	C₄	#14556572	1	1	yes	characteristic
127	C₂	—	2	1	no	—
128	C₂	—	2	2	no	—
129	C₂	—	4	2	no	—
130	C₂	#17988459	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989354

C₂

yes

maximal, characteristic

#17988635

C₂

yes

maximal, complemented

#17988571

C₂

yes

maximal, characteristic

#17988352

C₂

yes

maximal, complemented

#408×C₇₃

C₂

yes

maximal, characteristic

#14556598

—

C₂×#11924012

—

C₂×#11924012

C₂²

yes

—

C₂×#11924012

C₂²

yes

—

#14556526

—

#14556510

C₄

yes

—

#14556508

C₄

yes

—

C₂×#41×C₇₃

C₂²

yes

characteristic

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂²⋊C₈×C₇₃

—

—

—

—

C₂×C₄

yes

—

#11924012

D₄

yes

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

—

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

C₂×C₄

yes

characteristic

C₂×D₄×C₇₃

C₂×C₄

yes

characteristic

C₂×D₄×C₇₃

Q₈

yes

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×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

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic

#341

—

C₂×#41

C₂×D₇₃

yes

characteristic

#131

—

146

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

C₂×M₁₆

C₂×D₇₃

yes

characteristic

C₂²×C₈

C₂×D₇₃

yes

characteristic

#108

—

146

—

#101

—

#100

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

C₄×D₇₃

yes

characteristic

C₂×D₄

Dic₁₄₆

yes

—

C₂×D₄

C₄×D₇₃

yes

characteristic

C₂²×C₄

C₂²⋊D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

100

C₂×C₈

—

146

—

101

C₂×C₈

—

146

—

102

C₂³

#11924007

yes

—

103

C₂³

C₂×Dic₁₄₆

yes

characteristic

104

Q₈

—

105

D₄

—

106

D₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

#11924007

yes

—

110

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

111

C₂×C₄

D₄×D₇₃

yes

—

112

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

113

C₂×C₄

#11924027

yes

—

114

C₈

—

115

C₈

—

116

C₈

—

146

—

117

C₈

—

146

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

C₂×#11924007

yes

characteristic

122

C₂²

#14556568

yes

—

123

C₄

—

124

C₄

#14556551

yes

—

125

C₄

#14556559

yes

characteristic

126

C₄

#14556572

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#17988459

yes

characteristic

	subgroup	G/H
center	C₄	#14556559
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#408×C₇₃	C₂
socle	C₂×C₇₃	#385
hypercenter	#408	D₇₃
hypocenter	C₇₃	#1858
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #408

subgroup

G/H

center

C₄

#14556559

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#408×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #408

N	H ≅ G/N	type
2. #17988635	C₂	semidirect
4. #17988352	C₂	semidirect
66. C₇₃	#1858	semidirect

H ≅ G/N

type

2. #17988635

C₂

semidirect

4. #17988352

C₂

semidirect

66. C₇₃

#1858

semidirect

Subgroups — #22610150

Conjugacy classes of subgroups

Complements