Group #22620344 — subgroups

Subgroups — #494×D₇₃ #22620344

Order 9344.

552 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 165 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×Q₁₆×D₇₃	C₂	1	4	yes	maximal
2	C₄⋊Q₈×D₇₃	C₂	1	2	yes	maximal
3	#17988967	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988966	C₂	1	2	yes	maximal, complemented
5	#17988965	C₂	1	4	yes	maximal, complemented
6	C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
7	#494×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×D₇₃	C₂²	1	4	yes	—
9	C₂×Dic₂₉₂	C₂²	1	4	yes	—
10	C₂×#11924018	C₂²	1	8	yes	—
11	Q₁₆×D₇₃	—	2	16	no	—
12	C₂×C₈×D₇₃	C₂²	1	2	yes	—
13	#14556591	C₂²	1	2	yes	—
14	#14556590	—	2	4	no	—
15	#14556589	C₂²	1	4	yes	—
16	C₄⋊C₄×D₇₃	—	2	4	no	—
17	C₄²×D₇₃	C₂²	1	1	yes	characteristic
18	C₄×#10596831	C₂²	1	1	yes	characteristic
19	C₈×Dic₇₃	C₂²	1	2	yes	—
20	C₂×Q₁₆×C₇₃	C₂²	1	4	yes	—
21	C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
22	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₄₆	—	2	4	no	—
24	C₂×Dic₁₄₆	C₂³	1	4	yes	—
25	Q₈×D₇₃	—	2	16	no	—
26	C₂×C₄×D₇₃	—	2	4	no	—
27	C₂×C₄×D₇₃	D₄	1	2	yes	—
28	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
29	Dic₂₉₂	—	2	8	no	—
30	#11924018	—	2	16	no	—
31	C₂×#10596831	C₂³	1	2	yes	—
32	C₈×D₇₃	D₄	1	8	yes	—
33	C₄⋊Dic₇₃	—	2	4	no	—
34	#11924007	—	2	8	no	—
35	C₄×Dic₇₃	D₄	1	2	yes	—
36	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
37	C₂×Q₈×C₇₃	C₂³	1	4	yes	—
38	Q₁₆×C₇₃	—	2	8	no	—
39	C₂×C₈×C₇₃	C₂³	1	2	yes	—
40	C₄⋊C₄×C₇₃	—	2	4	no	—
41	C₄²×C₇₃	C₂³	1	1	yes	characteristic
42	C₂²×D₇₃	C₂×D₄	1	1	yes	characteristic
43	Q₈×C₇₃	—	2	8	no	—
44	C₂×C₄×C₇₃	—	2	4	no	—
45	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
47	C₂×Dic₇₃	—	2	4	no	—
48	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
50	C₄×D₇₃	—	4	8	no	—
51	C₄×D₇₃	Q₁₆	1	8	yes	complemented
52	C₄×D₇₃	C₂×D₄	1	4	yes	—
53	Dic₁₄₆	—	2	8	no	—
54	Dic₁₄₆	—	4	8	no	—
55	C₈×C₇₃	C₂×D₄	1	4	yes	—
56	#10596831	C₂×D₄	1	4	yes	—
57	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
58	C₂×D₇₃	#127	1	2	yes	—
59	C₂×D₇₃	C₂×Q₁₆	1	4	yes	—
60	C₄×C₇₃	—	4	4	no	—
61	C₄×C₇₃	C₂×Q₁₆	1	4	yes	complemented
62	C₄×C₇₃	C₂²×D₄	1	2	yes	—
63	Dic₇₃	—	4	4	no	—
64	Dic₇₃	#127	1	2	yes	—
65	Dic₇₃	C₂×Q₁₆	1	4	yes	complemented
66	C₂×C₇₃	C₂×#127	1	1	yes	characteristic
67	C₂×C₇₃	C₂²×Q₁₆	1	2	yes	—
68	D₇₃	#494	1	4	yes	direct product factor
69	C₂×#494	—	73	1	no	maximal, Sylow
70	C₇₃	C₂×#494	1	1	yes	characteristic, complemented, Sylow
71	C₂²×Q₁₆	—	73	4	no	—
72	C₂×C₄⋊Q₈	—	73	2	no	—
73	#494	—	73	4	no	—
74	#494	—	73	2	no	—
75	#494	—	73	1	no	—
76	#494	D₇₃	1	1	yes	characteristic, direct product factor
77	C₂×C₄×C₈	—	73	1	no	—
78	C₂²×Q₈	—	73	4	no	—
79	C₂×Q₁₆	—	73	8	no	—
80	C₂×Q₁₆	—	73	4	no	—
81	C₂×Q₁₆	—	146	16	no	—
82	C₂×Q₁₆	C₂×D₇₃	1	4	yes	—
83	C₂²×C₈	—	73	2	no	—
84	C₄⋊Q₈	—	73	4	no	—
85	C₄⋊Q₈	—	73	2	no	—
86	C₄⋊Q₈	—	146	4	no	—
87	C₄⋊Q₈	C₂×D₇₃	1	2	yes	—
88	C₂×C₄⋊C₄	—	146	4	no	—
89	C₂×C₄²	—	73	1	no	—
90	C₄×C₈	—	73	2	no	—
91	C₄×C₈	—	73	1	no	—
92	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
93	C₂×Q₈	—	73	4	no	—
94	C₂×Q₈	—	146	4	no	—
95	C₂×Q₈	—	146	16	no	—
96	C₂×Q₈	C₂²×D₇₃	1	4	yes	—
97	C₂²×C₄	—	73	2	no	—
98	C₂²×C₄	—	73	1	no	—
99	C₂²×C₄	—	146	4	no	—
100	Q₁₆	—	2	8	no	—
101	Q₁₆	—	146	16	no	—
102	Q₁₆	—	146	8	no	—
103	C₂×C₈	—	73	2	no	—
104	C₂×C₈	—	73	8	no	—
105	C₂×C₈	C₂²×D₇₃	1	2	yes	—
106	C₄⋊C₄	—	2	4	no	—
107	C₄⋊C₄	—	146	8	no	—
108	C₄⋊C₄	—	146	4	no	—
109	C₄²	—	73	2	no	—
110	C₄²	—	73	1	no	—
111	C₄²	C₂²×D₇₃	1	1	yes	characteristic
112	C₂³	—	73	1	no	—
113	Q₈	—	2	8	no	—
114	Q₈	—	292	8	no	—
115	Q₈	—	146	8	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	292	8	no	—
118	C₂×C₄	—	73	2	no	—
119	C₂×C₄	—	73	1	no	—
120	C₂×C₄	—	73	8	no	—
121	C₂×C₄	—	73	4	no	—
122	C₂×C₄	—	146	4	no	—
123	C₂×C₄	D₄×D₇₃	1	2	yes	—
124	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
125	C₈	—	73	4	no	—
126	C₈	D₄×D₇₃	1	4	yes	—
127	C₂²	—	73	2	no	—
128	C₂²	—	73	4	no	—
129	C₂²	C₂×D₄×D₇₃	1	1	yes	characteristic
130	C₄	—	4	4	no	—
131	C₄	—	292	4	no	—
132	C₄	—	73	2	no	—
133	C₄	—	73	4	no	—
134	C₄	Q₁₆×D₇₃	1	4	yes	complemented
135	C₄	C₂×D₄×D₇₃	1	2	yes	—
136	C₂	—	73	4	no	—
137	C₂	#127×D₇₃	1	1	yes	characteristic
138	C₂	C₂×Q₁₆×D₇₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₁₆×D₇₃

C₂

yes

maximal

C₄⋊Q₈×D₇₃

C₂

yes

maximal

#17988967

C₂

yes

maximal, characteristic, complemented

#17988966

C₂

yes

maximal, complemented

#17988965

C₂

yes

maximal, complemented

C₄×C₈×D₇₃

C₂

yes

maximal, characteristic

#494×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₇₃

C₂²

yes

—

C₂×Dic₂₉₂

C₂²

yes

—

C₂×#11924018

C₂²

yes

—

Q₁₆×D₇₃

—

C₂×C₈×D₇₃

C₂²

yes

—

#14556591

C₂²

yes

—

#14556590

—

#14556589

C₂²

yes

—

C₄⋊C₄×D₇₃

—

C₄²×D₇₃

C₂²

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

—

C₂×Q₁₆×C₇₃

C₂²

yes

—

C₄⋊Q₈×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂³

yes

—

Q₈×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

D₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

Dic₂₉₂

—

#11924018

—

C₂×#10596831

C₂³

yes

—

C₈×D₇₃

D₄

yes

—

C₄⋊Dic₇₃

—

#11924007

—

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×Q₈×C₇₃

C₂³

yes

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂²×D₇₃

C₂×D₄

yes

characteristic

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

—

C₄×D₇₃

—

C₄×D₇₃

Q₁₆

yes

complemented

C₄×D₇₃

C₂×D₄

yes

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂×D₄

yes

—

#10596831

C₂×D₄

yes

—

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₂×D₇₃

#127

yes

—

C₂×D₇₃

C₂×Q₁₆

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×Q₁₆

yes

complemented

C₄×C₇₃

C₂²×D₄

yes

—

Dic₇₃

—

Dic₇₃

#127

yes

—

Dic₇₃

C₂×Q₁₆

yes

complemented

C₂×C₇₃

C₂×#127

yes

characteristic

C₂×C₇₃

C₂²×Q₁₆

yes

—

D₇₃

#494

yes

direct product factor

C₂×#494

—

maximal, Sylow

C₇₃

C₂×#494

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

—

—

—

—

D₇₃

yes

characteristic, direct product factor

C₂×C₄×C₈

—

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

146

—

C₂×Q₁₆

C₂×D₇₃

yes

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

C₂×D₇₃

yes

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

C₂²×D₇₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

100

Q₁₆

—

101

Q₁₆

—

146

—

102

Q₁₆

—

146

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

C₂²×D₇₃

yes

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

146

—

108

C₄⋊C₄

—

146

—

109

C₄²

—

110

C₄²

—

111

C₄²

C₂²×D₇₃

yes

characteristic

112

C₂³

—

113

Q₈

—

114

Q₈

—

292

—

115

Q₈

—

146

—

116

C₂×C₄

—

117

C₂×C₄

—

292

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

146

—

123

C₂×C₄

D₄×D₇₃

yes

—

124

C₂×C₄

C₂³×D₇₃

yes

characteristic

125

C₈

—

126

C₈

D₄×D₇₃

yes

—

127

C₂²

—

128

C₂²

—

129

C₂²

C₂×D₄×D₇₃

yes

characteristic

130

C₄

—

131

C₄

—

292

—

132

C₄

—

133

C₄

—

134

C₄

Q₁₆×D₇₃

yes

complemented

135

C₄

C₂×D₄×D₇₃

yes

—

136

C₂

—

137

C₂

#127×D₇₃

yes

characteristic

138

C₂

C₂×Q₁₆×D₇₃

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₃
Fitting	#494×C₇₃	C₂
socle	C₂²×C₇₃	C₂²×D₄
hypercenter	#494	D₇₃
hypocenter	C₇₃	C₂×#494
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

C₂×D₄×D₇₃

commutator

C₂×C₄×C₇₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₃

Fitting

#494×C₇₃

C₂

socle

C₂²×C₇₃

C₂²×D₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
3. #17988967	C₂	semidirect
4. #17988966	C₂	semidirect
5. #17988965	C₂	semidirect
7. #494×C₇₃	C₂	semidirect
51. C₄×D₇₃	Q₁₆	semidirect
61. C₄×C₇₃	C₂×Q₁₆	semidirect
65. Dic₇₃	C₂×Q₁₆	semidirect
68. D₇₃	#494	direct (N × H)
70. C₇₃	C₂×#494	semidirect
76. #494	D₇₃	direct (N × H)
134. C₄	Q₁₆×D₇₃	semidirect

H ≅ G/N

type

3. #17988967

C₂

semidirect

4. #17988966

C₂

semidirect

5. #17988965

C₂

semidirect

7. #494×C₇₃

C₂

semidirect

51. C₄×D₇₃

Q₁₆

semidirect

61. C₄×C₇₃

C₂×Q₁₆

semidirect

65. Dic₇₃

C₂×Q₁₆

semidirect

68. D₇₃

#494

direct (N × H)

70. C₇₃

C₂×#494

semidirect

76. #494

D₇₃

direct (N × H)

134. C₄

Q₁₆×D₇₃

semidirect

Subgroups — #494×D₇₃ #22620344

Conjugacy classes of subgroups

Complements

Subgroups — #494×D73 #22620344

Conjugacy classes of subgroups

Complements

Subgroups — #494×D₇₃ #22620344