Group #22618203 — subgroups

Subgroups — #22618203

Order 9344.

356 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 133 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	#17988529	C₂	1	4	yes	maximal
2	#17988526	C₂	1	2	yes	maximal
3	#17988508	C₂	1	4	yes	maximal
4	#17988507	C₂	1	2	yes	maximal
5	#17988453	C₂	1	2	yes	maximal
6	#382×C₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₁₄₆	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
11	C₂×#11924007	C₂²	1	4	yes	—
12	#14556498	C₂²	1	4	yes	—
13	#14556498	C₂²	1	4	yes	—
14	#14556498	C₂²	1	2	yes	—
15	#14556498	C₂²	1	4	yes	—
16	#14556498	C₂²	1	2	yes	—
17	C₂×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
20	#95×C₇₃	C₂²	1	4	yes	—
21	C₂×Dic₁₄₆	—	4	4	no	—
22	C₂×Dic₁₄₆	—	4	2	no	—
23	C₂²×Dic₇₃	C₂³	1	4	yes	—
24	C₂²×Dic₇₃	C₂³	1	4	yes	—
25	C₄⋊Dic₇₃	—	4	2	no	—
26	C₄⋊Dic₇₃	—	4	2	no	—
27	C₄⋊Dic₇₃	—	4	2	no	—
28	#11924007	—	4	4	no	—
29	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
30	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
31	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
32	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
33	C₄⋊C₄×C₇₃	—	4	1	no	—
34	C₄⋊C₄×C₇₃	—	4	1	no	—
35	C₄²×C₇₃	Q₈	1	4	yes	complemented
36	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
37	C₂×C₄×C₇₃	—	2	1	no	—
38	C₂×C₄×C₇₃	—	2	2	no	—
39	C₂×C₄×C₇₃	—	2	2	no	—
40	C₂×C₄×C₇₃	—	2	1	no	—
41	C₂×C₄×C₇₃	—	2	2	no	—
42	C₂×C₄×C₇₃	—	2	2	no	—
43	C₂×C₄×C₇₃	—	2	4	no	—
44	C₂×C₄×C₇₃	—	2	4	no	—
45	C₂×C₄×C₇₃	C₂×Q₈	1	4	yes	—
46	C₂×C₄×C₇₃	C₂×Q₈	1	2	yes	—
47	C₂×Dic₇₃	—	2	4	no	—
48	C₂×Dic₇₃	—	2	4	no	—
49	C₂×Dic₇₃	—	2	4	no	—
50	C₂×Dic₇₃	—	2	4	no	—
51	C₂×Dic₇₃	—	2	4	no	—
52	C₂×Dic₇₃	—	2	4	no	—
53	Dic₁₄₆	—	4	8	no	—
54	C₂²×C₇₃	C₂²×Q₈	1	1	yes	characteristic
55	C₂²×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
56	C₂²×C₇₃	H(5,𝔽₂)	1	2	yes	—
57	C₂²×C₇₃	2₋¹⁺⁴	1	2	yes	—
58	C₂²×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
59	C₄×C₇₃	—	2	4	no	—
60	C₄×C₇₃	—	2	2	no	—
61	C₄×C₇₃	—	4	2	no	—
62	C₄×C₇₃	—	4	2	no	—
63	Dic₇₃	—	4	4	no	—
64	Dic₇₃	—	4	4	no	—
65	C₂×C₇₃	#544	1	2	yes	—
66	C₂×C₇₃	#544	1	1	yes	characteristic
67	C₂×C₇₃	H(3,𝔽₄)	1	1	yes	characteristic
68	C₂×C₇₃	#563	1	1	yes	characteristic
69	C₂×C₇₃	#563	1	2	yes	—
70	#2844	—	73	1	no	maximal, Sylow
71	C₇₃	#2844	1	1	yes	characteristic, complemented, Sylow
72	#400	—	73	2	no	—
73	#400	—	73	4	no	—
74	#395	—	73	2	no	—
75	#395	—	73	4	no	—
76	#382	—	73	2	no	—
77	#382	D₇₃	1	1	yes	characteristic
78	C₂²×Q₈	—	73	2	no	—
79	C₂×C₄⋊C₄	—	73	2	no	—
80	C₂×C₄⋊C₄	—	73	2	no	—
81	C₂×C₄⋊C₄	—	73	4	no	—
82	C₂×C₄⋊C₄	—	73	2	no	—
83	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
84	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
85	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
86	#95	—	73	4	no	—
87	#95	—	73	4	no	—
88	#95	—	73	2	no	—
89	#95	—	73	4	no	—
90	#95	—	73	2	no	—
91	#95	C₂×D₇₃	1	4	yes	—
92	C₂×Q₈	—	292	2	no	—
93	C₂×Q₈	—	292	4	no	—
94	C₂²×C₄	—	73	4	no	—
95	C₂²×C₄	—	73	4	no	—
96	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
97	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
98	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
99	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
100	C₄⋊C₄	—	4	1	no	—
101	C₄⋊C₄	—	4	1	no	—
102	C₄⋊C₄	—	292	4	no	—
103	C₄⋊C₄	—	292	2	no	—
104	C₄⋊C₄	—	292	2	no	—
105	C₄⋊C₄	—	292	2	no	—
106	C₄²	Dic₁₄₆	1	4	yes	complemented
107	C₂³	C₂³×D₇₃	1	1	yes	characteristic
108	Q₈	—	292	8	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	146	4	no	—
118	C₂×C₄	—	146	4	no	—
119	C₂×C₄	—	146	4	no	—
120	C₂×C₄	—	146	4	no	—
121	C₂×C₄	—	146	4	no	—
122	C₂×C₄	—	146	4	no	—
123	C₂×C₄	C₂×Dic₁₄₆	1	4	yes	—
124	C₂×C₄	C₂×Dic₁₄₆	1	2	yes	—
125	C₂²	C₂²×Dic₁₄₆	1	1	yes	characteristic
126	C₂²	#14556636	1	1	yes	characteristic
127	C₂²	#14556637	1	2	yes	—
128	C₂²	#14556638	1	2	yes	—
129	C₂²	#14556639	1	1	yes	characteristic
130	C₄	—	2	4	no	—
131	C₄	—	2	2	no	—
132	C₄	—	4	2	no	—
133	C₄	—	4	2	no	—
134	C₄	—	292	4	no	—
135	C₄	—	292	4	no	—
136	C₂	#17989215	1	2	yes	—
137	C₂	#17989218	1	1	yes	characteristic
138	C₂	#17989329	1	1	yes	characteristic
139	C₂	#17989337	1	1	yes	characteristic
140	C₂	#17989341	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988529

C₂

yes

maximal

#17988526

C₂

yes

maximal

#17988508

C₂

yes

maximal

#17988507

C₂

yes

maximal

#17988453

C₂

yes

maximal

#382×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#95×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

Q₈

yes

complemented

C₂³×C₇₃

C₂⁴

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

C₂²×C₇₃

C₂²×Q₈

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₂²×C₇₃

2₋¹⁺⁴

yes

—

C₂²×C₇₃

2₋¹⁺⁴

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#544

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

#2844

—

maximal, Sylow

C₇₃

#2844

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₃

yes

characteristic

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

C₂×D₇₃

yes

characteristic

C₂×C₄²

C₂×D₇₃

yes

—

—

—

—

—

C₂×D₇₃

yes

—

C₂×Q₈

—

292

—

C₂×Q₈

—

292

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂²×C₄

C₂²×D₇₃

yes

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

292

—

103

C₄⋊C₄

—

292

—

104

C₄⋊C₄

—

292

—

105

C₄⋊C₄

—

292

—

106

C₄²

Dic₁₄₆

yes

complemented

107

C₂³

C₂³×D₇₃

yes

characteristic

108

Q₈

—

292

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

146

—

118

C₂×C₄

—

146

—

119

C₂×C₄

—

146

—

120

C₂×C₄

—

146

—

121

C₂×C₄

—

146

—

122

C₂×C₄

—

146

—

123

C₂×C₄

C₂×Dic₁₄₆

yes

—

124

C₂×C₄

C₂×Dic₁₄₆

yes

—

125

C₂²

C₂²×Dic₁₄₆

yes

characteristic

126

C₂²

#14556636

yes

characteristic

127

C₂²

#14556637

yes

—

128

C₂²

#14556638

yes

—

129

C₂²

#14556639

yes

characteristic

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

292

—

135

C₄

—

292

—

136

C₂

#17989215

yes

—

137

C₂

#17989218

yes

characteristic

138

C₂

#17989329

yes

characteristic

139

C₂

#17989337

yes

characteristic

140

C₂

#17989341

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂⁴
Fitting	#382×C₇₃	C₂
hypercenter	#382	D₇₃
hypocenter	C₇₃	#2844
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂⁴

Fitting

#382×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
35. C₄²×C₇₃	Q₈	semidirect
71. C₇₃	#2844	semidirect
106. C₄²	Dic₁₄₆	semidirect

H ≅ G/N

type

35. C₄²×C₇₃

Q₈

semidirect

71. C₇₃

#2844

semidirect

106. C₄²

Dic₁₄₆

semidirect

Subgroups — #22618203

Conjugacy classes of subgroups

Complements