Group #22608196 — subgroups

Subgroups — #22608196

Order 9344.

608 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 229 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	C₂²×C₄⋊Dic₇₃	C₂	1	3	yes	maximal
2	C₂×#14556498	C₂	1	3	yes	maximal
3	C₂×#95×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₇₃	C₂²	1	3	yes	—
5	C₂³×Dic₇₃	C₂²	1	1	yes	characteristic
6	C₂×C₄⋊Dic₇₃	—	2	12	no	—
7	C₂×C₄⋊Dic₇₃	—	2	6	no	—
8	#14556498	—	2	6	no	—
9	C₂³×C₄×C₇₃	C₂²	1	3	yes	—
10	#95×C₇₃	C₄	1	4	yes	complemented
11	C₂²×Dic₇₃	—	2	3	no	—
12	C₂²×Dic₇₃	—	2	3	no	—
13	C₂²×Dic₇₃	—	2	6	no	—
14	C₂²×Dic₇₃	—	2	6	no	—
15	C₂²×Dic₇₃	—	2	3	no	—
16	C₂²×Dic₇₃	—	2	3	no	—
17	C₂²×Dic₇₃	D₄	1	6	yes	—
18	C₂²×Dic₇₃	Q₈	1	2	yes	—
19	C₄⋊Dic₇₃	—	2	24	no	—
20	C₂⁴×C₇₃	C₂³	1	1	yes	characteristic
21	C₂²×C₄×C₇₃	—	2	6	no	—
22	C₂²×C₄×C₇₃	—	2	6	no	—
23	C₂²×C₄×C₇₃	C₂×C₄	1	6	yes	—
24	C₂²×C₄×C₇₃	D₄	1	6	yes	—
25	C₂²×C₄×C₇₃	Q₈	1	6	yes	—
26	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
27	C₂³×C₇₃	C₂×D₄	1	3	yes	—
28	C₂³×C₇₃	C₂×D₄	1	3	yes	—
29	C₂³×C₇₃	C₂×Q₈	1	1	yes	characteristic
30	C₂³×C₇₃	C₂×Q₈	1	3	yes	—
31	C₂³×C₇₃	#41	1	3	yes	—
32	C₂³×C₇₃	#41	1	1	yes	characteristic
33	C₂×C₄×C₇₃	—	2	12	no	—
34	C₂×C₄×C₇₃	—	2	6	no	—
35	C₂×C₄×C₇₃	—	2	12	no	—
36	C₂×C₄×C₇₃	—	2	6	no	—
37	C₂×C₄×C₇₃	C₄⋊C₄	1	12	yes	complemented
38	C₂×Dic₇₃	—	2	12	no	—
39	C₂×Dic₇₃	—	2	6	no	—
40	C₂×Dic₇₃	—	2	6	no	—
41	C₂×Dic₇₃	—	4	3	no	—
42	C₂×Dic₇₃	—	4	6	no	—
43	C₂×Dic₇₃	—	4	3	no	—
44	C₂×Dic₇₃	—	4	3	no	—
45	C₂×Dic₇₃	—	4	1	no	—
46	C₂²×C₇₃	C₂×C₄⋊C₄	1	3	yes	—
47	C₂²×C₇₃	C₄×D₄	1	3	yes	—
48	C₂²×C₇₃	C₄×Q₈	1	1	yes	characteristic
49	C₂²×C₇₃	#120	1	3	yes	—
50	C₂²×C₇₃	#121	1	3	yes	—
51	C₂²×C₇₃	C₂²⋊Q₈	1	6	yes	—
52	C₂²×C₇₃	C₂²⋊Q₈	1	3	yes	—
53	C₂²×C₇₃	#123	1	3	yes	—
54	C₂²×C₇₃	#125	1	3	yes	—
55	C₂²×C₇₃	#127	1	1	yes	characteristic
56	C₂²×C₇₃	C₄⋊Q₈	1	3	yes	—
57	C₂²×C₇₃	C₄⋊Q₈	1	3	yes	—
58	C₄×C₇₃	—	2	12	no	—
59	Dic₇₃	—	4	6	no	—
60	Dic₇₃	—	4	2	no	—
61	C₂×C₇₃	#384	1	1	yes	characteristic
62	C₂×C₇₃	#385	1	3	yes	—
63	C₂×C₇₃	#389	1	3	yes	—
64	C₂×C₇₃	#392	1	1	yes	characteristic
65	C₂×C₇₃	#395	1	3	yes	—
66	C₂×C₇₃	#398	1	3	yes	—
67	C₂×C₇₃	#399	1	1	yes	characteristic
68	#1444	—	73	1	no	maximal, Sylow
69	C₇₃	#1444	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₄⋊C₄	—	73	3	no	—
71	C₂×#95	—	73	3	no	—
72	C₂×#95	D₇₃	1	1	yes	characteristic
73	C₂³×C₄	—	73	3	no	—
74	C₂³×C₄	—	73	1	no	—
75	C₂³×C₄	C₂×D₇₃	1	3	yes	—
76	C₂×C₄⋊C₄	—	146	12	no	—
77	C₂×C₄⋊C₄	—	146	6	no	—
78	#95	—	146	6	no	—
79	#95	Dic₇₃	1	4	yes	complemented
80	C₂⁴	C₂²×D₇₃	1	1	yes	characteristic
81	C₂²×C₄	—	2	6	no	—
82	C₂²×C₄	—	2	6	no	—
83	C₂²×C₄	—	73	6	no	—
84	C₂²×C₄	—	73	2	no	—
85	C₂²×C₄	—	146	6	no	—
86	C₂²×C₄	—	146	3	no	—
87	C₂²×C₄	—	146	3	no	—
88	C₂²×C₄	—	146	6	no	—
89	C₂²×C₄	—	146	3	no	—
90	C₂²×C₄	—	146	3	no	—
91	C₂²×C₄	Dic₁₄₆	1	6	yes	—
92	C₂²×C₄	D₂₉₂	1	6	yes	—
93	C₂²×C₄	C₂×Dic₇₃	1	6	yes	—
94	C₄⋊C₄	—	146	24	no	—
95	C₂³	C₂²×Dic₇₃	1	1	yes	characteristic
96	C₂³	D₄×D₇₃	1	3	yes	—
97	C₂³	C₂×D₂₉₂	1	3	yes	—
98	C₂³	Q₈×D₇₃	1	1	yes	characteristic
99	C₂³	C₂×Dic₁₄₆	1	3	yes	—
100	C₂³	#11924027	1	3	yes	—
101	C₂³	#11924029	1	1	yes	characteristic
102	C₂×C₄	—	2	12	no	—
103	C₂×C₄	—	2	6	no	—
104	C₂×C₄	—	2	12	no	—
105	C₂×C₄	—	2	6	no	—
106	C₂×C₄	—	292	3	no	—
107	C₂×C₄	—	292	6	no	—
108	C₂×C₄	—	292	3	no	—
109	C₂×C₄	—	292	3	no	—
110	C₂×C₄	—	292	1	no	—
111	C₂×C₄	—	146	12	no	—
112	C₂×C₄	—	146	6	no	—
113	C₂×C₄	—	146	6	no	—
114	C₂×C₄	C₄⋊Dic₇₃	1	12	yes	complemented
115	C₂²	C₂×C₄⋊Dic₇₃	1	3	yes	—
116	C₂²	D₄×Dic₇₃	1	3	yes	—
117	C₂²	Q₈×Dic₇₃	1	1	yes	characteristic
118	C₂²	#14556561	1	3	yes	—
119	C₂²	#14556566	1	3	yes	—
120	C₂²	#14556568	1	6	yes	—
121	C₂²	#14556571	1	3	yes	—
122	C₂²	#14556575	1	3	yes	—
123	C₂²	#14556582	1	3	yes	—
124	C₂²	#14556588	1	1	yes	characteristic
125	C₂²	#14556590	1	3	yes	—
126	C₂²	#14556591	1	3	yes	—
127	C₄	—	2	12	no	—
128	C₄	—	292	6	no	—
129	C₄	—	292	2	no	—
130	C₂	#17988457	1	1	yes	characteristic
131	C₂	#17988462	1	3	yes	—
132	C₂	#17988486	1	3	yes	—
133	C₂	#17988497	1	1	yes	characteristic
134	C₂	#17988508	1	3	yes	—
135	C₂	#17988519	1	3	yes	—
136	C₂	#17988524	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₇₃

C₂

yes

maximal

C₂×#14556498

C₂

yes

maximal

C₂×#95×C₇₃

C₂

yes

maximal, characteristic

C₂³×Dic₇₃

C₂²

yes

—

C₂³×Dic₇₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

#14556498

—

C₂³×C₄×C₇₃

C₂²

yes

—

#95×C₇₃

C₄

yes

complemented

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

—

C₂²×Dic₇₃

Q₈

yes

—

C₄⋊Dic₇₃

—

C₂⁴×C₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

Q₈

yes

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂³×C₇₃

C₂×D₄

yes

—

C₂³×C₇₃

C₂×D₄

yes

—

C₂³×C₇₃

C₂×Q₈

yes

characteristic

C₂³×C₇₃

C₂×Q₈

yes

—

C₂³×C₇₃

#41

yes

—

C₂³×C₇₃

#41

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

complemented

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

—

C₂²×C₇₃

C₄×D₄

yes

—

C₂²×C₇₃

C₄×Q₈

yes

characteristic

C₂²×C₇₃

#120

yes

—

C₂²×C₇₃

#121

yes

—

C₂²×C₇₃

C₂²⋊Q₈

yes

—

C₂²×C₇₃

C₂²⋊Q₈

yes

—

C₂²×C₇₃

#123

yes

—

C₂²×C₇₃

#125

yes

—

C₂²×C₇₃

#127

yes

characteristic

C₂²×C₇₃

C₄⋊Q₈

yes

—

C₂²×C₇₃

C₄⋊Q₈

yes

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#384

yes

characteristic

C₂×C₇₃

#385

yes

—

C₂×C₇₃

#389

yes

—

C₂×C₇₃

#392

yes

characteristic

C₂×C₇₃

#395

yes

—

C₂×C₇₃

#398

yes

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂²×C₄⋊C₄

—

C₂×#95

—

C₂×#95

D₇₃

yes

characteristic

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₇₃

yes

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

—

146

—

#95

—

146

—

#95

Dic₇₃

yes

complemented

C₂⁴

C₂²×D₇₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

Dic₁₄₆

yes

—

C₂²×C₄

D₂₉₂

yes

—

C₂²×C₄

C₂×Dic₇₃

yes

—

C₄⋊C₄

—

146

—

C₂³

C₂²×Dic₇₃

yes

characteristic

C₂³

D₄×D₇₃

yes

—

C₂³

C₂×D₂₉₂

yes

—

C₂³

Q₈×D₇₃

yes

characteristic

C₂³

C₂×Dic₁₄₆

yes

—

100

C₂³

#11924027

yes

—

101

C₂³

#11924029

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

292

—

107

C₂×C₄

—

292

—

108

C₂×C₄

—

292

—

109

C₂×C₄

—

292

—

110

C₂×C₄

—

292

—

111

C₂×C₄

—

146

—

112

C₂×C₄

—

146

—

113

C₂×C₄

—

146

—

114

C₂×C₄

C₄⋊Dic₇₃

yes

complemented

115

C₂²

C₂×C₄⋊Dic₇₃

yes

—

116

C₂²

D₄×Dic₇₃

yes

—

117

C₂²

Q₈×Dic₇₃

yes

characteristic

118

C₂²

#14556561

yes

—

119

C₂²

#14556566

yes

—

120

C₂²

#14556568

yes

—

121

C₂²

#14556571

yes

—

122

C₂²

#14556575

yes

—

123

C₂²

#14556582

yes

—

124

C₂²

#14556588

yes

characteristic

125

C₂²

#14556590

yes

—

126

C₂²

#14556591

yes

—

127

C₄

—

128

C₄

—

292

—

129

C₄

—

292

—

130

C₂

#17988457

yes

characteristic

131

C₂

#17988462

yes

—

132

C₂

#17988486

yes

—

133

C₂

#17988497

yes

characteristic

134

C₂

#17988508

yes

—

135

C₂

#17988519

yes

—

136

C₂

#17988524

yes

characteristic

	subgroup	G/H
center, Frattini	C₂⁴	C₂²×D₇₃
commutator	C₂³×C₇₃	C₂²×C₄
Fitting	C₂×#95×C₇₃	C₂
socle	C₂⁴×C₇₃	C₂³
hypercenter	C₂×#95	D₇₃
hypocenter	C₇₃	#1444
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂⁴

C₂²×D₇₃

commutator

C₂³×C₇₃

C₂²×C₄

Fitting

C₂×#95×C₇₃

C₂

socle

C₂⁴×C₇₃

C₂³

hypercenter

C₂×#95

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂⁴ ◁ C₂×#95

N	H ≅ G/N	type
10. #95×C₇₃	C₄	semidirect
37. C₂×C₄×C₇₃	C₄⋊C₄	semidirect
69. C₇₃	#1444	semidirect
79. #95	Dic₇₃	semidirect
114. C₂×C₄	C₄⋊Dic₇₃	semidirect

H ≅ G/N

type

10. #95×C₇₃

C₄

semidirect

37. C₂×C₄×C₇₃

C₄⋊C₄

semidirect

69. C₇₃

#1444

semidirect

79. #95

Dic₇₃

semidirect

114. C₂×C₄

C₄⋊Dic₇₃

semidirect

Subgroups — #22608196

Conjugacy classes of subgroups

Complements