Group #22618311 — subgroups

Subgroups — #22618311

Order 9344.

408 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 149 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	#17988491	C₂	1	3	yes	maximal
2	#17988484	C₂	1	3	yes	maximal
3	#17988474	C₂	1	3	yes	maximal
4	#17988470	C₂	1	3	yes	maximal
5	#17988455	C₂	1	1	yes	maximal, characteristic
6	C₄²×Dic₇₃	C₂	1	1	yes	maximal, characteristic
7	#383×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₇₃	C₂²	1	3	yes	—
10	C₂×#11924007	C₂²	1	3	yes	—
11	C₂×#11924007	C₂²	1	3	yes	—
12	C₂×C₄×Dic₇₃	C₂²	1	3	yes	—
13	C₂×C₄×Dic₇₃	C₂²	1	3	yes	—
14	#14556498	C₂²	1	3	yes	—
15	#14556498	C₂²	1	3	yes	—
16	#14556498	C₂²	1	3	yes	—
17	#14556498	C₂²	1	3	yes	—
18	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
19	#95×C₇₃	C₂²	1	3	yes	—
20	#95×C₇₃	C₂²	1	3	yes	—
21	C₂×Dic₁₄₆	—	2	6	no	—
22	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
23	C₂²×Dic₇₃	C₂³	1	3	yes	—
24	C₂²×Dic₇₃	C₂³	1	3	yes	—
25	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₇₃	—	2	6	no	—
27	#11924007	—	2	6	no	—
28	#11924007	—	2	6	no	—
29	C₄×Dic₇₃	—	2	6	no	—
30	C₄×Dic₇₃	—	2	6	no	—
31	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
33	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
34	C₄²×C₇₃	Q₈	1	4	yes	complemented
35	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
36	C₂×C₄×C₇₃	—	2	3	no	—
37	C₂×C₄×C₇₃	—	2	3	no	—
38	C₂×C₄×C₇₃	—	2	3	no	—
39	C₂×C₄×C₇₃	—	2	3	no	—
40	C₂×C₄×C₇₃	—	2	3	no	—
41	C₂×C₄×C₇₃	—	2	3	no	—
42	C₂×C₄×C₇₃	C₂×Q₈	1	6	yes	—
43	C₂×Dic₇₃	—	2	3	no	—
44	C₂×Dic₇₃	—	2	3	no	—
45	C₂×Dic₇₃	—	2	3	no	—
46	C₂×Dic₇₃	—	2	3	no	—
47	C₂×Dic₇₃	—	2	3	no	—
48	C₂×Dic₇₃	—	2	3	no	—
49	C₂×Dic₇₃	#41	1	6	yes	—
50	C₂×Dic₇₃	#41	1	6	yes	—
51	Dic₁₄₆	—	4	4	no	—
52	C₂²×C₇₃	C₂²×Q₈	1	1	yes	characteristic
53	C₂²×C₇₃	C₂×#41	1	3	yes	—
54	C₂²×C₇₃	C₂×#41	1	3	yes	—
55	C₄×C₇₃	—	2	6	no	—
56	C₄×C₇₃	—	4	1	no	—
57	C₄×C₇₃	—	4	3	no	—
58	Dic₇₃	—	2	6	no	—
59	Dic₇₃	—	4	1	no	—
60	Dic₇₃	—	4	3	no	—
61	Dic₇₃	#126	1	4	yes	—
62	C₂×C₇₃	C₂×#126	1	1	yes	characteristic
63	C₂×C₇₃	#529	1	3	yes	—
64	C₂×C₇₃	#533	1	3	yes	—
65	#2863	—	73	1	no	maximal, Sylow
66	C₇₃	#2863	1	1	yes	characteristic, complemented, Sylow
67	#391	—	73	3	no	—
68	#389	—	73	3	no	—
69	#387	—	73	3	no	—
70	#387	—	73	3	no	—
71	#383	—	73	1	no	—
72	#383	D₇₃	1	1	yes	characteristic
73	C₄³	—	73	1	no	—
74	C₂²×Q₈	—	73	1	no	—
75	C₂×C₄⋊C₄	—	73	3	no	—
76	C₂×C₄⋊C₄	—	73	3	no	—
77	C₂×C₄⋊C₄	—	73	3	no	—
78	C₂×C₄²	—	73	3	no	—
79	C₂×C₄²	—	73	3	no	—
80	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
81	#95	—	73	3	no	—
82	#95	—	73	3	no	—
83	#95	—	73	3	no	—
84	#95	—	73	3	no	—
85	#95	C₂×D₇₃	1	3	yes	—
86	#95	C₂×D₇₃	1	3	yes	—
87	C₂×Q₈	—	146	6	no	—
88	C₂²×C₄	—	73	1	no	—
89	C₂²×C₄	—	73	3	no	—
90	C₂²×C₄	—	73	1	no	—
91	C₂²×C₄	—	73	3	no	—
92	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
93	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
94	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
95	C₄⋊C₄	—	146	6	no	—
96	C₄⋊C₄	—	146	6	no	—
97	C₄⋊C₄	—	146	6	no	—
98	C₄²	—	146	6	no	—
99	C₄²	—	146	6	no	—
100	C₄²	Dic₁₄₆	1	4	yes	complemented
101	C₂³	C₂³×D₇₃	1	1	yes	characteristic
102	Q₈	—	292	4	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	2	3	no	—
105	C₂×C₄	—	2	3	no	—
106	C₂×C₄	—	2	3	no	—
107	C₂×C₄	—	2	3	no	—
108	C₂×C₄	—	2	3	no	—
109	C₂×C₄	—	73	6	no	—
110	C₂×C₄	—	73	6	no	—
111	C₂×C₄	—	146	3	no	—
112	C₂×C₄	—	146	3	no	—
113	C₂×C₄	—	146	3	no	—
114	C₂×C₄	—	146	3	no	—
115	C₂×C₄	—	146	3	no	—
116	C₂×C₄	—	146	3	no	—
117	C₂×C₄	C₂×Dic₁₄₆	1	6	yes	—
118	C₂²	C₂²×Dic₁₄₆	1	1	yes	characteristic
119	C₂²	#41×D₇₃	1	3	yes	—
120	C₂²	#41×D₇₃	1	3	yes	—
121	C₄	—	2	6	no	—
122	C₄	—	4	3	no	—
123	C₄	—	4	1	no	—
124	C₄	—	292	3	no	—
125	C₄	—	292	1	no	—
126	C₄	—	73	4	no	—
127	C₄	—	146	6	no	—
128	C₂	#126×D₇₃	1	1	yes	characteristic
129	C₂	#17989120	1	3	yes	—
130	C₂	#17989140	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988491

C₂

yes

maximal

#17988484

C₂

yes

maximal

#17988474

C₂

yes

maximal

#17988470

C₂

yes

maximal

#17988455

C₂

yes

maximal, characteristic

C₄²×Dic₇₃

C₂

yes

maximal, characteristic

#383×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#95×C₇₃

C₂²

yes

—

#95×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

C₂³

yes

characteristic

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

characteristic

C₄⋊Dic₇₃

—

#11924007

—

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

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×Q₈

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

#41

yes

—

C₂×Dic₇₃

#41

yes

—

Dic₁₄₆

—

C₂²×C₇₃

C₂²×Q₈

yes

characteristic

C₂²×C₇₃

C₂×#41

yes

—

C₂²×C₇₃

C₂×#41

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

#126

yes

—

C₂×C₇₃

C₂×#126

yes

characteristic

C₂×C₇₃

#529

yes

—

C₂×C₇₃

#533

yes

—

#2863

—

maximal, Sylow

C₇₃

#2863

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₃

yes

characteristic

C₄³

—

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₃

yes

—

—

—

—

C₂×D₇₃

yes

—

#95

C₂×D₇₃

yes

—

C₂×Q₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

146

—

C₄²

—

146

—

100

C₄²

Dic₁₄₆

yes

complemented

101

C₂³

C₂³×D₇₃

yes

characteristic

102

Q₈

—

292

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

146

—

112

C₂×C₄

—

146

—

113

C₂×C₄

—

146

—

114

C₂×C₄

—

146

—

115

C₂×C₄

—

146

—

116

C₂×C₄

—

146

—

117

C₂×C₄

C₂×Dic₁₄₆

yes

—

118

C₂²

C₂²×Dic₁₄₆

yes

characteristic

119

C₂²

#41×D₇₃

yes

—

120

C₂²

#41×D₇₃

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

292

—

125

C₄

—

292

—

126

C₄

—

127

C₄

—

146

—

128

C₂

#126×D₇₃

yes

characteristic

129

C₂

#17989120

yes

—

130

C₂

#17989140

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂⁴
Fitting	#383×C₇₃	C₂
hypercenter	#383	D₇₃
hypocenter	C₇₃	#2863
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂⁴

Fitting

#383×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
34. C₄²×C₇₃	Q₈	semidirect
66. C₇₃	#2863	semidirect
100. C₄²	Dic₁₄₆	semidirect

H ≅ G/N

type

34. C₄²×C₇₃

Q₈

semidirect

66. C₇₃

#2863

semidirect

100. C₄²

Dic₁₄₆

semidirect

Subgroups — #22618311

Conjugacy classes of subgroups

Complements