Group #22626579 — subgroups

Subgroups — #22626579

Order 9344.

484 conjugacy classes of subgroups; only the 204 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 204 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×#14556679	C₂	1	2	yes	maximal
2	#17989594	C₂	1	6	yes	maximal, complemented
3	#17989592	C₂	1	3	yes	maximal, complemented
4	#17989588	C₂	1	3	yes	maximal, complemented
5	C₄×#11924029	C₂	1	1	yes	maximal, characteristic
6	#14556679	—	2	8	no	—
7	C₂×#11924038	C₂²	1	6	yes	—
8	C₂×#11924036	C₂²	1	6	yes	—
9	#14556658	C₂²	1	1	yes	characteristic
10	#14556658	C₂²	1	3	yes	—
11	#14556658	C₂²	1	6	yes	—
12	C₄⋊#10596833	C₂²	1	6	yes	—
13	C₂×#11924029	C₂²	1	1	yes	characteristic
14	Q₈×Dic₇₃	C₄	1	1	yes	characteristic
15	C₄×D₂₉₂	C₄	1	3	yes	—
16	#14556553	C₄	1	3	yes	—
17	#14556549	C₂²	1	3	yes	—
18	C₄²×D₇₃	C₂²	1	3	yes	—
19	C₄×Q₈×C₇₃	C₄	1	1	yes	characteristic
20	#11924038	—	2	12	no	—
21	#11924036	—	2	12	no	—
22	C₂×#10596833	C₂³	1	2	yes	—
23	C₂×#10596833	C₂³	1	6	yes	—
24	#11924029	D₄	1	4	yes	—
25	#11924029	Q₈	1	4	yes	—
26	C₂×D₂₉₂	C₂×C₄	1	3	yes	—
27	C₂×C₄×D₇₃	C₂×C₄	1	3	yes	—
28	C₂×C₄×D₇₃	C₂×C₄	1	3	yes	—
29	C₂×C₄×D₇₃	C₂³	1	3	yes	—
30	C₄⋊Dic₇₃	C₂×C₄	1	3	yes	—
31	#11924005	C₂×C₄	1	6	yes	—
32	C₄×Dic₇₃	C₂×C₄	1	3	yes	—
33	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
34	C₄×Dic₇₃	C₂³	1	3	yes	—
35	C₂×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₄⋊C₄×C₇₃	C₂×C₄	1	3	yes	—
37	C₄²×C₇₃	C₂×C₄	1	3	yes	—
38	C₂²×D₇₃	C₂²×C₄	1	3	yes	—
39	Q₈×C₇₃	C₄⋊C₄	1	4	yes	—
40	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₇₃	C₂²×C₄	1	3	yes	—
42	C₂×C₄×C₇₃	C₂²×C₄	1	3	yes	—
43	C₂×Dic₇₃	C₂²×C₄	1	3	yes	—
44	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
46	D₂₉₂	C₄⋊C₄	1	12	yes	—
47	C₄×D₇₃	—	2	6	no	—
48	C₄×D₇₃	—	4	3	no	—
49	C₄×D₇₃	C₂×D₄	1	6	yes	—
50	C₄×D₇₃	C₂×Q₈	1	6	yes	—
51	#10596833	—	2	2	no	—
52	#10596833	—	2	6	no	—
53	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
54	C₂×D₇₃	—	2	3	no	—
55	C₂×D₇₃	—	2	3	no	—
56	C₂×D₇₃	C₂×C₄⋊C₄	1	6	yes	—
57	C₄×C₇₃	—	2	3	no	—
58	C₄×C₇₃	—	2	1	no	—
59	C₄×C₇₃	C₂×C₄⋊C₄	1	6	yes	—
60	Dic₇₃	—	2	3	no	—
61	Dic₇₃	#131	1	2	yes	complemented
62	Dic₇₃	C₂²×D₄	1	1	yes	characteristic
63	Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
64	C₂×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₇₃	C₂×#131	1	1	yes	characteristic
66	C₂×C₇₃	#568	1	1	yes	characteristic
67	D₇₃	—	2	6	no	—
68	#2906	—	73	1	no	maximal, Sylow
69	C₇₃	#2906	1	1	yes	characteristic, complemented, Sylow
70	C₂×#131	—	73	2	no	—
71	C₄×#41	—	73	1	no	—
72	#424	—	73	6	no	—
73	#423	—	73	3	no	—
74	C₂×C₄⋊C₈	—	73	3	no	—
75	C₂×#41	—	73	1	no	—
76	#131	—	146	8	no	—
77	C₂×M₁₆	—	73	6	no	—
78	C₂²×C₈	—	73	6	no	—
79	C₄×Q₈	—	73	1	no	—
80	C₄×Q₈	#64408	1	1	yes	characteristic
81	C₄×D₄	—	73	3	no	—
82	C₄×D₄	—	73	3	no	—
83	#117	—	73	3	no	—
84	C₂×C₄²	—	73	3	no	—
85	C₄⋊C₈	—	73	1	no	—
86	C₄⋊C₈	—	73	3	no	—
87	C₄⋊C₈	—	73	6	no	—
88	C₄⋊C₈	—	73	6	no	—
89	#41	—	73	4	no	—
90	#41	—	73	4	no	—
91	C₂×Q₈	C₂×#64408	1	1	yes	characteristic
92	C₂×D₄	—	73	3	no	—
93	C₂²×C₄	—	73	3	no	—
94	C₂²×C₄	—	73	3	no	—
95	C₂²×C₄	—	73	3	no	—
96	M₁₆	—	146	12	no	—
97	C₂×C₈	—	73	2	no	—
98	C₂×C₈	—	73	6	no	—
99	C₂×C₈	—	146	12	no	—
100	C₄⋊C₄	—	73	3	no	—
101	C₄⋊C₄	C₂×#64408	1	3	yes	—
102	C₂²⋊C₄	—	73	6	no	—
103	C₄²	—	73	3	no	—
104	C₄²	—	73	1	no	—
105	C₄²	—	73	3	no	—
106	C₄²	C₂×#64408	1	3	yes	—
107	C₂³	—	73	3	no	—
108	Q₈	C₄⋊#64408	1	4	yes	—
109	D₄	—	73	12	no	—
110	C₂×C₄	—	292	3	no	—
111	C₂×C₄	—	73	1	no	—
112	C₂×C₄	—	73	1	no	—
113	C₂×C₄	—	73	6	no	—
114	C₂×C₄	—	73	6	no	—
115	C₂×C₄	—	73	3	no	—
116	C₂×C₄	—	146	6	no	—
117	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
118	C₂×C₄	C₂²×#64408	1	3	yes	—
119	C₂×C₄	C₂²×#64408	1	3	yes	—
120	C₈	—	146	2	no	—
121	C₈	—	146	6	no	—
122	C₂²	—	73	6	no	—
123	C₂²	—	146	3	no	—
124	C₂²	—	146	3	no	—
125	C₂²	C₂³×#64408	1	1	yes	characteristic
126	C₄	—	2	3	no	—
127	C₄	—	2	1	no	—
128	C₄	—	73	1	no	—
129	C₄	—	73	1	no	—
130	C₄	—	73	2	no	—
131	C₄	—	146	3	no	—
132	C₄	C₂×C₄⋊#64408	1	6	yes	—
133	C₂	—	146	6	no	—
134	C₂	C₂²×C₄⋊#64408	1	1	yes	characteristic
135	C₂	D₇₃⋊#131	1	1	yes	characteristic
136	C₂	#17989667	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556679

C₂

yes

maximal

#17989594

C₂

yes

maximal, complemented

#17989592

C₂

yes

maximal, complemented

#17989588

C₂

yes

maximal, complemented

C₄×#11924029

C₂

yes

maximal, characteristic

#14556679

—

C₂×#11924038

C₂²

yes

—

C₂×#11924036

C₂²

yes

—

#14556658

C₂²

yes

characteristic

#14556658

C₂²

yes

—

#14556658

C₂²

yes

—

C₄⋊#10596833

C₂²

yes

—

C₂×#11924029

C₂²

yes

characteristic

Q₈×Dic₇₃

C₄

yes

characteristic

C₄×D₂₉₂

C₄

yes

—

#14556553

C₄

yes

—

#14556549

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

—

C₄×Q₈×C₇₃

C₄

yes

—

—

C₂³

yes

—

C₂×#10596833

C₂³

yes

—

#11924029

D₄

yes

—

#11924029

Q₈

yes

—

C₂×D₂₉₂

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924005

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₄×Dic₇₃

C₂³

yes

—

C₂×Q₈×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

—

C₂²×D₇₃

C₂²×C₄

yes

—

Q₈×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂⁴

yes

characteristic

D₂₉₂

C₄⋊C₄

yes

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

C₂×D₄

yes

—

C₄×D₇₃

C₂×Q₈

yes

—

#10596833

—

#10596833

—

C₂²×C₇₃

C₂³×C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₂×C₄⋊C₄

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄⋊C₄

yes

—

Dic₇₃

—

Dic₇₃

#131

yes

complemented

Dic₇₃

C₂²×D₄

yes

characteristic

Dic₇₃

C₂²×Q₈

yes

characteristic

C₂×C₇₃

C₂²×C₄⋊C₄

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#2906

—

maximal, Sylow

C₇₃

#2906

yes

characteristic, complemented, Sylow

C₂×#131

—

C₄×#41

—

#424

—

#423

—

C₂×C₄⋊C₈

—

C₂×#41

—

#131

—

146

—

C₂×M₁₆

—

C₂²×C₈

—

C₄×Q₈

—

C₄×Q₈

#64408

yes

characteristic

C₄×D₄

—

C₄×D₄

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#41

—

#41

—

C₂×Q₈

C₂×#64408

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

100

C₄⋊C₄

—

101

C₄⋊C₄

C₂×#64408

yes

—

102

C₂²⋊C₄

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₄²

C₂×#64408

yes

—

107

C₂³

—

108

Q₈

C₄⋊#64408

yes

—

109

D₄

—

110

C₂×C₄

—

292

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

146

—

117

C₂×C₄

C₂²×#64408

yes

characteristic

118

C₂×C₄

C₂²×#64408

yes

—

119

C₂×C₄

C₂²×#64408

yes

—

120

C₈

—

146

—

121

C₈

—

146

—

122

C₂²

—

123

C₂²

—

146

—

124

C₂²

—

146

—

125

C₂²

C₂³×#64408

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

146

—

132

C₄

C₂×C₄⋊#64408

yes

—

133

C₂

—

146

—

134

C₂

C₂²×C₄⋊#64408

yes

characteristic

135

C₂

D₇₃⋊#131

yes

characteristic

136

C₂

#17989667

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂³×C₄
Fitting	C₄×Q₈×C₇₃	C₄
hypercenter	C₄×Q₈	#64408
hypocenter	C₇₃	#2906
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

subgroup

G/H

center, Frattini

C₂²

C₂³×#64408

commutator, socle

C₂²×C₇₃

C₂³×C₄

Fitting

C₄×Q₈×C₇₃

C₄

C₄×Q₈

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂² ◁ C₄×Q₈

N	H ≅ G/N	type
2. #17989594	C₂	semidirect
3. #17989592	C₂	semidirect
4. #17989588	C₂	semidirect
61. Dic₇₃	#131	semidirect
69. C₇₃	#2906	semidirect

H ≅ G/N

type

2. #17989594

C₂

semidirect

3. #17989592

C₂

semidirect

4. #17989588

C₂

semidirect

61. Dic₇₃

#131

semidirect

69. C₇₃

#2906

semidirect

Subgroups — #22626579

Conjugacy classes of subgroups

Complements