Group #22611351 — subgroups

Subgroups — #22611351

Order 9344.

222 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 79 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×#14556516	C₂	1	2	yes	maximal
2	#17988493	C₂	1	1	yes	maximal, characteristic
3	#17988453	C₂	1	1	yes	maximal, characteristic
4	#17988350	C₂	1	2	yes	maximal
5	#336×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
9	#14556516	—	2	4	no	—
10	#14556498	—	2	2	no	—
11	#14556498	—	2	2	no	—
12	C₂²×C₈×C₇₃	C₂²	1	2	yes	—
13	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₄₆	—	2	2	no	—
15	C₂×Dic₁₄₆	—	2	2	no	—
16	C₂×Dic₁₄₆	—	2	1	no	—
17	C₂×Dic₁₄₆	D₄	1	2	yes	—
18	C₂²×Dic₇₃	—	2	1	no	—
19	C₂²×Dic₇₃	—	2	2	no	—
20	C₂²×Dic₇₃	—	2	1	no	—
21	C₄⋊Dic₇₃	—	2	2	no	—
22	C₄⋊Dic₇₃	—	2	2	no	—
23	C₄⋊Dic₇₃	—	2	2	no	—
24	C₂²×C₄×C₇₃	D₄	1	2	yes	—
25	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
26	C₂×C₈×C₇₃	—	2	2	no	—
27	C₂×C₈×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	—	2	2	no	—
29	C₄²×C₇₃	—	2	2	no	—
30	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	—	2	2	no	—
33	C₂×C₄×C₇₃	—	2	2	no	—
34	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	#41	1	2	yes	—
36	C₂×C₄×C₇₃	#41	1	2	yes	—
37	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
38	C₂×Dic₇₃	—	2	2	no	—
39	C₂×Dic₇₃	—	4	1	no	—
40	C₂×Dic₇₃	—	4	1	no	—
41	C₂×Dic₇₃	—	4	2	no	—
42	C₂×Dic₇₃	—	4	1	no	—
43	C₂×Dic₇₃	—	4	2	no	—
44	C₂×Dic₇₃	—	4	2	no	—
45	C₂×Dic₇₃	—	4	2	no	—
46	Dic₁₄₆	—	2	4	no	—
47	Dic₁₄₆	—	4	2	no	—
48	C₈×C₇₃	—	4	2	no	—
49	C₂²×C₇₃	#121	1	1	yes	characteristic
50	C₂²×C₇₃	#123	1	1	yes	characteristic
51	C₂²×C₇₃	#124	1	1	yes	characteristic
52	C₂²×C₇₃	#135	1	2	yes	—
53	C₂²×C₇₃	#137	1	2	yes	—
54	C₄×C₇₃	—	4	2	no	—
55	C₄×C₇₃	#123	1	2	yes	—
56	C₄×C₇₃	#126	1	2	yes	—
57	Dic₇₃	—	4	2	no	—
58	Dic₇₃	—	8	2	no	—
59	Dic₇₃	—	8	1	no	—
60	C₂×C₇₃	#397	1	1	yes	characteristic
61	C₂×C₇₃	#464	1	2	yes	—
62	C₂×C₇₃	#485	1	2	yes	—
63	C₂×C₇₃	#488	1	1	yes	characteristic
64	C₂×C₇₃	#491	1	1	yes	characteristic
65	#2074	—	73	1	no	maximal, Sylow
66	C₇₃	#2074	1	1	yes	characteristic, complemented, Sylow
67	C₂×#103	—	73	2	no	—
68	#391	—	73	1	no	—
69	#382	—	73	1	no	—
70	#340	—	73	2	no	—
71	#336	D₇₃	1	1	yes	characteristic
72	C₂²×Q₈	—	73	1	no	—
73	C₂²×C₈	C₂×D₇₃	1	2	yes	—
74	C₂×C₄⋊C₄	—	73	1	no	—
75	C₂×C₄⋊C₄	—	73	2	no	—
76	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
77	#103	—	146	4	no	—
78	#95	—	146	2	no	—
79	#95	—	146	2	no	—
80	C₂×Q₈	—	73	2	no	—
81	C₂×Q₈	—	146	2	no	—
82	C₂×Q₈	—	146	2	no	—
83	C₂×Q₈	—	146	1	no	—
84	C₂²×C₄	—	146	2	no	—
85	C₂²×C₄	—	146	1	no	—
86	C₂²×C₄	—	146	1	no	—
87	C₂²×C₄	D₂₉₂	1	2	yes	—
88	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₄⋊C₄	—	146	2	no	—
93	C₄⋊C₄	—	146	2	no	—
94	C₄⋊C₄	—	146	2	no	—
95	C₄²	—	2	2	no	—
96	C₂³	C₂×D₂₉₂	1	1	yes	characteristic
97	Q₈	—	292	2	no	—
98	Q₈	—	146	4	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	292	1	no	—
103	C₂×C₄	—	292	1	no	—
104	C₂×C₄	—	292	2	no	—
105	C₂×C₄	—	292	1	no	—
106	C₂×C₄	—	292	2	no	—
107	C₂×C₄	—	292	2	no	—
108	C₂×C₄	—	292	2	no	—
109	C₂×C₄	—	146	2	no	—
110	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
111	C₂×C₄	#11924027	1	2	yes	—
112	C₂×C₄	#11924028	1	2	yes	—
113	C₂×C₄	#11924029	1	1	yes	characteristic
114	C₈	—	4	2	no	—
115	C₂²	#14556566	1	1	yes	characteristic
116	C₂²	#14556575	1	1	yes	characteristic
117	C₂²	#14556579	1	1	yes	characteristic
118	C₂²	#14556613	1	2	yes	—
119	C₂²	#14556624	1	2	yes	—
120	C₄	—	4	2	no	—
121	C₄	—	292	2	no	—
122	C₄	—	584	1	no	—
123	C₄	—	584	2	no	—
124	C₄	#14556573	1	2	yes	—
125	C₄	#14556586	1	2	yes	—
126	C₂	#17988514	1	1	yes	characteristic
127	C₂	#17988810	1	2	yes	—
128	C₂	#17988929	1	2	yes	—
129	C₂	#17988942	1	1	yes	characteristic
130	C₂	#17988956	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556516

C₂

yes

maximal

#17988493

C₂

yes

maximal, characteristic

#17988453

C₂

yes

maximal, characteristic

#17988350

C₂

yes

maximal

#336×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

—

—

C₂²×C₈×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₂²×C₇₃

#137

yes

—

C₄×C₇₃

—

C₄×C₇₃

#123

yes

—

C₄×C₇₃

#126

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#397

yes

characteristic

C₂×C₇₃

#464

yes

—

C₂×C₇₃

#485

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₃

yes

characteristic

C₂²×Q₈

—

C₂²×C₈

C₂×D₇₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

#103

—

146

—

#95

—

146

—

#95

—

146

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

D₂₉₂

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

C₂³

C₂×D₂₉₂

yes

characteristic

Q₈

—

292

—

Q₈

—

146

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

292

—

103

C₂×C₄

—

292

—

104

C₂×C₄

—

292

—

105

C₂×C₄

—

292

—

106

C₂×C₄

—

292

—

107

C₂×C₄

—

292

—

108

C₂×C₄

—

292

—

109

C₂×C₄

—

146

—

110

C₂×C₄

D₄×D₇₃

yes

characteristic

111

C₂×C₄

#11924027

yes

—

112

C₂×C₄

#11924028

yes

—

113

C₂×C₄

#11924029

yes

characteristic

114

C₈

—

115

C₂²

#14556566

yes

characteristic

116

C₂²

#14556575

yes

characteristic

117

C₂²

#14556579

yes

characteristic

118

C₂²

#14556613

yes

—

119

C₂²

#14556624

yes

—

120

C₄

—

121

C₄

—

292

—

122

C₄

—

584

—

123

C₄

—

584

—

124

C₄

#14556573

yes

—

125

C₄

#14556586

yes

—

126

C₂

#17988514

yes

characteristic

127

C₂

#17988810

yes

—

128

C₂

#17988929

yes

—

129

C₂

#17988942

yes

characteristic

130

C₂

#17988956

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₂₉₂
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#336×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	#336	D₇₃
hypocenter	C₇₃	#2074
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₂₉₂

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#336×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
66. C₇₃	#2074	semidirect

H ≅ G/N

type

66. C₇₃

#2074

semidirect

Subgroups — #22611351

Conjugacy classes of subgroups

Complements