Group #22611378 — subgroups

Subgroups — #22611378

Order 9344.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14556523	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988589	C₂	1	2	yes	maximal
3	#17988553	C₂	1	1	yes	maximal, characteristic
4	#17988355	C₂	1	2	yes	maximal, complemented
5	#341×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924028	C₂²	1	1	yes	characteristic
7	C₂×#11924012	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
9	#14556523	—	2	2	no	—
10	#14556516	—	2	2	no	—
11	#14556513	—	2	2	no	—
12	#14556503	—	2	2	no	—
13	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
14	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	#11924028	—	2	2	no	—
16	#11924028	—	2	2	no	—
17	C₂×Dic₁₄₆	D₄	1	1	yes	characteristic
18	C₂×D₂₉₂	D₄	1	1	yes	characteristic
19	C₂×C₂²⋊D₇₃	—	2	1	no	—
20	C₂²×Dic₇₃	—	2	2	no	—
21	C₂×C₄×D₇₃	—	2	1	no	—
22	#11924012	—	2	2	no	—
23	C₂×#10596831	—	2	1	no	—
24	C₄⋊Dic₇₃	—	2	2	no	—
25	C₄⋊Dic₇₃	—	2	2	no	—
26	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
27	M₁₆×C₇₃	—	2	2	no	—
28	M₁₆×C₇₃	—	2	2	no	—
29	C₂×C₈×C₇₃	—	2	2	no	—
30	C₂×C₈×C₇₃	—	2	2	no	—
31	C₂×C₈×C₇₃	D₄	1	2	yes	—
32	C₂³×C₇₃	#41	1	1	yes	characteristic
33	C₂²×D₇₃	—	2	1	no	—
34	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	#41	1	2	yes	—
37	C₂×C₄×C₇₃	#41	1	2	yes	—
38	C₂²⋊D₇₃	—	4	2	no	—
39	C₂×Dic₇₃	—	2	1	no	—
40	C₂×Dic₇₃	—	4	2	no	—
41	C₂×Dic₇₃	—	8	2	no	—
42	D₂₉₂	—	2	2	no	—
43	C₄×D₇₃	—	4	1	no	—
44	C₄×D₇₃	—	4	1	no	—
45	Dic₁₄₆	—	2	2	no	—
46	C₈×C₇₃	—	2	2	no	—
47	C₈×C₇₃	—	4	2	no	—
48	#10596831	—	4	1	no	—
49	C₂²×C₇₃	—	2	2	no	—
50	C₂²×C₇₃	#121	1	1	yes	characteristic
51	C₂²×C₇₃	#126	1	2	yes	—
52	C₂×D₇₃	—	4	1	no	—
53	C₂×D₇₃	—	4	2	no	—
54	C₄×C₇₃	#123	1	2	yes	—
55	C₄×C₇₃	#123	1	1	yes	characteristic
56	C₄×C₇₃	#124	1	1	yes	characteristic
57	Dic₇₃	—	4	1	no	—
58	Dic₇₃	—	8	2	no	—
59	C₂×C₇₃	—	2	2	no	—
60	C₂×C₇₃	#397	1	1	yes	characteristic
61	C₂×C₇₃	#471	1	2	yes	—
62	D₇₃	—	8	1	no	—
63	#2079	—	73	1	no	maximal, Sylow
64	C₇₃	#2079	1	1	yes	characteristic, complemented, Sylow
65	C₂×#106	—	73	1	no	—
66	#417	—	73	2	no	—
67	#408	—	73	1	no	—
68	#343	—	73	2	no	—
69	#341	D₇₃	1	1	yes	characteristic, complemented
70	C₂×#41	—	73	1	no	—
71	C₂×M₁₆	—	73	1	no	—
72	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
73	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
74	C₂×C₄⋊C₄	—	73	2	no	—
75	#106	—	146	2	no	—
76	#103	—	146	2	no	—
77	#102	—	146	2	no	—
78	C₂²⋊C₈	—	146	2	no	—
79	#41	—	146	2	no	—
80	#41	—	146	2	no	—
81	C₂×Q₈	—	73	1	no	—
82	C₂×D₄	—	73	1	no	—
83	C₂×D₄	—	146	1	no	—
84	C₂²×C₄	—	146	1	no	—
85	C₂²×C₄	—	146	2	no	—
86	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
87	M₁₆	—	2	2	no	—
88	M₁₆	—	2	2	no	—
89	M₁₆	—	146	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	146	1	no	—
93	C₂×C₈	D₂₉₂	1	2	yes	—
94	C₄⋊C₄	—	146	2	no	—
95	C₄⋊C₄	—	146	2	no	—
96	C₂³	—	146	1	no	—
97	C₂³	#11924029	1	1	yes	characteristic
98	Q₈	—	146	2	no	—
99	D₄	—	292	2	no	—
100	D₄	—	146	2	no	—
101	C₂×C₄	—	292	1	no	—
102	C₂×C₄	—	292	1	no	—
103	C₂×C₄	—	292	2	no	—
104	C₂×C₄	—	584	2	no	—
105	C₂×C₄	—	146	1	no	—
106	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
107	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
108	C₂×C₄	#11924027	1	2	yes	—
109	C₂×C₄	#11924028	1	2	yes	—
110	C₈	—	2	2	no	—
111	C₈	—	4	2	no	—
112	C₈	—	292	1	no	—
113	C₂²	—	2	2	no	—
114	C₂²	—	292	1	no	—
115	C₂²	—	292	2	no	—
116	C₂²	#14556566	1	1	yes	characteristic
117	C₂²	#14556586	1	2	yes	—
118	C₄	—	292	1	no	—
119	C₄	—	584	2	no	—
120	C₄	#14556573	1	2	yes	—
121	C₄	#14556575	1	1	yes	characteristic
122	C₄	#14556579	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	584	1	no	—
125	C₂	#17988514	1	1	yes	characteristic
126	C₂	#17988851	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556523

C₂

yes

maximal, characteristic, complemented

#17988589

C₂

yes

maximal

#17988553

C₂

yes

maximal, characteristic

#17988355

C₂

yes

maximal, complemented

#341×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924028

C₂²

yes

characteristic

C₂×#11924012

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

—

—

—

—

—

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#11924028

—

#11924028

—

C₂×Dic₁₄₆

D₄

yes

characteristic

C₂×D₂₉₂

D₄

yes

characteristic

C₂×C₂²⋊D₇₃

—

C₂²×Dic₇₃

—

C₂×C₄×D₇₃

—

#11924012

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₂³×C₇₃

#41

yes

characteristic

C₂²×D₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#121

yes

characteristic

C₂²×C₇₃

#126

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

#123

yes

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#397

yes

characteristic

C₂×C₇₃

#471

yes

—

D₇₃

—

#2079

—

maximal, Sylow

C₇₃

#2079

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₃

yes

characteristic, complemented

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

#106

—

146

—

#103

—

146

—

#102

—

146

—

C₂²⋊C₈

—

146

—

#41

—

146

—

#41

—

146

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

D₂₉₂

yes

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₂³

—

146

—

C₂³

#11924029

yes

characteristic

Q₈

—

146

—

D₄

—

292

—

100

D₄

—

146

—

101

C₂×C₄

—

292

—

102

C₂×C₄

—

292

—

103

C₂×C₄

—

292

—

104

C₂×C₄

—

584

—

105

C₂×C₄

—

146

—

106

C₂×C₄

D₄×D₇₃

yes

characteristic

107

C₂×C₄

C₂×D₂₉₂

yes

characteristic

108

C₂×C₄

#11924027

yes

—

109

C₂×C₄

#11924028

yes

—

110

C₈

—

111

C₈

—

112

C₈

—

292

—

113

C₂²

—

114

C₂²

—

292

—

115

C₂²

—

292

—

116

C₂²

#14556566

yes

characteristic

117

C₂²

#14556586

yes

—

118

C₄

—

292

—

119

C₄

—

584

—

120

C₄

#14556573

yes

—

121

C₄

#14556575

yes

characteristic

122

C₄

#14556579

yes

characteristic

123

C₂

—

124

C₂

—

584

—

125

C₂

#17988514

yes

characteristic

126

C₂

#17988851

yes

—

	subgroup	G/H
center	C₂²	#14556566
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#341×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#341	D₇₃
hypocenter	C₇₃	#2079
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#14556566

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#341×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
1. C₂×#14556523	C₂	semidirect
4. #17988355	C₂	semidirect
5. #341×C₇₃	C₂	semidirect
64. C₇₃	#2079	semidirect
69. #341	D₇₃	semidirect

H ≅ G/N

type

1. C₂×#14556523

C₂

semidirect

4. #17988355

C₂

semidirect

5. #341×C₇₃

C₂

semidirect

64. C₇₃

#2079

semidirect

69. #341

D₇₃

semidirect

Subgroups — #22611378

Conjugacy classes of subgroups

Complements