Group #22611820 — subgroups

Subgroups — #22611820

Order 9344.

142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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	#17989028	C₂	1	1	yes	maximal, characteristic
2	#17988710	C₂	1	1	yes	maximal, characteristic
3	#17988409	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988403	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988396	C₂	1	1	yes	maximal, characteristic
6	#17988365	C₂	1	1	yes	maximal, characteristic, complemented
7	#441×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#14556613	C₂²	1	1	yes	characteristic
9	#14556597	—	2	1	no	—
10	#14556537	C₄	1	2	yes	complemented
11	#14556534	C₄	1	2	yes	complemented
12	#14556531	C₂²	1	1	yes	characteristic
13	#14556531	C₂²	1	1	yes	characteristic
14	#14556527	C₂²	1	1	yes	characteristic
15	#14556519	—	2	1	no	—
16	C₂×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₄×Q₈×C₇₃	—	2	1	no	—
18	#106×C₇₃	C₂²	1	1	yes	characteristic
19	#103×C₇₃	—	2	1	no	—
20	#97×C₇₃	C₂²	1	1	yes	characteristic
21	#11924028	—	2	1	no	—
22	Dic₂₉₂	C₂×C₄	1	1	yes	characteristic
23	#11924017	—	2	1	no	—
24	D₅₈₄	C₂×C₄	1	1	yes	characteristic
25	#11924012	—	2	1	no	—
26	#11924011	—	4	1	no	—
27	C₈×D₇₃	—	4	1	no	—
28	#11924003	—	2	1	no	—
29	#11924003	C₂×C₄	1	2	yes	—
30	C₂×Q₈×C₇₃	—	2	1	no	—
31	Q₁₆×C₇₃	—	2	1	no	—
32	Q₁₆×C₇₃	C₂×C₄	1	2	yes	—
33	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
34	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
35	C₄⋊C₄×C₇₃	—	2	1	no	—
36	C₄⋊C₄×C₇₃	—	4	1	no	—
37	C₄²×C₇₃	—	4	1	no	—
38	C₄²×C₇₃	D₄	1	1	yes	characteristic
39	Q₈×C₇₃	—	2	2	no	—
40	Q₈×C₇₃	—	4	1	no	—
41	C₂×C₄×C₇₃	—	2	1	no	—
42	C₂×C₄×C₇₃	—	4	1	no	—
43	C₂×C₄×C₇₃	—	4	1	no	—
44	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
45	C₂²⋊D₇₃	—	4	1	no	—
46	D₂₉₂	—	2	1	no	—
47	C₄×D₇₃	—	4	1	no	—
48	Dic₁₄₆	—	2	1	no	—
49	C₈×C₇₃	—	2	1	no	—
50	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
51	C₈×C₇₃	#41	1	1	yes	characteristic
52	#10596831	—	4	1	no	—
53	C₂²×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
54	C₂×D₇₃	—	4	1	no	—
55	C₄×C₇₃	—	4	1	no	—
56	C₄×C₇₃	—	4	2	no	—
57	C₄×C₇₃	—	8	1	no	—
58	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
59	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
60	Dic₇₃	—	4	1	no	—
61	C₂×C₇₃	—	2	1	no	—
62	C₂×C₇₃	#442	1	1	yes	characteristic
63	D₇₃	—	8	1	no	—
64	#2180	—	73	1	no	maximal, Sylow
65	C₇₃	#2180	1	1	yes	characteristic, complemented, Sylow
66	#510	—	73	1	no	—
67	#444	—	73	1	no	—
68	#441	D₇₃	1	1	yes	characteristic, complemented
69	#365	—	73	1	no	—
70	#362	—	73	1	no	—
71	#360	—	73	1	no	—
72	#347	—	73	1	no	—
73	#135	—	73	1	no	—
74	C₂×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
75	#131	—	146	1	no	—
76	C₄×Q₈	—	2	1	no	—
77	Q₃₂	—	73	2	no	—
78	SD₃₂	—	73	2	no	—
79	M₃₂	—	73	1	no	—
80	M₃₂	—	73	1	no	—
81	#108	—	73	1	no	—
82	#106	C₂×D₇₃	1	1	yes	characteristic
83	#104	—	146	1	no	—
84	#103	—	2	1	no	—
85	#97	C₂×D₇₃	1	1	yes	characteristic
86	#41	—	146	1	no	—
87	C₂×Q₈	—	2	1	no	—
88	Q₁₆	—	2	1	no	—
89	Q₁₆	—	73	1	no	—
90	Q₁₆	C₄×D₇₃	1	2	yes	—
91	SD₁₆	—	146	1	no	—
92	D₈	—	73	1	no	—
93	M₁₆	—	292	1	no	—
94	M₁₆	—	146	1	no	—
95	C₂×C₈	—	292	1	no	—
96	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
97	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
98	C₄⋊C₄	—	2	1	no	—
99	C₄⋊C₄	—	4	1	no	—
100	C₄²	—	4	1	no	—
101	C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
102	C₁₆	—	73	2	no	—
103	C₁₆	—	146	1	no	—
104	Q₈	—	2	2	no	—
105	Q₈	—	4	1	no	—
106	Q₈	—	146	1	no	—
107	D₄	—	292	1	no	—
108	D₄	—	146	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	4	1	no	—
112	C₂×C₄	—	292	1	no	—
113	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
114	C₈	—	2	1	no	—
115	C₈	—	292	1	no	—
116	C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
117	C₈	#11924028	1	1	yes	characteristic
118	C₂²	—	292	1	no	—
119	C₂²	#14556617	1	1	yes	characteristic
120	C₄	—	4	1	no	—
121	C₄	—	4	2	no	—
122	C₄	—	8	1	no	—
123	C₄	—	292	1	no	—
124	C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
125	C₄	#14556616	1	1	yes	characteristic
126	C₂	—	2	1	no	—
127	C₂	—	584	1	no	—
128	C₂	#17988697	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989028

C₂

yes

maximal, characteristic

#17988710

C₂

yes

maximal, characteristic

#17988409

C₂

yes

maximal, characteristic, complemented

#17988403

C₂

yes

maximal, characteristic, complemented

#17988396

C₂

yes

maximal, characteristic

#17988365

C₂

yes

maximal, characteristic, complemented

#441×C₇₃

C₂

yes

maximal, characteristic, complemented

#14556613

C₂²

yes

characteristic

#14556597

—

#14556537

C₄

yes

complemented

#14556534

C₄

yes

complemented

#14556531

C₂²

yes

characteristic

#14556531

C₂²

yes

characteristic

#14556527

C₂²

yes

characteristic

#14556519

—

C₂×Q₁₆×C₇₃

C₂²

yes

characteristic

C₄×Q₈×C₇₃

—

#106×C₇₃

C₂²

yes

characteristic

#103×C₇₃

—

#97×C₇₃

C₂²

yes

characteristic

#11924028

—

Dic₂₉₂

C₂×C₄

yes

characteristic

#11924017

—

D₅₈₄

C₂×C₄

yes

characteristic

#11924012

—

#11924011

—

C₈×D₇₃

—

#11924003

—

#11924003

C₂×C₄

yes

—

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²⋊D₇₃

—

D₂₉₂

—

C₄×D₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

C₂²×C₄

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

AGL(1,ℤ/8)

yes

characteristic

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

AGL(1,ℤ/8)

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#442

yes

characteristic

D₇₃

—

#2180

—

maximal, Sylow

C₇₃

#2180

yes

characteristic, complemented, Sylow

#510

—

#444

—

#441

D₇₃

yes

characteristic, complemented

—

—

—

—

—

C₂×Q₁₆

C₂×D₇₃

yes

characteristic

#131

—

146

—

C₄×Q₈

—

Q₃₂

—

SD₃₂

—

M₃₂

—

M₃₂

—

#108

—

#106

C₂×D₇₃

yes

characteristic

#104

—

146

—

#103

—

#97

C₂×D₇₃

yes

characteristic

#41

—

146

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

C₄×D₇₃

yes

—

SD₁₆

—

146

—

D₈

—

M₁₆

—

292

—

M₁₆

—

146

—

C₂×C₈

—

292

—

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄²

—

101

C₄²

C₂²⋊D₇₃

yes

characteristic

102

C₁₆

—

103

C₁₆

—

146

—

104

Q₈

—

105

Q₈

—

106

Q₈

—

146

—

107

D₄

—

292

—

108

D₄

—

146

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

292

—

113

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

114

C₈

—

115

C₈

—

292

—

116

C₈

C₂×C₄×D₇₃

yes

characteristic

117

C₈

#11924028

yes

characteristic

118

C₂²

—

292

—

119

C₂²

#14556617

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

292

—

124

C₄

C₄×C₂²⋊D₇₃

yes

characteristic

125

C₄

#14556616

yes

characteristic

126

C₂

—

127

C₂

—

584

—

128

C₂

#17988697

yes

characteristic

	subgroup	G/H
center	C₂	#17988697
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#441×C₇₃	C₂
socle	C₂×C₇₃	#442
hypercenter	#441	D₇₃
hypocenter	C₇₃	#2180
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #441

subgroup

G/H

center

C₂

#17988697

commutator

C₈×C₇₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#441×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #441

N	H ≅ G/N	type
3. #17988409	C₂	semidirect
4. #17988403	C₂	semidirect
6. #17988365	C₂	semidirect
7. #441×C₇₃	C₂	semidirect
10. #14556537	C₄	semidirect
11. #14556534	C₄	semidirect
65. C₇₃	#2180	semidirect
68. #441	D₇₃	semidirect

H ≅ G/N

type

3. #17988409

C₂

semidirect

4. #17988403

C₂

semidirect

6. #17988365

C₂

semidirect

7. #441×C₇₃

C₂

semidirect

10. #14556537

C₄

semidirect

11. #14556534

C₄

semidirect

65. C₇₃

#2180

semidirect

68. #441

D₇₃

semidirect

Subgroups — #22611820

Conjugacy classes of subgroups

Complements