Group #22610719 — subgroups

Subgroups — #22610719

Order 9344.

184 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 85 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	#17988635	C₂	1	2	yes	maximal
2	C₂×#14556527	C₂	1	1	yes	maximal, characteristic
3	#17988542	C₂	1	1	yes	maximal, characteristic
4	#17988358	C₂	1	2	yes	maximal
5	C₂×#108×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	C₂²	1	2	yes	—
7	C₂×#11924012	C₂²	1	1	yes	characteristic
8	#14556550	C₂²	1	1	yes	characteristic
9	#14556527	C₄	1	4	yes	complemented
10	#14556526	—	2	4	no	—
11	#14556501	—	2	1	no	—
12	C₈×Dic₇₃	—	2	1	no	—
13	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
14	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	#108×C₇₃	—	2	1	no	—
16	#108×C₇₃	—	2	1	no	—
17	#11924012	—	2	1	no	—
18	#11924012	—	2	2	no	—
19	#11924012	C₂×C₄	1	4	yes	—
20	#11924012	D₄	1	2	yes	—
21	C₂×#10596831	—	2	1	no	—
22	C₂×#10596831	—	2	2	no	—
23	C₄⋊Dic₇₃	—	2	1	no	—
24	C₂²⋊Dic₇₃	Q₈	1	2	yes	—
25	C₄×Dic₇₃	—	2	1	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	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
32	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
33	C₂×C₈×C₇₃	Q₈	1	2	yes	—
34	C₂³×C₇₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
40	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
41	C₂×Dic₇₃	—	2	2	no	—
42	C₈×C₇₃	—	4	2	no	—
43	C₈×C₇₃	C₄⋊C₄	1	2	yes	—
44	C₈×C₇₃	C₄⋊C₄	1	2	yes	—
45	#10596831	—	2	4	no	—
46	#10596831	—	2	2	no	—
47	C₂²×C₇₃	—	4	1	no	—
48	C₂²×C₇₃	C₄×Q₈	1	1	yes	characteristic
49	C₂²×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
51	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
53	C₄×C₇₃	#121	1	1	yes	characteristic
54	C₄×C₇₃	#125	1	1	yes	characteristic
55	Dic₇₃	—	4	2	no	—
56	C₂×C₇₃	—	2	1	no	—
57	C₂×C₇₃	—	2	1	no	—
58	C₂×C₇₃	—	2	1	no	—
59	C₂×C₇₃	#389	1	1	yes	characteristic
60	#1953	—	73	1	no	maximal, Sylow
61	C₇₃	#1953	1	1	yes	characteristic, complemented, Sylow
62	#430	—	73	2	no	—
63	C₂×#108	—	73	1	no	—
64	C₂×#108	D₇₃	1	1	yes	characteristic
65	#405	—	73	1	no	—
66	#344	—	73	2	no	—
67	C₂×M₁₆	—	73	2	no	—
68	C₂×M₁₆	—	73	1	no	—
69	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
70	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
71	#117	—	73	1	no	—
72	#108	—	2	1	no	—
73	#108	—	2	1	no	—
74	#108	—	73	4	no	—
75	#108	—	146	4	no	—
76	#97	—	146	1	no	—
77	C₄×C₈	—	146	1	no	—
78	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
79	M₁₆	—	2	2	no	—
80	M₁₆	—	2	2	no	—
81	M₁₆	—	73	4	no	—
82	M₁₆	—	73	2	no	—
83	M₁₆	—	146	1	no	—
84	M₁₆	—	146	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	146	2	no	—
87	C₂×C₈	—	146	1	no	—
88	C₂×C₈	Dic₁₄₆	1	2	yes	—
89	C₂×C₈	C₄×D₇₃	1	2	yes	—
90	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
91	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
92	C₄⋊C₄	—	146	1	no	—
93	C₂²⋊C₄	—	73	2	no	—
94	C₄²	—	146	1	no	—
95	C₂³	Q₈×D₇₃	1	1	yes	characteristic
96	C₂×C₄	—	146	2	no	—
97	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
98	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
99	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
100	C₂×C₄	C₂×Dic₁₄₆	1	1	yes	characteristic
101	C₂×C₄	#11924027	1	1	yes	characteristic
102	C₂×C₄	#11924029	1	1	yes	characteristic
103	C₈	—	4	2	no	—
104	C₈	—	146	4	no	—
105	C₈	—	146	2	no	—
106	C₈	#11924007	1	2	yes	—
107	C₈	#11924007	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	#14556556	1	1	yes	characteristic
110	C₂²	#14556567	1	1	yes	characteristic
111	C₂²	#14556590	1	1	yes	characteristic
112	C₄	—	292	2	no	—
113	C₄	C₂×#11924007	1	1	yes	characteristic
114	C₄	#14556553	1	1	yes	characteristic
115	C₄	#14556562	1	1	yes	characteristic
116	C₄	#14556582	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	1	no	—
119	C₂	—	2	1	no	—
120	C₂	#17988483	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988635

C₂

yes

maximal

C₂×#14556527

C₂

yes

maximal, characteristic

#17988542

C₂

yes

maximal, characteristic

#17988358

C₂

yes

maximal

C₂×#108×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

C₂×#11924012

C₂²

yes

characteristic

#14556550

C₂²

yes

characteristic

#14556527

C₄

yes

complemented

#14556526

—

#14556501

—

C₈×Dic₇₃

—

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#108×C₇₃

—

#108×C₇₃

—

#11924012

—

#11924012

—

#11924012

C₂×C₄

yes

—

#11924012

D₄

yes

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

Q₈

yes

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

Q₈

yes

—

C₂³×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×Dic₇₃

—

C₈×C₇₃

—

C₈×C₇₃

C₄⋊C₄

yes

—

C₈×C₇₃

C₄⋊C₄

yes

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄×Q₈

yes

characteristic

C₂²×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₇₃

C₄⋊Q₈

yes

characteristic

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

C₄×D₄

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#430

—

C₂×#108

—

C₂×#108

D₇₃

yes

characteristic

#405

—

#344

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₂²×C₈

C₂×D₇₃

yes

—

—

—

—

—

146

—

#97

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

Dic₁₄₆

yes

—

C₂×C₈

C₄×D₇₃

yes

—

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

C₄²

—

146

—

C₂³

Q₈×D₇₃

yes

characteristic

C₂×C₄

—

146

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

C₂×C₄

D₄×D₇₃

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

100

C₂×C₄

C₂×Dic₁₄₆

yes

characteristic

101

C₂×C₄

#11924027

yes

characteristic

102

C₂×C₄

#11924029

yes

characteristic

103

C₈

—

104

C₈

—

146

—

105

C₈

—

146

—

106

C₈

#11924007

yes

—

107

C₈

#11924007

yes

—

108

C₂²

—

109

C₂²

#14556556

yes

characteristic

110

C₂²

#14556567

yes

characteristic

111

C₂²

#14556590

yes

characteristic

112

C₄

—

292

—

113

C₄

C₂×#11924007

yes

characteristic

114

C₄

#14556553

yes

characteristic

115

C₄

#14556562

yes

characteristic

116

C₄

#14556582

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

#17988483

yes

characteristic

	subgroup	G/H
center	C₄	#14556562
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂×#108×C₇₃	C₂
socle	C₂×C₇₃	#389
hypercenter	C₂×#108	D₇₃
hypocenter	C₇₃	#1953
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₄

#14556562

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂×#108×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
9. #14556527	C₄	semidirect
61. C₇₃	#1953	semidirect

H ≅ G/N

type

9. #14556527

C₄

semidirect

61. C₇₃

#1953

semidirect

Subgroups — #22610719

Conjugacy classes of subgroups

Complements