Group #22610104 — subgroups

Subgroups — #22610104

Order 9344.

212 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14556527	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556526	C₂	1	2	yes	maximal
3	#17988610	C₂	1	2	yes	maximal
4	C₂×#14556501	C₂	1	1	yes	maximal, characteristic
5	C₂×#108×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	C₂²	1	2	yes	—
7	C₂²×#10596831	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
9	#14556527	—	2	2	no	—
10	#14556526	—	2	4	no	—
11	#14556520	—	2	4	no	—
12	#14556501	C₄	1	4	yes	—
13	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
14	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	#108×C₇₃	—	2	2	no	—
16	C₂²×Dic₇₃	Q₈	1	2	yes	—
17	#11924012	—	2	2	no	—
18	#11924012	—	2	2	no	—
19	C₂×#10596831	—	2	2	no	—
20	C₂×#10596831	C₂×C₄	1	2	yes	—
21	C₂×#10596831	D₄	1	2	yes	—
22	C₂×#10596831	Q₈	1	2	yes	—
23	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
24	C₄×Dic₇₃	D₄	1	2	yes	—
25	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
26	M₁₆×C₇₃	—	2	2	no	—
27	M₁₆×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	—	2	2	no	—
29	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₇₃	D₄	1	2	yes	—
31	C₂×C₈×C₇₃	Q₈	1	2	yes	—
32	C₂³×C₇₃	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
39	C₂×Dic₇₃	—	4	2	no	—
40	C₂×Dic₇₃	C₄⋊C₄	1	4	yes	—
41	C₈×C₇₃	—	4	2	no	—
42	C₈×C₇₃	C₄⋊C₄	1	4	yes	—
43	#10596831	—	4	2	no	—
44	#10596831	C₄⋊C₄	1	4	yes	—
45	C₂²×C₇₃	—	2	2	no	—
46	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
48	C₂²×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
49	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₇₃	#127	1	1	yes	characteristic
52	C₄×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
53	Dic₇₃	—	2	4	no	—
54	C₂×C₇₃	—	2	1	no	—
55	C₂×C₇₃	—	2	1	no	—
56	C₂×C₇₃	#384	1	1	yes	characteristic
57	C₂×C₇₃	#430	1	2	yes	—
58	#1849	—	73	1	no	maximal, Sylow
59	C₇₃	#1849	1	1	yes	characteristic, complemented, Sylow
60	C₂×#108	—	73	2	no	—
61	C₂×#108	—	73	1	no	—
62	C₂×#108	D₇₃	1	1	yes	characteristic
63	#423	—	73	2	no	—
64	C₂×#97	—	73	1	no	—
65	C₂×M₁₆	—	73	2	no	—
66	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
67	C₂²×C₈	—	73	1	no	—
68	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
69	C₂×C₄²	—	73	1	no	—
70	#108	—	2	2	no	—
71	#108	—	146	4	no	—
72	#108	—	146	2	no	—
73	C₄⋊C₈	—	146	4	no	—
74	#97	—	73	4	no	—
75	C₂²×C₄	—	73	2	no	—
76	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
77	M₁₆	—	2	2	no	—
78	M₁₆	—	2	2	no	—
79	M₁₆	—	146	2	no	—
80	M₁₆	—	146	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	73	2	no	—
83	C₂×C₈	—	73	2	no	—
84	C₂×C₈	—	73	2	no	—
85	C₂×C₈	—	146	2	no	—
86	C₂×C₈	Dic₁₄₆	1	2	yes	—
87	C₂×C₈	C₄×D₇₃	1	2	yes	—
88	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
89	C₄²	—	73	2	no	—
90	C₄²	—	73	2	no	—
91	C₂³	Q₈×D₇₃	1	1	yes	characteristic
92	C₂×C₄	—	292	2	no	—
93	C₂×C₄	—	73	4	no	—
94	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
95	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
96	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
97	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
98	C₂×C₄	Q₈×D₇₃	1	1	yes	characteristic
99	C₂×C₄	C₂×Dic₁₄₆	1	1	yes	characteristic
100	C₈	—	4	2	no	—
101	C₈	—	292	2	no	—
102	C₈	—	73	4	no	—
103	C₈	#11924007	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	C₄⋊C₄×D₇₃	1	1	yes	characteristic
106	C₂²	#14556589	1	1	yes	characteristic
107	C₂²	#14556590	1	1	yes	characteristic
108	C₄	—	146	4	no	—
109	C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
110	C₄	C₂×#11924007	1	1	yes	characteristic
111	C₄	#14556587	1	1	yes	characteristic
112	C₄	#14556590	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#17988456	1	1	yes	characteristic
116	C₂	#17988634	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556527

C₂

yes

maximal, characteristic

C₂×#14556526

C₂

yes

maximal

#17988610

C₂

yes

maximal

C₂×#14556501

C₂

yes

maximal, characteristic

C₂×#108×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

C₂²×#10596831

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

—

—

—

C₄

yes

—

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#108×C₇₃

—

C₂²×Dic₇₃

Q₈

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#10596831

D₄

yes

—

C₂×#10596831

Q₈

yes

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

D₄

yes

—

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×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₈×C₇₃

—

C₈×C₇₃

C₄⋊C₄

yes

—

#10596831

—

#10596831

C₄⋊C₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₃

C₄⋊Q₈

yes

characteristic

C₂²×C₇₃

C₄⋊Q₈

yes

characteristic

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

#127

yes

characteristic

C₄×C₇₃

C₄⋊Q₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#384

yes

characteristic

C₂×C₇₃

#430

yes

—

#1849

—

maximal, Sylow

C₇₃

#1849

yes

characteristic, complemented, Sylow

C₂×#108

—

C₂×#108

—

C₂×#108

D₇₃

yes

characteristic

#423

—

C₂×#97

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₂×C₄²

—

#108

—

#108

—

146

—

#108

—

146

—

C₄⋊C₈

—

146

—

#97

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

Dic₁₄₆

yes

—

C₂×C₈

C₄×D₇₃

yes

—

C₂×C₈

C₂²⋊D₇₃

yes

—

C₄²

—

C₄²

—

C₂³

Q₈×D₇₃

yes

characteristic

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

C₂×C₄

D₄×D₇₃

yes

characteristic

C₂×C₄

D₄×D₇₃

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₂×C₄

Q₈×D₇₃

yes

characteristic

C₂×C₄

C₂×Dic₁₄₆

yes

characteristic

100

C₈

—

101

C₈

—

292

—

102

C₈

—

103

C₈

#11924007

yes

—

104

C₂²

—

105

C₂²

C₄⋊C₄×D₇₃

yes

characteristic

106

C₂²

#14556589

yes

characteristic

107

C₂²

#14556590

yes

characteristic

108

C₄

—

146

—

109

C₄

C₄⋊C₄×D₇₃

yes

characteristic

110

C₄

C₂×#11924007

yes

characteristic

111

C₄

#14556587

yes

characteristic

112

C₄

#14556590

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#17988456

yes

characteristic

116

C₂

#17988634

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂×#108×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	C₂×#108	D₇₃
hypocenter	C₇₃	#1849
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂×#108×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₄⋊C₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
59. C₇₃	#1849	semidirect

H ≅ G/N

type

59. C₇₃

#1849

semidirect

Subgroups — #22610104

Conjugacy classes of subgroups

Complements