Group #22611196 — subgroups

Subgroups — #22611196

Order 9344.

256 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 71 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	#17988613	C₂	1	1	yes	maximal, characteristic
2	#17988596	C₂	1	2	yes	maximal
3	C₂×#14556510	C₂	1	2	yes	maximal
4	#17988352	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₁₆×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	#14556520	—	2	2	no	—
10	#14556515	—	2	4	no	—
11	#14556510	—	2	4	no	—
12	C₂²×Q₈×C₇₃	C₂²	1	2	yes	—
13	C₂×Q₁₆×C₇₃	—	2	4	no	—
14	C₂×Q₁₆×C₇₃	—	2	2	no	—
15	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	#11924012	—	2	2	no	—
17	#11924012	—	2	2	no	—
18	#11924012	—	2	2	no	—
19	C₂×#10596831	—	2	2	no	—
20	C₂×#10596831	—	2	1	no	—
21	C₄⋊Dic₇₃	D₄	1	2	yes	—
22	C₂²⋊Dic₇₃	—	2	1	no	—
23	C₄×Dic₇₃	—	2	1	no	—
24	C₂×Q₈×C₇₃	—	2	2	no	—
25	C₂×Q₈×C₇₃	—	2	2	no	—
26	C₂×Q₈×C₇₃	—	2	2	no	—
27	C₂×Q₈×C₇₃	—	2	2	no	—
28	C₂×Q₈×C₇₃	—	2	2	no	—
29	C₂×Q₈×C₇₃	D₄	1	4	yes	—
30	C₂²×C₄×C₇₃	—	2	2	no	—
31	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
32	Q₁₆×C₇₃	—	2	8	no	—
33	C₂×C₈×C₇₃	—	2	2	no	—
34	C₂×C₈×C₇₃	D₄	1	2	yes	—
35	C₂³×C₇₃	#41	1	1	yes	characteristic
36	Q₈×C₇₃	—	2	4	no	—
37	Q₈×C₇₃	—	2	4	no	—
38	Q₈×C₇₃	—	4	2	no	—
39	Q₈×C₇₃	—	4	2	no	—
40	C₂×C₄×C₇₃	—	2	4	no	—
41	C₂×C₄×C₇₃	—	4	2	no	—
42	C₂×C₄×C₇₃	—	4	2	no	—
43	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₇₃	#41	1	2	yes	—
47	C₂×Dic₇₃	—	2	2	no	—
48	C₈×C₇₃	—	2	2	no	—
49	#10596831	—	4	1	no	—
50	#10596831	—	4	2	no	—
51	C₂²×C₇₃	—	2	2	no	—
52	C₂²×C₇₃	#121	1	1	yes	characteristic
53	C₂²×C₇₃	#123	1	2	yes	—
54	C₄×C₇₃	—	4	4	no	—
55	C₄×C₇₃	#120	1	1	yes	characteristic
56	C₄×C₇₃	#121	1	2	yes	—
57	C₄×C₇₃	#124	1	1	yes	characteristic
58	Dic₇₃	—	4	2	no	—
59	C₂×C₇₃	—	2	2	no	—
60	C₂×C₇₃	#394	1	1	yes	characteristic
61	C₂×C₇₃	#473	1	2	yes	—
62	#2047	—	73	1	no	maximal, Sylow
63	C₇₃	#2047	1	1	yes	characteristic, complemented, Sylow
64	C₂²×Q₁₆	D₇₃	1	1	yes	characteristic
65	#424	—	73	1	no	—
66	#419	—	73	2	no	—
67	C₂×#101	—	73	2	no	—
68	#341	—	73	1	no	—
69	C₂²×Q₈	C₂×D₇₃	1	2	yes	—
70	C₂×Q₁₆	—	2	4	no	—
71	C₂×Q₁₆	—	2	2	no	—
72	C₂×M₁₆	—	73	2	no	—
73	C₂×M₁₆	—	73	1	no	—
74	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
75	#117	—	73	1	no	—
76	C₄⋊C₈	—	146	2	no	—
77	#103	—	146	4	no	—
78	#101	—	146	4	no	—
79	C₂×Q₈	—	2	2	no	—
80	C₂×Q₈	—	2	2	no	—
81	C₂×Q₈	—	2	2	no	—
82	C₂×Q₈	—	2	2	no	—
83	C₂×Q₈	—	2	2	no	—
84	C₂×Q₈	C₂²⋊D₇₃	1	4	yes	—
85	C₂²×C₄	—	2	2	no	—
86	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
87	Q₁₆	—	2	8	no	—
88	M₁₆	—	146	2	no	—
89	M₁₆	—	146	2	no	—
90	M₁₆	—	146	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	146	2	no	—
93	C₂×C₈	—	146	1	no	—
94	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
95	C₄⋊C₄	—	73	2	no	—
96	C₂²⋊C₄	—	146	1	no	—
97	C₄²	—	146	1	no	—
98	C₂³	#11924027	1	1	yes	characteristic
99	Q₈	—	2	4	no	—
100	Q₈	—	2	4	no	—
101	Q₈	—	4	2	no	—
102	Q₈	—	4	2	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	4	2	no	—
106	C₂×C₄	—	146	2	no	—
107	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
108	C₂×C₄	C₂×C₂²⋊D₇₃	1	2	yes	—
109	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
110	C₂×C₄	#11924027	1	2	yes	—
111	C₈	—	2	2	no	—
112	C₈	—	292	1	no	—
113	C₈	—	292	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	#14556562	1	1	yes	characteristic
116	C₂²	#14556572	1	2	yes	—
117	C₄	—	4	4	no	—
118	C₄	—	292	2	no	—
119	C₄	#14556560	1	1	yes	characteristic
120	C₄	#14556563	1	2	yes	—
121	C₄	#14556578	1	1	yes	characteristic
122	C₂	—	2	2	no	—
123	C₂	#17988501	1	1	yes	characteristic
124	C₂	#17988859	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988613

C₂

yes

maximal, characteristic

#17988596

C₂

yes

maximal

C₂×#14556510

C₂

yes

maximal

#17988352

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

C₂×#11924012

C₂²

yes

characteristic

#14556550

C₂²

yes

—

—

—

C₂²×Q₈×C₇₃

C₂²

yes

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂²×C₈×C₇₃

C₂²

yes

—

—

—

—

—

C₄⋊Dic₇₃

D₄

yes

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₂³×C₇₃

#41

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#121

yes

characteristic

C₂²×C₇₃

#123

yes

—

C₄×C₇₃

—

C₄×C₇₃

#120

yes

characteristic

C₄×C₇₃

#121

yes

—

C₄×C₇₃

#124

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#394

yes

characteristic

C₂×C₇₃

#473

yes

—

#2047

—

maximal, Sylow

C₇₃

#2047

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

D₇₃

yes

—

—

—

—

C₂²×Q₈

C₂×D₇₃

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

#117

—

C₄⋊C₈

—

146

—

#103

—

146

—

#101

—

146

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₇₃

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

Q₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂²⋊D₇₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

146

—

C₄²

—

146

—

C₂³

#11924027

yes

characteristic

Q₈

—

100

Q₈

—

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

146

—

107

C₂×C₄

D₄×D₇₃

yes

characteristic

108

C₂×C₄

C₂×C₂²⋊D₇₃

yes

—

109

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

110

C₂×C₄

#11924027

yes

—

111

C₈

—

112

C₈

—

292

—

113

C₈

—

292

—

114

C₂²

—

115

C₂²

#14556562

yes

characteristic

116

C₂²

#14556572

yes

—

117

C₄

—

118

C₄

—

292

—

119

C₄

#14556560

yes

characteristic

120

C₄

#14556563

yes

—

121

C₄

#14556578

yes

characteristic

122

C₂

—

123

C₂

#17988501

yes

characteristic

124

C₂

#17988859

yes

—

	subgroup	G/H
center	C₂²	#14556562
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂²×Q₁₆×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	C₂²×Q₁₆	D₇₃
hypocenter	C₇₃	#2047
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂²

#14556562

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂²×Q₁₆×C₇₃

C₂

socle

C₂²×C₇₃

#121

hypercenter

C₂²×Q₁₆

D₇₃

hypocenter

C₇₃

#2047

LCS

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
63. C₇₃	#2047	semidirect

H ≅ G/N

type

63. C₇₃

#2047

semidirect

Subgroups — #22611196

Conjugacy classes of subgroups

Complements