Group #22611372 — subgroups

Subgroups — #22611372

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	#17988586	C₂	1	2	yes	maximal
2	#17988553	C₂	1	1	yes	maximal, characteristic
3	#17988356	C₂	1	2	yes	maximal, complemented
4	#17988352	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#107×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924028	C₂²	1	1	yes	characteristic
7	C₂×#11924012	C₂²	1	2	yes	—
8	C₂×#11924012	C₂²	1	1	yes	characteristic
9	#14556514	—	2	2	no	—
10	#14556511	—	2	2	no	—
11	#14556503	—	2	2	no	—
12	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
14	#107×C₇₃	—	2	2	no	—
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	C₂×C₄×D₇₃	—	2	1	no	—
21	#11924012	—	2	2	no	—
22	#11924012	—	2	2	no	—
23	#11924012	—	2	2	no	—
24	C₂×#10596831	—	2	1	no	—
25	C₂×#10596831	—	2	2	no	—
26	C₂²×C₄×C₇₃	—	2	2	no	—
27	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
28	C₂×C₈×C₇₃	—	2	2	no	—
29	C₂×C₈×C₇₃	D₄	1	2	yes	—
30	C₄⋊C₄×C₇₃	—	2	2	no	—
31	C₄⋊C₄×C₇₃	—	2	2	no	—
32	C₂³×C₇₃	#41	1	1	yes	characteristic
33	C₂²×D₇₃	—	2	1	no	—
34	C₂×C₄×C₇₃	—	4	2	no	—
35	C₂×C₄×C₇₃	—	8	2	no	—
36	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	#41	1	2	yes	—
39	C₂×C₄×C₇₃	#41	1	2	yes	—
40	C₂²⋊D₇₃	—	4	2	no	—
41	C₂×Dic₇₃	—	2	1	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	#10596831	—	4	2	no	—
48	#10596831	—	4	1	no	—
49	C₂²×C₇₃	—	2	1	no	—
50	C₂²×C₇₃	—	2	1	no	—
51	C₂²×C₇₃	#121	1	1	yes	characteristic
52	C₂²×C₇₃	#126	1	2	yes	—
53	C₂×D₇₃	—	4	1	no	—
54	C₂×D₇₃	—	4	1	no	—
55	C₂×D₇₃	—	4	1	no	—
56	C₄×C₇₃	—	8	2	no	—
57	C₄×C₇₃	#123	1	1	yes	characteristic
58	C₄×C₇₃	#123	1	2	yes	—
59	C₄×C₇₃	#124	1	1	yes	characteristic
60	Dic₇₃	—	4	1	no	—
61	C₂×C₇₃	—	2	2	no	—
62	C₂×C₇₃	#397	1	1	yes	characteristic
63	C₂×C₇₃	#472	1	1	yes	characteristic
64	C₂×C₇₃	#473	1	1	yes	characteristic
65	D₇₃	—	8	1	no	—
66	#2078	—	73	1	no	maximal, Sylow
67	C₇₃	#2078	1	1	yes	characteristic, complemented, Sylow
68	C₂×#107	D₇₃	1	1	yes	characteristic, complemented
69	#417	—	73	2	no	—
70	#408	—	73	1	no	—
71	#343	—	73	2	no	—
72	#341	—	73	1	no	—
73	C₂×#41	—	73	1	no	—
74	C₂×M₁₆	—	73	2	no	—
75	C₂×M₁₆	—	73	1	no	—
76	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
77	C₂×C₄⋊C₄	C₂×D₇₃	1	2	yes	—
78	#107	—	2	2	no	—
79	#103	—	146	2	no	—
80	#102	—	146	2	no	—
81	C₂²⋊C₈	—	146	2	no	—
82	#41	—	146	2	no	—
83	#41	—	146	2	no	—
84	C₂×Q₈	—	73	1	no	—
85	C₂×D₄	—	73	1	no	—
86	C₂×D₄	—	146	1	no	—
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	—	146	1	no	—
89	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
90	M₁₆	—	146	2	no	—
91	M₁₆	—	146	2	no	—
92	M₁₆	—	146	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	146	2	no	—
95	C₂×C₈	—	146	1	no	—
96	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
97	C₄⋊C₄	—	2	2	no	—
98	C₄⋊C₄	—	2	2	no	—
99	C₂³	—	146	1	no	—
100	C₂³	#11924027	1	1	yes	characteristic
101	Q₈	—	146	2	no	—
102	D₄	—	292	2	no	—
103	D₄	—	146	2	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	8	2	no	—
106	C₂×C₄	—	292	1	no	—
107	C₂×C₄	—	292	1	no	—
108	C₂×C₄	—	146	1	no	—
109	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
110	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
111	C₂×C₄	#11924028	1	2	yes	—
112	C₂×C₄	#11924029	1	2	yes	—
113	C₈	—	2	2	no	—
114	C₈	—	292	2	no	—
115	C₈	—	292	1	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	292	1	no	—
119	C₂²	—	292	1	no	—
120	C₂²	—	292	1	no	—
121	C₂²	#14556562	1	1	yes	characteristic
122	C₂²	#14556586	1	2	yes	—
123	C₄	—	8	2	no	—
124	C₄	—	292	1	no	—
125	C₄	#14556574	1	1	yes	characteristic
126	C₄	#14556576	1	2	yes	—
127	C₄	#14556580	1	1	yes	characteristic
128	C₂	—	2	2	no	—
129	C₂	—	584	1	no	—
130	C₂	#17988513	1	1	yes	characteristic
131	C₂	#17988854	1	1	yes	characteristic
132	C₂	#17988859	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988586

C₂

yes

maximal

#17988553

C₂

yes

maximal, characteristic

#17988356

C₂

yes

maximal, complemented

#17988352

C₂

yes

maximal, characteristic, complemented

C₂×#107×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924028

C₂²

yes

characteristic

C₂×#11924012

C₂²

yes

—

C₂×#11924012

C₂²

yes

—

—

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

—

#107×C₇₃

—

#11924028

—

#11924028

—

C₂×Dic₁₄₆

D₄

yes

characteristic

C₂×D₂₉₂

D₄

yes

characteristic

C₂×C₂²⋊D₇₃

—

C₂×C₄×D₇₃

—

—

—

—

—

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂³×C₇₃

#41

yes

characteristic

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

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

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#121

yes

characteristic

C₂²×C₇₃

#126

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#123

yes

characteristic

C₄×C₇₃

#123

yes

—

C₄×C₇₃

#124

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#2078

—

maximal, Sylow

C₇₃

#2078

yes

characteristic, complemented, Sylow

C₂×#107

D₇₃

yes

characteristic, complemented

—

—

—

—

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

C₂×D₇₃

yes

—

#107

—

#103

—

146

—

#102

—

146

—

C₂²⋊C₈

—

146

—

#41

—

146

—

#41

—

146

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

146

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂²⋊D₇₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂³

—

146

—

100

C₂³

#11924027

yes

characteristic

101

Q₈

—

146

—

102

D₄

—

292

—

103

D₄

—

146

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

292

—

107

C₂×C₄

—

292

—

108

C₂×C₄

—

146

—

109

C₂×C₄

D₄×D₇₃

yes

characteristic

110

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

111

C₂×C₄

#11924028

yes

—

112

C₂×C₄

#11924029

yes

—

113

C₈

—

114

C₈

—

292

—

115

C₈

—

292

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

292

—

119

C₂²

—

292

—

120

C₂²

—

292

—

121

C₂²

#14556562

yes

characteristic

122

C₂²

#14556586

yes

—

123

C₄

—

124

C₄

—

292

—

125

C₄

#14556574

yes

characteristic

126

C₄

#14556576

yes

—

127

C₄

#14556580

yes

characteristic

128

C₂

—

129

C₂

—

584

—

130

C₂

#17988513

yes

characteristic

131

C₂

#17988854

yes

characteristic

132

C₂

#17988859

yes

characteristic

	subgroup	G/H
center	C₂²	#14556562
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂×#107×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	C₂×#107	D₇₃
hypocenter	C₇₃	#2078
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂²

#14556562

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂×#107×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
3. #17988356	C₂	semidirect
4. #17988352	C₂	semidirect
5. C₂×#107×C₇₃	C₂	semidirect
67. C₇₃	#2078	semidirect
68. C₂×#107	D₇₃	semidirect

H ≅ G/N

type

3. #17988356

C₂

semidirect

4. #17988352

C₂

semidirect

5. C₂×#107×C₇₃

C₂

semidirect

67. C₇₃

#2078

semidirect

68. C₂×#107

D₇₃

semidirect

Subgroups — #22611372

Conjugacy classes of subgroups

Complements