Group #22625138 — subgroups

Subgroups — #22625138

Order 9344.

208 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 98 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	#17989603	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10596833	C₂	1	1	yes	maximal, characteristic
3	#17989429	C₂	1	2	yes	maximal, complemented
4	#17989429	C₂	1	2	yes	maximal, complemented
5	M₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10596833	C₄	1	2	yes	—
7	C₄⋊#10596833	C₄	1	2	yes	—
8	C₂²⋊#10596833	C₄	1	2	yes	—
9	C₄×#10596833	C₄	1	2	yes	—
10	C₄×#10596833	C₂²	1	1	yes	characteristic
11	C₄×#10596833	C₂²	1	1	yes	characteristic
12	C₄×#10596833	C₂²	1	2	yes	—
13	C₂×#11924012	C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
15	#14556501	C₄	1	2	yes	—
16	C₈×Dic₇₃	C₂²	1	2	yes	—
17	C₂×M₁₆×C₇₃	C₄	1	1	yes	characteristic
18	C₂×#10596833	—	2	4	no	—
19	C₂×#10596833	C₂×C₄	1	2	yes	—
20	C₂×#10596833	C₂×C₄	1	4	yes	—
21	C₂×#10596833	C₂×C₄	1	2	yes	—
22	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
24	#11924012	—	2	2	no	—
25	C₂×#10596831	C₂×C₄	1	2	yes	—
26	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
30	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
31	M₁₆×C₇₃	—	2	2	no	—
32	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
33	C₂³×C₇₃	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
35	C₂×C₄×C₇₃	M₁₆	1	2	yes	—
36	C₂×C₄×C₇₃	M₁₆	1	2	yes	—
37	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₇₃	—	2	2	no	—
39	C₂×Dic₇₃	—	2	2	no	—
40	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
41	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
42	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
43	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
44	#10596833	—	2	2	no	—
45	#10596833	—	2	4	no	—
46	#10596833	M₁₆	1	4	yes	complemented
47	C₈×C₇₃	—	2	2	no	—
48	#10596831	—	2	2	no	—
49	C₂²×C₇₃	—	2	1	no	—
50	C₂²×C₇₃	—	2	1	no	—
51	C₂²×C₇₃	#97	1	2	yes	—
52	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
53	C₄×C₇₃	#97	1	2	yes	—
54	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
55	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
56	Dic₇₃	—	2	1	no	—
57	Dic₇₃	—	2	1	no	—
58	Dic₇₃	C₂×M₁₆	1	2	yes	—
59	Dic₇₃	#131	1	2	yes	—
60	C₂×C₇₃	—	2	2	no	—
61	C₂×C₇₃	C₂×#97	1	1	yes	characteristic
62	C₂×C₇₃	C₄×M₁₆	1	1	yes	characteristic
63	C₂×C₇₃	#405	1	1	yes	characteristic
64	#1451	—	73	1	no	maximal, Sylow
65	C₇₃	#1451	1	1	yes	characteristic, complemented, Sylow
66	#431	—	73	1	no	—
67	C₄×M₁₆	—	73	1	no	—
68	C₂×C₄×C₈	—	73	1	no	—
69	#322	—	73	2	no	—
70	#322	—	73	2	no	—
71	C₂×M₁₆	—	73	1	no	—
72	C₂×M₁₆	#64408	1	1	yes	characteristic
73	C₂²×C₈	—	73	2	no	—
74	C₂×C₄²	—	73	1	no	—
75	C₄⋊C₈	—	73	2	no	—
76	C₂²⋊C₈	—	73	2	no	—
77	#97	—	73	2	no	—
78	C₄×C₈	—	73	1	no	—
79	C₄×C₈	—	73	1	no	—
80	C₄×C₈	—	73	2	no	—
81	C₄×C₈	—	73	2	no	—
82	C₄×C₈	—	73	2	no	—
83	C₂²×C₄	—	73	1	no	—
84	C₂²×C₄	—	73	1	no	—
85	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
86	M₁₆	—	2	2	no	—
87	M₁₆	—	146	2	no	—
88	C₂×C₈	—	73	2	no	—
89	C₂×C₈	—	73	2	no	—
90	C₂×C₈	—	73	4	no	—
91	C₂×C₈	—	73	2	no	—
92	C₂×C₈	—	146	4	no	—
93	C₂×C₈	C₂×#64408	1	2	yes	—
94	C₄²	—	73	1	no	—
95	C₄²	—	73	1	no	—
96	C₄²	—	73	1	no	—
97	C₄²	—	73	1	no	—
98	C₂³	C₄×#64408	1	1	yes	characteristic
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	—	73	1	no	—
102	C₂×C₄	—	73	1	no	—
103	C₂×C₄	—	146	2	no	—
104	C₂×C₄	—	146	2	no	—
105	C₂×C₄	C₄×#64408	1	1	yes	characteristic
106	C₂×C₄	#11924037	1	2	yes	—
107	C₂×C₄	#11924038	1	2	yes	—
108	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
109	C₈	—	2	2	no	—
110	C₈	—	73	4	no	—
111	C₈	—	146	2	no	—
112	C₈	—	146	4	no	—
113	C₈	—	146	2	no	—
114	C₂²	—	2	1	no	—
115	C₂²	—	2	1	no	—
116	C₂²	#14556646	1	2	yes	—
117	C₂²	C₂×C₄×#64408	1	1	yes	characteristic
118	C₄	—	73	2	no	—
119	C₄	—	73	2	no	—
120	C₄	—	146	1	no	—
121	C₄	—	146	1	no	—
122	C₄	#14556646	1	2	yes	—
123	C₄	C₂×#11924037	1	1	yes	characteristic
124	C₄	C₂×#11924038	1	1	yes	characteristic
125	C₂	—	2	2	no	—
126	C₂	C₂×#14556646	1	1	yes	characteristic
127	C₂	M₁₆×#64408	1	1	yes	characteristic
128	C₂	#17989553	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989603

C₂

yes

maximal, characteristic

C₂×C₄×#10596833

C₂

yes

maximal, characteristic

#17989429

C₂

yes

maximal, complemented

#17989429

C₂

yes

maximal, complemented

M₁₆×Dic₇₃

C₂

yes

maximal, characteristic

C₂²×#10596833

C₄

yes

—

C₄⋊#10596833

C₄

yes

—

C₂²⋊#10596833

C₄

yes

—

C₄×#10596833

C₄

yes

—

C₄×#10596833

C₂²

yes

characteristic

C₄×#10596833

C₂²

yes

characteristic

C₄×#10596833

C₂²

yes

—

C₂×#11924012

C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556501

C₄

yes

—

C₈×Dic₇₃

C₂²

yes

—

C₂×M₁₆×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

C₂×#10596833

C₂×C₄

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

#11924012

—

C₂×#10596831

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

—

C₂×C₄×C₇₃

M₁₆

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄²

yes

characteristic

C₂×Dic₇₃

C₄²

yes

characteristic

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂²×C₄

yes

—

—

M₁₆

yes

complemented

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#97

yes

—

C₂²×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

#97

yes

—

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

C₂×M₁₆

yes

—

Dic₇₃

#131

yes

—

C₂×C₇₃

—

C₂×C₇₃

C₂×#97

yes

characteristic

C₂×C₇₃

C₄×M₁₆

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#431

—

C₄×M₁₆

—

C₂×C₄×C₈

—

#322

—

#322

—

C₂×M₁₆

—

C₂×M₁₆

#64408

yes

characteristic

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄×#64408

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

146

—

104

C₂×C₄

—

146

—

105

C₂×C₄

C₄×#64408

yes

characteristic

106

C₂×C₄

#11924037

yes

—

107

C₂×C₄

#11924038

yes

—

108

C₂×C₄

C₂²×#64408

yes

characteristic

109

C₈

—

110

C₈

—

111

C₈

—

146

—

112

C₈

—

146

—

113

C₈

—

146

—

114

C₂²

—

115

C₂²

—

116

C₂²

#14556646

yes

—

117

C₂²

C₂×C₄×#64408

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

146

—

121

C₄

—

146

—

122

C₄

#14556646

yes

—

123

C₄

C₂×#11924037

yes

characteristic

124

C₄

C₂×#11924038

yes

characteristic

125

C₂

—

126

C₂

C₂×#14556646

yes

characteristic

127

C₂

M₁₆×#64408

yes

characteristic

128

C₂

#17989553

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂×C₄²
Fitting	C₂×M₁₆×C₇₃	C₄
hypercenter	C₂×M₁₆	#64408
hypocenter	C₇₃	#1451
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#64408

commutator, socle

C₂²×C₇₃

C₂×C₄²

Fitting

C₂×M₁₆×C₇₃

C₄

C₂×M₁₆

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
3. #17989429	C₂	semidirect
4. #17989429	C₂	semidirect
46. #10596833	M₁₆	semidirect
65. C₇₃	#1451	semidirect

H ≅ G/N

type

3. #17989429

C₂

semidirect

4. #17989429

C₂

semidirect

46. #10596833

M₁₆

semidirect

65. C₇₃

#1451

semidirect

Subgroups — #22625138

Conjugacy classes of subgroups

Complements