Group #22626937 — subgroups

Subgroups — #22626937

Order 9344.

180 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 69 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×C₄⋊#10596842	C₂	1	2	yes	maximal
2	C₂×C₈×#64408	C₂	1	1	yes	maximal, characteristic
3	C₂²×#10596842	—	2	2	no	—
4	C₄⋊#10596842	—	2	2	no	—
5	C₄⋊#10596842	C₄	1	4	yes	—
6	C₂×#11924036	C₄	1	1	yes	characteristic
7	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
8	C₈×#64408	—	2	2	no	—
9	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
10	C₂×#10596842	—	2	4	no	—
11	C₂×#10596842	—	4	2	no	—
12	C₂×#10596842	—	4	2	no	—
13	C₂²×#64408	D₄	1	1	yes	characteristic
14	C₂²×#64408	Q₈	1	1	yes	characteristic
15	#11924036	—	2	1	no	—
16	#11924036	C₈	1	2	yes	complemented
17	C₂×#10596833	—	2	1	no	—
18	C₄×#64408	C₂×C₄	1	2	yes	—
19	C₄×#64408	D₄	1	2	yes	—
20	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×#10596831	C₈	1	1	yes	characteristic, complemented
22	C₈×D₇₃	—	2	1	no	—
23	C₈×D₇₃	—	2	1	no	—
24	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic, complemented
25	C₂²×D₇₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂×#64408	—	2	1	no	—
27	C₂×#64408	—	2	1	no	—
28	C₂×#64408	C₂²⋊C₄	1	2	yes	—
29	C₂×#64408	C₄⋊C₄	1	2	yes	—
30	C₂×#64408	D₈	1	1	yes	characteristic
31	C₂×#64408	SD₁₆	1	2	yes	—
32	C₂×#64408	Q₁₆	1	1	yes	characteristic
33	#10596842	—	4	4	no	—
34	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
35	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
36	C₄×D₇₃	C₄²	1	1	yes	characteristic
37	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
39	C₄×D₇₃	M₁₆	1	1	yes	characteristic
40	#10596833	—	2	2	no	—
41	C₈×C₇₃	—	2	1	no	—
42	#10596831	—	2	1	no	—
43	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
44	C₂×D₇₃	#95	1	1	yes	characteristic
45	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
46	C₂×D₇₃	#106	1	1	yes	characteristic
47	C₂×D₇₃	#107	1	1	yes	characteristic
48	C₂×D₇₃	#108	1	1	yes	characteristic
49	C₂×D₇₃	#108	1	1	yes	characteristic
50	#64408	—	2	2	no	—
51	#64408	#102	1	2	yes	—
52	#64408	#103	1	2	yes	—
53	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
54	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
55	Dic₇₃	#97	1	1	yes	characteristic
56	Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
57	C₂×C₇₃	#334	1	1	yes	characteristic
58	C₂×C₇₃	#335	1	1	yes	characteristic
59	C₂×C₇₃	#336	1	1	yes	characteristic
60	D₇₃	#334	1	1	yes	characteristic
61	D₇₃	#335	1	1	yes	characteristic
62	D₇₃	#340	1	1	yes	characteristic
63	D₇₃	#341	1	1	yes	characteristic
64	#1277	—	73	1	no	maximal, Sylow
65	C₇₃	#1277	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₄⋊C₈	—	73	2	no	—
67	C₂×C₄×C₈	—	73	1	no	—
68	C₂²×C₈	—	73	1	no	—
69	C₂²×C₈	—	73	1	no	—
70	C₂²×C₈	—	146	2	no	—
71	C₂×C₄²	—	73	1	no	—
72	C₄⋊C₈	—	73	4	no	—
73	C₄⋊C₈	—	146	2	no	—
74	C₄×C₈	—	146	2	no	—
75	C₂²×C₄	—	73	1	no	—
76	C₂²×C₄	—	73	1	no	—
77	C₂²×C₄	—	73	1	no	—
78	C₂×C₈	—	292	2	no	—
79	C₂×C₈	—	292	2	no	—
80	C₂×C₈	—	73	2	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	146	1	no	—
83	C₂×C₈	—	146	1	no	—
84	C₂×C₈	—	146	4	no	—
85	C₂×C₈	—	146	1	no	—
86	C₂×C₈	—	146	1	no	—
87	C₂×C₈	#10596842	1	1	yes	characteristic, complemented
88	C₄²	—	73	2	no	—
89	C₄²	—	73	2	no	—
90	C₂³	—	73	1	no	—
91	C₂×C₄	—	73	2	no	—
92	C₂×C₄	—	73	1	no	—
93	C₂×C₄	—	73	2	no	—
94	C₂×C₄	—	73	1	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	2	no	—
101	C₂×C₄	—	146	1	no	—
102	C₂×C₄	—	146	1	no	—
103	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
104	C₈	—	2	1	no	—
105	C₈	—	292	4	no	—
106	C₈	—	146	2	no	—
107	C₈	—	146	1	no	—
108	C₂²	—	73	1	no	—
109	C₂²	—	73	1	no	—
110	C₂²	—	73	1	no	—
111	C₂²	—	73	1	no	—
112	C₂²	—	73	1	no	—
113	C₂²	—	73	1	no	—
114	C₂²	C₄⋊#10596842	1	1	yes	characteristic
115	C₄	—	73	2	no	—
116	C₄	—	73	2	no	—
117	C₄	—	73	1	no	—
118	C₄	—	73	1	no	—
119	C₄	—	146	2	no	—
120	C₄	C₄×#10596842	1	1	yes	characteristic
121	C₄	C₂²⋊#10596842	1	1	yes	characteristic
122	C₂	—	73	1	no	—
123	C₂	—	73	1	no	—
124	C₂	—	73	1	no	—
125	C₂	—	73	1	no	—
126	C₂	#17989676	1	1	yes	characteristic
127	C₂	#17989677	1	1	yes	characteristic
128	C₂	(C₂×#10596842)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#10596842

C₂

yes

maximal

C₂×C₈×#64408

C₂

yes

maximal, characteristic

C₂²×#10596842

—

C₄⋊#10596842

—

C₄⋊#10596842

C₄

yes

—

C₂×#11924036

C₄

yes

characteristic

C₂×C₄×#64408

C₂²

yes

characteristic

C₈×#64408

—

C₂×C₈×D₇₃

C₄

yes

—

—

—

C₂²×#64408

D₄

yes

characteristic

C₂²×#64408

Q₈

yes

characteristic

#11924036

—

#11924036

C₈

yes

complemented

C₂×#10596833

—

C₄×#64408

C₂×C₄

yes

—

C₄×#64408

D₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₈

yes

characteristic, complemented

C₈×D₇₃

—

C₈×D₇₃

—

C₂×C₈×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

C₄⋊C₄

yes

—

—

C₂²⋊C₄

yes

—

C₂×#64408

C₄⋊C₄

yes

—

C₂×#64408

D₈

yes

characteristic

C₂×#64408

SD₁₆

yes

—

C₂×#64408

Q₁₆

yes

characteristic

#10596842

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

M₁₆

yes

characteristic

C₄×D₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₄⋊C₈

yes

characteristic

C₂×D₇₃

#95

yes

characteristic

C₂×D₇₃

C₄⋊C₈

yes

C₂×D₇₃

yes

C₂×D₇₃

yes

C₂×D₇₃

yes

C₂×D₇₃

yes

—

yes

—

#64408

#103

yes

—

C₄×C₇₃

C₄×C₈

yes

characteristic

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

Dic₇₃

#97

yes

characteristic

Dic₇₃

C₂²⋊C₈

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

yes

D₇₃

yes

D₇₃

yes

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

#10596842

yes

characteristic, complemented

C₄²

—

C₄²

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

146

—

102

C₂×C₄

—

146

—

103

C₂×C₄

C₂×#10596842

yes

characteristic

104

C₈

—

105

C₈

—

292

—

106

C₈

—

146

—

107

C₈

—

146

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₄⋊#10596842

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

146

—

120

C₄

C₄×#10596842

yes

characteristic

121

C₄

C₂²⋊#10596842

yes

characteristic

122

C₂

—

123

C₂

—

124

C₂

—

125

C₂

—

126

C₂

#17989676

yes

characteristic

127

C₂

#17989677

yes

characteristic

128

C₂

(C₂×#10596842)⋊C₄

yes

characteristic

	subgroup	G/H
center	C₂²	C₄⋊#10596842
commutator	C₄×C₇₃	C₄×C₈
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₂×C₈×C₇₃	C₈
socle	C₂²×C₇₃	C₄⋊C₈
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	#1277
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

subgroup

G/H

center

C₂²

C₄⋊#10596842

commutator

C₄×C₇₃

C₄×C₈

Frattini

C₂×C₄

C₂×#10596842

Fitting

C₂×C₈×C₇₃

C₈

socle

C₂²×C₇₃

C₄⋊C₈

C₂×C₈

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

N	H ≅ G/N	type
16. #11924036	C₈	semidirect
21. C₂×#10596831	C₈	semidirect
24. C₂×C₈×C₇₃	C₈	semidirect
65. C₇₃	#1277	semidirect
87. C₂×C₈	#10596842	semidirect

H ≅ G/N

type

16. #11924036

C₈

semidirect

21. C₂×#10596831

C₈

semidirect

24. C₂×C₈×C₇₃

C₈

semidirect

65. C₇₃

#1277

semidirect

87. C₂×C₈

#10596842

semidirect

Subgroups — #22626937

Conjugacy classes of subgroups

Complements