Group #22627119 — subgroups

Subgroups — #22627119

Order 9344.

172 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 77 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×#14556687	C₂	1	2	yes	maximal
2	#17989690	C₂	1	2	yes	maximal, complemented
3	C₄⋊#11924040	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×#10596833	C₂	1	1	yes	maximal, characteristic
5	#14556687	—	2	4	no	—
6	C₂×#11924040	C₂²	1	4	yes	—
7	C₂²×#10596833	C₄	1	1	yes	characteristic
8	C₂²×#10596833	C₂²	1	1	yes	characteristic
9	C₄×#10596833	C₄	1	1	yes	characteristic
10	C₄×#10596833	C₄	1	1	yes	characteristic
11	C₄×#10596833	C₂²	1	1	yes	characteristic
12	C₄×#10596833	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₇₃	C₄	1	1	yes	characteristic
14	#11924040	—	2	4	no	—
15	C₂×#10596833	—	2	2	no	—
16	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
17	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
18	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
19	C₂×#10596833	D₄	1	2	yes	—
20	C₂×#10596833	Q₈	1	2	yes	—
21	C₂×#10596833	C₂³	1	1	yes	characteristic
22	C₂²×Dic₇₃	C₈	1	1	yes	characteristic
23	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₇₃	C₈	1	1	yes	characteristic
25	C₄×Dic₇₃	C₈	1	1	yes	characteristic
26	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₇₃	C₈	1	1	yes	characteristic
29	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	—	2	2	no	—
31	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
33	C₂×Dic₇₃	—	2	2	no	—
34	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
35	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
37	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
38	C₂×Dic₇₃	M₁₆	1	2	yes	—
39	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
40	#10596833	—	2	1	no	—
41	#10596833	—	2	1	no	—
42	#10596833	C₄⋊C₄	1	2	yes	—
43	#10596833	C₂×D₄	1	1	yes	characteristic
44	#10596833	C₂×Q₈	1	1	yes	characteristic
45	C₂²×C₇₃	—	2	1	no	—
46	C₂²×C₇₃	—	2	1	no	—
47	C₂²×C₇₃	C₄⋊C₈	1	2	yes	—
48	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
49	C₄×C₇₃	—	2	1	no	—
50	C₄×C₇₃	M₃₂	1	2	yes	complemented
51	Dic₇₃	—	2	1	no	—
52	Dic₇₃	C₄⋊C₈	1	2	yes	—
53	Dic₇₃	M₃₂	1	2	yes	complemented
54	Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
55	Dic₇₃	C₂×M₁₆	1	1	yes	characteristic
56	C₂×C₇₃	—	2	2	no	—
57	C₂×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
58	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
59	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
60	#2150	—	73	1	no	maximal, Sylow
61	C₇₃	#2150	1	1	yes	characteristic, complemented, Sylow
62	C₂×M₃₂	—	73	2	no	—
63	C₂×C₄×C₈	—	73	1	no	—
64	C₄⋊C₁₆	—	73	2	no	—
65	C₄⋊C₁₆	—	73	2	no	—
66	C₂²×C₈	—	73	1	no	—
67	C₂²×C₈	—	73	1	no	—
68	C₂×C₄²	—	73	1	no	—
69	M₃₂	—	146	4	no	—
70	C₂×C₁₆	—	73	4	no	—
71	C₄×C₈	—	73	1	no	—
72	C₄×C₈	—	73	1	no	—
73	C₄×C₈	—	73	1	no	—
74	C₄×C₈	—	73	1	no	—
75	C₂²×C₄	—	73	1	no	—
76	C₂²×C₄	—	73	1	no	—
77	C₂²×C₄	#10596842	1	1	yes	characteristic
78	C₂×C₈	—	73	1	no	—
79	C₂×C₈	—	73	2	no	—
80	C₂×C₈	—	73	2	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	146	2	no	—
85	C₄²	—	73	1	no	—
86	C₄²	—	73	1	no	—
87	C₄²	—	73	1	no	—
88	C₄²	—	73	1	no	—
89	C₁₆	—	146	4	no	—
90	C₂³	C₂×#10596842	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	73	2	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	—	146	2	no	—
99	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
100	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
101	C₈	—	73	1	no	—
102	C₈	—	73	2	no	—
103	C₈	—	73	1	no	—
104	C₈	—	146	1	no	—
105	C₈	—	146	1	no	—
106	C₂²	—	2	1	no	—
107	C₂²	—	2	1	no	—
108	C₂²	C₄⋊#10596842	1	2	yes	—
109	C₂²	C₂²×#10596842	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	73	1	no	—
112	C₄	—	73	1	no	—
113	C₄	—	73	2	no	—
114	C₄	—	73	2	no	—
115	C₄	—	146	1	no	—
116	C₄	#14556687	1	2	yes	complemented
117	C₂	—	2	2	no	—
118	C₂	C₂×C₄⋊#10596842	1	1	yes	characteristic
119	C₂	C₂×#14556687	1	1	yes	characteristic
120	C₂	#17989706	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556687

C₂

yes

maximal

#17989690

C₂

yes

maximal, complemented

C₄⋊#11924040

C₂

yes

maximal, complemented

C₂×C₄×#10596833

C₂

yes

maximal, characteristic

#14556687

—

C₂×#11924040

C₂²

yes

—

C₂²×#10596833

C₄

yes

characteristic

C₂²×#10596833

C₂²

yes

characteristic

C₄×#10596833

C₄

yes

characteristic

C₄×#10596833

C₄

yes

characteristic

C₄×#10596833

C₂²

yes

characteristic

C₄×#10596833

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₄

yes

—

—

C₂×C₄

yes

characteristic

C₂×#10596833

C₂×C₄

yes

characteristic

C₂×#10596833

C₂×C₄

yes

characteristic

C₂×#10596833

D₄

yes

—

C₂×#10596833

Q₈

yes

—

C₂×#10596833

C₂³

yes

characteristic

C₂²×Dic₇₃

C₈

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₈

yes

characteristic

C₄×Dic₇₃

C₈

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₈

yes

characteristic

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

M₁₆

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

—

—

C₄⋊C₄

yes

—

#10596833

C₂×D₄

yes

characteristic

#10596833

C₂×Q₈

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄⋊C₈

yes

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

M₃₂

yes

complemented

Dic₇₃

—

Dic₇₃

C₄⋊C₈

yes

—

Dic₇₃

M₃₂

yes

complemented

Dic₇₃

C₂×C₄⋊C₄

yes

characteristic

Dic₇₃

C₂×M₁₆

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄⋊C₈

yes

characteristic

C₂×C₇₃

C₂×M₃₂

yes

characteristic

C₂×C₇₃

C₂×M₃₂

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

146

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#10596842

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

146

—

C₂³

C₂×#10596842

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₂×#10596842

yes

characteristic

100

C₂×C₄

C₂×#10596842

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

—

104

C₈

—

146

—

105

C₈

—

146

—

106

C₂²

—

107

C₂²

—

108

C₂²

C₄⋊#10596842

yes

—

109

C₂²

C₂²×#10596842

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

146

—

116

C₄

#14556687

yes

complemented

117

C₂

—

118

C₂

C₂×C₄⋊#10596842

yes

characteristic

119

C₂

C₂×#14556687

yes

characteristic

120

C₂

#17989706

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#10596842
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	C₂²×C₄×C₇₃	C₈
hypercenter	C₂²×C₄	#10596842
hypocenter	C₇₃	#2150
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

subgroup

G/H

center, Frattini

C₂²

C₂²×#10596842

commutator, socle

C₂²×C₇₃

C₂²×C₈

Fitting

C₂²×C₄×C₇₃

C₈

C₂²×C₄

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂² ◁ C₂²×C₄

N	H ≅ G/N	type
2. #17989690	C₂	semidirect
3. C₄⋊#11924040	C₂	semidirect
50. C₄×C₇₃	M₃₂	semidirect
53. Dic₇₃	M₃₂	semidirect
61. C₇₃	#2150	semidirect
116. C₄	#14556687	semidirect

H ≅ G/N

type

2. #17989690

C₂

semidirect

3. C₄⋊#11924040

C₂

semidirect

50. C₄×C₇₃

M₃₂

semidirect

53. Dic₇₃

M₃₂

semidirect

61. C₇₃

#2150

semidirect

116. C₄

#14556687

semidirect

Subgroups — #22627119

Conjugacy classes of subgroups

Complements