Group #22618198 — subgroups

Subgroups — #22618198

Order 9344.

348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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	#17988529	C₂	1	3	yes	maximal
2	#17988521	C₂	1	3	yes	maximal
3	#17988519	C₂	1	3	yes	maximal
4	#17988508	C₂	1	3	yes	maximal
5	#17988457	C₂	1	1	yes	maximal, characteristic
6	#17988455	C₂	1	1	yes	maximal, characteristic
7	#383×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₇₃	C₂²	1	3	yes	—
10	C₂×C₄⋊Dic₇₃	C₂²	1	3	yes	—
11	C₂×C₄⋊Dic₇₃	C₂²	1	3	yes	—
12	C₂×#11924007	C₂²	1	3	yes	—
13	C₂×#11924007	C₂²	1	3	yes	—
14	#14556498	C₂²	1	3	yes	—
15	#14556498	C₂²	1	3	yes	—
16	#14556498	C₂²	1	3	yes	—
17	#14556498	C₂²	1	3	yes	—
18	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
19	#95×C₇₃	C₂²	1	3	yes	—
20	#95×C₇₃	C₂²	1	3	yes	—
21	C₂×Dic₁₄₆	—	4	3	no	—
22	C₂²×Dic₇₃	C₂³	1	3	yes	—
23	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
24	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₇₃	C₂³	1	3	yes	—
26	C₄⋊Dic₇₃	—	4	3	no	—
27	C₄⋊Dic₇₃	—	4	3	no	—
28	C₄⋊Dic₇₃	—	4	3	no	—
29	#11924007	—	4	3	no	—
30	#11924007	—	4	3	no	—
31	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
32	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
34	C₄²×C₇₃	Q₈	1	4	yes	complemented
35	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
36	C₂×C₄×C₇₃	—	2	3	no	—
37	C₂×C₄×C₇₃	—	2	3	no	—
38	C₂×C₄×C₇₃	—	2	3	no	—
39	C₂×C₄×C₇₃	—	2	3	no	—
40	C₂×C₄×C₇₃	—	2	6	no	—
41	C₂×C₄×C₇₃	C₂×Q₈	1	6	yes	—
42	C₂×Dic₇₃	—	2	3	no	—
43	C₂×Dic₇₃	—	2	3	no	—
44	C₂×Dic₇₃	—	2	3	no	—
45	C₂×Dic₇₃	—	2	3	no	—
46	C₂×Dic₇₃	—	2	3	no	—
47	C₂×Dic₇₃	—	2	3	no	—
48	C₂×Dic₇₃	—	2	6	no	—
49	Dic₁₄₆	—	4	4	no	—
50	C₂²×C₇₃	C₂²×Q₈	1	1	yes	characteristic
51	C₂²×C₇₃	H(5,𝔽₂)	1	3	yes	—
52	C₂²×C₇₃	2₋¹⁺⁴	1	3	yes	—
53	C₄×C₇₃	—	2	6	no	—
54	C₄×C₇₃	—	4	1	no	—
55	C₄×C₇₃	—	4	3	no	—
56	Dic₇₃	—	4	1	no	—
57	Dic₇₃	—	4	1	no	—
58	Dic₇₃	—	4	3	no	—
59	Dic₇₃	—	4	3	no	—
60	C₂×C₇₃	#544	1	3	yes	—
61	C₂×C₇₃	#560	1	1	yes	characteristic
62	C₂×C₇₃	#563	1	3	yes	—
63	#2843	—	73	1	no	maximal, Sylow
64	C₇₃	#2843	1	1	yes	characteristic, complemented, Sylow
65	#400	—	73	3	no	—
66	#398	—	73	3	no	—
67	#398	—	73	3	no	—
68	#395	—	73	3	no	—
69	#384	—	73	1	no	—
70	#383	—	73	1	no	—
71	#383	D₇₃	1	1	yes	characteristic
72	C₂²×Q₈	—	73	1	no	—
73	C₂×C₄⋊C₄	—	73	3	no	—
74	C₂×C₄⋊C₄	—	73	3	no	—
75	C₂×C₄⋊C₄	—	73	3	no	—
76	C₂×C₄⋊C₄	—	73	3	no	—
77	C₂×C₄⋊C₄	—	73	3	no	—
78	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
79	#95	—	73	3	no	—
80	#95	—	73	3	no	—
81	#95	—	73	3	no	—
82	#95	—	73	3	no	—
83	#95	C₂×D₇₃	1	3	yes	—
84	#95	C₂×D₇₃	1	3	yes	—
85	C₂×Q₈	—	292	3	no	—
86	C₂²×C₄	—	73	3	no	—
87	C₂²×C₄	—	73	1	no	—
88	C₂²×C₄	—	73	1	no	—
89	C₂²×C₄	—	73	3	no	—
90	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
91	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
92	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
93	C₄⋊C₄	—	292	3	no	—
94	C₄⋊C₄	—	292	3	no	—
95	C₄⋊C₄	—	292	3	no	—
96	C₄⋊C₄	—	292	3	no	—
97	C₄⋊C₄	—	292	3	no	—
98	C₄²	Dic₁₄₆	1	4	yes	complemented
99	C₂³	C₂³×D₇₃	1	1	yes	characteristic
100	Q₈	—	292	4	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	2	3	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	2	3	no	—
105	C₂×C₄	—	2	6	no	—
106	C₂×C₄	—	146	3	no	—
107	C₂×C₄	—	146	3	no	—
108	C₂×C₄	—	146	3	no	—
109	C₂×C₄	—	146	3	no	—
110	C₂×C₄	—	146	3	no	—
111	C₂×C₄	—	146	3	no	—
112	C₂×C₄	—	146	6	no	—
113	C₂×C₄	C₂×Dic₁₄₆	1	6	yes	—
114	C₂²	C₂²×Dic₁₄₆	1	1	yes	characteristic
115	C₂²	#14556637	1	3	yes	—
116	C₂²	#14556638	1	3	yes	—
117	C₄	—	2	6	no	—
118	C₄	—	4	1	no	—
119	C₄	—	4	3	no	—
120	C₄	—	292	1	no	—
121	C₄	—	292	1	no	—
122	C₄	—	292	3	no	—
123	C₄	—	292	3	no	—
124	C₂	#17989215	1	3	yes	—
125	C₂	#17989328	1	1	yes	characteristic
126	C₂	#17989339	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988529

C₂

yes

maximal

#17988521

C₂

yes

maximal

#17988519

C₂

yes

maximal

#17988508

C₂

yes

maximal

#17988457

C₂

yes

maximal, characteristic

#17988455

C₂

yes

maximal, characteristic

#383×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#95×C₇₃

C₂²

yes

—

#95×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

characteristic

C₂²×Dic₇₃

C₂³

yes

characteristic

C₂²×Dic₇₃

C₂³

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

#11924007

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

—

C₄²×C₇₃

Q₈

yes

complemented

C₂³×C₇₃

C₂⁴

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

C₂²×C₇₃

C₂²×Q₈

yes

characteristic

C₂²×C₇₃

H(5,𝔽₂)

yes

—

C₂²×C₇₃

2₋¹⁺⁴

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#544

yes

—

C₂×C₇₃

#560

yes

characteristic

C₂×C₇₃

#563

yes

—

#2843

—

maximal, Sylow

C₇₃

#2843

yes

characteristic, complemented, Sylow

—

—

—

—

—

—

D₇₃

yes

characteristic

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₇₃

yes

—

—

—

—

C₂×D₇₃

yes

—

#95

C₂×D₇₃

yes

—

C₂×Q₈

—

292

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂²×C₄

C₂²×D₇₃

yes

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄²

Dic₁₄₆

yes

complemented

C₂³

C₂³×D₇₃

yes

characteristic

100

Q₈

—

292

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

146

—

107

C₂×C₄

—

146

—

108

C₂×C₄

—

146

—

109

C₂×C₄

—

146

—

110

C₂×C₄

—

146

—

111

C₂×C₄

—

146

—

112

C₂×C₄

—

146

—

113

C₂×C₄

C₂×Dic₁₄₆

yes

—

114

C₂²

C₂²×Dic₁₄₆

yes

characteristic

115

C₂²

#14556637

yes

—

116

C₂²

#14556638

yes

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

292

—

121

C₄

—

292

—

122

C₄

—

292

—

123

C₄

—

292

—

124

C₂

#17989215

yes

—

125

C₂

#17989328

yes

characteristic

126

C₂

#17989339

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂⁴
Fitting	#383×C₇₃	C₂
hypercenter	#383	D₇₃
hypocenter	C₇₃	#2843
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂⁴

Fitting

#383×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
34. C₄²×C₇₃	Q₈	semidirect
64. C₇₃	#2843	semidirect
98. C₄²	Dic₁₄₆	semidirect

H ≅ G/N

type

34. C₄²×C₇₃

Q₈

semidirect

64. C₇₃

#2843

semidirect

98. C₄²

Dic₁₄₆

semidirect

Subgroups — #22618198

Conjugacy classes of subgroups

Complements