Group #22625005 — subgroups

Subgroups — #22625005

Order 9344.

136 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 52 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×#14556666	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556661	C₂	1	1	yes	maximal, characteristic
3	#107×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924038	—	2	1	no	—
5	#14556666	—	2	1	no	—
6	#14556666	C₄	1	2	yes	complemented
7	C₂×#11924031	—	2	1	no	—
8	#14556661	—	2	1	no	—
9	#14556661	C₄	1	2	yes	complemented
10	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×D₇₃	—	2	1	no	—
12	#14556525	C₄	1	1	yes	characteristic
13	#14556524	—	2	1	no	—
14	#107×C₇₃	C₄	1	1	yes	characteristic
15	#11924038	—	2	2	no	—
16	#11924038	—	4	1	no	—
17	C₂×#10596833	—	4	1	no	—
18	#11924031	—	2	2	no	—
19	C₂×C₄×D₇₃	—	4	1	no	—
20	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
21	C₂×#10596831	D₄	1	1	yes	characteristic
22	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
23	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
24	C₈×D₇₃	D₄	1	1	yes	characteristic
25	C₈×D₇₃	Q₈	1	1	yes	characteristic
26	C₄⋊Dic₇₃	—	2	1	no	—
27	#11924007	—	4	1	no	—
28	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₄⋊C₄×C₇₃	—	2	1	no	—
30	C₂²×D₇₃	SD₁₆	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	4	1	no	—
32	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×Dic₇₃	—	4	1	no	—
34	C₂×Dic₇₃	D₈	1	1	yes	characteristic
35	C₄×D₇₃	—	8	2	no	—
36	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₇₃	SD₁₆	1	1	yes	characteristic
39	C₄×D₇₃	Q₁₆	1	1	yes	characteristic
40	#10596833	—	4	2	no	—
41	C₈×C₇₃	C₄²	1	1	yes	characteristic
42	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
43	#10596831	C₂²⋊C₄	1	1	yes	characteristic
44	#10596831	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₇₃	#102	1	1	yes	characteristic
46	C₂×D₇₃	—	2	1	no	—
47	C₂×D₇₃	—	2	1	no	—
48	C₂×D₇₃	#103	1	1	yes	characteristic
49	C₂×D₇₃	#106	1	1	yes	characteristic
50	C₄×C₇₃	—	8	1	no	—
51	C₄×C₇₃	#95	1	1	yes	characteristic
52	C₄×C₇₃	#103	1	1	yes	characteristic
53	Dic₇₃	—	8	1	no	—
54	Dic₇₃	#102	1	1	yes	characteristic
55	Dic₇₃	#107	1	1	yes	characteristic
56	C₂×C₇₃	#340	1	1	yes	characteristic
57	C₂×C₇₃	#361	1	1	yes	characteristic
58	C₂×C₇₃	#362	1	1	yes	characteristic
59	D₇₃	—	2	1	no	—
60	D₇₃	—	2	1	no	—
61	#1387	—	73	1	no	maximal, Sylow
62	C₇₃	#1387	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₃₂	—	73	1	no	—
64	C₂×#108	—	73	1	no	—
65	C₂×#107	—	73	1	no	—
66	C₂×M₁₆	—	146	1	no	—
67	C₂²×C₈	—	73	1	no	—
68	C₂×C₄⋊C₄	—	146	1	no	—
69	M₃₂	—	73	2	no	—
70	M₃₂	—	146	1	no	—
71	C₂×C₁₆	—	146	1	no	—
72	#108	—	73	2	no	—
73	#108	—	146	1	no	—
74	#107	—	73	1	no	—
75	#107	—	146	1	no	—
76	#107	#64408	1	1	yes	characteristic
77	C₂²×C₄	—	292	1	no	—
78	C₂²×C₄	—	73	1	no	—
79	M₁₆	—	292	1	no	—
80	M₁₆	—	146	2	no	—
81	C₂×C₈	—	292	1	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	73	1	no	—
85	C₂×C₈	—	73	1	no	—
86	C₂×C₈	—	73	1	no	—
87	C₂×C₈	C₂×#64408	1	1	yes	characteristic
88	C₄⋊C₄	—	2	1	no	—
89	C₄⋊C₄	—	292	1	no	—
90	C₄⋊C₄	—	146	1	no	—
91	C₁₆	—	146	2	no	—
92	C₂³	—	73	1	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	—	292	1	no	—
95	C₂×C₄	—	584	2	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	1	no	—
101	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
102	C₈	—	292	2	no	—
103	C₈	—	73	1	no	—
104	C₈	—	73	1	no	—
105	C₈	C₄×#64408	1	1	yes	characteristic
106	C₈	C₄⋊#64408	1	1	yes	characteristic
107	C₂²	—	73	1	no	—
108	C₂²	—	73	1	no	—
109	C₂²	—	146	1	no	—
110	C₂²	—	146	1	no	—
111	C₂²	#14556653	1	1	yes	characteristic
112	C₄	—	8	1	no	—
113	C₄	—	584	1	no	—
114	C₄	—	73	1	no	—
115	C₄	—	73	1	no	—
116	C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
117	C₄	#14556654	1	1	yes	characteristic
118	C₂	—	146	1	no	—
119	C₂	—	146	1	no	—
120	C₂	#17989460	1	1	yes	characteristic
121	C₂	#17989505	1	1	yes	characteristic
122	C₂	#17989506	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556666

C₂

yes

maximal, characteristic

C₂×#14556661

C₂

yes

maximal, characteristic

#107×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924038

—

#14556666

—

#14556666

C₄

yes

—

—

C₄

yes

complemented

C₂×C₈×D₇₃

C₂²

yes

characteristic

C₄⋊C₄×D₇₃

—

#14556525

C₄

yes

characteristic

#14556524

—

#107×C₇₃

C₄

yes

—

—

—

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×#10596831

D₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

Q₈

yes

characteristic

C₄⋊Dic₇₃

—

#11924007

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂²×D₇₃

SD₁₆

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

D₈

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

SD₁₆

yes

characteristic

C₄×D₇₃

Q₁₆

yes

characteristic

#10596833

—

C₈×C₇₃

C₄²

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

#10596831

C₂²⋊C₄

yes

characteristic

#10596831

C₄⋊C₄

yes

characteristic

C₂²×C₇₃

#102

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

yes

C₂×D₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

D₇₃

—

#1387

—

maximal, Sylow

C₇₃

#1387

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×#108

—

C₂×#107

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

146

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

#108

—

#108

—

146

—

#107

—

#107

—

146

—

#107

#64408

yes

characteristic

C₂²×C₄

—

292

—

C₂²×C₄

—

M₁₆

—

292

—

M₁₆

—

146

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₂²⋊#64408

yes

characteristic

102

C₈

—

292

—

103

C₈

—

104

C₈

—

105

C₈

C₄×#64408

yes

characteristic

106

C₈

C₄⋊#64408

yes

characteristic

107

C₂²

—

108

C₂²

—

109

C₂²

—

146

—

110

C₂²

—

146

—

111

C₂²

#14556653

yes

characteristic

112

C₄

—

113

C₄

—

584

—

114

C₄

—

115

C₄

—

116

C₄

(C₂×#64408)⋊C₄

yes

characteristic

117

C₄

#14556654

yes

characteristic

118

C₂

—

146

—

119

C₂

—

146

—

120

C₂

#17989460

yes

characteristic

121

C₂

#17989505

yes

characteristic

122

C₂

#17989506

yes

characteristic

	subgroup	G/H
center	C₂²	#14556653
commutator	C₈×C₇₃	C₄²
Frattini	C₂×C₈	C₂×#64408
Fitting	#107×C₇₃	C₄
socle	C₂²×C₇₃	#102
hypercenter	#107	#64408
hypocenter	C₇₃	#1387
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

subgroup

G/H

center

C₂²

#14556653

commutator

C₈×C₇₃

C₄²

Frattini

C₂×C₈

C₂×#64408

Fitting

#107×C₇₃

C₄

C₂²×C₇₃

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

N	H ≅ G/N	type
6. #14556666	C₄	semidirect
9. #14556661	C₄	semidirect
62. C₇₃	#1387	semidirect

H ≅ G/N

type

6. #14556666

C₄

semidirect

9. #14556661

C₄

semidirect

62. C₇₃

#1387

semidirect

Subgroups — #22625005

Conjugacy classes of subgroups

Complements