Group #22626844 — subgroups

Subgroups — #22626844

Order 9344.

314 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 144 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	#17989639	C₂	1	4	yes	maximal, complemented
2	#17989637	C₂	1	4	yes	maximal, complemented
3	#17989612	C₂	1	4	yes	maximal
4	#17989609	C₂	1	2	yes	maximal
5	#17989143	C₂	1	1	yes	maximal, characteristic
6	#14556658	C₂²	1	4	yes	—
7	C₄⋊#10596833	C₂²	1	2	yes	—
8	C₄⋊#10596833	C₂²	1	4	yes	—
9	C₄⋊#10596833	C₂²	1	2	yes	—
10	#14556648	C₂²	1	4	yes	—
11	#14556646	C₂²	1	4	yes	—
12	#14556646	C₂²	1	4	yes	—
13	C₄×#10596833	C₂²	1	4	yes	—
14	#14556590	C₄	1	2	yes	—
15	#14556583	C₄	1	1	yes	characteristic
16	#14556569	C₄	1	4	yes	—
17	#14556556	C₂²	1	4	yes	—
18	#14556549	C₂²	1	2	yes	—
19	C₄²×D₇₃	C₂²	1	1	yes	characteristic
20	#125×C₇₃	C₄	1	1	yes	characteristic
21	C₂×#10596833	C₂³	1	4	yes	—
22	C₂×#10596833	C₂³	1	4	yes	—
23	C₂×Dic₁₄₆	C₂×C₄	1	4	yes	—
24	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
27	#11924007	C₂×C₄	1	4	yes	—
28	#11924007	C₂×C₄	1	4	yes	—
29	#11924005	C₂×C₄	1	4	yes	—
30	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₇₃	C₂³	1	2	yes	—
32	C₄×Dic₇₃	C₂³	1	4	yes	—
33	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
34	C₄⋊C₄×C₇₃	C₂×C₄	1	4	yes	—
35	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
39	C₂×C₄×C₇₃	C₂²×C₄	1	4	yes	—
40	C₂×Dic₇₃	C₂²×C₄	1	2	yes	—
41	C₂×Dic₇₃	C₂²×C₄	1	4	yes	—
42	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
43	C₄×D₇₃	—	2	1	no	—
44	C₄×D₇₃	—	2	1	no	—
45	C₄×D₇₃	—	4	2	no	—
46	Dic₁₄₆	—	4	4	no	—
47	#10596833	—	2	4	no	—
48	#10596833	—	2	4	no	—
49	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
50	C₂×D₇₃	—	2	1	no	—
51	C₂×D₇₃	—	2	2	no	—
52	C₄×C₇₃	—	2	1	no	—
53	C₄×C₇₃	—	2	4	no	—
54	C₄×C₇₃	—	2	2	no	—
55	Dic₇₃	—	2	2	no	—
56	Dic₇₃	—	2	4	no	—
57	Dic₇₃	2₋¹⁺⁴	1	1	yes	characteristic
58	Dic₇₃	2₋¹⁺⁴	1	1	yes	characteristic
59	C₂×C₇₃	#519	1	1	yes	characteristic
60	C₂×C₇₃	#568	1	2	yes	—
61	D₇₃	—	4	1	no	—
62	#2987	—	73	1	no	maximal, Sylow
63	C₇₃	#2987	1	1	yes	characteristic, complemented, Sylow
64	#533	—	73	1	no	—
65	#446	—	73	4	no	—
66	#446	—	73	4	no	—
67	#433	—	73	4	no	—
68	#432	—	73	2	no	—
69	C₄⋊Q₈	—	73	2	no	—
70	#125	—	73	1	no	—
71	#125	#64408	1	1	yes	characteristic
72	C₂²⋊Q₈	—	73	4	no	—
73	C₄×Q₈	—	73	4	no	—
74	#117	—	73	2	no	—
75	C₂×C₄²	—	73	1	no	—
76	C₄⋊C₈	—	73	2	no	—
77	C₄⋊C₈	—	73	2	no	—
78	C₄⋊C₈	—	73	4	no	—
79	C₄⋊C₈	—	73	4	no	—
80	C₂²⋊C₈	—	73	4	no	—
81	#97	—	73	4	no	—
82	#97	—	73	4	no	—
83	C₄×C₈	—	73	4	no	—
84	C₂×Q₈	—	73	4	no	—
85	C₂²×C₄	—	73	2	no	—
86	C₂²×C₄	—	73	1	no	—
87	C₂×C₈	—	73	4	no	—
88	C₂×C₈	—	73	4	no	—
89	C₄⋊C₄	—	73	4	no	—
90	C₄⋊C₄	—	73	4	no	—
91	C₄⋊C₄	—	73	2	no	—
92	C₄⋊C₄	C₂×#64408	1	2	yes	—
93	C₄⋊C₄	C₂×#64408	1	4	yes	—
94	C₂²⋊C₄	—	73	4	no	—
95	C₄²	—	73	1	no	—
96	C₄²	—	73	4	no	—
97	C₄²	—	73	2	no	—
98	C₄²	C₂×#64408	1	1	yes	characteristic
99	C₂³	—	73	1	no	—
100	Q₈	—	292	4	no	—
101	C₂×C₄	—	292	2	no	—
102	C₂×C₄	—	73	1	no	—
103	C₂×C₄	—	73	2	no	—
104	C₂×C₄	—	73	4	no	—
105	C₂×C₄	—	146	1	no	—
106	C₂×C₄	—	146	1	no	—
107	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
108	C₂×C₄	C₂²×#64408	1	2	yes	—
109	C₂×C₄	C₂²×#64408	1	4	yes	—
110	C₈	—	146	4	no	—
111	C₈	—	146	4	no	—
112	C₂²	—	146	1	no	—
113	C₂²	—	146	2	no	—
114	C₂²	C₂³×#64408	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	2	2	no	—
117	C₄	—	2	4	no	—
118	C₄	—	73	1	no	—
119	C₄	—	73	1	no	—
120	C₄	—	146	2	no	—
121	C₄	—	146	4	no	—
122	C₂	—	292	1	no	—
123	C₂	#17989655	1	1	yes	characteristic
124	C₂	#17989666	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989639

C₂

yes

maximal, complemented

#17989637

C₂

yes

maximal, complemented

#17989612

C₂

yes

maximal

#17989609

C₂

yes

maximal

#17989143

C₂

yes

maximal, characteristic

#14556658

C₂²

yes

—

C₄⋊#10596833

C₂²

yes

—

C₄⋊#10596833

C₂²

yes

—

C₄⋊#10596833

C₂²

yes

—

#14556648

C₂²

yes

—

#14556646

C₂²

yes

—

#14556646

C₂²

yes

—

C₄×#10596833

C₂²

yes

—

#14556590

C₄

yes

—

#14556583

C₄

yes

characteristic

#14556569

C₄

yes

—

#14556556

C₂²

yes

—

#14556549

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

#125×C₇₃

C₄

yes

characteristic

C₂×#10596833

C₂³

yes

—

C₂×#10596833

C₂³

yes

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

C₂×C₄

yes

—

#11924007

C₂×C₄

yes

—

#11924005

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂³

yes

—

C₄×Dic₇₃

C₂³

yes

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂⁴

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

#10596833

—

#10596833

—

C₂²×C₇₃

C₂³×C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

2₋¹⁺⁴

yes

characteristic

Dic₇₃

2₋¹⁺⁴

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

D₇₃

—

#2987

—

maximal, Sylow

C₇₃

#2987

yes

characteristic, complemented, Sylow

—

—

—

—

—

C₄⋊Q₈

—

—

yes

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×#64408

yes

—

C₄⋊C₄

C₂×#64408

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

100

Q₈

—

292

—

101

C₂×C₄

—

292

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

146

—

106

C₂×C₄

—

146

—

107

C₂×C₄

C₂²×#64408

yes

characteristic

108

C₂×C₄

C₂²×#64408

yes

—

109

C₂×C₄

C₂²×#64408

yes

—

110

C₈

—

146

—

111

C₈

—

146

—

112

C₂²

—

146

—

113

C₂²

—

146

—

114

C₂²

C₂³×#64408

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

146

—

121

C₄

—

146

—

122

C₂

—

292

—

123

C₂

#17989655

yes

characteristic

124

C₂

#17989666

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂³×C₄
Fitting	#125×C₇₃	C₄
hypercenter	#125	#64408
hypocenter	C₇₃	#2987
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #125

subgroup

G/H

center, Frattini

C₂²

C₂³×#64408

commutator, socle

C₂²×C₇₃

C₂³×C₄

Fitting

#125×C₇₃

C₄

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂² ◁ #125

N	H ≅ G/N	type
1. #17989639	C₂	semidirect
2. #17989637	C₂	semidirect
63. C₇₃	#2987	semidirect

H ≅ G/N

type

1. #17989639

C₂

semidirect

2. #17989637

C₂

semidirect

63. C₇₃

#2987

semidirect

Subgroups — #22626844

Conjugacy classes of subgroups

Complements