Group #22625849 — subgroups

Subgroups — #22625849

Order 9344.

216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 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×#14556658	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#10596833	C₂	1	1	yes	maximal, characteristic
3	#17989453	C₂	1	4	yes	maximal
4	#17988432	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10596833	C₂²	1	2	yes	—
6	C₂²×#10596833	C₂²	1	2	yes	—
7	#14556658	—	2	2	no	—
8	C₄⋊#10596833	—	2	2	no	—
9	C₂×C₄×Dic₇₃	C₂²	1	2	yes	—
10	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
11	#14556498	C₄	1	2	yes	—
12	#14556498	C₄	1	1	yes	characteristic
13	#95×C₇₃	C₄	1	1	yes	characteristic
14	C₂×#10596833	—	2	2	no	—
15	C₂×#10596833	—	2	2	no	—
16	C₂×#10596833	—	2	4	no	—
17	C₂×#10596833	—	2	4	no	—
18	C₂²×Dic₇₃	C₂×C₄	1	2	yes	—
19	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
21	C₄×Dic₇₃	—	2	2	no	—
22	C₄×Dic₇₃	—	2	2	no	—
23	C₄×Dic₇₃	D₄	1	2	yes	—
24	C₄×Dic₇₃	Q₈	1	2	yes	—
25	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₇₃	—	2	2	no	—
29	C₂×C₄×C₇₃	—	2	2	no	—
30	C₂×C₄×C₇₃	—	2	2	no	—
31	C₂×C₄×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
33	C₂×Dic₇₃	—	2	1	no	—
34	C₂×Dic₇₃	—	2	1	no	—
35	C₂×Dic₇₃	—	2	2	no	—
36	C₂×Dic₇₃	—	2	2	no	—
37	C₂×Dic₇₃	—	2	2	no	—
38	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
39	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×Dic₇₃	#41	1	2	yes	—
42	C₂×Dic₇₃	#41	1	2	yes	—
43	#10596833	—	4	2	no	—
44	#10596833	—	4	2	no	—
45	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₇₃	#117	1	2	yes	—
47	C₂²×C₇₃	#131	1	2	yes	—
48	C₂²×C₇₃	#131	1	1	yes	characteristic
49	C₂²×C₇₃	#131	1	1	yes	characteristic
50	C₄×C₇₃	—	2	2	no	—
51	C₄×C₇₃	—	4	2	no	—
52	Dic₇₃	—	2	2	no	—
53	Dic₇₃	—	4	2	no	—
54	Dic₇₃	#124	1	1	yes	characteristic
55	Dic₇₃	#124	1	1	yes	characteristic
56	Dic₇₃	#125	1	2	yes	—
57	C₂×C₇₃	#382	1	1	yes	characteristic
58	C₂×C₇₃	#424	1	1	yes	characteristic
59	C₂×C₇₃	#424	1	1	yes	characteristic
60	C₂×C₇₃	#433	1	2	yes	—
61	C₂×C₇₃	#433	1	2	yes	—
62	#1832	—	73	1	no	maximal, Sylow
63	C₇₃	#1832	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₄⋊C₈	—	73	1	no	—
65	C₂×C₄⋊C₈	—	73	1	no	—
66	#376	—	73	1	no	—
67	#336	—	73	4	no	—
68	C₂²×C₈	—	73	2	no	—
69	C₂²×C₈	—	73	2	no	—
70	C₂×C₄²	—	73	1	no	—
71	C₂×C₄²	—	73	2	no	—
72	C₄⋊C₈	—	146	2	no	—
73	C₄⋊C₈	—	146	2	no	—
74	#95	—	73	2	no	—
75	#95	—	73	1	no	—
76	#95	#64408	1	1	yes	characteristic
77	C₂²×C₄	—	73	1	no	—
78	C₂²×C₄	—	73	1	no	—
79	C₂²×C₄	—	73	2	no	—
80	C₂²×C₄	C₂×#64408	1	2	yes	—
81	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
82	C₂×C₈	—	146	2	no	—
83	C₂×C₈	—	146	2	no	—
84	C₂×C₈	—	146	4	no	—
85	C₂×C₈	—	146	4	no	—
86	C₄²	—	73	2	no	—
87	C₄²	—	73	2	no	—
88	C₄²	—	146	2	no	—
89	C₄²	—	146	2	no	—
90	C₂³	C₂²×#64408	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	2	no	—
98	C₂×C₄	—	73	2	no	—
99	C₂×C₄	—	73	2	no	—
100	C₂×C₄	—	146	2	no	—
101	C₂×C₄	—	146	2	no	—
102	C₂×C₄	—	146	2	no	—
103	C₂×C₄	—	146	1	no	—
104	C₂×C₄	—	146	1	no	—
105	C₂×C₄	C₄⋊#64408	1	2	yes	—
106	C₈	—	292	2	no	—
107	C₈	—	292	2	no	—
108	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
109	C₂²	#14556670	1	2	yes	—
110	C₂²	#14556678	1	2	yes	—
111	C₂²	#14556678	1	1	yes	characteristic
112	C₂²	#14556679	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	4	2	no	—
115	C₄	—	292	2	no	—
116	C₄	—	73	1	no	—
117	C₄	—	73	1	no	—
118	C₄	—	73	2	no	—
119	C₄	—	146	2	no	—
120	C₂	#17989531	1	1	yes	characteristic
121	C₂	#17989593	1	1	yes	characteristic
122	C₂	#17989594	1	1	yes	characteristic
123	C₂	#17989611	1	2	yes	—
124	C₂	#17989612	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556658

C₂

yes

maximal, characteristic

C₂×C₄⋊#10596833

C₂

yes

maximal, characteristic

#17989453

C₂

yes

maximal

#17988432

C₂

yes

maximal, characteristic

C₂²×#10596833

C₂²

yes

—

C₂²×#10596833

C₂²

yes

—

#14556658

—

C₄⋊#10596833

—

C₂×C₄×Dic₇₃

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556498

C₄

yes

—

#14556498

C₄

yes

characteristic

#95×C₇₃

C₄

yes

—

—

—

—

C₂²×Dic₇₃

C₂×C₄

yes

—

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂³

yes

characteristic

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

Q₈

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

characteristic

C₂×Dic₇₃

#41

yes

—

C₂×Dic₇₃

#41

yes

—

#10596833

—

#10596833

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₃

#117

yes

—

C₂²×C₇₃

#131

yes

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

yes

Dic₇₃

yes

Dic₇₃

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

#433

yes

—

#1832

—

maximal, Sylow

C₇₃

#1832

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

#376

—

#336

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

146

—

C₄⋊C₈

—

146

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₄²

—

146

—

C₂³

C₂²×#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

146

—

101

C₂×C₄

—

146

—

102

C₂×C₄

—

146

—

103

C₂×C₄

—

146

—

104

C₂×C₄

—

146

—

105

C₂×C₄

C₄⋊#64408

yes

—

106

C₈

—

292

—

107

C₈

—

292

—

108

C₂²

C₂×C₄⋊#64408

yes

characteristic

109

C₂²

#14556670

yes

—

110

C₂²

#14556678

yes

—

111

C₂²

#14556678

yes

characteristic

112

C₂²

#14556679

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

292

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

146

—

120

C₂

#17989531

yes

characteristic

121

C₂

#17989593

yes

characteristic

122

C₂

#17989594

yes

characteristic

123

C₂

#17989611

yes

—

124

C₂

#17989612

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#64408
commutator, socle	C₂³×C₇₃	C₂²×C₄
Fitting	#95×C₇₃	C₄
hypercenter	#95	#64408
hypocenter	C₇₃	#1832
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#64408

commutator, socle

C₂³×C₇₃

C₂²×C₄

Fitting

#95×C₇₃

C₄

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
63. C₇₃	#1832	semidirect

H ≅ G/N

type

63. C₇₃

#1832

semidirect

Subgroups — #22625849

Conjugacy classes of subgroups

Complements