Group #22625873 — subgroups

Subgroups — #22625873

Order 9344.

212 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 86 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×#14556662	C₂	1	2	yes	maximal
2	C₂×#14556661	C₂	1	2	yes	maximal
3	#17989592	C₂	1	1	yes	maximal, characteristic
4	#17989591	C₂	1	1	yes	maximal, characteristic
5	#97×D₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924038	C₂²	1	2	yes	—
7	C₂×#11924038	C₂²	1	1	yes	characteristic
8	C₂×#11924038	C₂²	1	1	yes	characteristic
9	#14556662	—	2	4	no	—
10	#14556661	—	2	4	no	—
11	#14556658	—	2	2	no	—
12	C₄⋊#10596833	—	2	2	no	—
13	C₂×C₈×D₇₃	C₂²	1	2	yes	—
14	C₄²×D₇₃	C₂²	1	1	yes	characteristic
15	#14556502	C₄	1	1	yes	characteristic
16	#14556501	C₄	1	2	yes	—
17	#97×C₇₃	C₄	1	1	yes	characteristic
18	#11924038	—	2	2	no	—
19	#11924038	—	2	2	no	—
20	#11924038	—	2	2	no	—
21	#11924038	—	2	2	no	—
22	C₂×#10596833	—	2	2	no	—
23	C₂×#10596833	—	2	1	no	—
24	C₂×#10596833	—	2	1	no	—
25	C₂×C₄×D₇₃	Q₈	1	2	yes	—
26	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
27	C₂×#10596831	C₂×C₄	1	2	yes	—
28	C₈×D₇₃	D₄	1	4	yes	—
29	C₈×D₇₃	Q₈	1	4	yes	—
30	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₇₃	D₄	1	2	yes	—
32	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
33	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₇₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
38	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
39	C₄×D₇₃	—	4	2	no	—
40	C₄×D₇₃	C₂×D₄	1	2	yes	—
41	C₄×D₇₃	C₂×Q₈	1	2	yes	—
42	#10596833	—	4	2	no	—
43	#10596833	—	4	1	no	—
44	#10596833	—	4	1	no	—
45	C₈×C₇₃	C₄⋊C₄	1	4	yes	—
46	#10596831	C₄⋊C₄	1	4	yes	—
47	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×D₇₃	—	2	2	no	—
49	C₂×D₇₃	C₄⋊Q₈	1	2	yes	—
50	C₄×C₇₃	—	2	2	no	—
51	C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
52	Dic₇₃	—	2	2	no	—
53	Dic₇₃	#127	1	1	yes	characteristic
54	Dic₇₃	C₄⋊Q₈	1	1	yes	characteristic
55	C₂×C₇₃	#384	1	1	yes	characteristic
56	C₂×C₇₃	#430	1	2	yes	—
57	D₇₃	—	2	2	no	—
58	#1849	—	73	1	no	maximal, Sylow
59	C₇₃	#1849	1	1	yes	characteristic, complemented, Sylow
60	C₂×#108	—	73	2	no	—
61	C₂×#108	—	73	2	no	—
62	#423	—	73	1	no	—
63	#423	—	73	1	no	—
64	C₂×#97	—	73	1	no	—
65	C₂×M₁₆	—	73	2	no	—
66	C₂×M₁₆	—	73	1	no	—
67	C₂×M₁₆	—	73	1	no	—
68	C₂²×C₈	—	73	2	no	—
69	C₂×C₄²	—	73	1	no	—
70	#108	—	146	4	no	—
71	#108	—	146	4	no	—
72	C₄⋊C₈	—	146	2	no	—
73	C₄⋊C₈	—	146	2	no	—
74	#97	—	73	2	no	—
75	#97	—	73	1	no	—
76	#97	#64408	1	1	yes	characteristic
77	C₂²×C₄	—	73	2	no	—
78	C₂²×C₄	—	73	1	no	—
79	M₁₆	—	146	2	no	—
80	M₁₆	—	146	2	no	—
81	M₁₆	—	146	2	no	—
82	M₁₆	—	146	2	no	—
83	C₂×C₈	—	73	2	no	—
84	C₂×C₈	—	73	4	no	—
85	C₂×C₈	—	73	4	no	—
86	C₂×C₈	—	146	2	no	—
87	C₂×C₈	—	146	1	no	—
88	C₂×C₈	—	146	1	no	—
89	C₂×C₈	C₂×#64408	1	2	yes	—
90	C₄²	—	73	2	no	—
91	C₄²	—	73	1	no	—
92	C₄²	C₂×#64408	1	1	yes	characteristic
93	C₂³	—	73	1	no	—
94	C₂×C₄	—	292	2	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	2	no	—
97	C₂×C₄	—	73	2	no	—
98	C₂×C₄	—	73	2	no	—
99	C₂×C₄	C₄⋊#64408	1	2	yes	—
100	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
101	C₈	—	292	2	no	—
102	C₈	—	292	1	no	—
103	C₈	—	292	1	no	—
104	C₈	—	73	4	no	—
105	C₈	C₄⋊#64408	1	4	yes	—
106	C₂²	—	73	2	no	—
107	C₂²	—	146	2	no	—
108	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	73	1	no	—
111	C₄	—	73	1	no	—
112	C₄	—	146	2	no	—
113	C₄	C₂×C₄⋊#64408	1	2	yes	—
114	C₂	—	146	2	no	—
115	C₂	#17989533	1	1	yes	characteristic
116	C₂	#17989602	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556662

C₂

yes

maximal

C₂×#14556661

C₂

yes

maximal

#17989592

C₂

yes

maximal, characteristic

#17989591

C₂

yes

maximal, characteristic

#97×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924038

C₂²

yes

—

C₂×#11924038

C₂²

yes

characteristic

C₂×#11924038

C₂²

yes

—

—

—

—

C₂×C₈×D₇₃

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

#14556502

C₄

yes

characteristic

#14556501

C₄

yes

—

#97×C₇₃

C₄

yes

—

—

—

—

—

—

—

C₂×C₄×D₇₃

Q₈

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₂×#10596831

C₂×C₄

yes

—

C₈×D₇₃

D₄

yes

—

C₈×D₇₃

Q₈

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

C₂×D₄

yes

—

C₄×D₇₃

C₂×Q₈

yes

—

#10596833

—

#10596833

—

#10596833

—

C₈×C₇₃

C₄⋊C₄

yes

—

#10596831

C₄⋊C₄

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄⋊Q₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄⋊C₄

yes

—

Dic₇₃

—

Dic₇₃

#127

yes

characteristic

Dic₇₃

C₄⋊Q₈

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

D₇₃

—

#1849

—

maximal, Sylow

C₇₃

#1849

yes

characteristic, complemented, Sylow

—

—

—

—

C₂×#97

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

146

—

#108

—

146

—

C₄⋊C₈

—

146

—

C₄⋊C₈

—

146

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊#64408

yes

—

100

C₂×C₄

C₂²×#64408

yes

characteristic

101

C₈

—

292

—

102

C₈

—

292

—

103

C₈

—

292

—

104

C₈

—

105

C₈

C₄⋊#64408

yes

—

106

C₂²

—

107

C₂²

—

146

—

108

C₂²

C₂×C₄⋊#64408

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

146

—

113

C₄

C₂×C₄⋊#64408

yes

—

114

C₂

—

146

—

115

C₂

#17989533

yes

characteristic

116

C₂

#17989602

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#97×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	#97	#64408
hypocenter	C₇₃	#1849
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#97×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄⋊C₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
59. C₇₃	#1849	semidirect

H ≅ G/N

type

59. C₇₃

#1849

semidirect

Subgroups — #22625873

Conjugacy classes of subgroups

Complements