Group #22611485 — subgroups

Subgroups — #22611485

Order 9344.

210 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 67 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	#17988636	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988614	C₂	1	2	yes	maximal, complemented
3	#17988605	C₂	1	2	yes	maximal
4	#17988555	C₂	1	1	yes	maximal, characteristic
5	H(3,ℤ/4)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924028	C₂²	1	1	yes	characteristic
7	C₂×#11924012	C₂²	1	2	yes	—
8	C₂²×#10596831	C₂²	1	1	yes	characteristic
9	#14556527	—	2	2	no	—
10	C₄⋊#10596831	—	2	4	no	—
11	#14556519	—	2	4	no	—
12	#14556503	—	2	2	no	—
13	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	#117×C₇₃	C₂²	1	2	yes	—
15	#11924028	—	2	2	no	—
16	#11924028	—	2	2	no	—
17	C₂×Dic₁₄₆	Q₈	1	1	yes	characteristic
18	C₂×D₂₉₂	Q₈	1	1	yes	characteristic
19	C₂×C₂²⋊D₇₃	—	2	1	no	—
20	C₂×C₄×D₇₃	—	2	1	no	—
21	#11924012	—	2	2	no	—
22	#11924012	—	2	2	no	—
23	C₂×#10596831	—	2	1	no	—
24	C₂×#10596831	—	2	2	no	—
25	C₂×#10596831	—	2	2	no	—
26	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
27	M₁₆×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	D₄	1	2	yes	—
29	C₄⋊C₄×C₇₃	—	2	2	no	—
30	C₂²⋊C₄×C₇₃	—	2	2	no	—
31	C₄²×C₇₃	D₄	1	4	yes	—
32	C₂³×C₇₃	#41	1	1	yes	characteristic
33	C₂²×D₇₃	—	2	1	no	—
34	C₂×C₄×C₇₃	—	2	4	no	—
35	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₇₃	#41	1	2	yes	—
39	C₂²⋊D₇₃	—	4	2	no	—
40	C₂×Dic₇₃	—	2	1	no	—
41	D₂₉₂	—	2	2	no	—
42	C₄×D₇₃	—	4	1	no	—
43	C₄×D₇₃	—	4	1	no	—
44	Dic₁₄₆	—	2	2	no	—
45	C₈×C₇₃	—	2	2	no	—
46	#10596831	—	4	1	no	—
47	#10596831	—	4	2	no	—
48	C₂²×C₇₃	—	4	1	no	—
49	C₂²×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₇₃	#123	1	2	yes	—
51	C₂×D₇₃	—	4	2	no	—
52	C₂×D₇₃	—	4	1	no	—
53	C₄×C₇₃	—	4	4	no	—
54	C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
55	C₄×C₇₃	#123	1	1	yes	characteristic
56	C₄×C₇₃	#127	1	1	yes	characteristic
57	Dic₇₃	—	4	1	no	—
58	C₂×C₇₃	—	2	2	no	—
59	C₂×C₇₃	—	2	1	no	—
60	C₂×C₇₃	#399	1	1	yes	characteristic
61	D₇₃	—	8	1	no	—
62	#2098	—	73	1	no	maximal, Sylow
63	C₇₃	#2098	1	1	yes	characteristic, complemented, Sylow
64	#430	—	73	1	no	—
65	#424	—	73	2	no	—
66	#421	—	73	2	no	—
67	#408	—	73	1	no	—
68	H(3,ℤ/4)	D₇₃	1	1	yes	characteristic, complemented
69	C₂×#41	—	73	1	no	—
70	C₂×M₁₆	—	73	2	no	—
71	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
72	C₂²×C₈	—	73	1	no	—
73	#117	C₂×D₇₃	1	2	yes	—
74	#108	—	146	2	no	—
75	C₄⋊C₈	—	146	4	no	—
76	#104	—	146	4	no	—
77	C₂²⋊C₈	—	146	2	no	—
78	#41	—	146	2	no	—
79	#41	—	146	2	no	—
80	C₂×Q₈	—	73	1	no	—
81	C₂×D₄	—	73	1	no	—
82	C₂×D₄	—	146	1	no	—
83	C₂²×C₄	—	146	1	no	—
84	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
85	M₁₆	—	2	2	no	—
86	M₁₆	—	146	2	no	—
87	M₁₆	—	146	2	no	—
88	C₂×C₈	—	146	1	no	—
89	C₂×C₈	—	146	2	no	—
90	C₂×C₈	—	146	2	no	—
91	C₂×C₈	D₂₉₂	1	2	yes	—
92	C₄⋊C₄	—	2	2	no	—
93	C₂²⋊C₄	—	2	2	no	—
94	C₄²	D₂₉₂	1	4	yes	—
95	C₂³	—	146	1	no	—
96	C₂³	#11924027	1	1	yes	characteristic
97	Q₈	—	146	2	no	—
98	D₄	—	292	2	no	—
99	D₄	—	146	2	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	292	1	no	—
102	C₂×C₄	—	292	1	no	—
103	C₂×C₄	—	146	1	no	—
104	C₂×C₄	C₂×D₂₉₂	1	2	yes	—
105	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
106	C₂×C₄	Q₈×D₇₃	1	1	yes	characteristic
107	C₂×C₄	#11924027	1	2	yes	—
108	C₈	—	2	2	no	—
109	C₈	—	292	1	no	—
110	C₈	—	292	2	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	292	2	no	—
113	C₂²	—	292	1	no	—
114	C₂²	#14556571	1	1	yes	characteristic
115	C₂²	#14556575	1	2	yes	—
116	C₄	—	4	4	no	—
117	C₄	—	292	1	no	—
118	C₄	#14556571	1	2	yes	—
119	C₄	#14556575	1	1	yes	characteristic
120	C₄	#14556588	1	1	yes	characteristic
121	C₂	—	2	2	no	—
122	C₂	—	2	1	no	—
123	C₂	—	584	1	no	—
124	C₂	#17988524	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988636

C₂

yes

maximal, characteristic, complemented

#17988614

C₂

yes

maximal, complemented

#17988605

C₂

yes

maximal

#17988555

C₂

yes

maximal, characteristic

H(3,ℤ/4)×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924028

C₂²

yes

characteristic

C₂×#11924012

C₂²

yes

—

C₂²×#10596831

C₂²

yes

—

—

—

—

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

#117×C₇₃

C₂²

yes

—

#11924028

—

#11924028

—

C₂×Dic₁₄₆

Q₈

yes

characteristic

C₂×D₂₉₂

Q₈

yes

characteristic

C₂×C₂²⋊D₇₃

—

C₂×C₄×D₇₃

—

—

—

—

—

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

D₄

yes

—

C₂³×C₇₃

#41

yes

characteristic

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₇₃

#123

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#399

yes

characteristic

D₇₃

—

#2098

—

maximal, Sylow

C₇₃

#2098

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₃

yes

characteristic, complemented

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

characteristic

C₂²×C₈

—

#117

C₂×D₇₃

yes

—

#108

—

146

—

C₄⋊C₈

—

146

—

#104

—

146

—

C₂²⋊C₈

—

146

—

#41

—

146

—

#41

—

146

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

D₂₉₂

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₂₉₂

yes

—

C₂³

—

146

—

C₂³

#11924027

yes

characteristic

Q₈

—

146

—

D₄

—

292

—

D₄

—

146

—

100

C₂×C₄

—

101

C₂×C₄

—

292

—

102

C₂×C₄

—

292

—

103

C₂×C₄

—

146

—

104

C₂×C₄

C₂×D₂₉₂

yes

—

105

C₂×C₄

C₂×D₂₉₂

yes

characteristic

106

C₂×C₄

Q₈×D₇₃

yes

characteristic

107

C₂×C₄

#11924027

yes

—

108

C₈

—

109

C₈

—

292

—

110

C₈

—

292

—

111

C₂²

—

112

C₂²

—

292

—

113

C₂²

—

292

—

114

C₂²

#14556571

yes

characteristic

115

C₂²

#14556575

yes

—

116

C₄

—

117

C₄

—

292

—

118

C₄

#14556571

yes

—

119

C₄

#14556575

yes

characteristic

120

C₄

#14556588

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

584

—

124

C₂

#17988524

yes

characteristic

	subgroup	G/H
center	C₄	#14556588
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	H(3,ℤ/4)×C₇₃	C₂
socle	C₂×C₇₃	#399
hypercenter	H(3,ℤ/4)	D₇₃
hypocenter	C₇₃	#2098
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#14556588

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

H(3,ℤ/4)×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
1. #17988636	C₂	semidirect
2. #17988614	C₂	semidirect
5. H(3,ℤ/4)×C₇₃	C₂	semidirect
63. C₇₃	#2098	semidirect
68. H(3,ℤ/4)	D₇₃	semidirect

H ≅ G/N

type

1. #17988636

C₂

semidirect

2. #17988614

C₂

semidirect

5. H(3,ℤ/4)×C₇₃

C₂

semidirect

63. C₇₃

#2098

semidirect

68. H(3,ℤ/4)

D₇₃

semidirect

Subgroups — #22611485

Conjugacy classes of subgroups

Complements