Group #22626141 — subgroups

Subgroups — #22626141

Order 9344.

184 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 102 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×#14556664	C₂	1	1	yes	maximal, characteristic
3	#17989476	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989475	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989473	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#11924031	C₂	1	1	yes	maximal, characteristic, complemented
7	#17988544	C₂	1	1	yes	maximal, characteristic
8	#14556666	C₄	1	4	yes	complemented
9	#14556664	C₄	1	4	yes	complemented
10	C₂×#11924031	C₂²	1	1	yes	characteristic
11	C₂×#11924031	C₂²	1	1	yes	characteristic
12	C₂×#11924031	C₂²	1	1	yes	characteristic
13	C₂×#11924031	C₂²	1	1	yes	characteristic
14	C₂×#11924011	C₄	1	1	yes	characteristic
15	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
16	#14556548	C₄	1	1	yes	characteristic
17	#14556501	C₄	1	1	yes	characteristic
18	C₄×#10596831	C₂²	1	1	yes	characteristic
19	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
20	#97×C₇₃	C₄	1	1	yes	characteristic
21	#11924031	C₂×C₄	1	2	yes	—
22	#11924031	C₂×C₄	1	2	yes	—
23	#11924031	C₂×C₄	1	2	yes	—
24	#11924031	C₂×C₄	1	2	yes	—
25	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
26	#11924011	C₈	1	4	yes	—
27	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
28	C₂×#10596831	C₂³	1	1	yes	characteristic
29	C₈×D₇₃	C₂×C₄	1	2	yes	—
30	C₈×D₇₃	C₂×C₄	1	2	yes	—
31	#11924007	C₈	1	2	yes	—
32	#11924005	C₈	1	2	yes	—
33	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
39	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
41	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
42	C₄×D₇₃	C₄²	1	2	yes	—
43	C₄×D₇₃	C₂×C₈	1	2	yes	—
44	C₈×C₇₃	C₄²	1	2	yes	—
45	C₈×C₇₃	C₂×C₈	1	2	yes	—
46	#10596831	C₂×C₈	1	2	yes	—
47	#10596831	C₂²×C₄	1	1	yes	characteristic
48	#10596831	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
50	C₂×D₇₃	—	2	2	no	—
51	C₂×D₇₃	C₄×C₈	1	2	yes	—
52	C₄×C₇₃	—	2	2	no	—
53	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
54	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
55	Dic₇₃	—	2	2	no	—
56	Dic₇₃	C₄×C₈	1	2	yes	—
57	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
58	C₂×C₇₃	#504	1	2	yes	—
59	D₇₃	—	2	2	no	—
60	#2108	—	73	1	no	maximal, Sylow
61	C₇₃	#2108	1	1	yes	characteristic, complemented, Sylow
62	C₂×M₃₂	—	73	1	no	—
63	C₂²×C₁₆	—	73	1	no	—
64	#405	—	73	1	no	—
65	#346	—	73	1	no	—
66	#346	—	73	1	no	—
67	C₄×C₁₆	—	73	1	no	—
68	C₄×C₁₆	—	73	1	no	—
69	C₂×M₁₆	—	73	1	no	—
70	C₂²×C₈	—	73	1	no	—
71	#117	—	73	1	no	—
72	M₃₂	—	73	4	no	—
73	C₂×C₁₆	—	73	1	no	—
74	C₂×C₁₆	—	73	1	no	—
75	C₂×C₁₆	—	73	1	no	—
76	C₂×C₁₆	—	73	1	no	—
77	C₂×C₁₆	—	73	4	no	—
78	#97	—	73	1	no	—
79	#97	#64408	1	1	yes	characteristic
80	C₄×C₈	—	73	1	no	—
81	C₄×C₈	—	73	1	no	—
82	C₂²×C₄	—	73	1	no	—
83	M₁₆	—	73	4	no	—
84	C₂×C₈	—	73	1	no	—
85	C₂×C₈	—	73	1	no	—
86	C₂×C₈	—	73	2	no	—
87	C₂×C₈	—	73	2	no	—
88	C₂×C₈	C₂×#64408	1	1	yes	characteristic
89	C₂×C₈	C₂×#64408	1	1	yes	characteristic
90	C₄⋊C₄	—	73	2	no	—
91	C₂²⋊C₄	—	73	2	no	—
92	C₄²	—	73	1	no	—
93	C₄²	C₂×#64408	1	1	yes	characteristic
94	C₁₆	—	73	2	no	—
95	C₁₆	—	73	2	no	—
96	C₁₆	—	73	2	no	—
97	C₁₆	—	73	2	no	—
98	C₂³	—	73	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	2	no	—
101	C₂×C₄	—	73	2	no	—
102	C₂×C₄	—	73	2	no	—
103	C₂×C₄	#11924036	1	2	yes	—
104	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
105	C₈	—	73	2	no	—
106	C₈	—	73	1	no	—
107	C₈	—	73	1	no	—
108	C₈	C₄×#64408	1	2	yes	—
109	C₈	#11924036	1	2	yes	—
110	C₂²	—	73	2	no	—
111	C₂²	—	146	2	no	—
112	C₂²	C₂×#11924036	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	73	2	no	—
115	C₄	—	146	2	no	—
116	C₄	C₂×C₄×#64408	1	1	yes	characteristic
117	C₄	C₂×#11924036	1	1	yes	characteristic
118	C₂	—	146	2	no	—
119	C₂	C₄×#11924036	1	1	yes	characteristic
120	C₂	#17989646	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556666

C₂

yes

maximal, characteristic

C₂×#14556664

C₂

yes

maximal, characteristic

#17989476

C₂

yes

maximal, characteristic, complemented

#17989475

C₂

yes

maximal, characteristic, complemented

#17989473

C₂

yes

maximal, characteristic, complemented

C₄×#11924031

C₂

yes

maximal, characteristic, complemented

#17988544

C₂

yes

maximal, characteristic

#14556666

C₄

yes

complemented

#14556664

C₄

yes

complemented

C₂×#11924031

C₂²

yes

characteristic

C₂×#11924031

C₂²

yes

characteristic

C₂×#11924031

C₂²

yes

characteristic

C₂×#11924031

C₂²

yes

characteristic

C₂×#11924011

C₄

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556548

C₄

yes

characteristic

#14556501

C₄

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

#97×C₇₃

C₄

yes

characteristic

#11924031

C₂×C₄

yes

—

#11924031

C₂×C₄

yes

—

#11924031

C₂×C₄

yes

—

#11924031

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

#11924011

C₈

yes

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂³

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

—

C₈×D₇₃

C₂×C₄

yes

—

#11924007

C₈

yes

—

#11924005

C₈

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

—

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₄²

yes

—

C₄×D₇₃

C₂×C₈

yes

—

C₈×C₇₃

C₄²

yes

—

C₈×C₇₃

C₂×C₈

yes

—

#10596831

C₂×C₈

yes

—

#10596831

C₂²×C₄

yes

characteristic

#10596831

C₂²×C₄

yes

characteristic

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄×C₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

Dic₇₃

C₄×C₈

yes

—

C₂×C₇₃

C₂×C₄×C₈

yes

characteristic

C₂×C₇₃

#504

yes

—

D₇₃

—

#2108

—

maximal, Sylow

C₇₃

#2108

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

#11924036

yes

—

104

C₂×C₄

C₂²×#64408

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

C₄×#64408

yes

—

109

C₈

#11924036

yes

—

110

C₂²

—

111

C₂²

—

146

—

112

C₂²

C₂×#11924036

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

146

—

116

C₄

C₂×C₄×#64408

yes

characteristic

117

C₄

C₂×#11924036

yes

characteristic

118

C₂

—

146

—

119

C₂

C₄×#11924036

yes

characteristic

120

C₂

#17989646

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator	C₂×C₇₃	C₂×C₄×C₈
Fitting	#97×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₈
hypercenter	#97	#64408
hypocenter	C₇₃	#2108
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#64408

commutator

C₂×C₇₃

C₂×C₄×C₈

Fitting

#97×C₇₃

C₄

socle

C₂²×C₇₃

C₂²×C₈

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
3. #17989476	C₂	semidirect
4. #17989475	C₂	semidirect
5. #17989473	C₂	semidirect
6. C₄×#11924031	C₂	semidirect
8. #14556666	C₄	semidirect
9. #14556664	C₄	semidirect
61. C₇₃	#2108	semidirect

H ≅ G/N

type

3. #17989476

C₂

semidirect

4. #17989475

C₂

semidirect

5. #17989473

C₂

semidirect

6. C₄×#11924031

C₂

semidirect

8. #14556666

C₄

semidirect

9. #14556664

C₄

semidirect

61. C₇₃

#2108

semidirect

Subgroups — #22626141

Conjugacy classes of subgroups

Complements