Group #22611837 — subgroups

Subgroups — #22611837

Order 9344.

126 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 71 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	C₈×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11924003	C₂	1	1	yes	maximal, characteristic
3	#17988405	C₂	1	1	yes	maximal, characteristic
4	#17988405	C₂	1	1	yes	maximal, characteristic
5	#17988362	C₂	1	1	yes	maximal, characteristic
6	C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
7	#346×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₁₄₆	C₄	1	1	yes	characteristic
9	C₂×#11924003	C₂²	1	1	yes	characteristic
10	C₂×#11924003	C₂²	1	1	yes	characteristic
11	C₄⋊#10596831	C₄	1	1	yes	characteristic
12	#14556520	C₄	1	1	yes	characteristic
13	#14556520	C₄	1	1	yes	characteristic
14	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
15	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
18	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₄₆	C₈	1	1	yes	characteristic
20	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
21	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
22	C₄⋊Dic₇₃	C₈	1	1	yes	characteristic
23	#11924007	C₈	1	1	yes	characteristic
24	#11924007	C₈	1	1	yes	characteristic
25	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
27	#11924003	—	2	1	no	—
28	#11924003	—	2	1	no	—
29	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
31	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
32	C₁₆×C₇₃	—	2	1	no	—
33	C₁₆×C₇₃	Q₈	1	2	yes	complemented
34	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
38	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
39	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
40	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
41	Dic₁₄₆	—	2	2	no	—
42	C₈×C₇₃	—	2	1	no	—
43	C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
44	C₈×C₇₃	#41	1	1	yes	characteristic
45	#10596831	—	2	1	no	—
46	#10596831	—	2	1	no	—
47	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
48	C₄×C₇₃	—	2	1	no	—
49	C₄×C₇₃	—	2	1	no	—
50	C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
51	C₄×C₇₃	#131	1	1	yes	characteristic
52	Dic₇₃	—	2	1	no	—
53	Dic₇₃	—	2	1	no	—
54	Dic₇₃	—	2	1	no	—
55	Dic₇₃	M₃₂	1	2	yes	—
56	C₂×C₇₃	C₈×Q₈	1	1	yes	characteristic
57	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
58	C₂×C₇₃	#504	1	1	yes	characteristic
59	#2183	—	73	1	no	maximal, Sylow
60	C₇₃	#2183	1	1	yes	characteristic, complemented, Sylow
61	C₈×Q₈	—	73	1	no	—
62	C₄⋊C₁₆	—	73	1	no	—
63	C₄⋊C₁₆	—	73	1	no	—
64	C₄⋊C₁₆	—	73	1	no	—
65	#346	—	73	1	no	—
66	#346	D₇₃	1	1	yes	characteristic
67	C₄×C₁₆	—	73	1	no	—
68	C₄×Q₈	—	73	1	no	—
69	C₂×C₁₆	—	73	1	no	—
70	C₂×C₁₆	—	73	1	no	—
71	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
72	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
73	C₄⋊C₈	—	73	1	no	—
74	C₄⋊C₈	—	73	1	no	—
75	C₄⋊C₈	—	73	1	no	—
76	C₄×C₈	—	73	1	no	—
77	C₄×C₈	—	73	1	no	—
78	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
79	C₂×Q₈	—	73	1	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
83	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
84	C₄⋊C₄	—	73	1	no	—
85	C₄⋊C₄	—	73	1	no	—
86	C₄⋊C₄	—	73	1	no	—
87	C₄²	—	73	1	no	—
88	C₄²	—	73	1	no	—
89	C₄²	C₄×D₇₃	1	1	yes	characteristic
90	C₁₆	—	2	1	no	—
91	C₁₆	—	146	1	no	—
92	C₁₆	—	146	1	no	—
93	C₁₆	Dic₁₄₆	1	2	yes	complemented
94	Q₈	—	146	2	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
100	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	—	146	1	no	—
104	C₈	—	146	1	no	—
105	C₈	C₂×Dic₁₄₆	1	1	yes	characteristic
106	C₈	#11924028	1	1	yes	characteristic
107	C₂²	C₂×C₈×D₇₃	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	73	2	no	—
111	C₄	—	146	1	no	—
112	C₄	—	146	1	no	—
113	C₄	—	146	1	no	—
114	C₄	C₄×Dic₁₄₆	1	1	yes	characteristic
115	C₄	#14556597	1	1	yes	characteristic
116	C₂	C₈×Dic₁₄₆	1	1	yes	characteristic
117	C₂	M₃₂×D₇₃	1	1	yes	characteristic
118	C₂	#17989005	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₁₄₆

C₂

yes

maximal, characteristic

C₄⋊#11924003

C₂

yes

maximal, characteristic

#17988405

C₂

yes

maximal, characteristic

#17988405

C₂

yes

maximal, characteristic

#17988362

C₂

yes

maximal, characteristic

C₁₆×Dic₇₃

C₂

yes

maximal, characteristic

#346×C₇₃

C₂

yes

maximal, characteristic

C₄×Dic₁₄₆

C₄

yes

characteristic

C₂×#11924003

C₂²

yes

characteristic

C₂×#11924003

C₂²

yes

characteristic

C₄⋊#10596831

C₄

yes

characteristic

#14556520

C₄

yes

characteristic

#14556520

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

C₈

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₄⋊Dic₇₃

C₈

yes

characteristic

#11924007

C₈

yes

characteristic

#11924007

C₈

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

#11924003

—

#11924003

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₁₆×C₇₃

—

C₁₆×C₇₃

Q₈

yes

complemented

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

C₂×Q₈

yes

C₈×C₇₃

yes

—

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄×Q₈

yes

characteristic

C₄×C₇₃

#131

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

M₃₂

yes

—

C₂×C₇₃

C₈×Q₈

yes

characteristic

C₂×C₇₃

C₂×M₃₂

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₈×Q₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

#346

—

#346

D₇₃

yes

characteristic

C₄×C₁₆

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

C₂×C₁₆

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₄×D₇₃

yes

characteristic

C₁₆

—

C₁₆

—

146

—

C₁₆

—

146

—

C₁₆

Dic₁₄₆

yes

complemented

Q₈

—

146

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₇₃

yes

characteristic

100

C₂×C₄

C₈×D₇₃

yes

characteristic

101

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

102

C₈

—

103

C₈

—

146

—

104

C₈

—

146

—

105

C₈

C₂×Dic₁₄₆

yes

characteristic

106

C₈

#11924028

yes

characteristic

107

C₂²

C₂×C₈×D₇₃

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

146

—

112

C₄

—

146

—

113

C₄

—

146

—

114

C₄

C₄×Dic₁₄₆

yes

characteristic

115

C₄

#14556597

yes

characteristic

116

C₂

C₈×Dic₁₄₆

yes

characteristic

117

C₂

M₃₂×D₇₃

yes

characteristic

118

C₂

#17989005

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₇₃
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	#346×C₇₃	C₂
hypercenter	#346	D₇₃
hypocenter	C₇₃	#2183
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₇₃

commutator, socle

C₂²×C₇₃

C₂²×C₈

Fitting

#346×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
33. C₁₆×C₇₃	Q₈	semidirect
60. C₇₃	#2183	semidirect
93. C₁₆	Dic₁₄₆	semidirect

H ≅ G/N

type

33. C₁₆×C₇₃

Q₈

semidirect

60. C₇₃

#2183

semidirect

93. C₁₆

Dic₁₄₆

semidirect

Subgroups — #22611837

Conjugacy classes of subgroups

Complements