Group #22611800 — subgroups

Subgroups — #22611800

Order 9344.

148 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 61 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×#14556537	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₂₉₂	C₂	1	1	yes	maximal, characteristic
3	#17988414	C₂	1	1	yes	maximal, characteristic
4	#17988391	C₂	1	1	yes	maximal, characteristic
5	#17988390	C₂	1	1	yes	maximal, characteristic
6	#17988363	C₂	1	1	yes	maximal, characteristic
7	C₄×Q₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
9	C₄×Dic₁₄₆	—	2	1	no	—
10	#14556537	C₄	1	4	yes	complemented
11	C₂×#11924003	C₂²	1	1	yes	characteristic
12	C₂×#11924003	C₂²	1	1	yes	characteristic
13	#14556525	C₂²	1	1	yes	characteristic
14	#14556516	—	2	1	no	—
15	C₂×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
16	C₄×Q₈×C₇₃	—	2	1	no	—
17	#107×C₇₃	C₂²	1	1	yes	characteristic
18	#103×C₇₃	—	2	1	no	—
19	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×Dic₁₄₆	—	2	1	no	—
21	Dic₂₉₂	—	2	1	no	—
22	Dic₂₉₂	C₂×C₄	1	2	yes	—
23	C₄⋊Dic₇₃	—	2	1	no	—
24	#11924007	—	4	1	no	—
25	C₄×Dic₇₃	—	4	1	no	—
26	#11924003	—	2	1	no	—
27	#11924003	C₂×C₄	1	2	yes	—
28	C₂×Q₈×C₇₃	—	2	1	no	—
29	Q₁₆×C₇₃	—	2	1	no	—
30	Q₁₆×C₇₃	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
32	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
33	C₄⋊C₄×C₇₃	—	2	1	no	—
34	C₄⋊C₄×C₇₃	—	4	1	no	—
35	C₄²×C₇₃	—	4	1	no	—
36	C₄²×C₇₃	D₄	1	1	yes	characteristic
37	Q₈×C₇₃	—	2	2	no	—
38	Q₈×C₇₃	—	4	1	no	—
39	C₂×C₄×C₇₃	—	4	1	no	—
40	C₂×C₄×C₇₃	—	4	1	no	—
41	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
42	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
43	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
44	C₂×Dic₇₃	—	4	1	no	—
45	C₂×Dic₇₃	—	4	1	no	—
46	Dic₁₄₆	—	2	2	no	—
47	Dic₁₄₆	—	4	1	no	—
48	C₈×C₇₃	—	2	1	no	—
49	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
50	C₈×C₇₃	#41	1	1	yes	characteristic
51	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
52	C₄×C₇₃	—	2	1	no	—
53	C₄×C₇₃	—	2	1	no	—
54	C₄×C₇₃	—	4	2	no	—
55	C₄×C₇₃	—	8	1	no	—
56	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
57	C₄×C₇₃	#135	1	1	yes	characteristic
58	Dic₇₃	—	4	2	no	—
59	Dic₇₃	—	8	1	no	—
60	C₂×C₇₃	C₄×D₈	1	1	yes	characteristic
61	C₂×C₇₃	#510	1	1	yes	characteristic
62	C₂×C₇₃	#510	1	1	yes	characteristic
63	#2176	—	73	1	no	maximal, Sylow
64	C₇₃	#2176	1	1	yes	characteristic, complemented, Sylow
65	C₂×Q₃₂	—	73	1	no	—
66	C₄×Q₁₆	—	73	1	no	—
67	C₄×Q₁₆	D₇₃	1	1	yes	characteristic
68	#367	—	73	1	no	—
69	#358	—	73	1	no	—
70	#358	—	73	1	no	—
71	#346	—	73	1	no	—
72	C₂×Q₁₆	—	73	1	no	—
73	C₂×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
74	C₄×Q₈	—	2	1	no	—
75	C₄×Q₈	—	146	1	no	—
76	Q₃₂	—	73	4	no	—
77	C₂×C₁₆	—	73	1	no	—
78	C₂×C₁₆	—	73	1	no	—
79	#107	—	73	1	no	—
80	#107	C₂×D₇₃	1	1	yes	characteristic
81	#103	—	2	1	no	—
82	#103	—	146	1	no	—
83	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
84	C₂×Q₈	—	2	1	no	—
85	C₂×Q₈	—	146	1	no	—
86	Q₁₆	—	2	1	no	—
87	Q₁₆	—	73	2	no	—
88	Q₁₆	—	146	1	no	—
89	Q₁₆	C₄×D₇₃	1	2	yes	—
90	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
91	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
92	C₄⋊C₄	—	2	1	no	—
93	C₄⋊C₄	—	4	1	no	—
94	C₄⋊C₄	—	292	1	no	—
95	C₄⋊C₄	—	146	1	no	—
96	C₄²	—	4	1	no	—
97	C₄²	—	292	1	no	—
98	C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
99	C₁₆	—	73	2	no	—
100	C₁₆	—	146	1	no	—
101	Q₈	—	2	2	no	—
102	Q₈	—	4	1	no	—
103	Q₈	—	292	1	no	—
104	Q₈	—	146	2	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	292	1	no	—
108	C₂×C₄	—	292	1	no	—
109	C₂×C₄	#11924013	1	1	yes	characteristic
110	C₂×C₄	#11924013	1	1	yes	characteristic
111	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
112	C₈	—	2	1	no	—
113	C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
114	C₈	#11924028	1	1	yes	characteristic
115	C₂²	C₂×#11924013	1	1	yes	characteristic
116	C₄	—	2	1	no	—
117	C₄	—	2	1	no	—
118	C₄	—	4	2	no	—
119	C₄	—	8	1	no	—
120	C₄	—	292	2	no	—
121	C₄	—	584	1	no	—
122	C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
123	C₄	#14556611	1	1	yes	characteristic
124	C₂	C₄×#11924013	1	1	yes	characteristic
125	C₂	#17989027	1	1	yes	characteristic
126	C₂	#17989028	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556537

C₂

yes

maximal, characteristic

C₄×Dic₂₉₂

C₂

yes

maximal, characteristic

#17988414

C₂

yes

maximal, characteristic

#17988391

C₂

yes

maximal, characteristic

#17988390

C₂

yes

maximal, characteristic

#17988363

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₇₃

C₂

yes

maximal, characteristic

C₂×Dic₂₉₂

C₂²

yes

characteristic

C₄×Dic₁₄₆

—

#14556537

C₄

yes

complemented

C₂×#11924003

C₂²

yes

characteristic

C₂×#11924003

C₂²

yes

characteristic

#14556525

C₂²

yes

characteristic

#14556516

—

C₂×Q₁₆×C₇₃

C₂²

yes

characteristic

C₄×Q₈×C₇₃

—

#107×C₇₃

C₂²

yes

characteristic

#103×C₇₃

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

C₂×C₄

yes

—

C₄⋊Dic₇₃

—

#11924007

—

C₄×Dic₇₃

—

#11924003

—

#11924003

C₂×C₄

yes

—

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

C₂²×C₄

yes

characteristic

C₈×C₇₃

#41

yes

characteristic

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

#135

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

C₄×D₈

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₄×Q₁₆

—

C₄×Q₁₆

D₇₃

yes

—

—

—

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₇₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

146

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

C₂×D₇₃

yes

characteristic

#103

—

#103

—

146

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

146

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

146

—

Q₁₆

C₄×D₇₃

yes

—

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₄²

—

C₄²

—

292

—

C₄²

C₂²⋊D₇₃

yes

characteristic

C₁₆

—

100

C₁₆

—

146

—

101

Q₈

—

102

Q₈

—

103

Q₈

—

292

—

104

Q₈

—

146

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

292

—

108

C₂×C₄

—

292

—

109

C₂×C₄

#11924013

yes

characteristic

110

C₂×C₄

#11924013

yes

characteristic

111

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

112

C₈

—

113

C₈

C₂×C₄×D₇₃

yes

characteristic

114

C₈

#11924028

yes

characteristic

115

C₂²

C₂×#11924013

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

292

—

121

C₄

—

584

—

122

C₄

C₄×C₂²⋊D₇₃

yes

characteristic

123

C₄

#14556611

yes

characteristic

124

C₂

C₄×#11924013

yes

characteristic

125

C₂

#17989027

yes

characteristic

126

C₂

#17989028

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#11924013
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₄×Q₁₆×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	C₄×Q₁₆	D₇₃
hypocenter	C₇₃	#2176
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

subgroup

G/H

center

C₂²

C₂×#11924013

commutator

C₈×C₇₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₄×Q₁₆×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

hypercenter

C₄×Q₁₆

D₇₃

hypocenter

C₇₃

#2176

LCS

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

N	H ≅ G/N	type
10. #14556537	C₄	semidirect
64. C₇₃	#2176	semidirect

H ≅ G/N

type

10. #14556537

C₄

semidirect

64. C₇₃

#2176

semidirect

Subgroups — #22611800

Conjugacy classes of subgroups

Complements