Group #22618719 — subgroups

Subgroups — C₂×#17988695 #22618719

Order 9344.

480 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 205 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	C₂²×Dic₂₉₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₄₆	C₂	1	2	yes	maximal
3	#17988695	C₂	1	8	yes	maximal, direct product factor
4	C₂×#14556523	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556516	C₂	1	2	yes	maximal
6	C₂×#97×C₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₁₄₆	C₂²	1	2	yes	—
8	C₂×Dic₂₉₂	C₄	1	8	yes	complemented
9	C₂×Dic₂₉₂	C₂²	1	4	yes	—
10	C₄×Dic₁₄₆	—	2	4	no	—
11	C₄×Dic₁₄₆	C₂²	1	8	yes	—
12	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
13	C₂×#11924007	—	2	2	no	—
14	C₂×C₄×Dic₇₃	—	2	2	no	—
15	#14556523	C₂²	1	4	yes	—
16	#14556516	C₂²	1	8	yes	—
17	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
20	#97×C₇₃	C₂²	1	4	yes	—
21	C₂×Dic₁₄₆	—	2	2	no	—
22	C₂×Dic₁₄₆	—	2	4	no	—
23	C₂×Dic₁₄₆	C₂×C₄	1	8	yes	—
24	C₂×Dic₁₄₆	C₂³	1	4	yes	—
25	C₂²×Dic₇₃	—	2	2	no	—
26	C₂²×Dic₇₃	—	2	2	no	—
27	Dic₂₉₂	C₂×C₄	1	16	yes	complemented
28	C₄⋊Dic₇₃	—	2	2	no	—
29	C₄⋊Dic₇₃	C₂³	1	4	yes	—
30	#11924007	—	2	8	no	—
31	C₄×Dic₇₃	—	2	8	no	—
32	C₂²×C₄×C₇₃	D₄	1	2	yes	—
33	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
34	C₂×C₈×C₇₃	—	2	2	no	—
35	C₂×C₈×C₇₃	C₂×C₄	1	4	yes	—
36	C₂×C₈×C₇₃	C₂³	1	2	yes	—
37	C₂×C₈×C₇₃	C₂³	1	2	yes	—
38	C₄²×C₇₃	D₄	1	2	yes	—
39	C₄²×C₇₃	C₂³	1	2	yes	—
40	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₇₃	—	2	4	no	—
42	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₇₃	C₂×D₄	1	4	yes	—
44	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₇₃	#41	1	2	yes	—
46	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
47	C₂×Dic₇₃	—	2	8	no	—
48	C₂×Dic₇₃	—	2	4	no	—
49	C₂×Dic₇₃	—	2	4	no	—
50	C₂×Dic₇₃	—	4	4	no	—
51	Dic₁₄₆	—	2	8	no	—
52	Dic₁₄₆	—	2	4	no	—
53	Dic₁₄₆	C₂²×C₄	1	8	yes	—
54	C₈×C₇₃	—	2	2	no	—
55	C₈×C₇₃	C₂²×C₄	1	4	yes	—
56	C₂²×C₇₃	C₄×D₄	1	2	yes	—
57	C₂²×C₇₃	#137	1	4	yes	—
58	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
59	C₄×C₇₃	—	2	4	no	—
60	C₄×C₇₃	C₄×D₄	1	2	yes	—
61	C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
62	C₄×C₇₃	C₂×#41	1	1	yes	characteristic
63	Dic₇₃	—	2	8	no	—
64	Dic₇₃	—	4	4	no	—
65	C₂×C₇₃	#441	1	4	yes	complemented
66	C₂×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
67	C₂×C₇₃	C₂×#137	1	2	yes	—
68	C₂×#441	—	73	1	no	maximal, Sylow
69	C₇₃	C₂×#441	1	1	yes	characteristic, complemented, Sylow
70	C₂²×Q₁₆	—	73	1	no	—
71	C₂×C₄×Q₈	—	73	2	no	—
72	#441	—	73	8	no	—
73	C₂×#106	—	73	1	no	—
74	C₂×#103	—	73	2	no	—
75	C₂×#97	D₇₃	1	1	yes	characteristic
76	C₂²×Q₈	—	73	2	no	—
77	C₂×Q₁₆	—	73	8	no	—
78	C₂×Q₁₆	—	73	4	no	—
79	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
80	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
81	C₄×Q₈	—	73	8	no	—
82	C₄×Q₈	—	146	4	no	—
83	C₂×C₄⋊C₄	—	73	2	no	—
84	C₂×C₄⋊C₄	—	146	2	no	—
85	C₂×C₄²	—	146	2	no	—
86	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
87	#106	—	73	4	no	—
88	#103	—	73	8	no	—
89	#97	C₂×D₇₃	1	4	yes	—
90	C₂×Q₈	—	73	8	no	—
91	C₂×Q₈	—	73	4	no	—
92	C₂×Q₈	—	146	2	no	—
93	C₂×Q₈	—	146	4	no	—
94	C₂²×C₄	—	146	2	no	—
95	C₂²×C₄	—	146	2	no	—
96	C₂²×C₄	D₂₉₂	1	2	yes	—
97	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
98	Q₁₆	—	73	16	no	—
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	C₄×D₇₃	1	4	yes	—
101	C₂×C₈	C₂²×D₇₃	1	2	yes	—
102	C₂×C₈	C₂²×D₇₃	1	2	yes	—
103	C₄⋊C₄	—	73	4	no	—
104	C₄⋊C₄	—	146	8	no	—
105	C₄⋊C₄	—	146	2	no	—
106	C₄²	—	146	8	no	—
107	C₄²	D₂₉₂	1	2	yes	—
108	C₄²	C₂²×D₇₃	1	2	yes	—
109	C₂³	C₂×D₂₉₂	1	1	yes	characteristic
110	Q₈	—	73	8	no	—
111	Q₈	—	146	8	no	—
112	Q₈	—	146	4	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	292	4	no	—
115	C₂×C₄	—	146	4	no	—
116	C₂×C₄	—	146	8	no	—
117	C₂×C₄	—	146	4	no	—
118	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
119	C₂×C₄	C₂×D₂₉₂	1	4	yes	—
120	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
121	C₂×C₄	#11924028	1	2	yes	—
122	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	C₂×C₄×D₇₃	1	4	yes	—
125	C₂²	C₄×D₂₉₂	1	2	yes	—
126	C₂²	#14556624	1	4	yes	—
127	C₂²	C₂²×D₂₉₂	1	1	yes	characteristic
128	C₄	—	2	4	no	—
129	C₄	—	292	4	no	—
130	C₄	—	146	8	no	—
131	C₄	C₄×D₂₉₂	1	2	yes	—
132	C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
133	C₄	C₂×#11924028	1	1	yes	characteristic
134	C₂	#17988695	1	4	yes	direct product factor
135	C₂	C₂×C₄×D₂₉₂	1	1	yes	characteristic
136	C₂	C₂×#14556624	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₂₉₂

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₄₆

C₂

yes

maximal

#17988695

C₂

yes

maximal, direct product factor

C₂×#14556523

C₂

yes

maximal, characteristic

C₂×#14556516

C₂

yes

maximal

C₂×#97×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

C₂×Dic₂₉₂

C₄

yes

complemented

C₂×Dic₂₉₂

C₂²

yes

—

C₄×Dic₁₄₆

—

C₄×Dic₁₄₆

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

—

C₂×C₄×Dic₇₃

—

#14556523

C₂²

yes

—

#14556516

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#97×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

C₂×Dic₁₄₆

C₂³

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

Dic₂₉₂

C₂×C₄

yes

complemented

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂³

yes

—

#11924007

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂³

yes

—

C₂×C₈×C₇₃

C₂³

yes

—

C₄²×C₇₃

D₄

yes

—

C₄²×C₇₃

C₂³

yes

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

C₂²×C₄

yes

—

C₈×C₇₃

—

C₈×C₇₃

C₂²×C₄

yes

—

C₂²×C₇₃

C₄×D₄

yes

—

C₂²×C₇₃

#137

yes

—

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

—

C₄×C₇₃

C₂³×C₄

yes

characteristic

C₄×C₇₃

C₂×#41

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#441

yes

complemented

C₂×C₇₃

C₂×C₄×D₄

yes

characteristic

C₂×C₇₃

C₂×#137

yes

—

C₂×#441

—

maximal, Sylow

C₇₃

C₂×#441

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

C₂×C₄×Q₈

—

#441

—

C₂×#106

—

C₂×#103

—

C₂×#97

D₇₃

yes

characteristic

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

146

—

C₂×C₄²

C₂×D₇₃

yes

—

—

C₂×D₇₃

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

D₂₉₂

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

Q₁₆

—

C₂×C₈

—

100

C₂×C₈

C₄×D₇₃

yes

—

101

C₂×C₈

C₂²×D₇₃

yes

—

102

C₂×C₈

C₂²×D₇₃

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

146

—

105

C₄⋊C₄

—

146

—

106

C₄²

—

146

—

107

C₄²

D₂₉₂

yes

—

108

C₄²

C₂²×D₇₃

yes

—

109

C₂³

C₂×D₂₉₂

yes

characteristic

110

Q₈

—

111

Q₈

—

146

—

112

Q₈

—

146

—

113

C₂×C₄

—

114

C₂×C₄

—

292

—

115

C₂×C₄

—

146

—

116

C₂×C₄

—

146

—

117

C₂×C₄

—

146

—

118

C₂×C₄

C₂×C₄×D₇₃

yes

—

119

C₂×C₄

C₂×D₂₉₂

yes

—

120

C₂×C₄

C₂×D₂₉₂

yes

characteristic

121

C₂×C₄

#11924028

yes

—

122

C₂×C₄

C₂³×D₇₃

yes

characteristic

123

C₈

—

124

C₈

C₂×C₄×D₇₃

yes

—

125

C₂²

C₄×D₂₉₂

yes

—

126

C₂²

#14556624

yes

—

127

C₂²

C₂²×D₂₉₂

yes

characteristic

128

C₄

—

129

C₄

—

292

—

130

C₄

—

146

—

131

C₄

C₄×D₂₉₂

yes

—

132

C₄

C₂²×C₄×D₇₃

yes

characteristic

133

C₄

C₂×#11924028

yes

characteristic

134

C₂

#17988695

yes

direct product factor

135

C₂

C₂×C₄×D₂₉₂

yes

characteristic

136

C₂

C₂×#14556624

yes

—

	subgroup	G/H
center	C₂³	C₂×D₂₉₂
commutator	C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₇₃
Fitting	C₂×#97×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	C₂×#97	D₇₃
hypocenter	C₇₃	C₂×#441
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₂₉₂

commutator

C₄×C₇₃

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₇₃

Fitting

C₂×#97×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

hypercenter

C₂×#97

D₇₃

hypocenter

C₇₃

C₂×#441

LCS

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
3. #17988695	C₂	direct (N × H)
8. C₂×Dic₂₉₂	C₄	semidirect
27. Dic₂₉₂	C₂×C₄	semidirect
65. C₂×C₇₃	#441	semidirect
69. C₇₃	C₂×#441	semidirect
134. C₂	#17988695	direct (N × H)

H ≅ G/N

type

3. #17988695

C₂

direct (N × H)

8. C₂×Dic₂₉₂

C₄

semidirect

27. Dic₂₉₂

C₂×C₄

semidirect

65. C₂×C₇₃

#441

semidirect

69. C₇₃

C₂×#441

semidirect

134. C₂

#17988695

direct (N × H)

Subgroups — C₂×#17988695 #22618719

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17988695 #22618719

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17988695 #22618719