Finite Group Databasebeta

← #37549628

Subgroups — #37549628

Order 23168.

306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042250C211yesmaximal, characteristic
2C4×C22⋊#10624382C211yesmaximal, characteristic
3#26042149C214yesmaximal, complemented
4C2×#19153774C211yesmaximal, characteristic
5C2×#15668459C2212yes—
6C2×C22⋊#10624382—21no—
7C2×C4×#10624382C2212yes—
8#19153873—21no—
9C22⋊#13089685—21no—
10(C2×#10624382)⋊C4—21no—
11C22×C4×D181C2211yescharacteristic
12#19153774—21no—
13#19153774—21no—
14#19153774C412yescomplemented
15#19153774C2212yes—
16C2×C4⋊Dic181C411yescharacteristic, complemented
17C2×#15668426—21no—
18C2×C4×Dic181—21no—
19C2×C4⋊C4×C181C411yescharacteristic, complemented
20C22×#10624382—22no—
21#15668459—24no—
22C2×#13089685—22no—
23C22⋊#10624382—24no—
24C4×#10624382—24no—
25C23×D181D411yescharacteristic
26C22×Dic181—21no—
27C22×Dic181D411yescharacteristic
28C2×C4×D181—24no—
29C2×C4×D181C2×C411yescharacteristic
30C2×C4×D181D411yescharacteristic
31C2×C4×D181D411yescharacteristic
32C2×C4×D181C2311yescharacteristic
33C4⋊Dic181—21no—
34C4⋊Dic181C2×C412yes—
35#15668426—22no—
36#15668426—22no—
37C4×Dic181—22no—
38C4×Dic181—22no—
39C22×C4×C181—21no—
40C22×C4×C181C2×C411yescharacteristic
41C4⋊C4×C181—21no—
42C4⋊C4×C181C2×C412yes—
43C2×#10624382—24no—
44C2×#10624382—42no—
45C2×#10624382—42no—
46#13089685—42no—
47C22×D181—22no—
48C22×D181—22no—
49C22×D181—41no—
50C22×D181C22⋊C411yescharacteristic
51C22×D181C2×D411yescharacteristic
52C2×Dic181—22no—
53C2×Dic181—22no—
54C2×Dic181—42no—
55C2×Dic181C22⋊C411yescharacteristic
56C2×Dic181C2×D411yescharacteristic
57C4×D181—22no—
58C4×D181—22no—
59C4×D181—22no—
60C4×D181#4114yes—
61C23×C181C22⋊C411yescharacteristic
62C2×C4×C181—22no—
63C2×C4×C181—22no—
64C2×C4×C181—42no—
65C2×C4×C181C22⋊C411yescharacteristic
66C2×C4×C181C22×C411yescharacteristic
67C22×C181—21no—
68C22×C181—21no—
69C22×C181#10412yes—
70C22×C181C2×C22⋊C411yescharacteristic
71C2×D181—21no—
72C2×D181—21no—
73C2×D181—21no—
74C2×D181—21no—
75C2×D181—21no—
76C2×D181—44no—
77C2×D181#12312yes—
78#10624382—44no—
79C4×C181—21no—
80C4×C181—42no—
81C4×C181#11712yes—
82Dic181—21no—
83Dic181—42no—
84Dic181#12312yes—
85C2×C181—22no—
86C2×C181#38111yescharacteristic
87C2×C181C2×#10411yescharacteristic
88C2×C181#42111yescharacteristic
89D181—22no—
90D181—41no—
91C181#182611yescharacteristic, complemented, Sylow
92#1826—1811nomaximal, Sylow
93C2×#117—1811no—
94#407—1811no—
95C4×C22⋊C4—1811no—
96#339—1814no—
97C23×C4—1811no—
98C2×M16—1812no—
99#117—3621no—
100#117—3621no—
101#117—1812no—
102#117—1812no—
103C2×C4⋊C4—1811no—
104C2×C4⋊C4#1062438211yescharacteristic, complemented
105C2×C22⋊C4—3621no—
106C2×C22⋊C4—3621no—
107C2×C42—3621no—
108C2×C42—1812no—
109C22⋊C8—3621no—
110C22⋊C8—3621no—
111#95—3621no—
112C24—1811no—
113C22×C4—21no—
114C22×C4—3624no—
115C22×C4—3622no—
116C22×C4—3621no—
117C22×C4—1811no—
118C22×C4—1811no—
119C22×C4—1811no—
120C22×C4—1811no—
121C22×C4—1811no—
122C22×C4C2×#1062438211yescharacteristic
123M16—3624no—
124C2×C8—3622no—
125C4⋊C4—21no—
126C4⋊C4—3621no—
127C4⋊C4—1812no—
128C4⋊C4C2×#1062438212yes—
129C22⋊C4—3622no—
130C22⋊C4—3622no—
131C22⋊C4—3624no—
132C42—3622no—
133C42—3622no—
134C42—3624no—
135C23—3622no—
136C23—3622no—
137C23—1811no—
138C23—1811no—
139C23—7241no—
140C23C22⋊#1062438211yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—3622no—
145C2×C4—3622no—
146C2×C4—3622no—
147C2×C4—3622no—
148C2×C4—3624no—
149C2×C4—3622no—
150C2×C4—1811no—
151C2×C4—1811no—
152C2×C4—1814no—
153C2×C4—7242no—
154C2×C4—7242no—
155C2×C4—7242no—
156C2×C4C22⋊#1062438211yescharacteristic
157C2×C4C22×#1062438211yescharacteristic
158C8—7242no—
159C22—21no—
160C22—21no—
161C22—3621no—
162C22—3621no—
163C22—3621no—
164C22—3621no—
165C22—3621no—
166C22—1812no—
167C22—7244no—
168C22#1915388112yes—
169C22C2×C22⋊#1062438211yescharacteristic
170C4—21no—
171C4—42no—
172C4—3621no—
173C4—1812no—
174C4—7244no—
175C4—7242no—
176C4#1915389512yes—
177C2—22no—
178C2—3622no—
179C2—7241no—
180C2#2604222211yescharacteristic
181C2C2×#1915388111yescharacteristic
182C2#2604227711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC23×D181D4
cosocleC2×C4×D181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181#1826
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #26042149C2semidirect
14. #19153774C4semidirect
16. C2×C4⋊Dic181C4semidirect
19. C2×C4⋊C4×C181C4semidirect
91. C181#1826semidirect
104. C2×C4⋊C4#10624382semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260422502
C4×C22⋊#106243822
#260421492
C2×#191537742
#1826181