Finite Group Databasebeta

← #2022×C181 #37529965

Subgroups — #2022×C181 #37529965

Order 23168.

430 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 92 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#534×C181C211yesmaximal, characteristic
2C2×#123×C181C212yesmaximal, complemented
3C2×#99×C181C212yesmaximal, complemented
4#381×C181C211yesmaximal, characteristic, complemented
5#342×C181C211yesmaximal, characteristic, complemented
6C22×D4×C181C2212yes—
7C23×C4×C181C2211yescharacteristic
8#123×C181—22no—
9#123×C181—24no—
10#123×C181—24no—
11#121×C181—22no—
12#120×C181—22no—
13C2×C4⋊C4×C181—22no—
14C2×C22⋊C4×C181—22no—
15C2×C22⋊C4×C181C2211yescharacteristic
16C2×C22⋊C4×C181C2211yescharacteristic
17C2×C22⋊C4×C181C2212yes—
18#99×C181—24no—
19#95×C181—22no—
20C24×C181D412yes—
21C24×C181C2311yescharacteristic
22C2×D4×C181—22no—
23C2×D4×C181—22no—
24C2×D4×C181—22no—
25C2×D4×C181—22no—
26C2×D4×C181—22no—
27C2×D4×C181—22no—
28C2×D4×C181—22no—
29C22×C4×C181—21no—
30C22×C4×C181—22no—
31C22×C4×C181—22no—
32C22×C4×C181—22no—
33C22×C4×C181—21no—
34C22×C4×C181—21no—
35C22×C4×C181D412yes—
36C22×C4×C181D412yes—
37C22×C4×C181D412yescomplemented
38C4⋊C4×C181—28no—
39C4⋊C4×C181—22no—
40C22⋊C4×C181—28no—
41C22⋊C4×C181—24no—
42C22⋊C4×C181—22no—
43C22⋊C4×C181—22no—
44C22⋊C4×C181—22no—
45C22⋊C4×C181D414yescomplemented
46C23×C181—22no—
47C23×C181—22no—
48C23×C181—22no—
49C23×C181—42no—
50C23×C181—44no—
51C23×C181C2×D412yes—
52C23×C181C2×D411yescharacteristic
53C23×C181C2×D411yescharacteristic
54C23×C181C2×D412yes—
55C23×C181#4111yescharacteristic
56D4×C181—42no—
57D4×C181—42no—
58D4×C181—42no—
59D4×C181—42no—
60D4×C181—82no—
61C2×C4×C181—24no—
62C2×C4×C181—24no—
63C2×C4×C181—22no—
64C2×C4×C181—22no—
65C2×C4×C181—22no—
66C2×C4×C181—22no—
67C2×C4×C181—22no—
68C2×C4×C181—44no—
69C2×C4×C181—41no—
70C2×C4×C181—42no—
71C2×C4×C181—41no—
72C2×C4×C181—42no—
73C2×C4×C181—42no—
74C2×C4×C181—41no—
75C22×C181—22no—
76C22×C181—24no—
77C22×C181—41no—
78C22×C181—42no—
79C22×C181—41no—
80C22×C181—44no—
81C22×C181—42no—
82C22×C181—44no—
83C22×C181—82no—
84C22×C181#12012yes—
85C22×C181#12011yescharacteristic
86C22×C181#12111yescharacteristic
87C22×C181#12112yes—
88C22×C181#12711yescharacteristic
89C4×C181—44no—
90C4×C181—42no—
91C4×C181—42no—
92C4×C181—42no—
93C4×C181—81no—
94C2×C181—22no—
95C2×C181—21no—
96C2×C181—22no—
97C2×C181—21no—
98C2×C181—82no—
99C2×C181#39211yescharacteristic
100C2×C181#45812yes—
101C181#202211yescharacteristic, direct product factor, Sylow
102#2022C18111yesmaximal, characteristic, direct product factor, Sylow
103#534C2×C18111yescharacteristic
104C2×#123C2×C18112yescomplemented
105C2×#99C2×C18112yescomplemented
106#381C2×C18111yescharacteristic, complemented
107#342C2×C18111yescharacteristic, complemented
108C22×D4C22×C18112yes—
109C23×C4C22×C18111yescharacteristic
110#123—22no—
111#123—24no—
112#123—24no—
113#121—22no—
114#120—22no—
115C2×C4⋊C4—22no—
116C2×C22⋊C4—22no—
117C2×C22⋊C4C22×C18111yescharacteristic
118C2×C22⋊C4C22×C18111yescharacteristic
119C2×C22⋊C4C22×C18112yes—
120#99—24no—
121#95—22no—
122C24D4×C18112yes—
123C24C23×C18111yescharacteristic
124C2×D4—22no—
125C2×D4—22no—
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—22no—
131C22×C4—21no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4D4×C18112yes—
138C22×C4D4×C18112yes—
139C22×C4D4×C18112yescomplemented
140C4⋊C4—28no—
141C4⋊C4—22no—
142C22⋊C4—28no—
143C22⋊C4—24no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—22no—
147C22⋊C4D4×C18114yescomplemented
148C23—22no—
149C23—22no—
150C23—22no—
151C23—42no—
152C23—44no—
153C23C2×D4×C18112yes—
154C23C2×D4×C18111yescharacteristic
155C23C2×D4×C18111yescharacteristic
156C23C2×D4×C18112yes—
157C23#41×C18111yescharacteristic
158D4—42no—
159D4—42no—
160D4—42no—
161D4—42no—
162D4—82no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—44no—
171C2×C4—41no—
172C2×C4—42no—
173C2×C4—41no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—41no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—42no—
181C22—41no—
182C22—44no—
183C22—44no—
184C22—42no—
185C22—82no—
186C22#120×C18112yes—
187C22#120×C18111yescharacteristic
188C22#121×C18111yescharacteristic
189C22#121×C18112yes—
190C22#127×C18111yescharacteristic
191C4—44no—
192C4—42no—
193C4—42no—
194C4—42no—
195C4—81no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—82no—
201C2#392×C18111yescharacteristic
202C2#458×C18112yes—
subgroupG/H
center, socleC22×C181#120
commutator, Frattini, cosocleC24C23×C181
prime radical#534×C181C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C181 ◁ C24×C181 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#123×C181C2semidirect
3. C2×#99×C181C2semidirect
4. #381×C181C2semidirect
5. #342×C181C2semidirect
37. C22×C4×C181D4semidirect
45. C22⋊C4×C181D4semidirect
101. C181#2022direct (N × H)
102. #2022C181direct (N × H)
104. C2×#123C2×C181semidirect
105. C2×#99C2×C181semidirect
106. #381C2×C181semidirect
107. #342C2×C181semidirect
139. C22×C4D4×C181semidirect
147. C22⋊C4D4×C181semidirect

Maximal subgroups

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

subgroupindex
#534×C1812
C2×#123×C1812
C2×#99×C1812
#381×C1812
#342×C1812
#2022181