Finite Group Databasebeta

← #1609×C181 #37529552

Subgroups — #1609×C181 #37529552

Order 23168.

216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 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#539×C181C211yesmaximal, characteristic
2#483×C181C211yesmaximal, characteristic, complemented
3#480×C181C211yesmaximal, characteristic
4#398×C181C211yesmaximal, characteristic, complemented
5#328×C181C211yesmaximal, characteristic, complemented
6#327×C181C211yesmaximal, characteristic
7#324×C181C211yesmaximal, characteristic, complemented
8#126×C181—21no—
9#125×C181—21no—
10#123×C181—21no—
11#123×C181—21no—
12C22⋊Q8×C181—21no—
13C22⋊Q8×C181C2211yescharacteristic
14#121×C181C2211yescharacteristic
15C4×D4×C181—21no—
16C2×C4⋊C4×C181—21no—
17C2×C4⋊C4×C181C2211yescharacteristic
18C2×C4⋊C4×C181C2211yescharacteristic
19#107×C181—21no—
20#106×C181—21no—
21#103×C181—21no—
22#102×C181—21no—
23C22⋊C8×C181C2211yescharacteristic
24C22⋊C8×C181C2211yescharacteristic
25#95×C181—21no—
26#95×C181C2211yescharacteristic
27C2×Q8×C181D411yescharacteristic
28C2×D4×C181—21no—
29C2×D4×C181D411yescharacteristic
30C22×C4×C181—21no—
31C22×C4×C181—21no—
32C22×C4×C181—21no—
33C22×C4×C181D411yescharacteristic
34C22×C4×C181D411yescharacteristic
35C22×C4×C181C2311yescharacteristic
36C2×C8×C181—21no—
37C2×C8×C181—21no—
38C4⋊C4×C181—21no—
39C4⋊C4×C181—21no—
40C4⋊C4×C181—21no—
41C4⋊C4×C181—21no—
42C4⋊C4×C181—21no—
43C4⋊C4×C181—21no—
44C4⋊C4×C181—21no—
45C4⋊C4×C181—21no—
46C4⋊C4×C181—42no—
47C4⋊C4×C181D411yescharacteristic
48C4⋊C4×C181D411yescharacteristic
49C22⋊C4×C181—21no—
50C22⋊C4×C181—21no—
51C22⋊C4×C181—21no—
52C22⋊C4×C181—21no—
53C22⋊C4×C181—21no—
54C42×C181—21no—
55C23×C181—21no—
56C23×C181C2×D411yescharacteristic
57Q8×C181—41no—
58D4×C181—41no—
59D4×C181—41no—
60D4×C181—41no—
61C2×C4×C181—22no—
62C2×C4×C181—21no—
63C2×C4×C181—21no—
64C2×C4×C181—21no—
65C2×C4×C181—21no—
66C2×C4×C181—21no—
67C2×C4×C181—21no—
68C2×C4×C181—21no—
69C2×C4×C181—41no—
70C2×C4×C181—41no—
71C2×C4×C181—41no—
72C2×C4×C181—41no—
73C2×C4×C181—41no—
74C2×C4×C181—41no—
75C2×C4×C181—41no—
76C2×C4×C181—81no—
77C2×C4×C181C2×D411yescharacteristic
78C2×C4×C181C2×D411yescharacteristic
79C8×C181—41no—
80C8×C181—41no—
81C22×C181—21no—
82C22×C181—21no—
83C22×C181—41no—
84C22×C181—41no—
85C22×C181—41no—
86C22×C181#12011yescharacteristic
87C22×C181#13511yescharacteristic
88C22×C181AGL(1,ℤ/8)11yescharacteristic
89C4×C181—21no—
90C4×C181—21no—
91C4×C181—42no—
92C4×C181—41no—
93C4×C181—41no—
94C4×C181—41no—
95C4×C181—41no—
96C4×C181—41no—
97C4×C181—81no—
98C2×C181—21no—
99C2×C181—21no—
100C2×C181—81no—
101C2×C181#44911yescharacteristic
102C2×C181#45611yescharacteristic
103C2×C181#45811yescharacteristic
104C181#160911yescharacteristic, direct product factor, Sylow
105#1609C18111yesmaximal, characteristic, direct product factor, Sylow
106#539C2×C18111yescharacteristic
107#483C2×C18111yescharacteristic, complemented
108#480C2×C18111yescharacteristic
109#398C2×C18111yescharacteristic, complemented
110#328C2×C18111yescharacteristic, complemented
111#327C2×C18111yescharacteristic
112#324C2×C18111yescharacteristic, complemented
113#126—21no—
114#125—21no—
115#123—21no—
116#123—21no—
117C22⋊Q8—21no—
118C22⋊Q8C22×C18111yescharacteristic
119#121C22×C18111yescharacteristic
120C4×D4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C22×C18111yescharacteristic
123C2×C4⋊C4C22×C18111yescharacteristic
124#107—21no—
125#106—21no—
126#103—21no—
127#102—21no—
128C22⋊C8C22×C18111yescharacteristic
129C22⋊C8C22×C18111yescharacteristic
130#95—21no—
131#95C22×C18111yescharacteristic
132C2×Q8D4×C18111yescharacteristic
133C2×D4—21no—
134C2×D4D4×C18111yescharacteristic
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4D4×C18111yescharacteristic
139C22×C4D4×C18111yescharacteristic
140C22×C4C23×C18111yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—42no—
152C4⋊C4D4×C18111yescharacteristic
153C4⋊C4D4×C18111yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—21no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C42—21no—
160C23—21no—
161C23C2×D4×C18111yescharacteristic
162Q8—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—81no—
182C2×C4C2×D4×C18111yescharacteristic
183C2×C4C2×D4×C18111yescharacteristic
184C8—41no—
185C8—41no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#120×C18111yescharacteristic
192C22#135×C18111yescharacteristic
193C22AGL(1,ℤ/8)×C18111yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—41no—
200C4—41no—
201C4—41no—
202C4—81no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#449×C18111yescharacteristic
207C2#456×C18111yescharacteristic
208C2#458×C18111yescharacteristic
subgroupG/H
center, socleC22×C181#120
commutator, Frattini, cosocleC22×C4C23×C181
prime radical#121×C181C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C181 ◁ C22×C4×C181 ◁ G

Complements

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

NH ≅ G/Ntype
2. #483×C181C2semidirect
4. #398×C181C2semidirect
5. #328×C181C2semidirect
7. #324×C181C2semidirect
104. C181#1609direct (N × H)
105. #1609C181direct (N × H)
107. #483C2×C181semidirect
109. #398C2×C181semidirect
110. #328C2×C181semidirect
112. #324C2×C181semidirect

Maximal subgroups

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

subgroupindex
#539×C1812
#483×C1812
#480×C1812
#398×C1812
#328×C1812
#327×C1812
#324×C1812
#1609181