Finite Group Databasebeta

← #37549232

Subgroups — #37549232

Order 23168.

260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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#26042284C211yesmaximal, characteristic, complemented
2D181⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#26042138C212yesmaximal, complemented
4#26042137C212yesmaximal, complemented
5#26041826C211yesmaximal, characteristic
6C2×#15668459—21no—
7C2×D181⋊C8—21no—
8#19153883—21no—
9#19153883C2212yes—
10#19153883C2212yes—
11C4⋊#13089685—21no—
12C2×#15668449—21no—
13#19153815C2211yescharacteristic
14#19153812C2211yescharacteristic
15#19153802—21no—
16#19153791C411yescharacteristic
17#19153789—21no—
18#19153787C411yescharacteristic
19C4×D724C411yescharacteristic
20C4×C22⋊D181—21no—
21C42×D181C2211yescharacteristic
22C4×D4×C181C411yescharacteristic
23#15668459—42no—
24D181⋊C8—42no—
25C2×#13089685—22no—
26C2×#13089685—22no—
27#15668449—42no—
28#15668449—42no—
29C2×Dic362—21no—
30C2×D724—21no—
31C2×D724C2×C411yescharacteristic
32C2×C22⋊D181—21no—
33C2×C22⋊D181—21no—
34C2×C22⋊D181—21no—
35C2×C4×D181—21no—
36C2×C4×D181C2×C411yescharacteristic
37C2×C4×D181D411yescharacteristic
38C2×C4×D181D411yescharacteristic
39C4⋊Dic181C2×C411yescharacteristic
40#15668428—21no—
41C22⋊Dic181—21no—
42#15668426—21no—
43#15668426—21no—
44C4×Dic181D411yescharacteristic
45C4×Dic181D411yescharacteristic
46C4×Dic181C2311yescharacteristic
47C2×D4×C181C2×C411yescharacteristic
48C22×C4×C181—21no—
49C4⋊C4×C181C2×C411yescharacteristic
50C22⋊C4×C181—21no—
51C42×C181C2×C411yescharacteristic
52#13089685—42no—
53#13089685—42no—
54C22×D181—21no—
55C22×D181C22⋊C411yescharacteristic
56Dic362—41no—
57Dic362—41no—
58D724—41no—
59D724—42no—
60C22⋊D181—42no—
61C22⋊D181—41no—
62C22⋊D181—41no—
63C22⋊D181—41no—
64C22⋊D181—41no—
65C2×Dic181—21no—
66C2×Dic181C22⋊C411yescharacteristic
67C2×Dic181C2×D411yescharacteristic
68C2×Dic181C2×D411yescharacteristic
69C4×D181—21no—
70C4×D181—21no—
71C4×D181—41no—
72C4×D181—42no—
73C4×D181D812yes—
74C4×D181SD1612yes—
75C23×C181—21no—
76D4×C181—41no—
77C2×C4×C181—21no—
78C2×C4×C181—42no—
79C2×C4×C181C22⋊C411yescharacteristic
80C2×C4×C181C22⋊C411yescharacteristic
81C2×C4×C181C22×C411yescharacteristic
82C22×C181—41no—
83C22×C181—41no—
84C22×C181—41no—
85C22×C181C2×C22⋊C411yescharacteristic
86C2×D181—21no—
87C2×D181—21no—
88C2×D181—41no—
89C2×D181—41no—
90C2×D181—41no—
91C2×D181#10212yes—
92C4×C181—21no—
93C4×C181—21no—
94C4×C181—41no—
95C4×C181#10212yes—
96Dic181—21no—
97Dic181—41no—
98Dic181C2×D811yescharacteristic
99Dic181C2×SD1611yescharacteristic
100Dic181AGL(1,ℤ/8)11yescharacteristic
101Dic181#13711yescharacteristic
102C2×C181—81no—
103C2×C181#41311yescharacteristic
104C2×C181C2×#10211yescharacteristic
105C2×C181#41711yescharacteristic
106D181—22no—
107D181—81no—
108C181#154711yescharacteristic, complemented, Sylow
109#1547—1811nomaximal, Sylow
110#532—1811no—
111#423—1811no—
112C2×C4⋊C8—1811no—
113#332—1812no—
114#331—1812no—
115C2×#41—3621no—
116C2×M16—3621no—
117C22×C8—3621no—
118C4⋊Q8—1811no—
119#127—1811no—
120#124—3621no—
121#121—3621no—
122#121—1811no—
123#121—1811no—
124C4×D4—3621no—
125C4×D4—1811no—
126C4×D4#1062438211yescharacteristic
127C2×C42—1811no—
128C4⋊C8—3621no—
129C4⋊C8—3621no—
130C4⋊C8—1812no—
131C4⋊C8—1812no—
132#41—7242no—
133#41—7242no—
134C2×Q8—3621no—
135C2×D4—3621no—
136C2×D4—3621no—
137C2×D4—3621no—
138C2×D4—3621no—
139C2×D4—1811no—
140C2×D4C2×#1062438211yescharacteristic
141C22×C4—21no—
142C22×C4—3621no—
143C22×C4—1811no—
144C22×C4—1811no—
145C22×C4—1811no—
146M16—7242no—
147C2×C8—3622no—
148C2×C8—3622no—
149C2×C8—7242no—
150C4⋊C4—3621no—
151C4⋊C4—1811no—
152C4⋊C4C2×#1062438211yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—3621no—
155C22⋊C4—3621no—
156C22⋊C4—3621no—
157C42—1811no—
158C42—1811no—
159C42—1811no—
160C42C2×#1062438211yescharacteristic
161C23—21no—
162C23—3621no—
163C23—1811no—
164Q8—7241no—
165Q8—7241no—
166D4—41no—
167D4—7241no—
168D4—7242no—
169D4—7241no—
170D4—7241no—
171D4—7241no—
172D4—7241no—
173D4—7242no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—3621no—
177C2×C4—3621no—
178C2×C4—3621no—
179C2×C4—1811no—
180C2×C4—1811no—
181C2×C4—1811no—
182C2×C4—1812no—
183C2×C4—1812no—
184C2×C4—7241no—
185C2×C4—7242no—
186C2×C4C22⋊#1062438211yescharacteristic
187C2×C4C22⋊#1062438211yescharacteristic
188C2×C4C22×#1062438211yescharacteristic
189C8—7242no—
190C8—7242no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—3621no—
195C22—3621no—
196C22—1812no—
197C22—7241no—
198C22—7241no—
199C22—7241no—
200C22C2×C22⋊#1062438211yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—3621no—
205C4—1811no—
206C4—1811no—
207C4—1811no—
208C4—1811no—
209C4—7241no—
210C4#1915387812yes—
211C2—81no—
212C2—3622no—
213C2—14481no—
214C2#2604226511yescharacteristic
215C2C2×#1915387811yescharacteristic
216C2#2604227011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×D4×C181C4
socleC22×C181C2×C22⋊C4
prime radical#26041826C2
cosocleC4×Dic181C23
hypercenterC4×D4#10624382
hypocenterC181#1547
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26042284C2semidirect
2. D181⋊(C4⋊C8)C2semidirect
3. #26042138C2semidirect
4. #26042137C2semidirect
108. C181#1547semidirect

Maximal subgroups

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

subgroupindex
#260422842
D181⋊(C4⋊C8)2
#260421382
#260421372
#260418262
#1547181