Finite Group Databasebeta

← #27195597

Subgroups — #27195597

Order 13184.

598 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#15692990C211yesmaximal, characteristic
2C2×#15692935C212yesmaximal, complemented
3#20267647C211yesmaximal, characteristic, complemented
4#20267557C212yesmaximal, complemented
5C22×C22⋊C4×C103C211yesmaximal, characteristic, complemented
6C22×C22⋊D103C412yescomplemented
7C22×C22⋊D103C2211yescharacteristic
8#15692990—22no—
9#15692990—21no—
10#15692990—21no—
11C2×C22⋊Dic103—22no—
12C2×C22⋊Dic103C412yescomplemented
13C2×C22⋊Dic103C2212yes—
14C2×C22⋊Dic103C2211yescharacteristic
15#15692935—24no—
16C25×C103C2211yescharacteristic
17C23×C4×C103—21no—
18C2×C22⋊C4×C103—21no—
19C2×C22⋊C4×C103—24no—
20C2×C22⋊C4×C103C2212yes—
21C23×D103C2×C411yescharacteristic, complemented
22C2×C22⋊D103—22no—
23C2×C22⋊D103—22no—
24C2×C22⋊D103—22no—
25C2×C22⋊D103—21no—
26C2×C22⋊D103—21no—
27C2×C22⋊D103—22no—
28C2×C22⋊D103—44no—
29C22×Dic103—22no—
30C22×Dic103C2×C411yescharacteristic, complemented
31C22×Dic103C2×C412yescomplemented
32C22⋊Dic103—22no—
33C22⋊Dic103—22no—
34C22⋊Dic103—21no—
35C22⋊Dic103—21no—
36C22⋊Dic103—22no—
37C22⋊Dic103—22no—
38C22⋊Dic103—44no—
39C24×C103—22no—
40C24×C103—22no—
41C24×C103—44no—
42C24×C103C2×C412yes—
43C24×C103D412yes—
44C24×C103D411yescharacteristic
45C24×C103D411yescharacteristic
46C24×C103C2311yescharacteristic
47C22×C4×C103—24no—
48C22×C4×C103—22no—
49C22×C4×C103—44no—
50C22⋊C4×C103—24no—
51C22⋊C4×C103—22no—
52C22⋊C4×C103D414yescomplemented
53C23×C103—24no—
54C23×C103—21no—
55C23×C103—21no—
56C23×C103—24no—
57C23×C103—24no—
58C23×C103—24no—
59C23×C103—21no—
60C23×C103—24no—
61C23×C103—21no—
62C23×C103—42no—
63C23×C103—42no—
64C23×C103—42no—
65C23×C103—42no—
66C23×C103—48no—
67C23×C103—48no—
68C23×C103C22⋊C412yes—
69C23×C103C22⋊C412yes—
70C23×C103C22×C411yescharacteristic
71C23×C103C2×D411yescharacteristic
72C23×C103C2×D412yes—
73C23×C103C2×D411yescharacteristic
74C23×C103#4112yes—
75C22×D103—21no—
76C22×D103—22no—
77C22×D103—42no—
78C2×C4×C103—24no—
79C2×C4×C103—48no—
80C2×C4×C103—44no—
81C22⋊D103—44no—
82C22⋊D103—44no—
83C22⋊D103—41no—
84C22⋊D103—42no—
85C22⋊D103—41no—
86C2×Dic103—21no—
87C2×Dic103—22no—
88C2×Dic103—22no—
89C2×Dic103—42no—
90C2×Dic103—44no—
91C2×Dic103—42no—
92C22×C103—24no—
93C22×C103—24no—
94C22×C103—22no—
95C22×C103—22no—
96C22×C103—22no—
97C22×C103—22no—
98C22×C103—22no—
99C22×C103—22no—
100C22×C103—22no—
101C22×C103—22no—
102C22×C103—42no—
103C22×C103—42no—
104C22×C103—48no—
105C22×C103—48no—
106C22×C103—42no—
107C22×C103—42no—
108C22×C103#9914yescomplemented
109C22×C103C2×C22⋊C411yescharacteristic
110C22×C103C4×D412yes—
111C22×C103#12011yescharacteristic
112C22×C103#12112yes—
113C22×C103#12311yescharacteristic
114C2×D103—41no—
115C2×D103—42no—
116C2×D103—82no—
117C4×C103—44no—
118Dic103—41no—
119Dic103—42no—
120Dic103—82no—
121C2×C103—22no—
122C2×C103—21no—
123C2×C103—22no—
124C2×C103—24no—
125C2×C103—21no—
126C2×C103—42no—
127C2×C103#38611yescharacteristic
128C2×C103C2×#9912yes—
129D103—81no—
130#1898—1031nomaximal, Sylow
131C103#189811yescharacteristic, complemented, Sylow
132C2×#120—1031no—
133C22×C22⋊C4D10311yescharacteristic, complemented
134C2×#99—1032no—
135#379—1031no—
136#342—1032no—
137C25C2×D10311yescharacteristic
138C22×D4—1032no—
139C22×D4—1031no—
140C23×C4—21no—
141#120—2062no—
142#120—2061no—
143#120—2061no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—24no—
146C2×C22⋊C4—1032no—
147C2×C22⋊C4—1031no—
148C2×C22⋊C4—1032no—
149C2×C22⋊C4—2062no—
150C2×C22⋊C4C2×D10312yes—
151#99—2064no—
152C24—22no—
153C24—22no—
154C24—44no—
155C24—1031no—
156C24C4×D10312yes—
157C24D41212yes—
158C24C22⋊D10311yescharacteristic
159C24C22⋊D10311yescharacteristic
160C24C22×D10311yescharacteristic
161C2×D4—4124no—
162C2×D4—2062no—
163C2×D4—2062no—
164C2×D4—2062no—
165C2×D4—2061no—
166C2×D4—2061no—
167C2×D4—2062no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—44no—
171C22×C4—1032no—
172C22×C4—1031no—
173C22×C4—2062no—
174C22⋊C4—24no—
175C22⋊C4—22no—
176C22⋊C4—4124no—
177C22⋊C4—2062no—
178C22⋊C4—2062no—
179C22⋊C4—2062no—
180C22⋊C4—2062no—
181C22⋊C4—2061no—
182C22⋊C4—2061no—
183C22⋊C4C22⋊D10314yescomplemented
184C23—24no—
185C23—21no—
186C23—21no—
187C23—24no—
188C23—24no—
189C23—24no—
190C23—21no—
191C23—24no—
192C23—21no—
193C23—42no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—48no—
198C23—48no—
199C23—4122no—
200C23—2062no—
201C23—2061no—
202C23(C2×D103)⋊C412yes—
203C23(C2×D103)⋊C412yes—
204C23C2×C4×D10311yescharacteristic
205C23C2×C22⋊D10311yescharacteristic
206C23C2×C22⋊D10312yes—
207C23C2×D41211yescharacteristic
208C23#1311010512yes—
209D4—4124no—
210D4—4124no—
211D4—4121no—
212D4—4122no—
213D4—4121no—
214C2×C4—24no—
215C2×C4—48no—
216C2×C4—44no—
217C2×C4—4124no—
218C2×C4—4122no—
219C2×C4—4122no—
220C2×C4—2061no—
221C2×C4—2062no—
222C2×C4—2062no—
223C22—24no—
224C22—24no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—42no—
234C22—42no—
235C22—48no—
236C22—48no—
237C22—42no—
238C22—42no—
239C22—8242no—
240C22—4121no—
241C22—4122no—
242C22#1569293514yescomplemented
243C22C2×(C2×D103)⋊C411yescharacteristic
244C22C4×C22⋊D10312yes—
245C22#1569299011yescharacteristic
246C22#1569299512yes—
247C22#1569300411yescharacteristic
248C4—44no—
249C4—8242no—
250C4—4121no—
251C4—4122no—
252C2—21no—
253C2—22no—
254C2—24no—
255C2—21no—
256C2—22no—
257C2—42no—
258C2—8241no—
259C2#2026767011yescharacteristic
260C2C2×#1569293512yes—
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC23×C103C22×C4
FrattiniC24C22×D103
FittingC22×C22⋊C4×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC2×#15692990C2
cosocleC24×C103C23
hypercenterC22×C22⋊C4D103
hypocenterC103#1898
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15692935C2semidirect
3. #20267647C2semidirect
4. #20267557C2semidirect
5. C22×C22⋊C4×C103C2semidirect
6. C22×C22⋊D103C4semidirect
12. C2×C22⋊Dic103C4semidirect
21. C23×D103C2×C4semidirect
30. C22×Dic103C2×C4semidirect
31. C22×Dic103C2×C4semidirect
52. C22⋊C4×C103D4semidirect
108. C22×C103#99semidirect
131. C103#1898semidirect
133. C22×C22⋊C4D103semidirect
183. C22⋊C4C22⋊D103semidirect
242. C22#15692935semidirect

Maximal subgroups

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

subgroupindex
C2×#156929902
C2×#156929352
#202676472
#202675572
C22×C22⋊C4×C1032
#1898103