Finite Group Databasebeta

← #27205069

Subgroups — #27205069

Order 13184.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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#20268302C211yesmaximal, characteristic
2C22×C4⋊Dic103C211yesmaximal, characteristic, complemented
3#20268127C212yesmaximal, complemented
4#20268122C212yesmaximal, complemented
5#20268110C212yesmaximal, complemented
6#20268105C212yesmaximal, complemented
7#20267833C212yesmaximal, complemented
8#20267793C212yesmaximal, complemented
9#407×C103C211yesmaximal, characteristic, complemented
10C2×#13110105C2211yescharacteristic
11C23×Dic103—21no—
12#15693004—21no—
13#15693000C2211yescharacteristic
14#15693000C2211yescharacteristic
15#15692995C2211yescharacteristic
16#15692995C2211yescharacteristic
17#15692990—21no—
18C4×C22⋊D103—21no—
19C4×C22⋊D103—21no—
20#15692980C2211yescharacteristic
21C2×C4⋊Dic103—21no—
22C2×C4⋊Dic103—21no—
23C2×C4⋊Dic103—21no—
24C2×C4⋊Dic103C2212yes—
25C2×C4⋊Dic103C2212yes—
26C2×C4⋊Dic103C2212yes—
27#15692955C2214yescomplemented
28#15692953C2214yescomplemented
29#15692946C2214yescomplemented
30#15692943C2214yescomplemented
31C23×C4×C103C2211yescharacteristic
32C2×M16×C103C2212yes—
33C22⋊C8×C103C2212yes—
34C22⋊C8×C103C2212yes—
35#13110105—24no—
36C2×Dic206C2311yescharacteristic
37C2×D412C2311yescharacteristic
38C2×C22⋊D103—21no—
39C2×C22⋊D103—21no—
40C2×C22⋊D103—21no—
41C22×Dic103—22no—
42C22×Dic103—22no—
43C22×Dic103—22no—
44C22×Dic103—44no—
45C2×C4×D103—21no—
46C4⋊Dic103—22no—
47C4⋊Dic103—22no—
48C4⋊Dic103—22no—
49C4⋊Dic103C2314yes—
50C4⋊Dic103C2311yescharacteristic
51C4⋊Dic103C2311yescharacteristic
52Dic103⋊C4—21no—
53Dic103⋊C4—21no—
54C22⋊Dic103—21no—
55C22⋊Dic103—21no—
56C22⋊Dic103—21no—
57(C2×D103)⋊C4—21no—
58(C2×D103)⋊C4—21no—
59C4×Dic103—21no—
60C24×C103D411yescharacteristic
61C22×C4×C103—24no—
62C22×C4×C103D411yescharacteristic
63C22×C4×C103D411yescharacteristic
64C22×C4×C103D411yescharacteristic
65C22×C4×C103C2311yescharacteristic
66C22×C4×C103C2311yescharacteristic
67C22×C4×C103C2311yescharacteristic
68M16×C103—24no—
69C2×C8×C103C2314yes—
70C23×C103—22no—
71C23×C103—22no—
72C23×C103—22no—
73C23×C103C2×D411yescharacteristic
74C23×C103C2×D411yescharacteristic
75C23×C103C2×D411yescharacteristic
76C22×D103—21no—
77C2×C4×C103—22no—
78C2×C4×C103—22no—
79C2×C4×C103—22no—
80C2×C4×C103—22no—
81C2×C4×C103—22no—
82C2×C4×C103C2×D411yescharacteristic
83C2×C4×C103C2×D411yescharacteristic
84C2×C4×C103C2×D411yescharacteristic
85C2×C4×C103#4114yes—
86C2×C4×C103C2411yescharacteristic
87C22⋊D103—42no—
88C22⋊D103—42no—
89C22⋊D103—42no—
90C2×Dic103—21no—
91C2×Dic103—21no—
92C2×Dic103—21no—
93C2×Dic103—24no—
94C2×Dic103—44no—
95C2×Dic103—44no—
96C2×Dic103—44no—
97D412—22no—
98C4×D103—42no—
99Dic206—22no—
100C8×C103—24no—
101C22×C103—28no—
102C22×C103—21no—
103C22×C103—21no—
104C22×C103—21no—
105C22×C103—21no—
106C22×C103—21no—
107C22×C103—21no—
108C22×C103#12312yes—
109C22×C103AGL(1,ℤ/8)12yes—
110C22×C103#13712yes—
111C22×C103C22×D411yescharacteristic
112C2×D103—41no—
113C2×D103—41no—
114C2×D103—41no—
115C4×C103—21no—
116C4×C103—21no—
117C4×C103#12312yes—
118C4×C103C2×#4112yes—
119Dic103—41no—
120Dic103—44no—
121Dic103—41no—
122Dic103—41no—
123C2×C103—22no—
124C2×C103—22no—
125C2×C103—22no—
126C2×C103C2×#12311yescharacteristic
127C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C103C2×#13711yescharacteristic
129D103—81no—
130#3092—1031nomaximal, Sylow
131C103#309211yescharacteristic, complemented, Sylow
132#525—1031no—
133C22×C4⋊C4—1031no—
134#484—1032no—
135#483—1032no—
136#481—1032no—
137#480—1032no—
138#428—1032no—
139#417—1032no—
140#407D10311yescharacteristic, complemented
141C2×#41—1031no—
142C23×C4—2061no—
143C23×C4C2×D10311yescharacteristic
144C2×M16C2×D10312yes—
145#123—2061no—
146C22⋊Q8—1031no—
147C22⋊Q8—1031no—
148#121—1031no—
149#121—1031no—
150#120—2061no—
151C4×D4—2061no—
152C4×D4—2061no—
153#117—1031no—
154C2×C4⋊C4—1032no—
155C2×C4⋊C4—1032no—
156C2×C4⋊C4—1032no—
157C2×C4⋊C4—2061no—
158C2×C4⋊C4—2061no—
159C2×C4⋊C4—2061no—
160#107—1034no—
161#106—1034no—
162#103—1034no—
163#102—1034no—
164C22⋊C8C2×D10312yes—
165C22⋊C8C2×D10312yes—
166C24D41211yescharacteristic
167#41—2064no—
168C2×Q8—1031no—
169C2×D4—1031no—
170C2×D4—2061no—
171C2×D4—2061no—
172C2×D4—2061no—
173C22×C4—24no—
174C22×C4—4124no—
175C22×C4—2062no—
176C22×C4—2062no—
177C22×C4—2062no—
178C22×C4—2061no—
179C22×C4D41211yescharacteristic
180C22×C4D41211yescharacteristic
181C22×C4D41211yescharacteristic
182C22×C4C22×D10311yescharacteristic
183C22×C4C22×D10311yescharacteristic
184C22×C4C22×D10311yescharacteristic
185M16—24no—
186C2×C8C22×D10314yes—
187C4⋊C4—1034no—
188C4⋊C4—1031no—
189C4⋊C4—1031no—
190C4⋊C4—2061no—
191C4⋊C4—2061no—
192C4⋊C4—2062no—
193C4⋊C4—2062no—
194C4⋊C4—2062no—
195C22⋊C4—2061no—
196C22⋊C4—2061no—
197C22⋊C4—2061no—
198C22⋊C4—2061no—
199C22⋊C4—2061no—
200C42—2061no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—2061no—
205C23C2×D41211yescharacteristic
206C23C2×D41211yescharacteristic
207C23C2×D41211yescharacteristic
208Q8—2062no—
209D4—4122no—
210D4—4122no—
211D4—4122no—
212D4—2062no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—4124no—
219C2×C4—4124no—
220C2×C4—4124no—
221C2×C4—4122no—
222C2×C4—2061no—
223C2×C4—2061no—
224C2×C4—2061no—
225C2×C4—2064no—
226C2×C4C2×D41211yescharacteristic
227C2×C4C2×D41211yescharacteristic
228C2×C4C2×D41211yescharacteristic
229C2×C4#1311010414yes—
230C2×C4C23×D10311yescharacteristic
231C8—24no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—4121no—
240C22—4121no—
241C22—4121no—
242C22#1569300512yes—
243C22#1569304912yes—
244C22#1569305412yes—
245C22C22×D41211yescharacteristic
246C4—21no—
247C4—21no—
248C4—4121no—
249C4—4124no—
250C4—4121no—
251C4—4121no—
252C4#1569300512yes—
253C4C2×#1311010412yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—8241no—
258C2C2×#1569300511yescharacteristic
259C2C2×#1569304911yescharacteristic
260C2C2×#1569305411yescharacteristic
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#407×C103C2
socleC22×C103C22×D4
prime radical#20268302C2
hypercenter#407D103
hypocenterC103#3092
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic103C2semidirect
3. #20268127C2semidirect
4. #20268122C2semidirect
5. #20268110C2semidirect
6. #20268105C2semidirect
7. #20267833C2semidirect
8. #20267793C2semidirect
9. #407×C103C2semidirect
27. #15692955C22semidirect
28. #15692953C22semidirect
29. #15692946C22semidirect
30. #15692943C22semidirect
131. C103#3092semidirect
140. #407D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
C22×C4⋊Dic1032
#202681272
#202681222
#202681102
#202681052
#202678332
#202677932
#407×C1032
#3092103