Finite Group Databasebeta

← #27205059

Subgroups — #27205059

Order 13184.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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
2C2×#15692980C211yesmaximal, characteristic, complemented
3#20268133C212yesmaximal, complemented
4#20268127C211yesmaximal, characteristic, complemented
5#20268122C211yesmaximal, characteristic, complemented
6#20268116C212yesmaximal, complemented
7#20268110C211yesmaximal, characteristic, complemented
8#20268105C211yesmaximal, characteristic, complemented
9#20267829C212yesmaximal, complemented
10#20267788C212yesmaximal, complemented
11C2×C22⋊C8×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic
13#15693004—21no—
14#15693000C2211yescharacteristic
15#15693000C2211yescharacteristic
16#15692995C2211yescharacteristic
17#15692995C2211yescharacteristic
18#15692990—21no—
19C4×C22⋊D103—21no—
20C4×C22⋊D103—21no—
21#15692980—21no—
22#15692980—21no—
23#15692980C2212yes—
24#15692980C2211yescharacteristic
25#15692980C2212yes—
26C2×C4⋊Dic103C2211yescharacteristic
27C2×C4⋊Dic103C2211yescharacteristic
28C2×C22⋊Dic103—21no—
29C2×C4×Dic103—21no—
30#15692955C2212yescomplemented
31#15692955C2212yescomplemented
32#15692953C2212yescomplemented
33#15692953C2212yescomplemented
34#15692946C2212yescomplemented
35#15692946C2212yescomplemented
36#15692943C2212yescomplemented
37#15692943C2212yescomplemented
38C23×C4×C103C2211yescharacteristic
39C22×C8×C103C2212yes—
40C22⋊C8×C103C2211yescharacteristic
41C22⋊C8×C103C2211yescharacteristic
42C22⋊C8×C103C2212yes—
43#13110105—24no—
44C2×Dic206C2311yescharacteristic
45C2×D412C2311yescharacteristic
46C2×C22⋊D103—21no—
47C2×C22⋊D103—21no—
48C2×C22⋊D103—21no—
49C22×Dic103—21no—
50C22×Dic103—21no—
51C2×C4×D103—21no—
52C4⋊Dic103—21no—
53C4⋊Dic103—21no—
54C4⋊Dic103C2312yes—
55C4⋊Dic103C2312yes—
56C4⋊Dic103C2311yescharacteristic
57C4⋊Dic103C2311yescharacteristic
58Dic103⋊C4—21no—
59Dic103⋊C4—21no—
60C22⋊Dic103—22no—
61C22⋊Dic103—22no—
62C22⋊Dic103—21no—
63C22⋊Dic103—21no—
64C22⋊Dic103—21no—
65(C2×D103)⋊C4—21no—
66(C2×D103)⋊C4—21no—
67C4×Dic103—22no—
68C4×Dic103—22no—
69C4×Dic103—21no—
70C24×C103D411yescharacteristic
71C22×C4×C103—24no—
72C22×C4×C103D411yescharacteristic
73C22×C4×C103D411yescharacteristic
74C22×C4×C103D411yescharacteristic
75C22×C4×C103C2311yescharacteristic
76C22×C4×C103C2311yescharacteristic
77C22×C4×C103C2311yescharacteristic
78C2×C8×C103—24no—
79C2×C8×C103C2312yes—
80C2×C8×C103C2312yes—
81C23×C103—22no—
82C23×C103—22no—
83C23×C103—41no—
84C23×C103C2×D411yescharacteristic
85C23×C103C2×D411yescharacteristic
86C23×C103C2×D411yescharacteristic
87C22×D103—21no—
88C2×C4×C103—22no—
89C2×C4×C103—22no—
90C2×C4×C103—22no—
91C2×C4×C103—22no—
92C2×C4×C103—22no—
93C2×C4×C103C2×D411yescharacteristic
94C2×C4×C103C2×D411yescharacteristic
95C2×C4×C103C2×D411yescharacteristic
96C2×C4×C103#4114yes—
97C2×C4×C103C2411yescharacteristic
98C22⋊D103—42no—
99C22⋊D103—42no—
100C22⋊D103—42no—
101C2×Dic103—22no—
102C2×Dic103—22no—
103C2×Dic103—21no—
104C2×Dic103—21no—
105C2×Dic103—21no—
106C2×Dic103—42no—
107C2×Dic103—42no—
108D412—22no—
109C4×D103—42no—
110Dic206—22no—
111C8×C103—22no—
112C8×C103—22no—
113C22×C103—21no—
114C22×C103—21no—
115C22×C103—21no—
116C22×C103—21no—
117C22×C103—21no—
118C22×C103—21no—
119C22×C103—21no—
120C22×C103—44no—
121C22×C103#12312yes—
122C22×C103#13512yes—
123C22×C103C22×D411yescharacteristic
124C2×D103—41no—
125C2×D103—41no—
126C2×D103—41no—
127C4×C103—21no—
128C4×C103—21no—
129C4×C103#12312yes—
130C4×C103C2×#4112yes—
131Dic103—41no—
132Dic103—42no—
133Dic103—41no—
134Dic103—42no—
135Dic103—41no—
136C2×C103—22no—
137C2×C103—22no—
138C2×C103—41no—
139C2×C103C2×#12311yescharacteristic
140C2×C103C2×#13511yescharacteristic
141C2×C103#57511yescharacteristic
142D103—81no—
143#3091—1031nomaximal, Sylow
144C103#309111yescharacteristic, complemented, Sylow
145#525—1031no—
146C2×#117—1031no—
147#485—1032no—
148#484—1031no—
149#483—1031no—
150#482—1032no—
151#481—1031no—
152#480—1031no—
153#427—1032no—
154#416—1032no—
155C2×C22⋊C8D10311yescharacteristic, complemented
156C2×#41—1031no—
157C23×C4C2×D10311yescharacteristic
158C22×C8C2×D10312yes—
159#123—2061no—
160C22⋊Q8—1031no—
161C22⋊Q8—1031no—
162#121—1031no—
163#121—1031no—
164#120—2061no—
165C4×D4—2061no—
166C4×D4—2061no—
167#117—1032no—
168#117—1032no—
169#117—1031no—
170#117—2061no—
171#117—2061no—
172C2×C4⋊C4—1031no—
173C2×C4⋊C4—1031no—
174C2×C22⋊C4—2061no—
175C2×C42—2061no—
176#107—1032no—
177#107—1032no—
178#106—1032no—
179#106—1032no—
180#103—1032no—
181#103—1032no—
182#102—1032no—
183#102—1032no—
184C22⋊C8C2×D10311yescharacteristic
185C22⋊C8C2×D10311yescharacteristic
186C22⋊C8C2×D10312yes—
187C24D41211yescharacteristic
188#41—2064no—
189C2×Q8—1031no—
190C2×D4—1031no—
191C2×D4—2061no—
192C2×D4—2061no—
193C2×D4—2061no—
194C22×C4—24no—
195C22×C4—2061no—
196C22×C4—2061no—
197C22×C4—2061no—
198C22×C4D41211yescharacteristic
199C22×C4D41211yescharacteristic
200C22×C4D41211yescharacteristic
201C22×C4C22×D10311yescharacteristic
202C22×C4C22×D10311yescharacteristic
203C22×C4C22×D10311yescharacteristic
204C2×C8—24no—
205C2×C8C22×D10312yes—
206C2×C8C22×D10312yes—
207C4⋊C4—1032no—
208C4⋊C4—1032no—
209C4⋊C4—1031no—
210C4⋊C4—1031no—
211C4⋊C4—2061no—
212C4⋊C4—2061no—
213C4⋊C4—2061no—
214C4⋊C4—2061no—
215C22⋊C4—2062no—
216C22⋊C4—2062no—
217C22⋊C4—2061no—
218C22⋊C4—2061no—
219C22⋊C4—2061no—
220C22⋊C4—2061no—
221C22⋊C4—2061no—
222C42—2062no—
223C42—2062no—
224C42—2061no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—2061no—
229C23C2×D41211yescharacteristic
230C23C2×D41211yescharacteristic
231C23C2×D41211yescharacteristic
232Q8—2062no—
233D4—4122no—
234D4—4122no—
235D4—4122no—
236D4—2062no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—4122no—
243C2×C4—4122no—
244C2×C4—4122no—
245C2×C4—2062no—
246C2×C4—2062no—
247C2×C4—2061no—
248C2×C4—2061no—
249C2×C4—2061no—
250C2×C4C2×D41211yescharacteristic
251C2×C4C2×D41211yescharacteristic
252C2×C4C2×D41211yescharacteristic
253C2×C4#1311010414yes—
254C2×C4C23×D10311yescharacteristic
255C8—22no—
256C8—22no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—4121no—
266C22—4121no—
267C22—4121no—
268C22#1569300512yes—
269C22#1569304312yes—
270C22C22×D41211yescharacteristic
271C4—21no—
272C4—21no—
273C4—4121no—
274C4—4122no—
275C4—4121no—
276C4—4122no—
277C4—4121no—
278C4#1569300512yes—
279C4C2×#1311010412yes—
280C2—22no—
281C2—22no—
282C2—41no—
283C2—8241no—
284C2C2×#1569300511yescharacteristic
285C2C2×#1569304311yescharacteristic
286C2#2026859111yescharacteristic
subgroupG/H
centerC2×C4C2×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×C22⋊C8×C103C2
socleC22×C103C22×D4
prime radical#20268302C2
hypercenterC2×C22⋊C8D103
hypocenterC103#3091
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#15692980C2semidirect
3. #20268133C2semidirect
4. #20268127C2semidirect
5. #20268122C2semidirect
6. #20268116C2semidirect
7. #20268110C2semidirect
8. #20268105C2semidirect
9. #20267829C2semidirect
10. #20267788C2semidirect
11. C2×C22⋊C8×C103C2semidirect
30. #15692955C22semidirect
31. #15692955C22semidirect
32. #15692953C22semidirect
33. #15692953C22semidirect
34. #15692946C22semidirect
35. #15692946C22semidirect
36. #15692943C22semidirect
37. #15692943C22semidirect
144. C103#3091semidirect
155. C2×C22⋊C8D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
C2×#156929802
#202681332
#202681272
#202681222
#202681162
#202681102
#202681052
#202678292
#202677882
C2×C22⋊C8×C1032
#3091103