Finite Group Databasebeta

← #27205054

Subgroups — #27205054

Order 13184.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#20268301C211yesmaximal, characteristic
2C2×#15692979C211yesmaximal, characteristic, complemented
3#20268135C212yesmaximal, complemented
4#20268126C211yesmaximal, characteristic, complemented
5#20268122C211yesmaximal, characteristic, complemented
6#20268114C212yesmaximal, complemented
7#20268102C211yesmaximal, characteristic, complemented
8#20267826C212yesmaximal, complemented
9#20267784C212yesmaximal, complemented
10C22⋊C8×D103C211yesmaximal, characteristic, complemented
11#481×C103C211yesmaximal, characteristic, complemented
12C2×#13110104C2211yescharacteristic
13C22×C4×D103C2211yescharacteristic
14C2×C8×D103C2212yes—
15#15693003—21no—
16#15693001C2211yescharacteristic
17#15693000C2211yescharacteristic
18#15692992C2211yescharacteristic
19#15692989—21no—
20D4×Dic103—21no—
21(C22⋊D103)⋊C4—21no—
22#15692979—21no—
23#15692979—21no—
24#15692979C2212yes—
25#15692979C2211yescharacteristic
26#15692979C2212yes—
27C2×C4⋊Dic103C2211yescharacteristic
28C2×(C2×D103)⋊C4—21no—
29C2×C4×Dic103—21no—
30#15692954C2212yescomplemented
31#15692954C2212yescomplemented
32#15692953C2212yescomplemented
33#15692946C2212yescomplemented
34#15692944C2212yescomplemented
35#15692942C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic
37(C2×D103)⋊C8C2212yes—
38#121×C103C2211yescharacteristic
39C2×C4⋊C4×C103C2211yescharacteristic
40#106×C103C2212yescomplemented
41#102×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic
43C23×D103D411yescharacteristic
44#13110104—24no—
45C2×Dic206C2311yescharacteristic
46C2×C22⋊D103—21no—
47C2×C22⋊D103—21no—
48C22×Dic103—21no—
49C22×Dic103—21no—
50C22×Dic103D411yescharacteristic
51C2×C4×D103—24no—
52C2×C4×D103D411yescharacteristic
53C2×C4×D103D411yescharacteristic
54C2×C4×D103C2311yescharacteristic
55C2×C4×D103C2311yescharacteristic
56C2×C103⋊C8C2312yes—
57C8×D103—24no—
58C4⋊Dic103—21no—
59C4⋊Dic103—21no—
60C4⋊Dic103C2312yes—
61C4⋊Dic103C2311yescharacteristic
62Dic103⋊C4—21no—
63C22⋊Dic103—21no—
64C22⋊Dic103—21no—
65(C2×D103)⋊C4—22no—
66(C2×D103)⋊C4—22no—
67(C2×D103)⋊C4—21no—
68(C2×D103)⋊C4—21no—
69C4×Dic103—22no—
70C4×Dic103—22no—
71C4×Dic103—21no—
72C2×D4×C103—21no—
73C2×D4×C103C2311yescharacteristic
74C22×C4×C103—21no—
75C22×C4×C103C2311yescharacteristic
76C2×C8×C103C2312yes—
77C4⋊C4×C103—21no—
78C4⋊C4×C103C2312yes—
79C4⋊C4×C103C2311yescharacteristic
80C22⋊C4×C103—21no—
81C23×C103—21no—
82C23×C103C2×D411yescharacteristic
83C22×D103—22no—
84C22×D103—22no—
85C22×D103—41no—
86C22×D103C2×D411yescharacteristic
87C22×D103C2×D411yescharacteristic
88D4×C103—22no—
89D4×C103—42no—
90C2×C4×C103—22no—
91C2×C4×C103—21no—
92C2×C4×C103—22no—
93C2×C4×C103—42no—
94C2×C4×C103C2×D411yescharacteristic
95C2×C4×C103C2411yescharacteristic
96C22⋊D103—42no—
97C22⋊D103—42no—
98C2×Dic103—22no—
99C2×Dic103—22no—
100C2×Dic103—21no—
101C2×Dic103—21no—
102C2×Dic103—42no—
103C2×Dic103—42no—
104C2×Dic103C2×D411yescharacteristic
105C2×Dic103C2×D411yescharacteristic
106C4×D103—22no—
107C4×D103—22no—
108C4×D103—22no—
109C4×D103#4114yes—
110Dic206—22no—
111C8×C103—22no—
112C103⋊C8—22no—
113C22×C103—21no—
114C22×C103—21no—
115C22×C103—41no—
116C22×C103—41no—
117C22×C103—41no—
118C22×C103#13512yes—
119C22×C103C22×D411yescharacteristic
120C2×D103—21no—
121C2×D103—21no—
122C2×D103—21no—
123C2×D103—21no—
124C2×D103—21no—
125C2×D103—44no—
126C2×D103#12312yes—
127C4×C103—21no—
128C4×C103—41no—
129C4×C103—42no—
130C4×C103C2×#4112yes—
131Dic103—21no—
132Dic103—41no—
133Dic103—42no—
134Dic103—41no—
135Dic103#12312yes—
136C2×C103—22no—
137C2×C103—81no—
138C2×C103C2×#12311yescharacteristic
139C2×C103C2×#13511yescharacteristic
140C2×C103#57511yescharacteristic
141D103—22no—
142D103—41no—
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#481D10311yescharacteristic, complemented
152#480—1031no—
153#427—1032no—
154#416—1032no—
155C2×C22⋊C8—1031no—
156C2×#41—1031no—
157C23×C4—1031no—
158C22×C8—1032no—
159#123—2061no—
160C22⋊Q8—1031no—
161C22⋊Q8—1031no—
162#121—1031no—
163#121C2×D10311yescharacteristic
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⋊C4C2×D10311yescharacteristic
174C2×C22⋊C4—2061no—
175C2×C42—2061no—
176#107—1032no—
177#107—1032no—
178#106—1032no—
179#106C2×D10312yescomplemented
180#103—1032no—
181#103—1032no—
182#102—1032no—
183#102C2×D10312yescomplemented
184C22⋊C8—1031no—
185C22⋊C8—1032no—
186C22⋊C8C2×D10311yescharacteristic
187C24—1031no—
188#41—2064no—
189C2×Q8—1031no—
190C2×D4—21no—
191C2×D4—2061no—
192C2×D4—2061no—
193C2×D4C22×D10311yescharacteristic
194C22×C4—21no—
195C22×C4—1031no—
196C22×C4—1031no—
197C22×C4—1031no—
198C22×C4—1031no—
199C22×C4—1031no—
200C22×C4—2064no—
201C22×C4—2061no—
202C22×C4—2061no—
203C22×C4C22×D10311yescharacteristic
204C2×C8—1032no—
205C2×C8—2064no—
206C2×C8C22×D10312yes—
207C4⋊C4—21no—
208C4⋊C4—1032no—
209C4⋊C4—1031no—
210C4⋊C4—2061no—
211C4⋊C4—2061no—
212C4⋊C4—2061no—
213C4⋊C4C22×D10312yes—
214C4⋊C4C22×D10311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—2062no—
217C22⋊C4—2062no—
218C22⋊C4—2061no—
219C22⋊C4—2061no—
220C22⋊C4—2061no—
221C22⋊C4—2061no—
222C42—2062no—
223C42—2062no—
224C42—2061no—
225C23—21no—
226C23—1031no—
227C23—1031no—
228C23—4121no—
229C23—2062no—
230C23—2062no—
231C23D4×D10311yescharacteristic
232Q8—2062no—
233D4—22no—
234D4—42no—
235D4—4122no—
236D4—4122no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—1031no—
242C2×C4—1034no—
243C2×C4—1031no—
244C2×C4—4122no—
245C2×C4—4122no—
246C2×C4—2062no—
247C2×C4—2062no—
248C2×C4—2062no—
249C2×C4—2062no—
250C2×C4—2061no—
251C2×C4—2061no—
252C2×C4—2062no—
253C2×C4D4×D10311yescharacteristic
254C2×C4C23×D10311yescharacteristic
255C8—22no—
256C8—2062no—
257C22—21no—
258C22—21no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—1032no—
263C22—4124no—
264C22—2061no—
265C22—2061no—
266C22—2061no—
267C22—2061no—
268C22—2061no—
269C22#1569304212yes—
270C22C2×D4×D10311yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—1032no—
275C4—4121no—
276C4—4122no—
277C4—4121no—
278C4—2061no—
279C4#41×D10312yes—
280C2—22no—
281C2—81no—
282C2—4121no—
283C2—2062no—
284C2#123×D10311yescharacteristic
285C2C2×#1569304211yescharacteristic
286C2#2026858711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#481×C103C2
socleC22×C103C22×D4
prime radical#20268301C2
hypercenter#481D103
hypocenterC103#3091
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#15692979C2semidirect
3. #20268135C2semidirect
4. #20268126C2semidirect
5. #20268122C2semidirect
6. #20268114C2semidirect
7. #20268102C2semidirect
8. #20267826C2semidirect
9. #20267784C2semidirect
10. C22⋊C8×D103C2semidirect
11. #481×C103C2semidirect
30. #15692954C22semidirect
31. #15692954C22semidirect
32. #15692953C22semidirect
33. #15692946C22semidirect
34. #15692944C22semidirect
35. #15692942C22semidirect
40. #106×C103C22semidirect
41. #102×C103C22semidirect
144. C103#3091semidirect
151. #481D103semidirect
179. #106C2×D103semidirect
183. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683012
C2×#156929792
#202681352
#202681262
#202681222
#202681142
#202681022
#202678262
#202677842
C22⋊C8×D1032
#481×C1032
#3091103