Finite Group Databasebeta

← #27205074

Subgroups — #27205074

Order 13184.

414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 125 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#20268298C211yesmaximal, characteristic
2C2×#15692979C211yesmaximal, characteristic, complemented
3#20268131C212yesmaximal, complemented
4#20268130C212yesmaximal, complemented
5#20268114C212yesmaximal, complemented
6#20268113C212yesmaximal, complemented
7#20267833C211yesmaximal, characteristic, complemented
8#20267831C211yesmaximal, characteristic, complemented
9#20267792C211yesmaximal, characteristic, complemented
10#20267754C211yesmaximal, characteristic, complemented
11#417×C103C211yesmaximal, characteristic, complemented
12C22×C4×D103C2211yescharacteristic
13C2×#13110089C2211yescharacteristic
14#15693002—21no—
15#15692997C2211yescharacteristic
16#15692997C2211yescharacteristic
17#15692992C2211yescharacteristic
18#15692992C2211yescharacteristic
19#15692989—21no—
20C4×C22⋊D103—21no—
21C4×C22⋊D103—21no—
22#15692980C2211yescharacteristic
23#15692979—21no—
24#15692979—21no—
25#15692979C2212yes—
26#15692979C2212yes—
27C2×C4⋊Dic103C2211yescharacteristic
28C2×(C2×D103)⋊C4—21no—
29C2×C4×Dic103—21no—
30#15692955C2212yescomplemented
31#15692954C2212yescomplemented
32#15692953C2212yescomplemented
33#15692952C2212yescomplemented
34#15692945C2212yescomplemented
35#15692942C2212yescomplemented
36(C2×D103)⋊C8C2212yes—
37(C2×D103)⋊C8C2212yes—
38C2×#41×C103C2211yescharacteristic
39C2×M16×C103C2211yescharacteristic
40C2×C4⋊C4×C103C2211yescharacteristic
41#103×C103C2212yescomplemented
42#102×C103C2212yescomplemented
43C23×D103D411yescharacteristic
44C2×C22⋊D103—21no—
45C2×C22⋊D103—21no—
46C22×Dic103—21no—
47C22×Dic103D411yescharacteristic
48C2×C4×D103—22no—
49C2×C4×D103—22no—
50C2×C4×D103D411yescharacteristic
51C2×C4×D103D411yescharacteristic
52C2×C4×D103C2311yescharacteristic
53C2×C4×D103C2311yescharacteristic
54#13110089—22no—
55C2×C103⋊C8C2312yes—
56C4⋊Dic103—21no—
57C4⋊Dic103C2312yes—
58C4⋊Dic103C2311yescharacteristic
59C4⋊Dic103C2311yescharacteristic
60Dic103⋊C4—21no—
61Dic103⋊C4—21no—
62C22⋊Dic103—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—21no—
70C4×Dic103—22no—
71C4×Dic103—22no—
72#41×C103—22no—
73#41×C103—22no—
74C2×Q8×C103C2311yescharacteristic
75C2×D4×C103—21no—
76C2×D4×C103C2311yescharacteristic
77C22×C4×C103—21no—
78C22×C4×C103—21no—
79C22×C4×C103C2311yescharacteristic
80M16×C103—22no—
81C2×C8×C103C2312yes—
82C4⋊C4×C103—21no—
83C4⋊C4×C103C2312yes—
84C23×C103—21no—
85C23×C103C2×D411yescharacteristic
86C22×D103—22no—
87C22×D103—41no—
88C22×D103—41no—
89C22×D103C2×D411yescharacteristic
90C22×D103C2×D411yescharacteristic
91Q8×C103—21no—
92Q8×C103—21no—
93D4×C103—21no—
94D4×C103—21no—
95D4×C103—42no—
96C2×C4×C103—22no—
97C2×C4×C103—21no—
98C2×C4×C103—42no—
99C2×C4×C103—42no—
100C2×C4×C103C2×D411yescharacteristic
101C2×C4×C103#4112yes—
102C2×C4×C103#4112yes—
103C2×C4×C103C2411yescharacteristic
104C22⋊D103—42no—
105C22⋊D103—42no—
106C2×Dic103—22no—
107C2×Dic103—22no—
108C2×Dic103—21no—
109C2×Dic103—21no—
110C2×Dic103—42no—
111C2×Dic103C2×D411yescharacteristic
112C2×Dic103C2×D411yescharacteristic
113C4×D103—22no—
114C4×D103—22no—
115C4×D103—21no—
116C4×D103—21no—
117C4×D103—21no—
118C4×D103—21no—
119C8×C103—22no—
120C103⋊C8—22no—
121C22×C103—21no—
122C22×C103—21no—
123C22×C103—41no—
124C22×C103—41no—
125C22×C103—41no—
126C22×C103#12312yes—
127C22×C103C22×D411yescharacteristic
128C2×D103—21no—
129C2×D103—21no—
130C2×D103—21no—
131C2×D103—21no—
132C2×D103—21no—
133C2×D103—21no—
134C2×D103—44no—
135C4×C103—41no—
136C4×C103—42no—
137C4×C103#12312yes—
138C4×C103C2×#4111yescharacteristic
139C4×C103C2×#4111yescharacteristic
140Dic103—21no—
141Dic103—21no—
142Dic103—42no—
143Dic103—41no—
144Dic103—41no—
145C2×C103—22no—
146C2×C103—81no—
147C2×C103C2×#12311yescharacteristic
148C2×C103#57511yescharacteristic
149C2×C103#57511yescharacteristic
150D103—41no—
151D103—41no—
152#3093—1031nomaximal, Sylow
153C103#309311yescharacteristic, complemented, Sylow
154#525—1031no—
155C2×#117—1031no—
156#485—1032no—
157#485—1032no—
158#482—1032no—
159#482—1032no—
160#428—1031no—
161#428—1031no—
162#417—1031no—
163#417D10311yescharacteristic, complemented
164#407—1031no—
165C2×#41C2×D10311yescharacteristic
166C23×C4—1031no—
167C2×M16—1031no—
168C2×M16C2×D10311yescharacteristic
169#123—2061no—
170C22⋊Q8—1031no—
171C22⋊Q8—1031no—
172#121—1031no—
173#121—1031no—
174#120—2061no—
175C4×D4—2061no—
176C4×D4—2061no—
177#117—1031no—
178#117—1032no—
179#117—1032no—
180#117—2061no—
181#117—2061no—
182C2×C4⋊C4—1031no—
183C2×C4⋊C4C2×D10311yescharacteristic
184C2×C22⋊C4—2061no—
185C2×C42—2061no—
186#107—1032no—
187#107—1032no—
188#106—1032no—
189#106—1032no—
190#103—1032no—
191#103C2×D10312yescomplemented
192#102—1032no—
193#102C2×D10312yescomplemented
194C22⋊C8—1032no—
195C22⋊C8—1032no—
196C24—1031no—
197#41—22no—
198#41—22no—
199C2×Q8C22×D10311yescharacteristic
200C2×D4—21no—
201C2×D4—2061no—
202C2×D4—2061no—
203C2×D4C22×D10311yescharacteristic
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—1031no—
207C22×C4—1031no—
208C22×C4—1031no—
209C22×C4—1031no—
210C22×C4—1031no—
211C22×C4—2061no—
212C22×C4—2062no—
213C22×C4—2062no—
214C22×C4C22×D10311yescharacteristic
215M16—22no—
216M16—2062no—
217C2×C8—1032no—
218C2×C8C22×D10312yes—
219C4⋊C4—21no—
220C4⋊C4—1032no—
221C4⋊C4—1031no—
222C4⋊C4—1031no—
223C4⋊C4—2061no—
224C4⋊C4—2061no—
225C4⋊C4—2061no—
226C4⋊C4C22×D10312yes—
227C22⋊C4—2062no—
228C22⋊C4—2062no—
229C22⋊C4—2061no—
230C22⋊C4—2061no—
231C22⋊C4—2061no—
232C22⋊C4—2061no—
233C22⋊C4—2061no—
234C42—2062no—
235C42—2062no—
236C42—2061no—
237C23—21no—
238C23—1031no—
239C23—1031no—
240C23—4121no—
241C23—4121no—
242C23—2062no—
243C23D4×D10311yescharacteristic
244Q8—21no—
245Q8—21no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—4122no—
250D4—4122no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—1031no—
256C2×C4—1031no—
257C2×C4—4122no—
258C2×C4—2062no—
259C2×C4—2061no—
260C2×C4—2061no—
261C2×C4—2062no—
262C2×C4—2061no—
263C2×C4—2061no—
264C2×C4—2061no—
265C2×C4—2061no—
266C2×C4—2062no—
267C2×C4—2062no—
268C2×C4D4×D10311yescharacteristic
269C2×C4#1311010412yes—
270C2×C4#1311010512yes—
271C2×C4C23×D10311yescharacteristic
272C8—22no—
273C8—2062no—
274C22—21no—
275C22—21no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—4124no—
280C22—2061no—
281C22—2061no—
282C22—2061no—
283C22—2061no—
284C22—2061no—
285C22—2061no—
286C22#1569300312yes—
287C22C2×D4×D10311yescharacteristic
288C4—41no—
289C4—42no—
290C4—4121no—
291C4—4122no—
292C4—4121no—
293C4—2061no—
294C4—2061no—
295C4#1569300312yes—
296C4C2×#1311010411yescharacteristic
297C4C2×#1311010511yescharacteristic
298C2—22no—
299C2—81no—
300C2—4121no—
301C2—4121no—
302C2C2×#1569300311yescharacteristic
303C2#2026858711yescharacteristic
304C2#2026859011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#417×C103C2
socleC22×C103C22×D4
prime radical#20268298C2
hypercenter#417D103
hypocenterC103#3093
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#15692979C2semidirect
3. #20268131C2semidirect
4. #20268130C2semidirect
5. #20268114C2semidirect
6. #20268113C2semidirect
7. #20267833C2semidirect
8. #20267831C2semidirect
9. #20267792C2semidirect
10. #20267754C2semidirect
11. #417×C103C2semidirect
30. #15692955C22semidirect
31. #15692954C22semidirect
32. #15692953C22semidirect
33. #15692952C22semidirect
34. #15692945C22semidirect
35. #15692942C22semidirect
41. #103×C103C22semidirect
42. #102×C103C22semidirect
153. C103#3093semidirect
163. #417D103semidirect
191. #103C2×D103semidirect
193. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202682982
C2×#156929792
#202681312
#202681302
#202681142
#202681132
#202678332
#202678312
#202677922
#202677542
#417×C1032
#3093103