Finite Group Databasebeta

← #27205928

Subgroups — #27205928

Order 13184.

420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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#20268304C211yesmaximal, characteristic
2C2×#15692997C211yesmaximal, characteristic, complemented
3#20268131C212yesmaximal, complemented
4#20268119C211yesmaximal, characteristic, complemented
5#20268105C211yesmaximal, characteristic, complemented
6#20268029C212yesmaximal, complemented
7#20268023C212yesmaximal, complemented
8#20267952C212yesmaximal, complemented
9#20267930C211yesmaximal, characteristic, complemented
10C22⋊C8×D103C211yesmaximal, characteristic, complemented
11#451×C103C211yesmaximal, characteristic, complemented
12C2×#13110106C2211yescharacteristic
13C22×C4×D103C2211yescharacteristic
14C2×#13110092C2212yescomplemented
15C2×C8×D103C2212yes—
16#15693006—21no—
17#15692997—21no—
18#15692997—21no—
19#15692997C2211yescharacteristic
20#15692997C2212yes—
21#15692997C2212yes—
22#15692996C2211yescharacteristic
23#15692995C2211yescharacteristic
24#15692991—21no—
25#15692983—21no—
26(C22⋊D103)⋊C4—21no—
27#15692979C2211yescharacteristic
28C2×C4⋊Dic103C2211yescharacteristic
29C2×Dic103⋊C4—21no—
30C2×(C2×D103)⋊C4—21no—
31#15692955C2212yescomplemented
32#15692952C2212yescomplemented
33#15692945C2212yescomplemented
34#15692945C2212yescomplemented
35#15692943C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic
37(C2×D103)⋊C8C2212yes—
38C22×Q8×C103C2211yescharacteristic
39C2×Q16×C103C2212yescomplemented
40C22⋊Q8×C103C2211yescharacteristic
41#103×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic
43C23×D103D411yescharacteristic
44#13110106—42no—
45C2×D412—21no—
46C2×D412—21no—
47C2×D412C2311yescharacteristic
48C2×C22⋊D103—21no—
49C22×Dic103—21no—
50C22×Dic103D411yescharacteristic
51C2×C4×D103—21no—
52C2×C4×D103—42no—
53C2×C4×D103D411yescharacteristic
54C2×C4×D103D411yescharacteristic
55C2×C4×D103C2311yescharacteristic
56C2×C4×D103C2311yescharacteristic
57#13110092—42no—
58C2×C103⋊C8C2312yes—
59C8×D103—42no—
60C4⋊Dic103—21no—
61C4⋊Dic103C2312yes—
62C4⋊Dic103C2311yescharacteristic
63Dic103⋊C4—22no—
64Dic103⋊C4—22no—
65Dic103⋊C4—21no—
66(C2×D103)⋊C4—22no—
67(C2×D103)⋊C4—22no—
68(C2×D103)⋊C4—21no—
69(C2×D103)⋊C4—21no—
70(C2×D103)⋊C4—21no—
71(C2×D103)⋊C4—21no—
72C4×Dic103—21no—
73C2×Q8×C103—21no—
74C2×Q8×C103—42no—
75C2×Q8×C103C2311yescharacteristic
76C2×Q8×C103C2312yes—
77C22×C4×C103—21no—
78C22×C4×C103C2311yescharacteristic
79Q16×C103—42no—
80C2×C8×C103C2312yes—
81C4⋊C4×C103—21no—
82C4⋊C4×C103C2311yescharacteristic
83C22⋊C4×C103—21no—
84C23×C103C2×D411yescharacteristic
85C22×D103—22no—
86C22×D103—22no—
87C22×D103—21no—
88C22×D103—41no—
89C22×D103C2×D411yescharacteristic
90C22×D103C2×D411yescharacteristic
91Q8×C103—22no—
92Q8×C103—22no—
93Q8×C103—22no—
94Q8×C103—42no—
95C2×C4×C103—22no—
96C2×C4×C103—21no—
97C2×C4×C103—21no—
98C2×C4×C103—22no—
99C2×C4×C103—42no—
100C2×C4×C103C2×D411yescharacteristic
101C2×C4×C103C2411yescharacteristic
102C22⋊D103—42no—
103C2×Dic103—21no—
104C2×Dic103—22no—
105C2×Dic103—41no—
106C2×Dic103—42no—
107C2×Dic103C2×D411yescharacteristic
108C2×Dic103C2×D411yescharacteristic
109D412—22no—
110D412—42no—
111D412—42no—
112C4×D103—22no—
113C4×D103—22no—
114C4×D103—41no—
115C4×D103—41no—
116C4×D103—42no—
117C8×C103—22no—
118C103⋊C8—22no—
119C22×C103—21no—
120C22×C103—21no—
121C22×C103#13512yes—
122C22×C103C22×D411yescharacteristic
123C2×D103—21no—
124C2×D103—21no—
125C2×D103—21no—
126C2×D103—21no—
127C2×D103—21no—
128C2×D103—44no—
129C2×D103—41no—
130C2×D103—41no—
131C2×D103—41no—
132C2×D103#13712yes—
133C4×C103—21no—
134C4×C103—41no—
135C4×C103—42no—
136C4×C103—41no—
137C4×C103H(5,𝔽2)12yes—
138Dic103—21no—
139Dic103—21no—
140Dic103—42no—
141Dic103—41no—
142C2×C103—22no—
143C2×C103#53411yescharacteristic
144C2×C103C2×#13511yescharacteristic
145C2×C103C2×#13711yescharacteristic
146D103—22no—
147D103—41no—
148D103—81no—
149#3190—1031nomaximal, Sylow
150C103#319011yescharacteristic, complemented, Sylow
151#525—1031no—
152C2×C22⋊Q8—1031no—
153#485—1032no—
154#483—1031no—
155#480—1031no—
156#467—1032no—
157#465—1032no—
158#452—1032no—
159#451D10311yescharacteristic, complemented
160#448—1031no—
161C2×C22⋊C8—1031no—
162C2×#41—1031no—
163C22×Q8C2×D10311yescharacteristic
164C23×C4—1031no—
165C2×Q16C2×D10312yescomplemented
166C2×SD16—1032no—
167C22×C8—1032no—
168#123—2061no—
169C22⋊Q8—1032no—
170C22⋊Q8—1032no—
171C22⋊Q8—1031no—
172C22⋊Q8—2061no—
173C22⋊Q8—2061no—
174C22⋊Q8C2×D10311yescharacteristic
175#121—1031no—
176#121—1031no—
177#120—2061no—
178C4×D4—2061no—
179C4×D4—2061no—
180#117—1031no—
181C2×C4⋊C4—1031no—
182C2×C4⋊C4—2061no—
183C2×C22⋊C4—2061no—
184#107—1032no—
185#106—1032no—
186#103—1032no—
187#103—1032no—
188#103C2×D10312yescomplemented
189#102—1032no—
190C22⋊C8—1031no—
191C22⋊C8—1032no—
192C22⋊C8C2×D10311yescharacteristic
193C24—1031no—
194#41—4122no—
195C2×Q8—21no—
196C2×Q8—42no—
197C2×Q8C22×D10311yescharacteristic
198C2×Q8C22×D10312yes—
199C2×D4—1031no—
200C2×D4—2061no—
201C2×D4—2061no—
202C2×D4—2061no—
203C22×C4—21no—
204C22×C4—1031no—
205C22×C4—1031no—
206C22×C4—1031no—
207C22×C4—1031no—
208C22×C4—1031no—
209C22×C4—4122no—
210C22×C4—2061no—
211C22×C4—2061no—
212C22×C4C22×D10311yescharacteristic
213Q16—42no—
214SD16—4122no—
215C2×C8—1032no—
216C2×C8—4122no—
217C2×C8C22×D10312yes—
218C4⋊C4—21no—
219C4⋊C4—1032no—
220C4⋊C4—1031no—
221C4⋊C4—2062no—
222C4⋊C4—2062no—
223C4⋊C4—2061no—
224C4⋊C4—2061no—
225C4⋊C4C22×D10311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2061no—
228C22⋊C4—2062no—
229C22⋊C4—2062no—
230C22⋊C4—2061no—
231C22⋊C4—2061no—
232C22⋊C4—2061no—
233C42—2061no—
234C23—1031no—
235C23—1031no—
236C23—4121no—
237C23—2062no—
238C23—2061no—
239C23—2062no—
240C23D4×D10311yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—22no—
244Q8—42no—
245D4—4122no—
246D4—4122no—
247D4—4122no—
248D4—2062no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—1031no—
255C2×C4—1031no—
256C2×C4—4121no—
257C2×C4—4121no—
258C2×C4—4122no—
259C2×C4—4122no—
260C2×C4—4121no—
261C2×C4—2061no—
262C2×C4—2062no—
263C2×C4—2062no—
264C2×C4—2062no—
265C2×C4D4×D10311yescharacteristic
266C2×C4C23×D10311yescharacteristic
267C8—22no—
268C8—2062no—
269C22—21no—
270C22—21no—
271C22—1032no—
272C22—4124no—
273C22—4121no—
274C22—4121no—
275C22—4121no—
276C22—2061no—
277C22—2061no—
278C22—2061no—
279C22—2061no—
280C22—2061no—
281C22#1569304412yes—
282C22C2×D4×D10311yescharacteristic
283C4—21no—
284C4—41no—
285C4—42no—
286C4—41no—
287C4—4122no—
288C4—4121no—
289C4—2061no—
290C4—2061no—
291C4#1569306612yes—
292C2—22no—
293C2—8241no—
294C2—4121no—
295C2—2062no—
296C2#2026835111yescharacteristic
297C2C2×#1569304411yescharacteristic
298C2#137×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#451×C103C2
socleC22×C103C22×D4
prime radical#20268304C2
hypercenter#451D103
hypocenterC103#3190
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×#15692997C2semidirect
3. #20268131C2semidirect
4. #20268119C2semidirect
5. #20268105C2semidirect
6. #20268029C2semidirect
7. #20268023C2semidirect
8. #20267952C2semidirect
9. #20267930C2semidirect
10. C22⋊C8×D103C2semidirect
11. #451×C103C2semidirect
14. C2×#13110092C22semidirect
31. #15692955C22semidirect
32. #15692952C22semidirect
33. #15692945C22semidirect
34. #15692945C22semidirect
35. #15692943C22semidirect
39. C2×Q16×C103C22semidirect
41. #103×C103C22semidirect
150. C103#3190semidirect
159. #451D103semidirect
165. C2×Q16C2×D103semidirect
188. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683042
C2×#156929972
#202681312
#202681192
#202681052
#202680292
#202680232
#202679522
#202679302
C22⋊C8×D1032
#451×C1032
#3190103