Finite Group Databasebeta

← #27205058

Subgroups — #27205058

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#20268304C211yesmaximal, characteristic
2C2×#15692979C211yesmaximal, characteristic, complemented
3#20268130C212yesmaximal, complemented
4#20268124C211yesmaximal, characteristic, complemented
5#20268117C212yesmaximal, complemented
6#20268110C211yesmaximal, characteristic, complemented
7#20268104C211yesmaximal, characteristic, complemented
8#20267826C212yesmaximal, complemented
9#20267786C212yesmaximal, complemented
10C22⋊C8×D103C211yesmaximal, characteristic, complemented
11#483×C103C211yesmaximal, characteristic, complemented
12C2×#13110106C2211yescharacteristic
13C22×C4×D103C2211yescharacteristic
14C2×C8×D103C2212yes—
15#15693006—21no—
16#15692997C2211yescharacteristic
17#15692996C2211yescharacteristic
18#15692995C2211yescharacteristic
19#15692991—21no—
20#15692983—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#15692945C2212yescomplemented
34#15692943C2212yescomplemented
35#15692941C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic
37(C2×D103)⋊C8C2212yes—
38C22⋊Q8×C103C2211yescharacteristic
39C2×C4⋊C4×C103C2211yescharacteristic
40#106×C103C2212yescomplemented
41#103×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic
43C23×D103D411yescharacteristic
44#13110106—24no—
45C2×D412—21no—
46C2×D412—21no—
47C2×D412C2311yescharacteristic
48C2×C22⋊D103—21no—
49C22×Dic103—21no—
50C22×Dic103D411yescharacteristic
51C2×C4×D103—24no—
52C2×C4×D103—21no—
53C2×C4×D103D411yescharacteristic
54C2×C4×D103D411yescharacteristic
55C2×C4×D103C2311yescharacteristic
56C2×C4×D103C2311yescharacteristic
57C2×C103⋊C8C2312yes—
58C8×D103—24no—
59C4⋊Dic103—21no—
60C4⋊Dic103C2312yes—
61C4⋊Dic103C2311yescharacteristic
62Dic103⋊C4—21no—
63(C2×D103)⋊C4—22no—
64(C2×D103)⋊C4—22no—
65(C2×D103)⋊C4—21no—
66(C2×D103)⋊C4—21no—
67(C2×D103)⋊C4—21no—
68(C2×D103)⋊C4—21no—
69C4×Dic103—22no—
70C4×Dic103—22no—
71C4×Dic103—21no—
72C2×Q8×C103C2311yescharacteristic
73C22×C4×C103—21no—
74C22×C4×C103C2311yescharacteristic
75C2×C8×C103C2312yes—
76C4⋊C4×C103—21no—
77C4⋊C4×C103—21no—
78C4⋊C4×C103C2312yes—
79C4⋊C4×C103C2311yescharacteristic
80C22⋊C4×C103—21no—
81C23×C103C2×D411yescharacteristic
82C22×D103—22no—
83C22×D103—22no—
84C22×D103—21no—
85C22×D103—41no—
86C22×D103C2×D411yescharacteristic
87C22×D103C2×D411yescharacteristic
88Q8×C103—22no—
89C2×C4×C103—22no—
90C2×C4×C103—21no—
91C2×C4×C103—21no—
92C2×C4×C103—22no—
93C2×C4×C103—42no—
94C2×C4×C103C2×D411yescharacteristic
95C2×C4×C103C2411yescharacteristic
96C22⋊D103—42no—
97C2×Dic103—22no—
98C2×Dic103—22no—
99C2×Dic103—21no—
100C2×Dic103—42no—
101C2×Dic103C2×D411yescharacteristic
102C2×Dic103C2×D411yescharacteristic
103D412—22no—
104D412—42no—
105D412—42no—
106C4×D103—22no—
107C4×D103—22no—
108C4×D103—22no—
109C4×D103—42no—
110C4×D103#4114yes—
111C8×C103—22no—
112C103⋊C8—22no—
113C22×C103—21no—
114C22×C103—21no—
115C22×C103#13512yes—
116C22×C103C22×D411yescharacteristic
117C2×D103—21no—
118C2×D103—21no—
119C2×D103—21no—
120C2×D103—21no—
121C2×D103—21no—
122C2×D103—44no—
123C2×D103—41no—
124C2×D103—41no—
125C2×D103—41no—
126C2×D103#12312yes—
127C4×C103—21no—
128C4×C103—41no—
129C4×C103—42no—
130C4×C103—41no—
131C4×C103C2×#4112yes—
132Dic103—21no—
133Dic103—41no—
134Dic103—42no—
135Dic103#12312yes—
136C2×C103—22no—
137C2×C103C2×#12311yescharacteristic
138C2×C103C2×#13511yescharacteristic
139C2×C103#57511yescharacteristic
140D103—22no—
141D103—41no—
142D103—81no—
143#3091—1031nomaximal, Sylow
144C103#309111yescharacteristic, complemented, Sylow
145#525—1031no—
146C2×#117—1031no—
147#485—1032no—
148#484—1031no—
149#483D10311yescharacteristic, complemented
150#482—1032no—
151#481—1031no—
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⋊Q8C2×D10311yescharacteristic
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⋊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#103C2×D10312yescomplemented
182#102—1032no—
183#102—1032no—
184C22⋊C8—1031no—
185C22⋊C8—1032no—
186C22⋊C8C2×D10311yescharacteristic
187C24—1031no—
188#41—2064no—
189C2×Q8C22×D10311yescharacteristic
190C2×D4—1031no—
191C2×D4—2061no—
192C2×D4—2061no—
193C2×D4—2061no—
194C22×C4—21no—
195C22×C4—1031no—
196C22×C4—1031no—
197C22×C4—1031no—
198C22×C4—1031no—
199C22×C4—1031no—
200C22×C4—2061no—
201C22×C4—2064no—
202C22×C4—2061no—
203C22×C4C22×D10311yescharacteristic
204C2×C8—1032no—
205C2×C8—2064no—
206C2×C8C22×D10312yes—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—1032no—
210C4⋊C4—1031no—
211C4⋊C4—2061no—
212C4⋊C4—2061no—
213C4⋊C4C22×D10312yes—
214C4⋊C4C22×D10311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—2061no—
217C22⋊C4—2062no—
218C22⋊C4—2062no—
219C22⋊C4—2061no—
220C22⋊C4—2061no—
221C22⋊C4—2061no—
222C42—2062no—
223C42—2062no—
224C42—2061no—
225C23—1031no—
226C23—1031no—
227C23—4121no—
228C23—2062no—
229C23—2061no—
230C23—2062no—
231C23D4×D10311yescharacteristic
232Q8—22no—
233D4—4122no—
234D4—4122no—
235D4—4122no—
236D4—2062no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—1031no—
243C2×C4—1034no—
244C2×C4—1031no—
245C2×C4—4122no—
246C2×C4—4122no—
247C2×C4—2062no—
248C2×C4—2062no—
249C2×C4—2062no—
250C2×C4—2062no—
251C2×C4—2061no—
252C2×C4—2062no—
253C2×C4D4×D10311yescharacteristic
254C2×C4C23×D10311yescharacteristic
255C8—22no—
256C8—2062no—
257C22—21no—
258C22—21no—
259C22—1032no—
260C22—4124no—
261C22—4121no—
262C22—4121no—
263C22—4121no—
264C22—2061no—
265C22—2061no—
266C22—2061no—
267C22—2061no—
268C22—2061no—
269C22#1569304212yes—
270C22C2×D4×D10311yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—41no—
275C4—1032no—
276C4—4121no—
277C4—4122no—
278C4—2061no—
279C4#41×D10312yes—
280C2—22no—
281C2—8241no—
282C2—4121no—
283C2—2062no—
284C2#123×D10311yescharacteristic
285C2C2×#1569304211yescharacteristic
286C2#2026859011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#483×C103C2
socleC22×C103C22×D4
prime radical#20268304C2
hypercenter#483D103
hypocenterC103#3091
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. C2×#15692979C2semidirect
3. #20268130C2semidirect
4. #20268124C2semidirect
5. #20268117C2semidirect
6. #20268110C2semidirect
7. #20268104C2semidirect
8. #20267826C2semidirect
9. #20267786C2semidirect
10. C22⋊C8×D103C2semidirect
11. #483×C103C2semidirect
30. #15692954C22semidirect
31. #15692954C22semidirect
32. #15692953C22semidirect
33. #15692945C22semidirect
34. #15692943C22semidirect
35. #15692941C22semidirect
40. #106×C103C22semidirect
41. #103×C103C22semidirect
144. C103#3091semidirect
149. #483D103semidirect
179. #106C2×D103semidirect
181. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683042
C2×#156929792
#202681302
#202681242
#202681172
#202681102
#202681042
#202678262
#202677862
C22⋊C8×D1032
#483×C1032
#3091103