Finite Group Databasebeta

← #27204751

Subgroups — #27204751

Order 13184.

500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#15693040C211yesmaximal, characteristic, complemented
2C2×M16×D103C211yesmaximal, characteristic, complemented
3#20268301C212yesmaximal, complemented
4#20268050C211yesmaximal, characteristic, complemented
5#20268049C211yesmaximal, characteristic, complemented
6#20268041C211yesmaximal, characteristic, complemented
7#20268036C212yesmaximal, complemented
8#20268035C212yesmaximal, complemented
9#20267826C211yesmaximal, characteristic, complemented
10#20267784C212yesmaximal, complemented
11#469×C103C211yesmaximal, characteristic, complemented
12C2×#13110104C2212yes—
13C22×C4×D103C2211yescharacteristic
14#15693040—24no—
15C2×Dic412C2211yescharacteristic, complemented
16C2×#13110093C2212yescomplemented
17C2×#13110089C2211yescharacteristic
18C2×#13110088C2211yescharacteristic
19C2×#13110088C2211yescharacteristic
20M16×D103—24no—
21C2×C8×D103C2211yescharacteristic
22C2×C8×D103C2211yescharacteristic
23#15693003—22no—
24#15693001C2212yes—
25#15693000C2212yes—
26#15692992C2212yes—
27#15692989—22no—
28D4×Dic103—22no—
29(C22⋊D103)⋊C4—22no—
30#15692979C2212yes—
31#15692954C2212yescomplemented
32#15692953C2211yescharacteristic, complemented
33#15692946C2212yescomplemented
34#15692944C2212yescomplemented
35#15692942C2212yescomplemented
36C2×D8×C103C2211yescharacteristic, complemented
37C2×M16×C103C2211yescharacteristic
38#121×C103C2212yes—
39#106×C103C2211yescharacteristic, complemented
40#102×C103C2212yescomplemented
41C23×D103D411yescharacteristic
42#13110104—24no—
43#13110104—24no—
44C2×Dic206C2312yes—
45C2×C22⋊D103—22no—
46C2×C22⋊D103—22no—
47C22×Dic103—22no—
48C22×Dic103D411yescharacteristic
49C2×C4×D103—22no—
50C2×C4×D103—22no—
51C2×C4×D103D411yescharacteristic
52C2×C4×D103D411yescharacteristic
53C2×C4×D103C2311yescharacteristic
54C2×C4×D103C2311yescharacteristic
55Dic412—22no—
56#13110093—24no—
57#13110089—22no—
58#13110088—22no—
59#13110088—22no—
60C2×C103⋊C8C2311yescharacteristic
61C2×C103⋊C8C2311yescharacteristic
62C8×D103—22no—
63C8×D103D414yescomplemented
64C4⋊Dic103—22no—
65C4⋊Dic103C2312yes—
66Dic103⋊C4—22no—
67C22⋊Dic103—22no—
68C22⋊Dic103—22no—
69(C2×D103)⋊C4—22no—
70(C2×D103)⋊C4—22no—
71C4×Dic103—22no—
72C2×D4×C103—22no—
73C2×D4×C103C2312yes—
74C22×C4×C103C2311yescharacteristic
75D8×C103—22no—
76M16×C103—22no—
77C2×C8×C103C2311yescharacteristic
78C2×C8×C103C2311yescharacteristic
79C4⋊C4×C103C2312yes—
80C22⋊C4×C103—22no—
81C23×C103—22no—
82C23×C103C2×D411yescharacteristic
83C22×D103—22no—
84C22×D103—42no—
85C22×D103C2×D411yescharacteristic
86C22×D103C2×D411yescharacteristic
87D4×C103—22no—
88D4×C103—22no—
89D4×C103—44no—
90C2×C4×C103—21no—
91C2×C4×C103—21no—
92C2×C4×C103—22no—
93C2×C4×C103C2×D411yescharacteristic
94C2×C4×C103C2411yescharacteristic
95C22⋊D103—44no—
96C22⋊D103—44no—
97C2×Dic103—22no—
98C2×Dic103—22no—
99C2×Dic103—22no—
100C2×Dic103—44no—
101C2×Dic103C2×D411yescharacteristic
102C2×Dic103C2×D411yescharacteristic
103C4×D103—22no—
104C4×D103—21no—
105C4×D103—21no—
106C4×D103—22no—
107C4×D103C2×D412yes—
108C4×D103#4112yes—
109Dic206—22no—
110Dic206—22no—
111C8×C103—21no—
112C8×C103C2×D412yes—
113C103⋊C8—21no—
114C103⋊C8C2×D412yes—
115C22×C103—21no—
116C22×C103—22no—
117C22×C103—42no—
118C22×C103—42no—
119C22×C103—42no—
120C22×C103C22×D411yescharacteristic
121C2×D103—22no—
122C2×D103—21no—
123C2×D103—22no—
124C2×D103—44no—
125C2×D103#12112yes—
126C4×C103—21no—
127C4×C103—42no—
128C4×C103C22×D411yescharacteristic
129C4×C103C2×#4111yescharacteristic
130Dic103—21no—
131Dic103—42no—
132Dic103—42no—
133Dic103#12112yes—
134C2×C103—41no—
135C2×C103—82no—
136C2×C103C2×#12111yescharacteristic
137C2×C103#57512yes—
138D103—22no—
139D103—41no—
140#3054—1031nomaximal, Sylow
141C103#305411yescharacteristic, complemented, Sylow
142C2×#135—1031no—
143C22×M16—1031no—
144#525—1032no—
145#470—1031no—
146#470—1031no—
147#469—1031no—
148#469D10311yescharacteristic, complemented
149#468—1032no—
150#468—1032no—
151#427—1031no—
152#416—1032no—
153C2×#41—1032no—
154C23×C4—1031no—
155#135—2064no—
156C2×Q16—1031no—
157C2×SD16—1032no—
158C2×D8C2×D10311yescharacteristic, complemented
159C2×M16—1031no—
160C2×M16—1031no—
161C2×M16—1031no—
162C2×M16—2064no—
163C2×M16C2×D10311yescharacteristic
164C22×C8—1031no—
165C22×C8—1031no—
166#123—2062no—
167C22⋊Q8—1032no—
168C22⋊Q8—1032no—
169#121—1032no—
170#121C2×D10312yes—
171#120—2062no—
172C4×D4—2062no—
173C4×D4—2062no—
174#117—1032no—
175#107—1032no—
176#106—1031no—
177#106C2×D10311yescharacteristic, complemented
178#103—1032no—
179#103—1032no—
180#102—1032no—
181#102C2×D10312yescomplemented
182C24—1031no—
183#41—2064no—
184#41—2064no—
185C2×Q8—1032no—
186C2×D4—22no—
187C2×D4—2062no—
188C2×D4—2062no—
189C2×D4C22×D10312yes—
190C22×C4—1031no—
191C22×C4—1031no—
192C22×C4—1031no—
193C22×C4—1031no—
194C22×C4—1031no—
195C22×C4—2062no—
196C22×C4—2062no—
197C22×C4—2062no—
198C22×C4C22×D10311yescharacteristic
199Q16—2062no—
200SD16—2064no—
201D8—22no—
202M16—22no—
203M16—2062no—
204M16—2062no—
205M16—2062no—
206C2×C8—1031no—
207C2×C8—1034no—
208C2×C8—1031no—
209C2×C8—2062no—
210C2×C8C22×D10311yescharacteristic
211C2×C8C22×D10311yescharacteristic
212C4⋊C4—1032no—
213C4⋊C4—2062no—
214C4⋊C4—2062no—
215C4⋊C4C22×D10312yes—
216C22⋊C4—22no—
217C22⋊C4—2062no—
218C22⋊C4—2062no—
219C22⋊C4—2062no—
220C22⋊C4—2062no—
221C42—2062no—
222C23—22no—
223C23—1031no—
224C23—1031no—
225C23—4122no—
226C23—2062no—
227C23D4×D10311yescharacteristic
228Q8—2062no—
229Q8—2062no—
230D4—22no—
231D4—22no—
232D4—44no—
233D4—4124no—
234D4—4124no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—1031no—
239C2×C4—1032no—
240C2×C4—1032no—
241C2×C4—1031no—
242C2×C4—4124no—
243C2×C4—2062no—
244C2×C4—2062no—
245C2×C4—2062no—
246C2×C4—2062no—
247C2×C4—2062no—
248C2×C4—2061no—
249C2×C4—2061no—
250C2×C4D4×D10311yescharacteristic
251C2×C4C23×D10311yescharacteristic
252C8—21no—
253C8—1032no—
254C8—2061no—
255C8D4×D10312yes—
256C22—22no—
257C22—21no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—1032no—
262C22—4124no—
263C22—2062no—
264C22—2061no—
265C22—2062no—
266C22C2×D4×D10311yescharacteristic
267C4—21no—
268C4—42no—
269C4—1032no—
270C4—4122no—
271C4—4122no—
272C4—2061no—
273C4C2×D4×D10311yescharacteristic
274C4#41×D10311yescharacteristic
275C2—41no—
276C2—82no—
277C2—4121no—
278C2—2062no—
279C2#121×D10311yescharacteristic
280C2#2026858712yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#469×C103C2
socleC22×C103C22×D4
hypercenter#469D103
hypocenterC103#3054
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#15693040C2semidirect
2. C2×M16×D103C2semidirect
3. #20268301C2semidirect
4. #20268050C2semidirect
5. #20268049C2semidirect
6. #20268041C2semidirect
7. #20268036C2semidirect
8. #20268035C2semidirect
9. #20267826C2semidirect
10. #20267784C2semidirect
11. #469×C103C2semidirect
15. C2×Dic412C22semidirect
16. C2×#13110093C22semidirect
31. #15692954C22semidirect
32. #15692953C22semidirect
33. #15692946C22semidirect
34. #15692944C22semidirect
35. #15692942C22semidirect
36. C2×D8×C103C22semidirect
39. #106×C103C22semidirect
40. #102×C103C22semidirect
63. C8×D103D4semidirect
141. C103#3054semidirect
148. #469D103semidirect
158. C2×D8C2×D103semidirect
177. #106C2×D103semidirect
181. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930402
C2×M16×D1032
#202683012
#202680502
#202680492
#202680412
#202680362
#202680352
#202678262
#202677842
#469×C1032
#3054103