Finite Group Databasebeta

← #28348249

Subgroups — #28348249

Order 13696.

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

normal subgroups only

This group has 454 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#20293441C211yesmaximal, characteristic, complemented
2#20293439C212yesmaximal, complemented
3#20293429C211yesmaximal, characteristic, complemented
4#20293011C211yesmaximal, characteristic, complemented
5#20292903C211yesmaximal, characteristic, complemented
6#20292898C211yesmaximal, characteristic, complemented
7#20292890C212yesmaximal, complemented
8#20292806C212yesmaximal, complemented
9#20292801C212yesmaximal, complemented
10#20292745C211yesmaximal, characteristic, complemented
11#443×C107C211yesmaximal, characteristic, complemented
12#16812156C2212yescomplemented
13#16812155C2212yes—
14#16812142—22no—
15#16812142C2212yes—
16#16812139C2212yescomplemented
17#16812138—22no—
18#16812137—22no—
19#16812137C2212yescomplemented
20#16812136—22no—
21#16812134C2212yes—
22#16812132—21no—
23#16812131—22no—
24#16812131C2211yescharacteristic
25#16812128—21no—
26C2×Dic428C2211yescharacteristic, complemented
27Q16×D107—21no—
28C2×#13133807—22no—
29C2×#13133807C2212yescomplemented
30C2×D856C2211yescharacteristic
31D8×D107—21no—
32#16812115C2211yescharacteristic
33#16812115C2211yescharacteristic, complemented
34#16812097C2212yescomplemented
35#16812045C2211yescharacteristic, complemented
36#16812037C2211yescharacteristic
37#16812037C2211yescharacteristic, complemented
38#16812027C2212yescomplemented
39#16812025C2212yescomplemented
40#135×C107C2211yescharacteristic
41#131×C107C2212yescomplemented
42#108×C107C2211yescharacteristic, complemented
43#104×C107C2212yescomplemented
44C4×C8×C107C2211yescharacteristic, complemented
45#13133819—22no—
46#13133818—22no—
47#13133818—22no—
48#13133818C2311yescharacteristic
49#13133818C2311yescharacteristic
50#13133817—22no—
51#13133817—42no—
52C2×Dic214—22no—
53C2×Dic214C2312yes—
54Q8×D107—22no—
55C2×D428—22no—
56C2×D428C2312yes—
57D4×D107—22no—
58D4×D107—42no—
59Dic428—22no—
60Dic428—21no—
61Dic428—21no—
62Dic428D411yescharacteristic
63#13133808—22no—
64#13133807—22no—
65#13133807—22no—
66#13133807—22no—
67#13133807—22no—
68#13133807D411yescharacteristic
69#13133807D411yescharacteristic
70#13133806—22no—
71#13133805—22no—
72D856—22no—
73D856—21no—
74D856—21no—
75D856D411yescharacteristic
76#13133803—22no—
77#13133802C2311yescharacteristic
78#13133802C2311yescharacteristic
79#13133801—21no—
80#13133801—21no—
81C8×D107—21no—
82C8×D107—21no—
83(C2×D107)⋊C4—42no—
84#41×C107C2312yes—
85Q16×C107D411yescharacteristic
86SD16×C107D412yes—
87D8×C107D411yescharacteristic
88M16×C107—22no—
89M16×C107C2312yes—
90C2×C8×C107—22no—
91C2×C8×C107C2311yescharacteristic
92C2×C8×C107C2311yescharacteristic
93C42×C107C2311yescharacteristic
94C22×D107—22no—
95C22×D107—42no—
96Q8×C107C2×D412yes—
97D4×C107—22no—
98D4×C107C2×D412yes—
99C2×C4×C107—22no—
100C2×C4×C107—21no—
101C2×C4×C107C2411yescharacteristic
102C22⋊D107—21no—
103C22⋊D107—21no—
104C22⋊D107—42no—
105C22⋊D107—42no—
106C2×Dic107—22no—
107C2×Dic107—42no—
108D428—22no—
109D428—22no—
110D428—42no—
111D428C2×D411yescharacteristic
112D428C2×D411yescharacteristic
113C4×D107—21no—
114C4×D107—21no—
115C4×D107—42no—
116C4×D107—42no—
117Dic214—22no—
118Dic214—22no—
119Dic214—42no—
120Dic214C2×D411yescharacteristic
121Dic214C2×D411yescharacteristic
122C8×C107—22no—
123C8×C107C2×D411yescharacteristic
124C8×C107C2×D411yescharacteristic
125C8×C107C2×D411yescharacteristic
126C8×C107C2×D411yescharacteristic
127C107⋊C8—21no—
128C107⋊C8—21no—
129C22×C107—22no—
130C22×C107H(5,𝔽2)11yescharacteristic
131C2×D107—21no—
132C2×D107—21no—
133C2×D107—42no—
134C2×D107—82no—
135C2×D107—162no—
136C4×C107—22no—
137C4×C107—41no—
138C4×C107C22×D411yescharacteristic
139C4×C107C22×D411yescharacteristic
140Dic107—21no—
141Dic107—21no—
142Dic107—42no—
143C2×C107—21no—
144C2×C107—42no—
145C2×C107D4211yescharacteristic
146D107—41no—
147D107—41no—
148D107—82no—
149#3290—1071nomaximal, Sylow
150C107#329011yescharacteristic, complemented, Sylow
151#578—1071no—
152#577—1072no—
153#576—1071no—
154#495—1071no—
155#473—1071no—
156#472—1071no—
157#471—1072no—
158#455—1072no—
159#454—1072no—
160#443—1071no—
161#443D10711yescharacteristic, complemented
1622−1+4—1072no—
163H(5,𝔽2)—1072no—
164#137—1072no—
165#137—1072no—
166#137—2142no—
167#137—2142no—
168AGL(1,ℤ/8)—1072no—
169AGL(1,ℤ/8)—1072no—
170AGL(1,ℤ/8)—2142no—
171AGL(1,ℤ/8)—2142no—
172#135—1071no—
173#135—2142no—
174#135—2141no—
175#135—2141no—
176#135C2×D10711yescharacteristic
177C2×Q16—1071no—
178C2×Q16—2141no—
179C2×SD16—1072no—
180C2×SD16—2142no—
181C2×D8—1071no—
182C2×D8—2141no—
183#131—1071no—
184#131—1071no—
185#131C2×D10712yescomplemented
186#124—1072no—
187#108—1071no—
188#108C2×D10711yescharacteristic, complemented
189#104—1071no—
190#104—1071no—
191#104C2×D10712yescomplemented
192#101—1072no—
193#100—1072no—
194C4×C8C2×D10711yescharacteristic, complemented
195#41—1071no—
196#41—1071no—
197#41—4282no—
198#41—2142no—
199#41—2142no—
200#41—2142no—
201#41—2142no—
202#41C22×D10712yes—
203C2×Q8—1072no—
204C2×Q8—2142no—
205C2×Q8—2142no—
206C2×D4—1072no—
207C2×D4—4282no—
208C2×D4—2142no—
209C2×D4—2142no—
210Q16—1071no—
211Q16—2142no—
212Q16—2142no—
213Q16—2141no—
214Q16—2141no—
215Q16D42811yescharacteristic
216SD16—1071no—
217SD16—1071no—
218SD16—2142no—
219SD16—2142no—
220SD16—2142no—
221SD16—2142no—
222SD16—2142no—
223SD16—2142no—
224SD16D42812yes—
225D8—1071no—
226D8—2142no—
227D8—2142no—
228D8—2141no—
229D8—2141no—
230D8D42811yescharacteristic
231M16—22no—
232M16—1071no—
233M16—1071no—
234M16—2141no—
235M16—2141no—
236M16C22×D10712yes—
237C2×C8—22no—
238C2×C8—2141no—
239C2×C8—2141no—
240C2×C8C22×D10711yescharacteristic
241C2×C8C22×D10711yescharacteristic
242C22⋊C4—4282no—
243C42C22×D10711yescharacteristic
244C23—4282no—
245C23—2142no—
246Q8—1071no—
247Q8—1071no—
248Q8—4282no—
249Q8—2142no—
250Q8—2142no—
251Q8C2×D42812yes—
252D4—22no—
253D4—1071no—
254D4—1071no—
255D4—4282no—
256D4—4282no—
257D4—4282no—
258D4—2141no—
259D4—2141no—
260D4—2142no—
261D4—2142no—
262D4C2×D42812yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—4282no—
266C2×C4—4282no—
267C2×C4—4282no—
268C2×C4—2142no—
269C2×C4—2141no—
270C2×C4—2141no—
271C2×C4C23×D10711yescharacteristic
272C8—22no—
273C8—2141no—
274C8—2141no—
275C8D4×D10711yescharacteristic
276C8D4×D10711yescharacteristic
277C8C2×D42811yescharacteristic
278C8C2×D42811yescharacteristic
279C22—22no—
280C22—8562no—
281C22—4282no—
282C22—17122no—
283C22—2141no—
284C22—2141no—
285C22#1681215511yescharacteristic
286C4—22no—
287C4—41no—
288C4—4282no—
289C4—2141no—
290C4—2141no—
291C4C2×D4×D10711yescharacteristic
292C4C22×D42811yescharacteristic
293C2—21no—
294C2—42no—
295C2—8562no—
296C2—4281no—
297C2—4281no—
298C2D4×D42811yescharacteristic
subgroupG/H
centerC2D4×D428
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#443×C107C2
socleC2×C107D42
hypercenter#443D107
hypocenterC107#3290
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #20293441C2semidirect
2. #20293439C2semidirect
3. #20293429C2semidirect
4. #20293011C2semidirect
5. #20292903C2semidirect
6. #20292898C2semidirect
7. #20292890C2semidirect
8. #20292806C2semidirect
9. #20292801C2semidirect
10. #20292745C2semidirect
11. #443×C107C2semidirect
12. #16812156C22semidirect
16. #16812139C22semidirect
19. #16812137C22semidirect
26. C2×Dic428C22semidirect
29. C2×#13133807C22semidirect
33. #16812115C22semidirect
34. #16812097C22semidirect
35. #16812045C22semidirect
37. #16812037C22semidirect
38. #16812027C22semidirect
39. #16812025C22semidirect
41. #131×C107C22semidirect
42. #108×C107C22semidirect
43. #104×C107C22semidirect
44. C4×C8×C107C22semidirect
150. C107#3290semidirect
161. #443D107semidirect
185. #131C2×D107semidirect
188. #108C2×D107semidirect
191. #104C2×D107semidirect
194. C4×C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202934412
#202934392
#202934292
#202930112
#202929032
#202928982
#202928902
#202928062
#202928012
#202927452
#443×C1072
#3290107