Finite Group Databasebeta

← #27205958

Subgroups — #27205958

Order 13184.

466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 466 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#20268302C211yesmaximal, characteristic, complemented
2#20268121C211yesmaximal, characteristic, complemented
3#20268112C212yesmaximal, complemented
4#20268104C211yesmaximal, characteristic, complemented
5#20268042C212yesmaximal, complemented
6#20268035C212yesmaximal, complemented
7#20267942C211yesmaximal, characteristic, complemented
8#20267934C212yesmaximal, complemented
9#20267925C211yesmaximal, characteristic, complemented
10#20267755C211yesmaximal, characteristic, complemented
11C2×#121×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic, complemented
13C2×#13110093C2212yescomplemented
14C2×#13110090C2212yescomplemented
15C2×#13110089C2212yescomplemented
16#15693004—21no—
17#15693000C2211yescharacteristic
18#15693000C2211yescharacteristic, complemented
19#15692995C2211yescharacteristic
20#15692995C2211yescharacteristic, complemented
21#15692990—21no—
22C4×C22⋊D103—21no—
23C4×C22⋊D103—21no—
24#15692980C2211yescharacteristic, complemented
25#15692954C2212yescomplemented
26#15692952C2212yescomplemented
27#15692944C2212yescomplemented
28#15692942C2212yescomplemented
29#15692942C2212yescomplemented
30#15692941C2212yescomplemented
31C22⋊(C103⋊C8)C2211yescharacteristic
32C22⋊(C103⋊C8)C2211yescharacteristic
33C22⋊(C103⋊C8)C2212yescomplemented
34C22×D4×C103—21no—
35C22×D4×C103C2211yescharacteristic
36C23×C4×C103C2211yescharacteristic
37#121×C103—21no—
38#121×C103—21no—
39#121×C103C2212yes—
40#121×C103C2212yes—
41C2×C4⋊C4×C103C2211yescharacteristic
42C2×C22⋊C4×C103—21no—
43#13110105—42no—
44C2×Dic206C2311yescharacteristic
45C2×D412C2311yescharacteristic
46C2×C22⋊D103—21no—
47C2×C22⋊D103—21no—
48C2×C22⋊D103—21no—
49C2×C4×D103—21no—
50#13110093—42no—
51#13110090—42no—
52#13110089—42no—
53C2×C103⋊C8C2312yes—
54C2×C103⋊C8C2312yes—
55C4⋊Dic103C2311yescharacteristic
56C4⋊Dic103C2311yescharacteristic
57Dic103⋊C4—21no—
58Dic103⋊C4—21no—
59C22⋊Dic103—21no—
60C22⋊Dic103—21no—
61C22⋊Dic103—21no—
62(C2×D103)⋊C4—21no—
63(C2×D103)⋊C4—21no—
64C4×Dic103—21no—
65C24×C103—21no—
66C24×C103D411yescharacteristic
67C2×D4×C103—22no—
68C2×D4×C103—22no—
69C2×D4×C103—21no—
70C2×D4×C103—42no—
71C2×D4×C103—44no—
72C2×D4×C103C2312yes—
73C22×C4×C103—21no—
74C22×C4×C103—42no—
75C22×C4×C103D411yescharacteristic
76C22×C4×C103D411yescharacteristic
77C22×C4×C103D411yescharacteristic
78C22×C4×C103C2311yescharacteristic
79C22×C4×C103C2311yescharacteristic
80C22×C4×C103C2311yescharacteristic
81C4⋊C4×C103—21no—
82C4⋊C4×C103C2312yes—
83C22⋊C4×C103—22no—
84C22⋊C4×C103—22no—
85C23×C103—22no—
86C23×C103—22no—
87C23×C103—41no—
88C23×C103—41no—
89C23×C103—42no—
90C23×C103—42no—
91C23×C103—42no—
92C23×C103C2×D411yescharacteristic
93C23×C103C2×D411yescharacteristic
94C23×C103C2×D411yescharacteristic
95C22×D103—21no—
96D4×C103—22no—
97D4×C103—22no—
98D4×C103—42no—
99D4×C103—44no—
100D4×C103—44no—
101C2×C4×C103—22no—
102C2×C4×C103—22no—
103C2×C4×C103—22no—
104C2×C4×C103—22no—
105C2×C4×C103—41no—
106C2×C4×C103—41no—
107C2×C4×C103—41no—
108C2×C4×C103—42no—
109C2×C4×C103C2×D411yescharacteristic
110C2×C4×C103C2×D411yescharacteristic
111C2×C4×C103C2×D411yescharacteristic
112C2×C4×C103C2411yescharacteristic
113C22⋊D103—42no—
114C22⋊D103—42no—
115C22⋊D103—42no—
116C2×Dic103—21no—
117C2×Dic103—21no—
118C2×Dic103—21no—
119D412—22no—
120C4×D103—42no—
121Dic206—22no—
122C103⋊C8—22no—
123C103⋊C8—22no—
124C22×C103—21no—
125C22×C103—21no—
126C22×C103—21no—
127C22×C103—21no—
128C22×C103—21no—
129C22×C103—21no—
130C22×C103—21no—
131C22×C103—21no—
132C22×C103—44no—
133C22×C103—42no—
134C22×C103—42no—
135C22×C103—42no—
136C22×C103—84no—
137C22×C103AGL(1,ℤ/8)12yes—
138C22×C103C22×D411yescharacteristic
139C2×D103—41no—
140C2×D103—41no—
141C2×D103—41no—
142C4×C103—21no—
143C4×C103—21no—
144C4×C103—21no—
145C4×C103—42no—
146C4×C103H(5,𝔽2)12yes—
147Dic103—41no—
148Dic103—41no—
149Dic103—41no—
150C2×C103—22no—
151C2×C103—41no—
152C2×C103—41no—
153C2×C103—82no—
154C2×C103#53411yescharacteristic
155C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C103#57511yescharacteristic
157D103—81no—
158#3194—1031nomaximal, Sylow
159C103#319411yescharacteristic, complemented, Sylow
160#525—1031no—
161C2×#121D10311yescharacteristic, complemented
162#483—1031no—
163#482—1032no—
164#480—1031no—
165#469—1032no—
166#468—1032no—
167#450—1031no—
168#449—1032no—
169#447—1031no—
170#407—1031no—
171C2×#41—1031no—
172C22×D4—21no—
173C22×D4C2×D10311yescharacteristic
174C23×C4C2×D10311yescharacteristic
175C2×SD16—1032no—
176C2×D8—1032no—
177C2×M16—1032no—
178#123—2061no—
179C22⋊Q8—1031no—
180C22⋊Q8—1031no—
181#121—21no—
182#121—21no—
183#121—1031no—
184#121—1031no—
185#121C2×D10312yes—
186#121C2×D10312yes—
187#120—2061no—
188C4×D4—2061no—
189C4×D4—2061no—
190#117—1031no—
191C2×C4⋊C4C2×D10311yescharacteristic
192C2×C22⋊C4—21no—
193#107—1032no—
194#106—1032no—
195#103—1032no—
196#102—1032no—
197#102—1032no—
198#102—1032no—
199C22⋊C8—1031no—
200C22⋊C8—1031no—
201C22⋊C8—1032no—
202C24—21no—
203C24C22⋊D10311yescharacteristic
204#41—4122no—
205C2×Q8—1031no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—42no—
210C2×D4—44no—
211C2×D4—1031no—
212C2×D4—2061no—
213C2×D4—2061no—
214C2×D4—2061no—
215C2×D4C22×D10312yes—
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—2061no—
219C22×C4C22⋊D10311yescharacteristic
220C22×C4C22⋊D10311yescharacteristic
221C22×C4C22⋊D10311yescharacteristic
222C22×C4C22×D10311yescharacteristic
223C22×C4C22×D10311yescharacteristic
224C22×C4C22×D10311yescharacteristic
225SD16—4122no—
226D8—4122no—
227M16—4122no—
228C2×C8—1032no—
229C2×C8—1032no—
230C4⋊C4—21no—
231C4⋊C4—1031no—
232C4⋊C4—1031no—
233C4⋊C4—2061no—
234C4⋊C4—2061no—
235C4⋊C4C22×D10312yes—
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—2061no—
239C22⋊C4—2061no—
240C22⋊C4—2061no—
241C22⋊C4—2061no—
242C22⋊C4—2061no—
243C42—2061no—
244C23—22no—
245C23—22no—
246C23—41no—
247C23—41no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—2061no—
252C23C2×C22⋊D10311yescharacteristic
253C23C2×C22⋊D10311yescharacteristic
254C23C2×C22⋊D10311yescharacteristic
255Q8—2062no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—44no—
260D4—44no—
261D4—4122no—
262D4—4122no—
263D4—4122no—
264D4—2062no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—4122no—
274C2×C4—2061no—
275C2×C4—2061no—
276C2×C4—2061no—
277C2×C4C2×C22⋊D10311yescharacteristic
278C2×C4C2×C22⋊D10311yescharacteristic
279C2×C4C2×C22⋊D10311yescharacteristic
280C2×C4C23×D10311yescharacteristic
281C8—2062no—
282C8—2062no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—84no—
296C22—4121no—
297C22—4121no—
298C22—4121no—
299C22#1569304712yes—
300C22C22×C22⋊D10311yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—42no—
305C4—4121no—
306C4—4121no—
307C4—4121no—
308C4#1569306612yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—82no—
313C2—8241no—
314C2#2026835011yescharacteristic
315C2C2×#1569304711yescharacteristic
316C2#2026858911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#121×C103C2
socleC22×C103C22×D4
hypercenterC2×#121D103
hypocenterC103#3194
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #20268302C2semidirect
2. #20268121C2semidirect
3. #20268112C2semidirect
4. #20268104C2semidirect
5. #20268042C2semidirect
6. #20268035C2semidirect
7. #20267942C2semidirect
8. #20267934C2semidirect
9. #20267925C2semidirect
10. #20267755C2semidirect
11. C2×#121×C103C2semidirect
12. C2×#13110105C22semidirect
13. C2×#13110093C22semidirect
14. C2×#13110090C22semidirect
15. C2×#13110089C22semidirect
18. #15693000C22semidirect
20. #15692995C22semidirect
24. #15692980C22semidirect
25. #15692954C22semidirect
26. #15692952C22semidirect
27. #15692944C22semidirect
28. #15692942C22semidirect
29. #15692942C22semidirect
30. #15692941C22semidirect
33. C22⋊(C103⋊C8)C22semidirect
159. C103#3194semidirect
161. C2×#121D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
#202681212
#202681122
#202681042
#202680422
#202680352
#202679422
#202679342
#202679252
#202677552
C2×#121×C1032
#3194103