Finite Group Databasebeta

← #27206005

Subgroups — #27206005

Order 13184.

442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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#20268355C211yesmaximal, characteristic, complemented
2#20268115C212yesmaximal, complemented
3#20268112C212yesmaximal, complemented
4#20268042C212yesmaximal, complemented
5#20268025C212yesmaximal, complemented
6#20267925C212yesmaximal, complemented
7#20267924C212yesmaximal, complemented
8#20267758C211yesmaximal, characteristic, complemented
9#535×C103C211yesmaximal, characteristic, complemented
10C22×D412C2211yescharacteristic, complemented
11C2×#13110090C2212yes—
12C2×#13110090C2212yes—
13C2×#13110089C2211yescharacteristic, complemented
14C22×C103⋊C8C2211yescharacteristic, complemented
15#15693017—21no—
16#15693010—21no—
17#15692995C2212yes—
18#15692995C2212yescomplemented
19#15692989—21no—
20#15692989—21no—
21#15692980C2211yescharacteristic, complemented
22#15692954C2212yescomplemented
23#15692952C2212yescomplemented
24#15692942C2212yescomplemented
25#15692942C2212yescomplemented
26#15692941C2212yescomplemented
27#15692941C2212yescomplemented
28C22⋊(C103⋊C8)C2212yescomplemented
29C22⋊(C103⋊C8)C2212yescomplemented
30C2×#41×C103C2211yescharacteristic
31C22×D4×C103C2211yescharacteristic, complemented
32#127×C103—21no—
33#124×C103—21no—
34#121×C103C2212yes—
35#121×C103C2212yescomplemented
36#120×C103—21no—
37#120×C103—21no—
38#117×C103C2211yescharacteristic, complemented
39C23×D103—21no—
40C2×D412—21no—
41C2×D412—41no—
42C2×D412—41no—
43C2×D412C2312yes—
44C2×C22⋊D103—22no—
45C2×C22⋊D103—22no—
46#13110090—42no—
47#13110090—42no—
48#13110089—41no—
49C2×C103⋊C8—41no—
50C2×C103⋊C8C2312yes—
51C2×C103⋊C8C2312yes—
52C4⋊Dic103C2312yes—
53C22⋊Dic103—21no—
54(C2×D103)⋊C4—22no—
55(C2×D103)⋊C4—22no—
56C4×Dic103—21no—
57C24×C103—21no—
58#41×C103—41no—
59#41×C103—41no—
60C2×Q8×C103D411yescharacteristic
61C2×D4×C103—22no—
62C2×D4×C103—22no—
63C2×D4×C103—21no—
64C2×D4×C103—41no—
65C2×D4×C103—41no—
66C2×D4×C103D411yescharacteristic
67C2×D4×C103D411yescharacteristic
68C2×D4×C103D411yescharacteristic
69C2×D4×C103C2312yes—
70C22×C4×C103C2311yescharacteristic
71C22×C4×C103C2311yescharacteristic
72C22×C4×C103C2311yescharacteristic
73C4⋊C4×C103C2312yes—
74C22⋊C4×C103—21no—
75C22⋊C4×C103—22no—
76C22⋊C4×C103—22no—
77C42×C103—21no—
78C23×C103—22no—
79C23×C103—42no—
80C23×C103—82no—
81C23×C103C2×D411yescharacteristic
82C23×C103C2×D411yescharacteristic
83C23×C103C2×D411yescharacteristic
84C22×D103—22no—
85C22×D103—42no—
86C22×D103—82no—
87Q8×C103—41no—
88D4×C103—22no—
89D4×C103—22no—
90D4×C103—41no—
91D4×C103—41no—
92D4×C103—41no—
93D4×C103—42no—
94D4×C103—82no—
95D4×C103—82no—
96C2×C4×C103—21no—
97C2×C4×C103—21no—
98C2×C4×C103—21no—
99C2×C4×C103—21no—
100C2×C4×C103—21no—
101C2×C4×C103—21no—
102C2×C4×C103—22no—
103C2×C4×C103C2×D411yescharacteristic
104C2×C4×C103C2×D411yescharacteristic
105C2×C4×C103C2×D411yescharacteristic
106C2×C4×C103C2411yescharacteristic
107C22⋊D103—82no—
108C22⋊D103—82no—
109C2×Dic103—22no—
110D412—22no—
111D412—22no—
112D412—42no—
113C103⋊C8—22no—
114C103⋊C8—22no—
115C22×C103—21no—
116C22×C103—21no—
117C22×C103—21no—
118C22×C103—22no—
119C22×C103—22no—
120C22×C103—22no—
121C22×C103—42no—
122C22×C103—42no—
123C22×C103—42no—
124C22×C103—84no—
125C22×C103C22×D411yescharacteristic
126C2×D103—42no—
127C2×D103—42no—
128C2×D103—42no—
129C2×D103—84no—
130C4×C103—21no—
131C4×C103—21no—
132C4×C103—21no—
133C4×C103—42no—
134C4×C103H(5,𝔽2)11yescharacteristic
135C4×C103H(5,𝔽2)11yescharacteristic
136Dic103—42no—
137C2×C103—41no—
138C2×C103—41no—
139C2×C103—41no—
140C2×C103—82no—
141C2×C103#53411yescharacteristic
142C2×C103#57612yes—
143D103—82no—
144#3199—1031nomaximal, Sylow
145C103#319911yescharacteristic, complemented, Sylow
146#535—1031no—
147#535D10311yescharacteristic, complemented
148#482—1032no—
149#482—1032no—
150#469—1032no—
151#466—1032no—
152#447—1032no—
153#447—1032no—
154#408—1031no—
155C2×#41C2×D10311yescharacteristic
156C22×D4—1031no—
157C22×D4C2×D10311yescharacteristic, complemented
158C2×D8—1032no—
159C2×D8—1032no—
160C2×M16—1031no—
161C22×C8—1031no—
162#127—21no—
163#127—2061no—
164#124—21no—
165#124—2061no—
166#121—1032no—
167#121—1032no—
168#121C2×D10312yes—
169#121C2×D10312yescomplemented
170#120—21no—
171#120—21no—
172#120—2061no—
173#120—2061no—
174#117—1031no—
175#117C2×D10311yescharacteristic, complemented
176#107—1032no—
177#106—1032no—
178#102—1032no—
179#102—1032no—
180#102—1032no—
181#102—1032no—
182C22⋊C8—1032no—
183C22⋊C8—1032no—
184C24—21no—
185C24—2061no—
186#41—41no—
187#41—41no—
188C2×Q8C22⋊D10311yescharacteristic
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—1032no—
195C2×D4—4121no—
196C2×D4—4121no—
197C2×D4—2062no—
198C2×D4—2062no—
199C2×D4—2061no—
200C2×D4C22⋊D10311yescharacteristic
201C2×D4C22⋊D10311yescharacteristic
202C2×D4C22⋊D10311yescharacteristic
203C2×D4C22×D10312yes—
204C22×C4C22×D10311yescharacteristic
205C22×C4C22×D10311yescharacteristic
206C22×C4C22×D10311yescharacteristic
207D8—4122no—
208D8—4122no—
209M16—4121no—
210C2×C8—1032no—
211C2×C8—1032no—
212C2×C8—4121no—
213C4⋊C4—1032no—
214C4⋊C4C22×D10312yes—
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—2061no—
219C22⋊C4—2062no—
220C22⋊C4—2062no—
221C42—21no—
222C42—2061no—
223C23—22no—
224C23—42no—
225C23—82no—
226C23—8242no—
227C23—4122no—
228C23—2062no—
229C23C2×C22⋊D10311yescharacteristic
230C23C2×C22⋊D10311yescharacteristic
231C23C2×C22⋊D10311yescharacteristic
232Q8—41no—
233D4—22no—
234D4—22no—
235D4—41no—
236D4—41no—
237D4—41no—
238D4—42no—
239D4—82no—
240D4—82no—
241D4—8242no—
242D4—8242no—
243D4—4122no—
244D4—2062no—
245D4—2062no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—2062no—
254C2×C4C2×C22⋊D10311yescharacteristic
255C2×C4C2×C22⋊D10311yescharacteristic
256C2×C4C2×C22⋊D10311yescharacteristic
257C2×C4C23×D10311yescharacteristic
258C8—2062no—
259C8—2062no—
260C22—22no—
261C22—22no—
262C22—22no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—84no—
270C22—8244no—
271C22—4122no—
272C22—4122no—
273C22—4122no—
274C22C22×C22⋊D10311yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—42no—
279C4—4122no—
280C4#1569306611yescharacteristic
281C4#1569306611yescharacteristic
282C2—41no—
283C2—41no—
284C2—41no—
285C2—82no—
286C2—8242no—
287C2#2026835011yescharacteristic
288C2#2026859412yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#535×C103C2
socleC22×C103C22×D4
hypercenter#535D103
hypocenterC103#3199
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #20268355C2semidirect
2. #20268115C2semidirect
3. #20268112C2semidirect
4. #20268042C2semidirect
5. #20268025C2semidirect
6. #20267925C2semidirect
7. #20267924C2semidirect
8. #20267758C2semidirect
9. #535×C103C2semidirect
10. C22×D412C22semidirect
13. C2×#13110089C22semidirect
14. C22×C103⋊C8C22semidirect
18. #15692995C22semidirect
21. #15692980C22semidirect
22. #15692954C22semidirect
23. #15692952C22semidirect
24. #15692942C22semidirect
25. #15692942C22semidirect
26. #15692941C22semidirect
27. #15692941C22semidirect
28. C22⋊(C103⋊C8)C22semidirect
29. C22⋊(C103⋊C8)C22semidirect
31. C22×D4×C103C22semidirect
35. #121×C103C22semidirect
38. #117×C103C22semidirect
145. C103#3199semidirect
147. #535D103semidirect
157. C22×D4C2×D103semidirect
169. #121C2×D103semidirect
175. #117C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683552
#202681152
#202681122
#202680422
#202680252
#202679252
#202679242
#202677582
#535×C1032
#3199103