Finite Group Databasebeta

← #27206016

Subgroups — #27206016

Order 13184.

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

normal subgroups only

This group has 410 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#20268362C211yesmaximal, characteristic, complemented
2#20268132C212yesmaximal, complemented
3#20268112C212yesmaximal, complemented
4#20268035C212yesmaximal, complemented
5#20268018C212yesmaximal, complemented
6#20267942C212yesmaximal, complemented
7#20267929C212yesmaximal, complemented
8#20267758C211yesmaximal, characteristic, complemented
9#535×C103C211yesmaximal, characteristic
10C22×Dic206C2211yescharacteristic, complemented
11C2×#13110093C2212yes—
12C2×#13110093C2212yes—
13C2×#13110089C2211yescharacteristic, complemented
14C22×C103⋊C8C2211yescharacteristic, complemented
15#15693019—21no—
16#15693008—21no—
17#15693002—21no—
18#15693002—21no—
19#15693000C2212yes—
20#15693000C2212yescomplemented
21#15692980C2211yescharacteristic, complemented
22#15692954C2212yescomplemented
23#15692952C2212yescomplemented
24#15692944C2212yescomplemented
25#15692944C2212yescomplemented
26#15692942C2212yes—
27#15692942C2212yes—
28C22⋊(C103⋊C8)C2212yes—
29C22⋊(C103⋊C8)C2212yescomplemented
30C2×#41×C103C2211yescharacteristic
31C22×D4×C103C2211yescharacteristic
32#127×C103—21no—
33#124×C103—21no—
34#121×C103C2212yes—
35#121×C103C2212yes—
36#120×C103—21no—
37#120×C103—21no—
38#117×C103C2211yescharacteristic
39C2×Dic206—21no—
40C2×Dic206—41no—
41C2×Dic206—41no—
42C2×Dic206C2312yes—
43C22×Dic103—21no—
44#13110093—42no—
45#13110093—42no—
46#13110089—41no—
47C2×C103⋊C8—41no—
48C2×C103⋊C8C2312yes—
49C2×C103⋊C8C2312yes—
50C4⋊Dic103C2312yes—
51Dic103⋊C4—22no—
52Dic103⋊C4—22no—
53C22⋊Dic103—21no—
54C22⋊Dic103—22no—
55C22⋊Dic103—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
84Q8×C103—41no—
85D4×C103—22no—
86D4×C103—22no—
87D4×C103—41no—
88D4×C103—41no—
89D4×C103—41no—
90D4×C103—42no—
91D4×C103—82no—
92D4×C103—82no—
93C2×C4×C103—21no—
94C2×C4×C103—21no—
95C2×C4×C103—21no—
96C2×C4×C103—21no—
97C2×C4×C103—21no—
98C2×C4×C103—21no—
99C2×C4×C103—22no—
100C2×C4×C103C2×D411yescharacteristic
101C2×C4×C103C2×D411yescharacteristic
102C2×C4×C103C2×D411yescharacteristic
103C2×C4×C103C2411yescharacteristic
104C2×Dic103—22no—
105C2×Dic103—22no—
106C2×Dic103—42no—
107Dic206—22no—
108Dic206—22no—
109Dic206—42no—
110C103⋊C8—22no—
111C103⋊C8—22no—
112C22×C103—21no—
113C22×C103—21no—
114C22×C103—21no—
115C22×C103—22no—
116C22×C103—22no—
117C22×C103—22no—
118C22×C103—42no—
119C22×C103—42no—
120C22×C103—42no—
121C22×C103—84no—
122C22×C103C22×D411yescharacteristic
123C4×C103—21no—
124C4×C103—21no—
125C4×C103—21no—
126C4×C103—42no—
127C4×C103H(5,𝔽2)11yescharacteristic
128C4×C103H(5,𝔽2)11yescharacteristic
129Dic103—42no—
130Dic103—42no—
131C2×C103—41no—
132C2×C103—41no—
133C2×C103—41no—
134C2×C103—82no—
135C2×C103#53411yescharacteristic
136C2×C103#57712yes—
137#3200—1031nomaximal, Sylow
138C103#320011yescharacteristic, complemented, Sylow
139#536—1031no—
140#535D10311yescharacteristic
141#485—1032no—
142#482—1032no—
143#468—1032no—
144#465—1032no—
145#450—1032no—
146#448—1032no—
147#408—1031no—
148C2×#41C2×D10311yescharacteristic
149C22×Q8—1031no—
150C22×D4C2×D10311yescharacteristic
151C2×SD16—1032no—
152C2×SD16—1032no—
153C2×M16—1031no—
154C22×C8—1031no—
155C4⋊Q8—2061no—
156#127—21no—
157#124—21no—
158#124—2061no—
159#123—2061no—
160#123—2061no—
161C22⋊Q8—1032no—
162C22⋊Q8—1032no—
163#121C2×D10312yes—
164#121C2×D10312yes—
165#120—21no—
166#120—21no—
167#117—1031no—
168#117C2×D10311yescharacteristic
169#107—1032no—
170#106—1032no—
171#103—1032no—
172#103—1032no—
173#102—1032no—
174#102—1032no—
175C22⋊C8—1032no—
176C22⋊C8—1032no—
177C24—21no—
178#41—41no—
179#41—41no—
180C2×Q8—1032no—
181C2×Q8—4121no—
182C2×Q8—4121no—
183C2×Q8—2061no—
184C2×Q8C22⋊D10311yescharacteristic
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4C22⋊D10311yescharacteristic
191C2×D4C22⋊D10311yescharacteristic
192C2×D4C22⋊D10311yescharacteristic
193C2×D4C22×D10312yes—
194C22×C4—2061no—
195C22×C4C22×D10311yescharacteristic
196C22×C4C22×D10311yescharacteristic
197C22×C4C22×D10311yescharacteristic
198SD16—4122no—
199SD16—4122no—
200M16—4121no—
201C2×C8—1032no—
202C2×C8—1032no—
203C2×C8—4121no—
204C4⋊C4—1032no—
205C4⋊C4—2062no—
206C4⋊C4—2062no—
207C4⋊C4C22×D10312yes—
208C22⋊C4—21no—
209C22⋊C4—22no—
210C22⋊C4—22no—
211C22⋊C4—2061no—
212C22⋊C4—2062no—
213C22⋊C4—2062no—
214C42—21no—
215C42—2061no—
216C23—22no—
217C23—42no—
218C23—82no—
219C23C2×C22⋊D10311yescharacteristic
220C23C2×C22⋊D10311yescharacteristic
221C23C2×C22⋊D10311yescharacteristic
222Q8—41no—
223Q8—4122no—
224Q8—2062no—
225Q8—2062no—
226D4—22no—
227D4—22no—
228D4—41no—
229D4—41no—
230D4—41no—
231D4—42no—
232D4—82no—
233D4—82no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—4122no—
242C2×C4—2062no—
243C2×C4—2062no—
244C2×C4C2×C22⋊D10311yescharacteristic
245C2×C4C2×C22⋊D10311yescharacteristic
246C2×C4C2×C22⋊D10311yescharacteristic
247C2×C4C23×D10311yescharacteristic
248C8—2062no—
249C8—2062no—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—84no—
260C22C22×C22⋊D10311yescharacteristic
261C4—21no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—4122no—
266C4—4122no—
267C4#1569306611yescharacteristic
268C4#1569306611yescharacteristic
269C2—41no—
270C2—41no—
271C2—41no—
272C2—82no—
273C2#2026835011yescharacteristic
274C2#2026860212yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting, prime radical#535×C103C2
socleC22×C103C22×D4
hypercenter#535D103
hypocenterC103#3200
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. #20268362C2semidirect
2. #20268132C2semidirect
3. #20268112C2semidirect
4. #20268035C2semidirect
5. #20268018C2semidirect
6. #20267942C2semidirect
7. #20267929C2semidirect
8. #20267758C2semidirect
10. C22×Dic206C22semidirect
13. C2×#13110089C22semidirect
14. C22×C103⋊C8C22semidirect
20. #15693000C22semidirect
21. #15692980C22semidirect
22. #15692954C22semidirect
23. #15692952C22semidirect
24. #15692944C22semidirect
25. #15692944C22semidirect
29. C22⋊(C103⋊C8)C22semidirect
138. C103#3200semidirect

Maximal subgroups

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

subgroupindex
#202683622
#202681322
#202681122
#202680352
#202680182
#202679422
#202679292
#202677582
#535×C1032
#3200103