Finite Group Databasebeta

← #27206011

Subgroups — #27206011

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#20268355C211yesmaximal, characteristic
2#20268129C212yesmaximal, complemented
3#20268115C212yesmaximal, complemented
4#20268039C212yesmaximal, complemented
5#20268022C212yesmaximal, complemented
6#20267941C212yesmaximal, complemented
7#20267930C212yesmaximal, complemented
8#20267758C211yesmaximal, characteristic, complemented
9#536×C103C211yesmaximal, characteristic, complemented
10C22×D412C2211yescharacteristic
11C2×#13110092C2212yes—
12C2×#13110092C2212yes—
13C2×#13110089C2211yescharacteristic, complemented
14C22×C103⋊C8C2211yescharacteristic, complemented
15#15693017—21no—
16#15693010—21no—
17#15692995C2212yes—
18#15692995C2212yes—
19#15692989—21no—
20#15692989—21no—
21#15692980C2211yescharacteristic
22#15692954C2212yescomplemented
23#15692952C2212yescomplemented
24#15692945C2212yescomplemented
25#15692945C2212yescomplemented
26#15692941C2212yes—
27#15692941C2212yes—
28C22⋊(C103⋊C8)C2212yes—
29C22⋊(C103⋊C8)C2212yescomplemented
30C2×#41×C103C2211yescharacteristic
31C22×Q8×C103C2211yescharacteristic, complemented
32C4⋊Q8×C103—21no—
33#124×C103—21no—
34#123×C103—21no—
35#123×C103—21no—
36C22⋊Q8×C103C2212yes—
37C22⋊Q8×C103C2212yescomplemented
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#13110092—42no—
47#13110092—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—
57#41×C103—41no—
58#41×C103—41no—
59C2×Q8×C103—21no—
60C2×Q8×C103—41no—
61C2×Q8×C103—41no—
62C2×Q8×C103D411yescharacteristic
63C2×Q8×C103C2312yes—
64C2×D4×C103D411yescharacteristic
65C2×D4×C103D411yescharacteristic
66C2×D4×C103D411yescharacteristic
67C22×C4×C103—21no—
68C22×C4×C103C2311yescharacteristic
69C22×C4×C103C2311yescharacteristic
70C22×C4×C103C2311yescharacteristic
71C4⋊C4×C103—22no—
72C4⋊C4×C103—22no—
73C4⋊C4×C103C2312yes—
74C22⋊C4×C103—21no—
75C22⋊C4×C103—22no—
76C22⋊C4×C103—22no—
77C42×C103—21no—
78C23×C103C2×D411yescharacteristic
79C23×C103C2×D411yescharacteristic
80C23×C103C2×D411yescharacteristic
81C22×D103—22no—
82C22×D103—42no—
83C22×D103—82no—
84Q8×C103—22no—
85Q8×C103—22no—
86Q8×C103—41no—
87Q8×C103—42no—
88D4×C103—41no—
89D4×C103—41no—
90D4×C103—41no—
91C2×C4×C103—21no—
92C2×C4×C103—21no—
93C2×C4×C103—21no—
94C2×C4×C103—21no—
95C2×C4×C103—21no—
96C2×C4×C103—21no—
97C2×C4×C103—22no—
98C2×C4×C103—22no—
99C2×C4×C103—42no—
100C2×C4×C103C2×D411yescharacteristic
101C2×C4×C103C2×D411yescharacteristic
102C2×C4×C103C2×D411yescharacteristic
103C2×C4×C103C2411yescharacteristic
104C22⋊D103—82no—
105C22⋊D103—82no—
106C2×Dic103—22no—
107D412—22no—
108D412—22no—
109D412—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×C103C22×D411yescharacteristic
119C2×D103—42no—
120C2×D103—42no—
121C2×D103—42no—
122C2×D103—84no—
123C4×C103—21no—
124C4×C103—21no—
125C4×C103—21no—
126C4×C103—42no—
127C4×C103—42no—
128C4×C103H(5,𝔽2)11yescharacteristic
129C4×C103H(5,𝔽2)11yescharacteristic
130Dic103—42no—
131C2×C103—41no—
132C2×C103—41no—
133C2×C103—41no—
134C2×C103#53411yescharacteristic
135C2×C103#57712yes—
136D103—82no—
137#3200—1031nomaximal, Sylow
138C103#320011yescharacteristic, complemented, Sylow
139#536D10311yescharacteristic, complemented
140#535—1031no—
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×Q8C2×D10311yescharacteristic, complemented
150C22×D4—1031no—
151C2×SD16—1032no—
152C2×SD16—1032no—
153C2×M16—1031no—
154C22×C8—1031no—
155C4⋊Q8—21no—
156#127—2061no—
157#124—21no—
158#124—2061no—
159#123—21no—
160#123—21no—
161C22⋊Q8C2×D10312yes—
162C22⋊Q8C2×D10312yescomplemented
163#121—1032no—
164#121—1032no—
165#120—2061no—
166#120—2061no—
167#117—1031no—
168#117C2×D10311yescharacteristic, complemented
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—2061no—
178#41—41no—
179#41—41no—
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8C22⋊D10311yescharacteristic
184C2×Q8C22×D10312yes—
185C2×D4—1032no—
186C2×D4—4121no—
187C2×D4—4121no—
188C2×D4—2062no—
189C2×D4—2062no—
190C2×D4—2061no—
191C2×D4C22⋊D10311yescharacteristic
192C2×D4C22⋊D10311yescharacteristic
193C2×D4C22⋊D10311yescharacteristic
194C22×C4—21no—
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—22no—
205C4⋊C4—22no—
206C4⋊C4—1032no—
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—8242no—
217C23—4122no—
218C23—2062no—
219C23C2×C22⋊D10311yescharacteristic
220C23C2×C22⋊D10311yescharacteristic
221C23C2×C22⋊D10311yescharacteristic
222Q8—22no—
223Q8—22no—
224Q8—41no—
225Q8—42no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—8242no—
230D4—8242no—
231D4—4122no—
232D4—2062no—
233D4—2062no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—42no—
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—8244no—
257C22—4122no—
258C22—4122no—
259C22—4122no—
260C22C22×C22⋊D10311yescharacteristic
261C4—21no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—42no—
266C4—4122no—
267C4#1569306611yescharacteristic
268C4#1569306611yescharacteristic
269C2—41no—
270C2—41no—
271C2—41no—
272C2—8242no—
273C2#2026835011yescharacteristic
274C2#2026859912yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#536×C103C2
socleC22×C103C22×D4
prime radical#20268355C2
hypercenter#536D103
hypocenterC103#3200
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #20268129C2semidirect
3. #20268115C2semidirect
4. #20268039C2semidirect
5. #20268022C2semidirect
6. #20267941C2semidirect
7. #20267930C2semidirect
8. #20267758C2semidirect
9. #536×C103C2semidirect
13. C2×#13110089C22semidirect
14. C22×C103⋊C8C22semidirect
22. #15692954C22semidirect
23. #15692952C22semidirect
24. #15692945C22semidirect
25. #15692945C22semidirect
29. C22⋊(C103⋊C8)C22semidirect
31. C22×Q8×C103C22semidirect
37. C22⋊Q8×C103C22semidirect
38. #117×C103C22semidirect
138. C103#3200semidirect
139. #536D103semidirect
149. C22×Q8C2×D103semidirect
162. C22⋊Q8C2×D103semidirect
168. #117C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683552
#202681292
#202681152
#202680392
#202680222
#202679412
#202679302
#202677582
#536×C1032
#3200103