Finite Group Databasebeta

← #27205496

Subgroups — #27205496

Order 13184.

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

normal subgroups only

This group has 404 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#20268422C211yesmaximal, characteristic, complemented
2#20268358C211yesmaximal, characteristic
3#20268154C212yesmaximal, complemented
4#20268149C212yesmaximal, complemented
5#20268144C212yesmaximal, complemented
6#20268136C212yesmaximal, complemented
7#20267796C211yesmaximal, characteristic, complemented
8#20267790C211yesmaximal, characteristic, complemented
9#20267788C211yesmaximal, characteristic, complemented
10#20267746C211yesmaximal, characteristic, complemented
11C2×#102×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic
13C2×#13110089C2211yescharacteristic
14#15693020—21no—
15#15693020C2212yescomplemented
16#15693017C2212yes—
17#15693012—21no—
18#15693012C2212yescomplemented
19#15693008C2212yes—
20#15693000—22no—
21#15692992—21no—
22#15692992—21no—
23#15692990—22no—
24#15692980C2211yescharacteristic
25#15692980C2211yescharacteristic
26#15692946C2211yescharacteristic, complemented
27#15692946C2211yescharacteristic, complemented
28#15692944C2212yescomplemented
29#15692943C2211yescharacteristic, complemented
30#15692943C2211yescharacteristic, complemented
31#15692942C2212yes—
32#15692942C2212yes—
33#15692941C2212yescomplemented
34#15692931C2212yescomplemented
35C8×Dic103C2212yescomplemented
36C22×D4×C103C2211yescharacteristic
37C22×C8×C103C2211yescharacteristic
38C2×C4⋊C4×C103C2211yescharacteristic
39#102×C103C2212yes—
40#102×C103C2212yes—
41#13110105—22no—
42#13110105—22no—
43C2×Dic206—22no—
44C2×Dic206C2311yescharacteristic
45C2×D412C2311yescharacteristic
46C2×C22⋊D103—21no—
47C2×C22⋊D103—22no—
48C2×C22⋊D103—22no—
49C2×C4×D103—21no—
50#13110089—22no—
51C2×C103⋊C8C2312yes—
52C4⋊Dic103—22no—
53C4⋊Dic103D411yescharacteristic
54C4⋊Dic103D411yescharacteristic
55C4⋊Dic103C2311yescharacteristic
56C4⋊Dic103C2311yescharacteristic
57Dic103⋊C4—22no—
58Dic103⋊C4—22no—
59C22⋊Dic103—21no—
60C22⋊Dic103—22no—
61C22⋊Dic103—22no—
62C22⋊Dic103D412yes—
63C4×Dic103—21no—
64C4×Dic103C2312yes—
65C24×C103—21no—
66C2×D4×C103—21no—
67C2×D4×C103—22no—
68C2×D4×C103—22no—
69C2×D4×C103C2312yes—
70C22×C4×C103—21no—
71C22×C4×C103C2311yescharacteristic
72C2×C8×C103—22no—
73C2×C8×C103C2311yescharacteristic
74C2×C8×C103C2311yescharacteristic
75C4⋊C4×C103—21no—
76C4⋊C4×C103C2312yes—
77C23×C103—22no—
78C23×C103—42no—
79C23×C103—81no—
80C23×C103—81no—
81C23×C103C2×D411yescharacteristic
82C22×D103—21no—
83D4×C103—22no—
84D4×C103—22no—
85D4×C103—42no—
86C2×C4×C103—22no—
87C2×C4×C103—81no—
88C2×C4×C103C2×D411yescharacteristic
89C2×C4×C103#4112yes—
90C2×C4×C103#4112yes—
91C2×C4×C103C2411yescharacteristic
92C22⋊D103—42no—
93C22⋊D103—82no—
94C22⋊D103—82no—
95C2×Dic103—21no—
96C2×Dic103—21no—
97C2×Dic103—21no—
98C2×Dic103C2×D412yes—
99C2×Dic103C2×D412yes—
100D412—21no—
101D412—21no—
102C4×D103—42no—
103Dic206—21no—
104Dic206—21no—
105Dic206—82no—
106C8×C103—21no—
107C8×C103—21no—
108C103⋊C8—22no—
109C22×C103—21no—
110C22×C103—21no—
111C22×C103—42no—
112C22×C103—42no—
113C22×C103—42no—
114C22×C103—84no—
115C22×C103#12412yes—
116C22×C103C22×D411yescharacteristic
117C2×D103—41no—
118C2×D103—41no—
119C2×D103—41no—
120C4×C103—42no—
121C4×C103#12412yes—
122C4×C103C2×#4111yescharacteristic
123C4×C103C2×#4111yescharacteristic
124Dic103—22no—
125Dic103—22no—
126Dic103—41no—
127Dic103—41no—
128Dic103—41no—
129C2×C103—22no—
130C2×C103—82no—
131C2×C103C2×#12411yescharacteristic
132C2×C103#57611yescharacteristic
133C2×C103#57711yescharacteristic
134D103—81no—
135#3136—1031nomaximal, Sylow
136C103#313611yescharacteristic, complemented, Sylow
137#544—1031no—
138#535—1031no—
139#490—1032no—
140#489—1032no—
141#488—1032no—
142#486—1032no—
143#418—1031no—
144#417—1031no—
145#416—1031no—
146C2×#102D10311yescharacteristic, complemented
147#405—1031no—
148C2×#41—1031no—
149C22×D4C2×D10311yescharacteristic
150C2×M16—1031no—
151C22×C8C2×D10311yescharacteristic
152C4⋊Q8—1032no—
153C4⋊Q8—2061no—
154#127—1032no—
155#125—1032no—
156#125—2061no—
157#124—1032no—
158C22⋊Q8—2062no—
159#121—2061no—
160#121—2061no—
161#120—2062no—
162#117—1031no—
163#117—1031no—
164C2×C4⋊C4C2×D10311yescharacteristic
165#103—1031no—
166#103—1031no—
167#103—1032no—
168#102—1032no—
169#102—1032no—
170#102—1031no—
171#102—1031no—
172#102—1032no—
173#102C2×D10312yes—
174#102C2×D10312yes—
175#97—1032no—
176C4×C8—1032no—
177C24—21no—
178#41—2062no—
179#41—2062no—
180C2×Q8—1031no—
181C2×Q8—2062no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—22no—
185C2×D4—1031no—
186C2×D4—2062no—
187C2×D4—2062no—
188C2×D4—2061no—
189C2×D4C22×D10312yes—
190C22×C4—21no—
191C22×C4—2061no—
192C22×C4C22×D10311yescharacteristic
193M16—2062no—
194C2×C8—22no—
195C2×C8—1032no—
196C2×C8C22×D10311yescharacteristic
197C2×C8C22×D10311yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—1031no—
200C4⋊C4—1031no—
201C4⋊C4—1031no—
202C4⋊C4—1031no—
203C4⋊C4—2062no—
204C4⋊C4—2062no—
205C4⋊C4—2062no—
206C4⋊C4C22×D10312yes—
207C22⋊C4—1032no—
208C22⋊C4—2062no—
209C22⋊C4—2062no—
210C22⋊C4—2061no—
211C42—1032no—
212C42—2061no—
213C23—22no—
214C23—42no—
215C23—81no—
216C23—81no—
217C23—2061no—
218C23D4×D10311yescharacteristic
219Q8—8242no—
220Q8—2061no—
221Q8—2061no—
222D4—22no—
223D4—22no—
224D4—42no—
225D4—8242no—
226D4—8242no—
227D4—4122no—
228D4—2061no—
229D4—2061no—
230C2×C4—22no—
231C2×C4—81no—
232C2×C4—1032no—
233C2×C4—1032no—
234C2×C4—4122no—
235C2×C4—2061no—
236C2×C4—2061no—
237C2×C4—2061no—
238C2×C4D4×D10311yescharacteristic
239C2×C4#1311010412yes—
240C2×C4#1311010512yes—
241C2×C4C23×D10311yescharacteristic
242C8—21no—
243C8—21no—
244C8—2062no—
245C22—21no—
246C22—21no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—84no—
251C22—4121no—
252C22—4121no—
253C22—4121no—
254C22#1569300712yes—
255C22C2×D4×D10311yescharacteristic
256C4—42no—
257C4—4121no—
258C4—4121no—
259C4—4121no—
260C4—2062no—
261C4—2062no—
262C4#1569300712yes—
263C4C2×#1311010411yescharacteristic
264C4C2×#1311010511yescharacteristic
265C2—22no—
266C2—82no—
267C2—8241no—
268C2C2×#1569300711yescharacteristic
269C2#2026859211yescharacteristic
270C2#2026859711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#102×C103C2
socleC22×C103C22×D4
prime radical#20268358C2
hypercenterC2×#102D103
hypocenterC103#3136
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #20268422C2semidirect
3. #20268154C2semidirect
4. #20268149C2semidirect
5. #20268144C2semidirect
6. #20268136C2semidirect
7. #20267796C2semidirect
8. #20267790C2semidirect
9. #20267788C2semidirect
10. #20267746C2semidirect
11. C2×#102×C103C2semidirect
15. #15693020C22semidirect
18. #15693012C22semidirect
26. #15692946C22semidirect
27. #15692946C22semidirect
28. #15692944C22semidirect
29. #15692943C22semidirect
30. #15692943C22semidirect
33. #15692941C22semidirect
34. #15692931C22semidirect
35. C8×Dic103C22semidirect
136. C103#3136semidirect
146. C2×#102D103semidirect

Maximal subgroups

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

subgroupindex
#202684222
#202683582
#202681542
#202681492
#202681442
#202681362
#202677962
#202677902
#202677882
#202677462
C2×#102×C1032
#3136103