Finite Group Databasebeta

← #27205980

Subgroups — #27205980

Order 13184.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#20268301C212yesmaximal, complemented
2#20268135C212yesmaximal, complemented
3#20268114C212yesmaximal, complemented
4#20268049C211yesmaximal, characteristic, complemented
5#20268035C212yesmaximal, complemented
6#20267954C212yesmaximal, complemented
7#20267933C212yesmaximal, complemented
8#20267754C211yesmaximal, characteristic, complemented
9#469×C103C211yesmaximal, characteristic, complemented
10C2×#13110104C2212yes—
11C22×C4×D103C2211yescharacteristic
12C2×Dic412C2211yescharacteristic, complemented
13C2×#13110093C2212yescomplemented
14C2×#13110089C2211yescharacteristic
15#15693003—22no—
16#15693001C2212yes—
17#15693000C2212yes—
18#15692992C2212yes—
19#15692989—22no—
20D4×Dic103—22no—
21(C22⋊D103)⋊C4—22no—
22#15692979C2212yes—
23#15692954C2212yescomplemented
24#15692953C2211yescharacteristic, complemented
25#15692946C2212yescomplemented
26#15692944C2212yescomplemented
27#15692942C2212yescomplemented
28(C2×D103)⋊C8C2212yes—
29(C2×D103)⋊C8C2212yes—
30C2×D8×C103C2211yescharacteristic, complemented
31C2×M16×C103C2211yescharacteristic
32#121×C103C2212yes—
33#106×C103C2211yescharacteristic, complemented
34#102×C103C2212yescomplemented
35C23×D103D411yescharacteristic
36#13110104—42no—
37#13110104—42no—
38C2×Dic206C2312yes—
39C2×C22⋊D103—22no—
40C2×C22⋊D103—22no—
41C22×Dic103—22no—
42C22×Dic103D411yescharacteristic
43C2×C4×D103—41no—
44C2×C4×D103—41no—
45C2×C4×D103D412yes—
46C2×C4×D103C2312yes—
47Dic412—41no—
48#13110093—42no—
49#13110089—41no—
50C2×C103⋊C8C2312yes—
51C4⋊Dic103—22no—
52C4⋊Dic103C2312yes—
53Dic103⋊C4—22no—
54C22⋊Dic103—22no—
55C22⋊Dic103—22no—
56(C2×D103)⋊C4—22no—
57(C2×D103)⋊C4—22no—
58C4×Dic103—22no—
59C2×D4×C103—22no—
60C2×D4×C103C2312yes—
61C22×C4×C103C2311yescharacteristic
62D8×C103—41no—
63M16×C103—41no—
64C2×C8×C103C2311yescharacteristic
65C2×C8×C103C2311yescharacteristic
66C4⋊C4×C103C2312yes—
67C22⋊C4×C103—22no—
68C23×C103—22no—
69C23×C103C2×D411yescharacteristic
70C22×D103—41no—
71C22×D103—42no—
72C22×D103C2×D412yes—
73D4×C103—22no—
74D4×C103—22no—
75D4×C103—44no—
76C2×C4×C103—21no—
77C2×C4×C103—21no—
78C2×C4×C103—22no—
79C2×C4×C103C2×D411yescharacteristic
80C2×C4×C103C2411yescharacteristic
81C22⋊D103—44no—
82C22⋊D103—44no—
83C2×Dic103—22no—
84C2×Dic103—22no—
85C2×Dic103—41no—
86C2×Dic103—44no—
87C2×Dic103C2×D412yes—
88C4×D103—22no—
89C4×D103—22no—
90C4×D103—42no—
91Dic206—22no—
92Dic206—22no—
93C8×C103—21no—
94C8×C103—21no—
95C103⋊C8—22no—
96C22×C103—21no—
97C22×C103—22no—
98C22×C103—42no—
99C22×C103—42no—
100C22×C103—42no—
101C22×C103C22×D411yescharacteristic
102C2×D103—22no—
103C2×D103—22no—
104C2×D103—22no—
105C2×D103—44no—
106C4×C103—21no—
107C4×C103—42no—
108C4×C103H(5,𝔽2)11yescharacteristic
109C4×C103H(5,𝔽2)11yescharacteristic
110Dic103—22no—
111Dic103—42no—
112Dic103—42no—
113C2×C103—41no—
114C2×C103—82no—
115C2×C103#53411yescharacteristic
116C2×C103#57512yes—
117D103—42no—
118#3197—1031nomaximal, Sylow
119C103#319711yescharacteristic, complemented, Sylow
120#525—1032no—
121#485—1032no—
122#482—1032no—
123#470—1031no—
124#469D10311yescharacteristic, complemented
125#468—1032no—
126#452—1032no—
127#449—1032no—
128#407—1031no—
129C2×#41—1032no—
130C23×C4—1031no—
131C2×Q16—1031no—
132C2×SD16—1032no—
133C2×D8C2×D10311yescharacteristic, complemented
134C2×M16—1031no—
135C2×M16C2×D10311yescharacteristic
136#123—2062no—
137C22⋊Q8—1032no—
138C22⋊Q8—1032no—
139#121—1032no—
140#121C2×D10312yes—
141#120—2062no—
142C4×D4—2062no—
143C4×D4—2062no—
144#117—1032no—
145#107—1032no—
146#106—1031no—
147#106C2×D10311yescharacteristic, complemented
148#103—1032no—
149#103—1032no—
150#102—1032no—
151#102C2×D10312yescomplemented
152C22⋊C8—1032no—
153C22⋊C8—1032no—
154C24—1031no—
155#41—4122no—
156#41—4122no—
157C2×Q8—1032no—
158C2×D4—22no—
159C2×D4—2062no—
160C2×D4—2062no—
161C2×D4C22×D10312yes—
162C22×C4—1031no—
163C22×C4—1032no—
164C22×C4—1032no—
165C22×C4—4121no—
166C22×C4—4121no—
167C22×C4—2062no—
168C22×C4C22×D10311yescharacteristic
169Q16—4121no—
170SD16—4122no—
171D8—41no—
172M16—41no—
173M16—4121no—
174C2×C8—1032no—
175C2×C8C22×D10311yescharacteristic
176C2×C8C22×D10311yescharacteristic
177C4⋊C4—1032no—
178C4⋊C4—2062no—
179C4⋊C4—2062no—
180C4⋊C4C22×D10312yes—
181C22⋊C4—22no—
182C22⋊C4—2062no—
183C22⋊C4—2062no—
184C22⋊C4—2062no—
185C22⋊C4—2062no—
186C42—2062no—
187C23—22no—
188C23—1032no—
189C23—4121no—
190C23—4122no—
191C23D4×D10311yescharacteristic
192Q8—2062no—
193Q8—2062no—
194D4—22no—
195D4—22no—
196D4—44no—
197D4—4124no—
198D4—4124no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—1032no—
203C2×C4—4122no—
204C2×C4—4124no—
205C2×C4—4121no—
206C2×C4—2062no—
207C2×C4—2062no—
208C2×C4—2062no—
209C2×C4—2062no—
210C2×C4D4×D10311yescharacteristic
211C2×C4C23×D10311yescharacteristic
212C8—21no—
213C8—21no—
214C8—2062no—
215C22—22no—
216C22—21no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—4124no—
221C22—2062no—
222C22—2062no—
223C22—2062no—
224C22C2×D4×D10311yescharacteristic
225C4—21no—
226C4—42no—
227C4—4122no—
228C4—4122no—
229C4—2062no—
230C4#1569306611yescharacteristic
231C4#1569306711yescharacteristic
232C2—41no—
233C2—82no—
234C2—4122no—
235C2#2026834911yescharacteristic
236C2#2026858712yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#469×C103C2
socleC22×C103C22×D4
hypercenter#469D103
hypocenterC103#3197
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20268301C2semidirect
2. #20268135C2semidirect
3. #20268114C2semidirect
4. #20268049C2semidirect
5. #20268035C2semidirect
6. #20267954C2semidirect
7. #20267933C2semidirect
8. #20267754C2semidirect
9. #469×C103C2semidirect
12. C2×Dic412C22semidirect
13. C2×#13110093C22semidirect
23. #15692954C22semidirect
24. #15692953C22semidirect
25. #15692946C22semidirect
26. #15692944C22semidirect
27. #15692942C22semidirect
30. C2×D8×C103C22semidirect
33. #106×C103C22semidirect
34. #102×C103C22semidirect
119. C103#3197semidirect
124. #469D103semidirect
133. C2×D8C2×D103semidirect
147. #106C2×D103semidirect
151. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683012
#202681352
#202681142
#202680492
#202680352
#202679542
#202679332
#202677542
#469×C1032
#3197103