Finite Group Databasebeta

← #27206004

Subgroups — #27206004

Order 13184.

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

normal subgroups only

This group has 442 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#20268357C212yesmaximal, complemented
2#20268118C212yesmaximal, complemented
3#20268113C212yesmaximal, complemented
4#20268042C212yesmaximal, complemented
5#20268027C211yesmaximal, characteristic, complemented
6#20267926C212yesmaximal, complemented
7#20267923C212yesmaximal, complemented
8#20267757C211yesmaximal, characteristic, complemented
9#466×C103C211yesmaximal, characteristic, complemented
10C2×#13110105C2211yescharacteristic
11C2×D4×D103C2212yescomplemented
12C2×D824C2211yescharacteristic
13C2×#13110090C2212yes—
14C2×#13110089C2211yescharacteristic, complemented
15#15693017—22no—
16#15693007—22no—
17#15692996C2212yes—
18#15692995C2212yescomplemented
19#15692992C2212yes—
20#15692991—22no—
21#15692989—22no—
22#15692979C2212yescomplemented
23#15692955C2211yescharacteristic, complemented
24#15692952C2212yescomplemented
25#15692943C2212yescomplemented
26#15692942C2212yescomplemented
27#15692941C2212yescomplemented
28(C2×D103)⋊C8C2212yescomplemented
29(C2×D103)⋊C8C2212yescomplemented
30C2×D8×C103C2211yescharacteristic
31C22×C8×C103C2211yescharacteristic, complemented
32#121×C103C2212yescomplemented
33#107×C103C2211yescharacteristic, complemented
34#102×C103C2212yescomplemented
35C23×D103—22no—
36#13110105—41no—
37#13110105—41no—
38C2×Dic206D411yescharacteristic
39C2×D412—22no—
40C2×D412D411yescharacteristic
41C2×D412C2312yes—
42C2×C22⋊D103—22no—
43C2×C22⋊D103—22no—
44C2×C22⋊D103—22no—
45C2×C22⋊D103D412yes—
46D4×D103—42no—
47D4×D103—42no—
48C2×C4×D103C2312yes—
49D824—41no—
50#13110090—42no—
51#13110089—41no—
52C2×C103⋊C8C2312yes—
53C4⋊Dic103C2312yes—
54C22⋊Dic103—22no—
55(C2×D103)⋊C4—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—
63C2×C8×C103—41no—
64C2×C8×C103C2311yescharacteristic
65C2×C8×C103C2311yescharacteristic
66C4⋊C4×C103C2312yes—
67C22⋊C4×C103—22no—
68C23×C103—22no—
69C23×C103C2×D411yescharacteristic
70C22×D103—22no—
71C22×D103—44no—
72C22×D103—82no—
73C22×D103—82no—
74C22×D103C2×D412yes—
75D4×C103—22no—
76D4×C103—22no—
77D4×C103—82no—
78C2×C4×C103—21no—
79C2×C4×C103—21no—
80C2×C4×C103—22no—
81C2×C4×C103C2×D411yescharacteristic
82C2×C4×C103C2411yescharacteristic
83C22⋊D103—42no—
84C22⋊D103—44no—
85C22⋊D103—82no—
86C22⋊D103—82no—
87C2×Dic103—22no—
88C2×Dic103C2×D412yes—
89D412—22no—
90D412—22no—
91D412—41no—
92D412—82no—
93C4×D103—22no—
94C4×D103—22no—
95Dic206—41no—
96C8×C103—21no—
97C8×C103—21no—
98C103⋊C8—22no—
99C22×C103—21no—
100C22×C103—21no—
101C22×C103—21no—
102C22×C103—42no—
103C22×C103—42no—
104C22×C103—42no—
105C22×C103C22×D411yescharacteristic
106C2×D103—22no—
107C2×D103—22no—
108C2×D103—22no—
109C2×D103—42no—
110C2×D103—42no—
111C2×D103—42no—
112C2×D103—88no—
113C4×C103—21no—
114C4×C103—42no—
115C4×C103H(5,𝔽2)11yescharacteristic
116C4×C103H(5,𝔽2)11yescharacteristic
117Dic103—22no—
118Dic103—42no—
119C2×C103—41no—
120C2×C103—82no—
121C2×C103#53411yescharacteristic
122C2×C103#57611yescharacteristic
123C2×C103#57611yescharacteristic
124D103—42no—
125D103—82no—
126#3199—1031nomaximal, Sylow
127C103#319911yescharacteristic, complemented, Sylow
128#535—1032no—
129#482—1032no—
130#482—1032no—
131#469—1032no—
132#466—1031no—
133#466D10311yescharacteristic, complemented
134#447—1032no—
135#447—1032no—
136#408—1031no—
137C2×#41—1031no—
138C22×D4—1032no—
139C2×D8—1032no—
140C2×D8—1031no—
141C2×D8C2×D10311yescharacteristic
142C2×M16—1031no—
143C22×C8C2×D10311yescharacteristic, complemented
144#127—2062no—
145#124—2062no—
146#121—1032no—
147#121—1032no—
148#121—1032no—
149#121C2×D10312yescomplemented
150#120—2062no—
151#120—2062no—
152#117—1032no—
153#107—1031no—
154#107C2×D10311yescharacteristic, complemented
155#106—1032no—
156#102—1032no—
157#102—1032no—
158#102—1032no—
159#102C2×D10312yescomplemented
160C22⋊C8—1032no—
161C22⋊C8—1032no—
162C24—2062no—
163#41—4121no—
164#41—4121no—
165C2×Q8—1031no—
166C2×D4—22no—
167C2×D4—1032no—
168C2×D4—1031no—
169C2×D4—1032no—
170C2×D4—4122no—
171C2×D4—4122no—
172C2×D4—2062no—
173C2×D4—2062no—
174C2×D4—2062no—
175C2×D4—2062no—
176C2×D4C22×D10312yes—
177C22×C4—1032no—
178C22×C4C22×D10311yescharacteristic
179D8—41no—
180D8—4121no—
181D8—4122no—
182M16—4121no—
183C2×C8—41no—
184C2×C8—1032no—
185C2×C8C22×D10311yescharacteristic
186C2×C8C22×D10311yescharacteristic
187C4⋊C4—1032no—
188C4⋊C4C22×D10312yes—
189C22⋊C4—22no—
190C22⋊C4—2062no—
191C22⋊C4—2062no—
192C22⋊C4—2062no—
193C22⋊C4—2062no—
194C42—2062no—
195C23—22no—
196C23—8242no—
197C23—8242no—
198C23—1032no—
199C23—4124no—
200C23—2062no—
201C23D4×D10311yescharacteristic
202Q8—4121no—
203D4—22no—
204D4—22no—
205D4—82no—
206D4—8242no—
207D4—8242no—
208D4—8242no—
209D4—4121no—
210D4—4122no—
211D4—4124no—
212D4—2062no—
213D4—2062no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—1032no—
218C2×C4—2062no—
219C2×C4—2062no—
220C2×C4—2062no—
221C2×C4D4×D10311yescharacteristic
222C2×C4C23×D10311yescharacteristic
223C8—21no—
224C8—21no—
225C8—2062no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—8248no—
233C22—4122no—
234C22—4122no—
235C22—4122no—
236C22—2062no—
237C22—2062no—
238C22—2062no—
239C22C2×D4×D10311yescharacteristic
240C4—21no—
241C4—42no—
242C4—4122no—
243C4—2062no—
244C4#1569306611yescharacteristic
245C4#1569306711yescharacteristic
246C2—41no—
247C2—82no—
248C2—8242no—
249C2—4122no—
250C2#2026834911yescharacteristic
251C2#2026859211yescharacteristic
252C2#2026859311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#466×C103C2
socleC22×C103C22×D4
hypercenter#466D103
hypocenterC103#3199
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #20268357C2semidirect
2. #20268118C2semidirect
3. #20268113C2semidirect
4. #20268042C2semidirect
5. #20268027C2semidirect
6. #20267926C2semidirect
7. #20267923C2semidirect
8. #20267757C2semidirect
9. #466×C103C2semidirect
11. C2×D4×D103C22semidirect
14. C2×#13110089C22semidirect
18. #15692995C22semidirect
22. #15692979C22semidirect
23. #15692955C22semidirect
24. #15692952C22semidirect
25. #15692943C22semidirect
26. #15692942C22semidirect
27. #15692941C22semidirect
28. (C2×D103)⋊C8C22semidirect
29. (C2×D103)⋊C8C22semidirect
31. C22×C8×C103C22semidirect
32. #121×C103C22semidirect
33. #107×C103C22semidirect
34. #102×C103C22semidirect
127. C103#3199semidirect
133. #466D103semidirect
143. C22×C8C2×D103semidirect
149. #121C2×D103semidirect
154. #107C2×D103semidirect
159. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683572
#202681182
#202681132
#202680422
#202680272
#202679262
#202679232
#202677572
#466×C1032
#3199103