Finite Group Databasebeta

← #27205931

Subgroups — #27205931

Order 13184.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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#20268134C212yesmaximal, complemented
3#20268113C212yesmaximal, complemented
4#20268032C211yesmaximal, characteristic, complemented
5#20268018C212yesmaximal, complemented
6#20267954C212yesmaximal, complemented
7#20267933C212yesmaximal, complemented
8C2×(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
9#466×C103C211yesmaximal, characteristic, complemented
10C2×#13110104C2212yes—
11C22×C4×D103C2211yescharacteristic
12C2×Dic412C2211yescharacteristic, complemented
13C2×#13110093C2212yescomplemented
14C22×C103⋊C8C2211yescharacteristic
15#15693003—22no—
16#15693001C2212yes—
17#15693000C2212yes—
18#15692992C2212yes—
19#15692989—22no—
20D4×Dic103—22no—
21(C22⋊D103)⋊C4—22no—
22#15692979C2212yes—
23#15692955C2211yescharacteristic, complemented
24#15692952C2212yescomplemented
25#15692946C2212yescomplemented
26#15692944C2212yescomplemented
27#15692942C2212yescomplemented
28(C2×D103)⋊C8C2212yes—
29(C2×D103)⋊C8C2212yes—
30C2×D8×C103C2211yescharacteristic, complemented
31C22×C8×C103C2211yescharacteristic
32#121×C103C2212yes—
33#107×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—
49C2×C103⋊C8—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—
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—41no—
72C22×D103—41no—
73C22×D103C2×D412yes—
74D4×C103—22no—
75D4×C103—22no—
76D4×C103—44no—
77C2×C4×C103—21no—
78C2×C4×C103—21no—
79C2×C4×C103—22no—
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103C2411yescharacteristic
82C22⋊D103—44no—
83C22⋊D103—44no—
84C2×Dic103—22no—
85C2×Dic103—22no—
86C2×Dic103—41no—
87C2×Dic103—44no—
88C2×Dic103C2×D412yes—
89C4×D103—22no—
90C4×D103—22no—
91C4×D103—42no—
92Dic206—22no—
93Dic206—22no—
94C8×C103—21no—
95C8×C103—21no—
96C103⋊C8—22no—
97C22×C103—21no—
98C22×C103—21no—
99C22×C103—42no—
100C22×C103—42no—
101C22×C103—42no—
102C22×C103#13512yes—
103C22×C103C22×D411yescharacteristic
104C2×D103—22no—
105C2×D103—22no—
106C2×D103—22no—
107C2×D103—44no—
108C4×C103—21no—
109C4×C103—42no—
110C4×C103H(5,𝔽2)11yescharacteristic
111C4×C103H(5,𝔽2)11yescharacteristic
112Dic103—22no—
113Dic103—42no—
114Dic103—42no—
115C2×C103—22no—
116C2×C103—82no—
117C2×C103#53411yescharacteristic
118C2×C103C2×#13511yescharacteristic
119C2×C103#57511yescharacteristic
120D103—42no—
121#3191—1031nomaximal, Sylow
122C103#319111yescharacteristic, complemented, Sylow
123#525—1032no—
124#485—1032no—
125#482—1032no—
126#467—1031no—
127#466D10311yescharacteristic, complemented
128#465—1032no—
129#452—1032no—
130#449—1032no—
131C2×C22⋊C8—1031no—
132C2×#41—1032no—
133C23×C4—1031no—
134C2×Q16—1031no—
135C2×SD16—1032no—
136C2×D8C2×D10311yescharacteristic, complemented
137C22×C8—1031no—
138C22×C8C2×D10311yescharacteristic
139#123—2062no—
140C22⋊Q8—1032no—
141C22⋊Q8—1032no—
142#121—1032no—
143#121C2×D10312yes—
144#120—2062no—
145C4×D4—2062no—
146C4×D4—2062no—
147#117—1032no—
148#107—1031no—
149#107C2×D10311yescharacteristic, complemented
150#106—1032no—
151#103—1032no—
152#103—1032no—
153#102—1032no—
154#102C2×D10312yescomplemented
155C22⋊C8—1032no—
156C22⋊C8—1032no—
157C24—1031no—
158#41—4122no—
159#41—4122no—
160C2×Q8—1032no—
161C2×D4—22no—
162C2×D4—2062no—
163C2×D4—2062no—
164C2×D4C22×D10312yes—
165C22×C4—1031no—
166C22×C4—1032no—
167C22×C4—1032no—
168C22×C4—4121no—
169C22×C4—4121no—
170C22×C4—2062no—
171C22×C4C22×D10311yescharacteristic
172Q16—4121no—
173SD16—4122no—
174D8—41no—
175C2×C8—41no—
176C2×C8—1032no—
177C2×C8—4121no—
178C2×C8C22×D10311yescharacteristic
179C2×C8C22×D10311yescharacteristic
180C4⋊C4—1032no—
181C4⋊C4—2062no—
182C4⋊C4—2062no—
183C4⋊C4C22×D10312yes—
184C22⋊C4—22no—
185C22⋊C4—2062no—
186C22⋊C4—2062no—
187C22⋊C4—2062no—
188C22⋊C4—2062no—
189C42—2062no—
190C23—22no—
191C23—1032no—
192C23—4121no—
193C23—4121no—
194C23—2062no—
195C23D4×D10311yescharacteristic
196Q8—2062no—
197Q8—2062no—
198D4—22no—
199D4—22no—
200D4—44no—
201D4—4124no—
202D4—4124no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—1032no—
207C2×C4—4122no—
208C2×C4—4124no—
209C2×C4—4121no—
210C2×C4—2062no—
211C2×C4—2062no—
212C2×C4—2062no—
213C2×C4—2062no—
214C2×C4D4×D10311yescharacteristic
215C2×C4C23×D10311yescharacteristic
216C8—21no—
217C8—21no—
218C8—2062no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—4124no—
225C22—2062no—
226C22—2062no—
227C22—2062no—
228C22#1569304012yes—
229C22C2×D4×D10311yescharacteristic
230C4—21no—
231C4—42no—
232C4—4122no—
233C4—4122no—
234C4—2062no—
235C4#1569306611yescharacteristic
236C4#1569306711yescharacteristic
237C2—22no—
238C2—82no—
239C2—4122no—
240C2#2026834911yescharacteristic
241C2C2×#1569304011yescharacteristic
242C2#2026858811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#466×C103C2
socleC22×C103C22×D4
hypercenter#466D103
hypocenterC103#3191
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. #20268301C2semidirect
2. #20268134C2semidirect
3. #20268113C2semidirect
4. #20268032C2semidirect
5. #20268018C2semidirect
6. #20267954C2semidirect
7. #20267933C2semidirect
8. C2×(C2×D103)⋊C8C2semidirect
9. #466×C103C2semidirect
12. C2×Dic412C22semidirect
13. C2×#13110093C22semidirect
23. #15692955C22semidirect
24. #15692952C22semidirect
25. #15692946C22semidirect
26. #15692944C22semidirect
27. #15692942C22semidirect
30. C2×D8×C103C22semidirect
33. #107×C103C22semidirect
34. #102×C103C22semidirect
122. C103#3191semidirect
127. #466D103semidirect
136. C2×D8C2×D103semidirect
149. #107C2×D103semidirect
154. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683012
#202681342
#202681132
#202680322
#202680182
#202679542
#202679332
C2×(C2×D103)⋊C82
#466×C1032
#3191103