Finite Group Databasebeta

← #28401361

Subgroups — #28401361

Order 14464.

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#20299108C212yesmaximal, complemented
2#20298941C212yesmaximal, complemented
3#20298920C212yesmaximal, complemented
4#20298839C211yesmaximal, characteristic, complemented
5#20298825C212yesmaximal, complemented
6#20298761C212yesmaximal, complemented
7#20298740C212yesmaximal, complemented
8C2×#16813534C211yesmaximal, characteristic, complemented
9#466×C113C211yesmaximal, characteristic, complemented
10C2×#14268646C2212yes—
11C22×C4×D113C2211yescharacteristic
12C2×Dic452C2211yescharacteristic, complemented
13C2×#14268635C2212yescomplemented
14C22×#11744751C2211yescharacteristic
15#16813604—22no—
16#16813602C2212yes—
17#16813601C2212yes—
18#16813593C2212yes—
19#16813590—22no—
20D4×Dic113—22no—
21#16813582—22no—
22#16813580C2212yes—
23#16813556C2211yescharacteristic, complemented
24#16813553C2212yescomplemented
25#16813547C2212yescomplemented
26#16813545C2212yescomplemented
27#16813543C2212yescomplemented
28#16813534C2212yes—
29#16813534C2212yes—
30C2×D8×C113C2211yescharacteristic, complemented
31C22×C8×C113C2211yescharacteristic
32#121×C113C2212yes—
33#107×C113C2211yescharacteristic, complemented
34#102×C113C2212yescomplemented
35C23×D113D411yescharacteristic
36#14268646—42no—
37#14268646—42no—
38C2×Dic226C2312yes—
39C2×C22⋊D113—22no—
40C2×C22⋊D113—22no—
41C22×Dic113—22no—
42C22×Dic113D411yescharacteristic
43C2×C4×D113—41no—
44C2×C4×D113—41no—
45C2×C4×D113D412yes—
46C2×C4×D113C2312yes—
47Dic452—41no—
48#14268635—42no—
49C2×#11744751—41no—
50C2×#11744751C2312yes—
51C4⋊Dic113—22no—
52C4⋊Dic113C2312yes—
53#14268626—22no—
54C22⋊Dic113—22no—
55C22⋊Dic113—22no—
56#14268624—22no—
57#14268624—22no—
58C4×Dic113—22no—
59C2×D4×C113—22no—
60C2×D4×C113C2312yes—
61C22×C4×C113C2311yescharacteristic
62D8×C113—41no—
63C2×C8×C113—41no—
64C2×C8×C113C2311yescharacteristic
65C2×C8×C113C2311yescharacteristic
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C23×C113—22no—
69C23×C113C2×D411yescharacteristic
70C22×D113—22no—
71C22×D113—41no—
72C22×D113—41no—
73C22×D113C2×D412yes—
74D4×C113—22no—
75D4×C113—22no—
76D4×C113—44no—
77C2×C4×C113—21no—
78C2×C4×C113—21no—
79C2×C4×C113—22no—
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2411yescharacteristic
82C22⋊D113—44no—
83C22⋊D113—44no—
84C2×Dic113—22no—
85C2×Dic113—22no—
86C2×Dic113—41no—
87C2×Dic113—44no—
88C2×Dic113C2×D412yes—
89C4×D113—22no—
90C4×D113—22no—
91C4×D113—42no—
92Dic226—22no—
93Dic226—22no—
94C8×C113—21no—
95C8×C113—21no—
96#11744751—22no—
97C22×C113—21no—
98C22×C113—21no—
99C22×C113—42no—
100C22×C113—42no—
101C22×C113—42no—
102C22×C113#13512yes—
103C22×C113C22×D411yescharacteristic
104C2×D113—22no—
105C2×D113—22no—
106C2×D113—22no—
107C2×D113—44no—
108C4×C113—21no—
109C4×C113—42no—
110C4×C113H(5,𝔽2)11yescharacteristic
111C4×C113H(5,𝔽2)11yescharacteristic
112Dic113—22no—
113Dic113—42no—
114Dic113—42no—
115C2×C113—22no—
116C2×C113—82no—
117C2×C113#53411yescharacteristic
118C2×C113C2×#13511yescharacteristic
119C2×C113#57511yescharacteristic
120D113—42no—
121#3191—1131nomaximal, Sylow
122C113#319111yescharacteristic, complemented, Sylow
123#525—1132no—
124#485—1132no—
125#482—1132no—
126#467—1131no—
127#466D11311yescharacteristic, complemented
128#465—1132no—
129#452—1132no—
130#449—1132no—
131C2×C22⋊C8—1131no—
132C2×#41—1132no—
133C23×C4—1131no—
134C2×Q16—1131no—
135C2×SD16—1132no—
136C2×D8C2×D11311yescharacteristic, complemented
137C22×C8—1131no—
138C22×C8C2×D11311yescharacteristic
139#123—2262no—
140C22⋊Q8—1132no—
141C22⋊Q8—1132no—
142#121—1132no—
143#121C2×D11312yes—
144#120—2262no—
145C4×D4—2262no—
146C4×D4—2262no—
147#117—1132no—
148#107—1131no—
149#107C2×D11311yescharacteristic, complemented
150#106—1132no—
151#103—1132no—
152#103—1132no—
153#102—1132no—
154#102C2×D11312yescomplemented
155C22⋊C8—1132no—
156C22⋊C8—1132no—
157C24—1131no—
158#41—4522no—
159#41—4522no—
160C2×Q8—1132no—
161C2×D4—22no—
162C2×D4—2262no—
163C2×D4—2262no—
164C2×D4C22×D11312yes—
165C22×C4—1131no—
166C22×C4—1132no—
167C22×C4—1132no—
168C22×C4—4521no—
169C22×C4—4521no—
170C22×C4—2262no—
171C22×C4C22×D11311yescharacteristic
172Q16—4521no—
173SD16—4522no—
174D8—41no—
175C2×C8—41no—
176C2×C8—1132no—
177C2×C8—4521no—
178C2×C8C22×D11311yescharacteristic
179C2×C8C22×D11311yescharacteristic
180C4⋊C4—1132no—
181C4⋊C4—2262no—
182C4⋊C4—2262no—
183C4⋊C4C22×D11312yes—
184C22⋊C4—22no—
185C22⋊C4—2262no—
186C22⋊C4—2262no—
187C22⋊C4—2262no—
188C22⋊C4—2262no—
189C42—2262no—
190C23—22no—
191C23—1132no—
192C23—4521no—
193C23—4521no—
194C23—2262no—
195C23D4×D11311yescharacteristic
196Q8—2262no—
197Q8—2262no—
198D4—22no—
199D4—22no—
200D4—44no—
201D4—4524no—
202D4—4524no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—1132no—
207C2×C4—4522no—
208C2×C4—4524no—
209C2×C4—4521no—
210C2×C4—2262no—
211C2×C4—2262no—
212C2×C4—2262no—
213C2×C4—2262no—
214C2×C4D4×D11311yescharacteristic
215C2×C4C23×D11311yescharacteristic
216C8—21no—
217C8—21no—
218C8—2262no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—4524no—
225C22—2262no—
226C22—2262no—
227C22—2262no—
228C22#1681364112yes—
229C22C2×D4×D11311yescharacteristic
230C4—21no—
231C4—42no—
232C4—4522no—
233C4—4522no—
234C4—2262no—
235C4#1681366711yescharacteristic
236C4#1681366811yescharacteristic
237C2—22no—
238C2—82no—
239C2—4522no—
240C2#2029915611yescharacteristic
241C2C2×#1681364111yescharacteristic
242C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#466×C113C2
socleC22×C113C22×D4
hypercenter#466D113
hypocenterC113#3191
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #20299108C2semidirect
2. #20298941C2semidirect
3. #20298920C2semidirect
4. #20298839C2semidirect
5. #20298825C2semidirect
6. #20298761C2semidirect
7. #20298740C2semidirect
8. C2×#16813534C2semidirect
9. #466×C113C2semidirect
12. C2×Dic452C22semidirect
13. C2×#14268635C22semidirect
23. #16813556C22semidirect
24. #16813553C22semidirect
25. #16813547C22semidirect
26. #16813545C22semidirect
27. #16813543C22semidirect
30. C2×D8×C113C22semidirect
33. #107×C113C22semidirect
34. #102×C113C22semidirect
122. C113#3191semidirect
127. #466D113semidirect
136. C2×D8C2×D113semidirect
149. #107C2×D113semidirect
154. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991082
#202989412
#202989202
#202988392
#202988252
#202987612
#202987402
C2×#168135342
#466×C1132
#3191113