Finite Group Databasebeta

← #28401183

Subgroups — #28401183

Order 14464.

364 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 115 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#20299153C211yesmaximal, characteristic, complemented
2#20299127C211yesmaximal, characteristic
3#20299004C211yesmaximal, characteristic, complemented
4#20298993C211yesmaximal, characteristic, complemented
5#20298967C211yesmaximal, characteristic, complemented
6#20298855C212yesmaximal, complemented
7#20298843C212yesmaximal
8#20298690C212yesmaximal, complemented
9#20298689C212yesmaximal, complemented
10#20298550C211yesmaximal, characteristic, complemented
11#489×C113C211yesmaximal, characteristic, complemented
12C2×#14268637C2212yes—
13C2×#14268635C2212yes—
14C2×#14268630C2212yes—
15#16813622C2211yescharacteristic
16#16813615—21no—
17#16813614C2211yescharacteristic
18#16813613—21no—
19#16813604—21no—
20#16813602C2212yes—
21#16813598—21no—
22#16813598C2211yescharacteristic
23#16813593C2211yescharacteristic
24Q8×Dic113—21no—
25Q8×Dic113C2211yescharacteristic
26#16813587C2212yes—
27D4×Dic113C2211yescharacteristic
28#16813582—21no—
29#16813580—21no—
30#16813578—21no—
31C42×D113C2211yescharacteristic
32#16813555C2212yes—
33#16813553C2212yes—
34#16813547C2212yes—
35#16813547C2212yes—
36#16813533C2211yescharacteristic
37C8×Dic113C2212yes—
38C4⋊Q8×C113C2211yescharacteristic
39#124×C113C2211yescharacteristic
40#103×C113C2212yes—
41#102×C113C2212yes—
42#97×C113C2211yescharacteristic
43C2×Dic226C2312yes—
44C2×C22⋊D113—21no—
45C22×Dic113—21no—
46C2×C4×D113D411yescharacteristic
47C2×C4×D113D411yescharacteristic
48C2×C4×D113C2311yescharacteristic
49#14268637—24no—
50#14268635—24no—
51#14268630—24no—
52C2×#11744751C2312yes—
53C4⋊Dic113—21no—
54C4⋊Dic113—21no—
55C4⋊Dic113—22no—
56C4⋊Dic113—21no—
57C4⋊Dic113C2311yescharacteristic
58C4⋊Dic113C2311yescharacteristic
59#14268626—21no—
60#14268626—21no—
61#14268626—21no—
62#14268626—22no—
63C22⋊Dic113—21no—
64C22⋊Dic113—21no—
65#14268624—22no—
66#14268624—21no—
67C4×Dic113—21no—
68C4×Dic113—22no—
69C4×Dic113D411yescharacteristic
70C4×Dic113D411yescharacteristic
71C4×Dic113C2311yescharacteristic
72C2×Q8×C113—21no—
73C2×Q8×C113C2311yescharacteristic
74C2×D4×C113C2311yescharacteristic
75C2×C8×C113C2312yes—
76C4⋊C4×C113—21no—
77C4⋊C4×C113C2312yes—
78C22⋊C4×C113—21no—
79C22⋊C4×C113—21no—
80C42×C113C2311yescharacteristic
81C23×C113—21no—
82C22×D113C2×D411yescharacteristic
83Q8×C113—22no—
84Q8×C113—42no—
85D4×C113—22no—
86C2×C4×C113—21no—
87C2×C4×C113—22no—
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2411yescharacteristic
91C22⋊D113—42no—
92C2×Dic113—22no—
93C2×Dic113—21no—
94C2×Dic113—21no—
95C2×Dic113—42no—
96C2×Dic113C2×D411yescharacteristic
97C2×Dic113C2×D411yescharacteristic
98C2×Dic113C2×D411yescharacteristic
99C4×D113—22no—
100C4×D113—22no—
101C4×D113—41no—
102Dic226—22no—
103Dic226—22no—
104C8×C113—22no—
105#11744751#4114yes—
106C22×C113—41no—
107C22×C113—41no—
108C22×C113—41no—
109C22×C113C22×D411yescharacteristic
110C2×D113—21no—
111C2×D113—21no—
112C2×D113—21no—
113C4×C113—21no—
114C4×C113—21no—
115C4×C113—41no—
116C4×C113—42no—
117C4×C113C2×#4112yes—
118Dic113—21no—
119Dic113—21no—
120Dic113—42no—
121Dic113—41no—
122Dic113—41no—
123Dic113#13712yes—
124C2×C113—81no—
125C2×C113#53211yescharacteristic
126C2×C113C2×#13711yescharacteristic
127C2×C113#57511yescharacteristic
128D113—41no—
129#3172—1131nomaximal, Sylow
130C113#317211yescharacteristic, complemented, Sylow
131#533—1131no—
132#529—1131no—
133#501—1131no—
134#497—1131no—
135#491—1131no—
136#489D11311yescharacteristic, complemented
137#470—1132no—
138#468—1132no—
139C4×Q16—1132no—
140C4×SD16—1132no—
141C4×M16—1131no—
142C2×Q16—1132no—
143C2×SD16—1132no—
144C2×M16—1132no—
145C4⋊Q8—1131no—
146C4⋊Q8C2×D11311yescharacteristic
147#126—2261no—
148#125—1131no—
149#125—2261no—
150#124C2×D11311yescharacteristic
151#123—2261no—
152C22⋊Q8—1131no—
153C22⋊Q8—1132no—
154C22⋊Q8—2261no—
155#121—1131no—
156C4×Q8—1131no—
157C4×Q8—1132no—
158C4×Q8—2261no—
159C4×D4—1131no—
160C4×D4—2261no—
161#117—2261no—
162#117—2261no—
163C2×C42—1131no—
164#107—1132no—
165#106—1132no—
166#103—1132no—
167#103—1132no—
168#103C2×D11312yes—
169#102C2×D11312yes—
170#97—1131no—
171#97C2×D11311yescharacteristic
172C4×C8—1132no—
173C2×Q8—21no—
174C2×Q8—1132no—
175C2×Q8C22×D11311yescharacteristic
176C2×D4—2261no—
177C2×D4C22×D11311yescharacteristic
178C22×C4—1131no—
179C22×C4—1131no—
180C22×C4—1131no—
181C22×C4—2261no—
182Q16—2264no—
183SD16—2264no—
184M16—2264no—
185C2×C8—1132no—
186C2×C8C22×D11312yes—
187C4⋊C4—21no—
188C4⋊C4—1131no—
189C4⋊C4—1131no—
190C4⋊C4—2261no—
191C4⋊C4—2262no—
192C4⋊C4—2261no—
193C4⋊C4—2262no—
194C4⋊C4—2261no—
195C4⋊C4—2261no—
196C4⋊C4—2261no—
197C4⋊C4—2261no—
198C4⋊C4C22×D11312yes—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—2262no—
202C22⋊C4—2261no—
203C22⋊C4—2261no—
204C22⋊C4—2261no—
205C42—1131no—
206C42—1131no—
207C42—1131no—
208C42—2261no—
209C42—2262no—
210C42C22×D11311yescharacteristic
211C23—21no—
212C23—1131no—
213Q8—22no—
214Q8—42no—
215Q8—2262no—
216Q8—2262no—
217D4—22no—
218D4—4522no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—1131no—
222C2×C4—1131no—
223C2×C4—1131no—
224C2×C4—4521no—
225C2×C4—4522no—
226C2×C4—2262no—
227C2×C4—2261no—
228C2×C4—2262no—
229C2×C4—2261no—
230C2×C4—2262no—
231C2×C4D4×D11311yescharacteristic
232C2×C4D4×D11311yescharacteristic
233C2×C4C23×D11311yescharacteristic
234C8—22no—
235C8—1134no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—2261no—
240C22—2261no—
241C22—2261no—
242C22C2×D4×D11311yescharacteristic
243C4—21no—
244C4—21no—
245C4—42no—
246C4—41no—
247C4—1132no—
248C4—4521no—
249C4—4521no—
250C4—4522no—
251C4—2261no—
252C4—2261no—
253C4#41×D11312yes—
254C2—81no—
255C2—4521no—
256C2#2029914711yescharacteristic
257C2#137×D11311yescharacteristic
258C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#489×C113C2
socleC22×C113C22×D4
prime radical#16813593C22
hypercenter#489D113
hypocenterC113#3172
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #20299153C2semidirect
3. #20299004C2semidirect
4. #20298993C2semidirect
5. #20298967C2semidirect
6. #20298855C2semidirect
8. #20298690C2semidirect
9. #20298689C2semidirect
10. #20298550C2semidirect
11. #489×C113C2semidirect
130. C113#3172semidirect
136. #489D113semidirect

Maximal subgroups

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

subgroupindex
#202991532
#202991272
#202990042
#202989932
#202989672
#202988552
#202988432
#202986902
#202986892
#202985502
#489×C1132
#3172113