Finite Group Databasebeta

← #28401182

Subgroups — #28401182

Order 14464.

364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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#20299133C211yesmaximal, characteristic
3#20298992C211yesmaximal, characteristic, complemented
4#20298968C211yesmaximal, characteristic, complemented
5#20298960C211yesmaximal, characteristic, complemented
6#20298857C212yesmaximal, complemented
7#20298845C212yesmaximal
8#20298692C212yesmaximal, complemented
9#20298685C212yesmaximal, complemented
10#20298550C211yesmaximal, characteristic, complemented
11#501×C113C211yesmaximal, characteristic, complemented
12C2×Dic452C2212yes—
13C2×#14268636C2212yes—
14C2×#14268630C2212yes—
15#16813622C2211yescharacteristic
16#16813617—21no—
17#16813613—21no—
18#16813610C2211yescharacteristic
19#16813607—21no—
20#16813602C2212yes—
21#16813602C2211yescharacteristic
22#16813598—21no—
23#16813597C2211yescharacteristic
24Q8×Dic113—21no—
25#16813587C2211yescharacteristic
26#16813587C2212yes—
27#16813584—21no—
28#16813584C2211yescharacteristic
29#16813580—21no—
30#16813580—21no—
31C42×D113C2211yescharacteristic
32#16813545C2212yes—
33#16813545C2212yes—
34#16813545C2212yes—
35#16813542C2212yes—
36#16813533C2211yescharacteristic
37C8×Dic113C2212yes—
38C4⋊Q8×C113C2211yescharacteristic
39#125×C113C2211yescharacteristic
40#107×C113C2212yes—
41#106×C113C2212yes—
42#97×C113C2211yescharacteristic
43C2×Dic226C2311yescharacteristic
44C2×Dic226C2312yes—
45C2×D452—21no—
46C2×D452C2311yescharacteristic
47C2×C4×D113—21no—
48C2×C4×D113D411yescharacteristic
49C2×C4×D113D411yescharacteristic
50C2×C4×D113C2311yescharacteristic
51Dic452—24no—
52#14268636—24no—
53#14268630—24no—
54C2×#11744751C2312yes—
55C4⋊Dic113—21no—
56C4⋊Dic113—21no—
57C4⋊Dic113—21no—
58C4⋊Dic113—22no—
59#14268626—22no—
60#14268626—21no—
61#14268624—22no—
62#14268624—21no—
63#14268624—21no—
64#14268624—21no—
65#14268624—21no—
66#14268624—21no—
67C4×Dic113—21no—
68C4×Dic113—22no—
69C4×Dic113D411yescharacteristic
70C4×Dic113D411yescharacteristic
71C4×Dic113C2311yescharacteristic
72C2×Q8×C113—21no—
73C2×C8×C113C2312yes—
74C4⋊C4×C113—21no—
75C4⋊C4×C113—21no—
76C4⋊C4×C113—21no—
77C4⋊C4×C113C2311yescharacteristic
78C4⋊C4×C113C2311yescharacteristic
79C4⋊C4×C113C2312yes—
80C42×C113C2311yescharacteristic
81C22×D113—21no—
82C22×D113C2×D411yescharacteristic
83Q8×C113—42no—
84C2×C4×C113—21no—
85C2×C4×C113—21no—
86C2×C4×C113—22no—
87C2×C4×C113C2×D411yescharacteristic
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113C2411yescharacteristic
90C2×Dic113—21no—
91C2×Dic113—22no—
92C2×Dic113C2×D411yescharacteristic
93C2×Dic113C2×D411yescharacteristic
94C2×Dic113C2×D411yescharacteristic
95D452—22no—
96D452—42no—
97C4×D113—22no—
98C4×D113—22no—
99C4×D113—41no—
100C4×D113—42no—
101Dic226—22no—
102Dic226—22no—
103Dic226—22no—
104C8×C113#4114yes—
105#11744751—22no—
106C22×C113C22×D411yescharacteristic
107C2×D113—21no—
108C2×D113—21no—
109C2×D113—21no—
110C2×D113—41no—
111C2×D113—41no—
112C2×D113—41no—
113C4×C113—21no—
114C4×C113—21no—
115C4×C113—41no—
116C4×C113—41no—
117C4×C113—42no—
118C4×C113C2×#4112yes—
119Dic113—21no—
120Dic113—21no—
121Dic113—42no—
122Dic113—41no—
123Dic113#13712yes—
124C2×C113#53211yescharacteristic
125C2×C113C2×#13711yescharacteristic
126C2×C113#57511yescharacteristic
127D113—41no—
128D113—81no—
129#3172—1131nomaximal, Sylow
130C113#317211yescharacteristic, complemented, Sylow
131#533—1131no—
132#529—1131no—
133#501D11311yescharacteristic, complemented
134#497—1131no—
135#491—1131no—
136#489—1131no—
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—2261no—
149#125C2×D11311yescharacteristic
150#124—1131no—
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#107C2×D11312yes—
165#106C2×D11312yes—
166#103—1132no—
167#103—1132no—
168#103—1132no—
169#102—1132no—
170#97—1131no—
171#97C2×D11311yescharacteristic
172C4×C8—1132no—
173C2×Q8—21no—
174C2×Q8—1131no—
175C2×Q8—1132no—
176C2×D4—1131no—
177C2×D4—2261no—
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—21no—
189C4⋊C4—21no—
190C4⋊C4—2261no—
191C4⋊C4—2262no—
192C4⋊C4—2261no—
193C4⋊C4—2262no—
194C4⋊C4—2261no—
195C4⋊C4—2261no—
196C4⋊C4C22×D11312yes—
197C4⋊C4C22×D11311yescharacteristic
198C4⋊C4C22×D11311yescharacteristic
199C22⋊C4—2261no—
200C22⋊C4—2261no—
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—1131no—
212C23—2261no—
213Q8—42no—
214Q8—2262no—
215Q8—2262no—
216Q8—2262no—
217D4—4522no—
218D4—2262no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—1131no—
223C2×C4—1131no—
224C2×C4—1131no—
225C2×C4—4521no—
226C2×C4—4522no—
227C2×C4—2262no—
228C2×C4—2261no—
229C2×C4—2262no—
230C2×C4—2262no—
231C2×C4D4×D11311yescharacteristic
232C2×C4D4×D11311yescharacteristic
233C2×C4C23×D11311yescharacteristic
234C8—2262no—
235C8#1426864814yes—
236C22—4521no—
237C22—4521no—
238C22—4521no—
239C22—2261no—
240C22—2261no—
241C22—2261no—
242C22C2×D4×D11311yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—42no—
248C4—1132no—
249C4—4521no—
250C4—4522no—
251C4—2261no—
252C4—2261no—
253C4C2×#1426864812yes—
254C2—9041no—
255C2—4521no—
256C2#2029914911yescharacteristic
257C2#137×D11311yescharacteristic
258C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#501×C113C2
socleC22×C113C22×D4
prime radical#16813597C22
hypercenter#501D113
hypocenterC113#3172
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #20299153C2semidirect
3. #20298992C2semidirect
4. #20298968C2semidirect
5. #20298960C2semidirect
6. #20298857C2semidirect
8. #20298692C2semidirect
9. #20298685C2semidirect
10. #20298550C2semidirect
11. #501×C113C2semidirect
130. C113#3172semidirect
133. #501D113semidirect

Maximal subgroups

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

subgroupindex
#202991532
#202991332
#202989922
#202989682
#202989602
#202988572
#202988452
#202986922
#202986852
#202985502
#501×C1132
#3172113