Finite Group Databasebeta

← #28401181

Subgroups — #28401181

Order 14464.

364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299155C211yesmaximal, characteristic, complemented
2#20299008C211yesmaximal, characteristic, complemented
3#20298993C211yesmaximal, characteristic, complemented
4#20298968C211yesmaximal, characteristic, complemented
5#20298957C211yesmaximal, characteristic, complemented
6#20298854C212yesmaximal, complemented
7#20298842C212yesmaximal
8C4×#14268637C212yesmaximal, complemented
9C4×#14268635C212yesmaximal, complemented
10C4×#14268631C211yesmaximal, characteristic, complemented
11#529×C113C211yesmaximal, characteristic
12C2×#14268637C2212yes—
13C2×#14268635C2212yes—
14C2×#14268631C2212yes—
15#16813622C2211yescharacteristic
16#16813622C2211yescharacteristic
17#16813614—21no—
18#16813601—21no—
19#16813601C2212yes—
20C4×Dic226—21no—
21C4×Dic226C2212yes—
22#16813581—21no—
23#16813555C2212yes—
24#16813553C2212yes—
25#16813546C2212yes—
26#16813545C2212yes—
27#16813545C2212yes—
28#16813543C2212yes—
29#16813533C2211yescharacteristic
30#16813533C2211yescharacteristic
31C4×#11744751C2212yes—
32#126×C113—21no—
33#125×C113C2211yescharacteristic
34#124×C113C2211yescharacteristic
35#123×C113—21no—
36C22⋊Q8×C113C2211yescharacteristic
37#121×C113C2211yescharacteristic
38C4×Q8×C113C2211yescharacteristic
39C4×D4×C113—21no—
40C4×D4×C113C2211yescharacteristic
41#117×C113—21no—
42C2×C42×C113C2211yescharacteristic
43C2×Dic226—21no—
44C2×Dic226C2312yes—
45#14268637—24no—
46#14268635—24no—
47#14268631—24no—
48C2×#11744751C2312yes—
49C2×#11744751C2312yes—
50C4⋊Dic113—21no—
51C4⋊Dic113—21no—
52C4⋊Dic113—21no—
53C4⋊Dic113C2312yes—
54#14268626—22no—
55#14268626—22no—
56C22⋊Dic113—22no—
57C4×Dic113—22no—
58C2×Q8×C113C2311yescharacteristic
59C2×D4×C113—21no—
60C2×D4×C113C2311yescharacteristic
61C22×C4×C113—21no—
62C22×C4×C113D411yescharacteristic
63C22×C4×C113D411yescharacteristic
64C22×C4×C113C2311yescharacteristic
65C4⋊C4×C113—21no—
66C4⋊C4×C113—21no—
67C4⋊C4×C113—21no—
68C4⋊C4×C113—21no—
69C4⋊C4×C113C2311yescharacteristic
70C4⋊C4×C113C2311yescharacteristic
71C22⋊C4×C113—21no—
72C22⋊C4×C113—21no—
73C22⋊C4×C113—21no—
74C22⋊C4×C113—21no—
75C22⋊C4×C113—21no—
76C42×C113—21no—
77C42×C113D411yescharacteristic
78C42×C113D411yescharacteristic
79C42×C113C2311yescharacteristic
80C42×C113C2311yescharacteristic
81C23×C113—21no—
82C23×C113C2×D411yescharacteristic
83Q8×C113—22no—
84D4×C113—22no—
85D4×C113—42no—
86C2×C4×C113—22no—
87C2×C4×C113—22no—
88C2×C4×C113—21no—
89C2×C4×C113—21no—
90C2×C4×C113—21no—
91C2×C4×C113—41no—
92C2×C4×C113—42no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2411yescharacteristic
99C2×Dic113—22no—
100C2×Dic113—22no—
101Dic226—22no—
102Dic226—22no—
103Dic226—42no—
104#11744751—22no—
105#11744751#4114yes—
106C22×C113—21no—
107C22×C113—21no—
108C22×C113—21no—
109C22×C113—41no—
110C22×C113—41no—
111C22×C113—41no—
112C22×C113C22×D411yescharacteristic
113C4×C113—21no—
114C4×C113—21no—
115C4×C113—21no—
116C4×C113—21no—
117C4×C113—41no—
118C4×C113—41no—
119C4×C113—41no—
120C4×C113#13712yes—
121C4×C113C2×#4112yes—
122Dic113—42no—
123Dic113—42no—
124C2×C113—41no—
125C2×C113—81no—
126C2×C113#53211yescharacteristic
127C2×C113C2×#13711yescharacteristic
128C2×C113#57511yescharacteristic
129#3172—1131nomaximal, Sylow
130C113#317211yescharacteristic, complemented, Sylow
131#533—1131no—
132#529D11311yescharacteristic
133#501—1131no—
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⋊Q8—1131no—
147#126—21no—
148#125—2261no—
149#125C2×D11311yescharacteristic
150#124C2×D11311yescharacteristic
151#123—21no—
152C22⋊Q8—1132no—
153C22⋊Q8—2261no—
154C22⋊Q8C2×D11311yescharacteristic
155#121C2×D11311yescharacteristic
156C4×Q8—1132no—
157C4×Q8—2261no—
158C4×Q8C2×D11311yescharacteristic
159C4×D4—21no—
160C4×D4C2×D11311yescharacteristic
161#117—21no—
162#117—2261no—
163C2×C42C2×D11311yescharacteristic
164#107—1132no—
165#106—1132no—
166#103—1132no—
167#103—1132no—
168#103—1132no—
169#102—1132no—
170#97—1131no—
171#97—1131no—
172C4×C8—1132no—
173C2×Q8—1132no—
174C2×Q8—2261no—
175C2×Q8C22×D11311yescharacteristic
176C2×D4—21no—
177C2×D4C22×D11311yescharacteristic
178C22×C4—21no—
179C22×C4C22⋊D11311yescharacteristic
180C22×C4C22⋊D11311yescharacteristic
181C22×C4C22×D11311yescharacteristic
182Q16—2264no—
183SD16—2264no—
184M16—2264no—
185C2×C8—1132no—
186C2×C8—1132no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—1132no—
192C4⋊C4—2261no—
193C4⋊C4—2261no—
194C4⋊C4—2262no—
195C4⋊C4—2262no—
196C4⋊C4—2261no—
197C4⋊C4C22×D11311yescharacteristic
198C4⋊C4C22×D11311yescharacteristic
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—21no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—2262no—
205C42—21no—
206C42—2262no—
207C42C22⋊D11311yescharacteristic
208C42C22⋊D11311yescharacteristic
209C42C22×D11311yescharacteristic
210C42C22×D11311yescharacteristic
211C23—21no—
212C23C2×C22⋊D11311yescharacteristic
213Q8—22no—
214Q8—4522no—
215Q8—2262no—
216Q8—2262no—
217D4—22no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—2262no—
227C2×C4—2262no—
228C2×C4C2×C22⋊D11311yescharacteristic
229C2×C4C2×C22⋊D11311yescharacteristic
230C2×C4C2×C22⋊D11311yescharacteristic
231C2×C4C2×C22⋊D11311yescharacteristic
232C2×C4C2×C22⋊D11311yescharacteristic
233C2×C4C23×D11311yescharacteristic
234C8—1134no—
235C8—2262no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22C22×C22⋊D11311yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—4522no—
251C4—4522no—
252C4#1681365212yes—
253C4#41×D11312yes—
254C2—41no—
255C2—81no—
256C2#2029914411yescharacteristic
257C2C2×#1681365211yescharacteristic
258C2#2029939611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#529×C113C2
socleC22×C113C22×D4
prime radical#121×C113C22
hypercenter#529D113
hypocenterC113#3172
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #20299155C2semidirect
2. #20299008C2semidirect
3. #20298993C2semidirect
4. #20298968C2semidirect
5. #20298957C2semidirect
6. #20298854C2semidirect
8. C4×#14268637C2semidirect
9. C4×#14268635C2semidirect
10. C4×#14268631C2semidirect
130. C113#3172semidirect

Maximal subgroups

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

subgroupindex
#202991552
#202990082
#202989932
#202989682
#202989572
#202988542
#202988422
C4×#142686372
C4×#142686352
C4×#142686312
#529×C1132
#3172113