Finite Group Databasebeta

← #28400497

Subgroups — #28400497

Order 14464.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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#20299109C211yesmaximal, characteristic
2#20298933C212yesmaximal, complemented
3#20298928C212yesmaximal, complemented
4#20298916C212yesmaximal, complemented
5#20298911C212yesmaximal, complemented
6#20298638C212yesmaximal, complemented
7#20298597C212yesmaximal, complemented
8#20298562C211yesmaximal, characteristic, complemented
9C22×C4⋊C4×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C2×#14268631C2212yes—
12#16813605—21no—
13#16813601C2211yescharacteristic
14#16813601C2211yescharacteristic
15#16813596C2211yescharacteristic
16#16813596C2211yescharacteristic
17#16813591—21no—
18C4×C22⋊D113—21no—
19C4×C22⋊D113—21no—
20#16813581C2211yescharacteristic
21#16813555C2214yescomplemented
22#16813553C2214yescomplemented
23#16813545C2214yescomplemented
24#16813542C2214yescomplemented
25C22⋊#11744751C2212yes—
26C22⋊#11744751C2212yes—
27C23×C4×C113—21no—
28C23×C4×C113C2211yescharacteristic
29C2×C4⋊C4×C113—21no—
30C2×C4⋊C4×C113—21no—
31C2×C4⋊C4×C113—21no—
32C2×C4⋊C4×C113C2212yes—
33C2×C4⋊C4×C113C2212yes—
34C2×C4⋊C4×C113C2212yes—
35#14268647—24no—
36C2×Dic226C2311yescharacteristic
37C2×D452C2311yescharacteristic
38C2×C22⋊D113—21no—
39C2×C22⋊D113—21no—
40C2×C22⋊D113—21no—
41C2×C4×D113—21no—
42#14268631—24no—
43C2×#11744751C2314yes—
44C4⋊Dic113C2311yescharacteristic
45C4⋊Dic113C2311yescharacteristic
46#14268626—21no—
47#14268626—21no—
48C22⋊Dic113—21no—
49C22⋊Dic113—21no—
50C22⋊Dic113—21no—
51#14268624—21no—
52#14268624—21no—
53C4×Dic113—21no—
54C24×C113D411yescharacteristic
55C22×C4×C113—24no—
56C22×C4×C113—22no—
57C22×C4×C113—22no—
58C22×C4×C113—22no—
59C22×C4×C113—44no—
60C22×C4×C113D411yescharacteristic
61C22×C4×C113D411yescharacteristic
62C22×C4×C113D411yescharacteristic
63C22×C4×C113C2311yescharacteristic
64C22×C4×C113C2311yescharacteristic
65C22×C4×C113C2311yescharacteristic
66C4⋊C4×C113—22no—
67C4⋊C4×C113—22no—
68C4⋊C4×C113—22no—
69C4⋊C4×C113C2314yes—
70C23×C113—22no—
71C23×C113—22no—
72C23×C113—22no—
73C23×C113C2×D411yescharacteristic
74C23×C113C2×D411yescharacteristic
75C23×C113C2×D411yescharacteristic
76C22×D113—21no—
77C2×C4×C113—22no—
78C2×C4×C113—22no—
79C2×C4×C113—22no—
80C2×C4×C113—22no—
81C2×C4×C113—22no—
82C2×C4×C113—24no—
83C2×C4×C113—44no—
84C2×C4×C113—44no—
85C2×C4×C113—44no—
86C2×C4×C113C2×D411yescharacteristic
87C2×C4×C113C2×D411yescharacteristic
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113#4114yes—
90C2×C4×C113C2411yescharacteristic
91C22⋊D113—42no—
92C22⋊D113—42no—
93C22⋊D113—42no—
94C2×Dic113—21no—
95C2×Dic113—21no—
96C2×Dic113—21no—
97D452—22no—
98C4×D113—42no—
99Dic226—22no—
100#11744751—24no—
101C22×C113—28no—
102C22×C113—21no—
103C22×C113—21no—
104C22×C113—21no—
105C22×C113—21no—
106C22×C113—21no—
107C22×C113—21no—
108C22×C113#12312yes—
109C22×C113AGL(1,ℤ/8)12yes—
110C22×C113#13712yes—
111C22×C113C22×D411yescharacteristic
112C2×D113—41no—
113C2×D113—41no—
114C2×D113—41no—
115C4×C113—21no—
116C4×C113—21no—
117C4×C113—44no—
118C4×C113#12312yes—
119C4×C113C2×#4112yes—
120Dic113—41no—
121Dic113—41no—
122Dic113—41no—
123C2×C113—22no—
124C2×C113—22no—
125C2×C113—22no—
126C2×C113C2×#12311yescharacteristic
127C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C113C2×#13711yescharacteristic
129D113—81no—
130#3092—1131nomaximal, Sylow
131C113#309211yescharacteristic, complemented, Sylow
132#525—1131no—
133C22×C4⋊C4D11311yescharacteristic, complemented
134#484—1132no—
135#483—1132no—
136#481—1132no—
137#480—1132no—
138#428—1132no—
139#417—1132no—
140#407—1131no—
141C2×#41—1131no—
142C23×C4—21no—
143C23×C4C2×D11311yescharacteristic
144C2×M16—1132no—
145#123—2261no—
146C22⋊Q8—1131no—
147C22⋊Q8—1131no—
148#121—1131no—
149#121—1131no—
150#120—2261no—
151C4×D4—2261no—
152C4×D4—2261no—
153#117—1131no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×D11312yes—
158C2×C4⋊C4C2×D11312yes—
159C2×C4⋊C4C2×D11312yes—
160#107—1134no—
161#106—1134no—
162#103—1134no—
163#102—1134no—
164C22⋊C8—1132no—
165C22⋊C8—1132no—
166C24C22⋊D11311yescharacteristic
167#41—2264no—
168C2×Q8—1131no—
169C2×D4—1131no—
170C2×D4—2261no—
171C2×D4—2261no—
172C2×D4—2261no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—44no—
178C22×C4—2261no—
179C22×C4C22⋊D11311yescharacteristic
180C22×C4C22⋊D11311yescharacteristic
181C22×C4C22⋊D11311yescharacteristic
182C22×C4C22×D11311yescharacteristic
183C22×C4C22×D11311yescharacteristic
184C22×C4C22×D11311yescharacteristic
185M16—2264no—
186C2×C8—1134no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—1131no—
191C4⋊C4—1131no—
192C4⋊C4—2261no—
193C4⋊C4—2261no—
194C4⋊C4C22×D11314yes—
195C22⋊C4—2261no—
196C22⋊C4—2261no—
197C22⋊C4—2261no—
198C22⋊C4—2261no—
199C22⋊C4—2261no—
200C42—2261no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—2261no—
205C23C2×C22⋊D11311yescharacteristic
206C23C2×C22⋊D11311yescharacteristic
207C23C2×C22⋊D11311yescharacteristic
208Q8—2262no—
209D4—4522no—
210D4—4522no—
211D4—4522no—
212D4—2262no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—4522no—
223C2×C4—2261no—
224C2×C4—2261no—
225C2×C4—2261no—
226C2×C4C2×C22⋊D11311yescharacteristic
227C2×C4C2×C22⋊D11311yescharacteristic
228C2×C4C2×C22⋊D11311yescharacteristic
229C2×C4#1426864714yes—
230C2×C4C23×D11311yescharacteristic
231C8—2264no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—4521no—
240C22—4521no—
241C22—4521no—
242C22#1681360512yes—
243C22#1681364812yes—
244C22#1681365312yes—
245C22C22×C22⋊D11311yescharacteristic
246C4—21no—
247C4—21no—
248C4—44no—
249C4—4521no—
250C4—4521no—
251C4—4521no—
252C4#1681360512yes—
253C4C2×#1426864712yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—9041no—
258C2C2×#1681360511yescharacteristic
259C2C2×#1681364811yescharacteristic
260C2C2×#1681365311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×C4⋊C4×C113C2
socleC22×C113C22×D4
prime radical#20299109C2
hypercenterC22×C4⋊C4D113
hypocenterC113#3092
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20298933C2semidirect
3. #20298928C2semidirect
4. #20298916C2semidirect
5. #20298911C2semidirect
6. #20298638C2semidirect
7. #20298597C2semidirect
8. #20298562C2semidirect
9. C22×C4⋊C4×C113C2semidirect
21. #16813555C22semidirect
22. #16813553C22semidirect
23. #16813545C22semidirect
24. #16813542C22semidirect
131. C113#3092semidirect
133. C22×C4⋊C4D113semidirect

Maximal subgroups

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

subgroupindex
#202991092
#202989332
#202989282
#202989162
#202989112
#202986382
#202985972
#202985622
C22×C4⋊C4×C1132
#3092113