Finite Group Databasebeta

← #28401627

Subgroups — #28401627

Order 14464.

420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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#20299204C211yesmaximal, characteristic, complemented
2#20299166C211yesmaximal, characteristic, complemented
3#20298988C211yesmaximal, characteristic, complemented
4#20298975C211yesmaximal, characteristic, complemented
5#20298964C211yesmaximal, characteristic, complemented
6#20298816C212yesmaximal, complemented
7#20298792C212yesmaximal, complemented
8#20298746C212yesmaximal, complemented
9#20298733C212yesmaximal, complemented
10#20298657C211yesmaximal, characteristic, complemented
11#488×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C2×D4×D113C2211yescharacteristic
14C2×#14268634C2212yescomplemented
15C2×D904C2212yes—
16C2×D904C2212yescomplemented
17C2×#14268632C2212yes—
18#16813619C2211yescharacteristic
19#16813619C2211yescharacteristic, complemented
20#16813618C2211yescharacteristic
21#16813611C2211yescharacteristic
22#16813607—22no—
23#16813597—22no—
24#16813597C2212yes—
25#16813595—22no—
26#16813592—22no—
27#16813584C2212yescomplemented
28#16813579C2211yescharacteristic
29#16813551C2212yescomplemented
30#16813542C2212yes—
31#16813542C2212yescomplemented
32#16813534C2212yes—
33#16813533C2211yescharacteristic, complemented
34#125×C113C2211yescharacteristic, complemented
35#124×C113C2211yescharacteristic
36#103×C113C2212yescomplemented
37#102×C113C2212yes—
38C4×C8×C113C2211yescharacteristic, complemented
39C23×D113—21no—
40#14268648—42no—
41C2×D452—21no—
42C2×D452—22no—
43C2×D452—22no—
44C2×D452—22no—
45C2×D452C2312yes—
46C2×D452C2311yescharacteristic
47C2×D452C2311yescharacteristic
48C2×C22⋊D113—21no—
49C2×C22⋊D113—22no—
50D4×D113—42no—
51C2×C4×D113—21no—
52C2×C4×D113—22no—
53C2×C4×D113C2311yescharacteristic
54#14268634—42no—
55D904—42no—
56D904—42no—
57#14268632—42no—
58C2×#11744751C2312yes—
59#14268626D412yes—
60#14268624—22no—
61#14268624—22no—
62#14268624—22no—
63#14268624D412yes—
64C4×Dic113C2311yescharacteristic
65C2×Q8×C113C2311yescharacteristic
66C2×D4×C113C2311yescharacteristic
67C2×C8×C113C2312yes—
68C4⋊C4×C113—22no—
69C4⋊C4×C113C2312yes—
70C22⋊C4×C113—22no—
71C42×C113C2311yescharacteristic
72C23×C113—21no—
73C22×D113—22no—
74C22×D113—21no—
75C22×D113—21no—
76C22×D113—42no—
77C22×D113—82no—
78C22×D113C2×D411yescharacteristic
79Q8×C113—22no—
80D4×C113—22no—
81C2×C4×C113—21no—
82C2×C4×C113—22no—
83C2×C4×C113C2×D412yes—
84C2×C4×C113C2411yescharacteristic
85C22⋊D113—42no—
86C22⋊D113—82no—
87C2×Dic113C2×D412yes—
88C2×Dic113C2×D411yescharacteristic
89D452—22no—
90D452—22no—
91D452—22no—
92D452—22no—
93D452—42no—
94D452—82no—
95D452—82no—
96D452—82no—
97C4×D113—22no—
98C4×D113—42no—
99C4×D113—82no—
100C8×C113—22no—
101#11744751—22no—
102C22×C113—41no—
103C22×C113—42no—
104C22×C113C22×D411yescharacteristic
105C2×D113—21no—
106C2×D113—22no—
107C2×D113—41no—
108C2×D113—41no—
109C2×D113—42no—
110C2×D113—42no—
111C2×D113—42no—
112C2×D113—42no—
113C2×D113—42no—
114C2×D113—84no—
115C4×C113—22no—
116C4×C113—41no—
117C4×C113—42no—
118C4×C113H(5,𝔽2)12yes—
119Dic113—21no—
120Dic113—22no—
121C2×C113—81no—
122C2×C113#53511yescharacteristic
123C2×C113#57612yes—
124D113—41no—
125D113—81no—
126D113—82no—
127D113—81no—
128#3220—1131nomaximal, Sylow
129C113#322011yescharacteristic, complemented, Sylow
130#540—1131no—
131#535—1131no—
132#496—1131no—
133#493—1131no—
134#490—1131no—
135#488D11311yescharacteristic, complemented
136#463—1132no—
137#459—1132no—
138#449—1132no—
139#447—1132no—
140#433—1131no—
141C2×#41—1131no—
142C22×D4—1131no—
143C2×SD16—1132no—
144C2×D8—1132no—
145C2×D8—1132no—
146C2×D8—1132no—
147#127—1131no—
148#127—1131no—
149#127—1131no—
150#125C2×D11311yescharacteristic, complemented
151#124—1131no—
152#124C2×D11311yescharacteristic
153#123—2262no—
154#121—1132no—
155#121—2262no—
156#121—2262no—
157#120—2262no—
158C4×D4—1132no—
159#117—1131no—
160C4⋊C8—1132no—
161#103C2×D11312yescomplemented
162#102—1132no—
163#102—1132no—
164#102C2×D11312yes—
165C22⋊C8—1132no—
166#97—1131no—
167C4×C8C2×D11311yescharacteristic, complemented
168C24—2261no—
169#41—4522no—
170C2×Q8C22×D11311yescharacteristic
171C2×D4—1131no—
172C2×D4—1131no—
173C2×D4—1132no—
174C2×D4—4522no—
175C2×D4—2262no—
176C2×D4—2261no—
177C2×D4—2262no—
178C2×D4—2261no—
179C2×D4—2262no—
180C2×D4—2262no—
181C2×D4C22×D11311yescharacteristic
182C22×C4—1131no—
183C22×C4—2262no—
184C22×C4—2261no—
185SD16—4522no—
186D8—4522no—
187D8—4522no—
188D8—4522no—
189C2×C8—1132no—
190C2×C8C22×D11312yes—
191C4⋊C4—22no—
192C4⋊C4—1132no—
193C4⋊C4C22×D11312yes—
194C22⋊C4—22no—
195C22⋊C4—1132no—
196C22⋊C4—2262no—
197C22⋊C4—2262no—
198C22⋊C4—2262no—
199C42—1131no—
200C42C22×D11311yescharacteristic
201C23—21no—
202C23—1131no—
203C23—9042no—
204C23—4522no—
205C23—2262no—
206C23—2261no—
207C23—2261no—
208Q8—22no—
209D4—22no—
210D4—9042no—
211D4—9042no—
212D4—9042no—
213D4—9042no—
214D4—4522no—
215D4—4522no—
216D4—2262no—
217D4—2262no—
218D4—2262no—
219D4—2262no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—1132no—
223C2×C4—1131no—
224C2×C4—9042no—
225C2×C4—4522no—
226C2×C4—2262no—
227C2×C4D4×D11312yes—
228C2×C4C23×D11311yescharacteristic
229C8—22no—
230C8—2262no—
231C22—42no—
232C22—41no—
233C22—9044no—
234C22—4522no—
235C22—4522no—
236C22—4522no—
237C22—4522no—
238C22—4521no—
239C22—4521no—
240C22—4522no—
241C22—2262no—
242C22—2261no—
243C22C2×D4×D11311yescharacteristic
244C4—22no—
245C4—42no—
246C4—41no—
247C4—2262no—
248C4—2261no—
249C4#1681366812yes—
250C2—81no—
251C2—9041no—
252C2—9042no—
253C2—9041no—
254C2—4521no—
255C2#2029916611yescharacteristic
256C2#2029940012yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#488×C113C2
socleC22×C113C22×D4
hypercenter#488D113
hypocenterC113#3220
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #20299204C2semidirect
2. #20299166C2semidirect
3. #20298988C2semidirect
4. #20298975C2semidirect
5. #20298964C2semidirect
6. #20298816C2semidirect
7. #20298792C2semidirect
8. #20298746C2semidirect
9. #20298733C2semidirect
10. #20298657C2semidirect
11. #488×C113C2semidirect
14. C2×#14268634C22semidirect
16. C2×D904C22semidirect
19. #16813619C22semidirect
27. #16813584C22semidirect
29. #16813551C22semidirect
31. #16813542C22semidirect
33. #16813533C22semidirect
34. #125×C113C22semidirect
36. #103×C113C22semidirect
38. C4×C8×C113C22semidirect
129. C113#3220semidirect
135. #488D113semidirect
150. #125C2×D113semidirect
161. #103C2×D113semidirect
167. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992042
#202991662
#202989882
#202989752
#202989642
#202988162
#202987922
#202987462
#202987332
#202986572
#488×C1132
#3220113