Finite Group Databasebeta

← #28401617

Subgroups — #28401617

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#20299202C211yesmaximal, characteristic, complemented
2#20299161C211yesmaximal, characteristic, complemented
3#20298985C211yesmaximal, characteristic, complemented
4#20298962C211yesmaximal, characteristic, complemented
5#20298953C211yesmaximal, characteristic, complemented
6#20298811C212yesmaximal, complemented
7#20298791C212yesmaximal, complemented
8#20298740C212yesmaximal, complemented
9#20298730C212yesmaximal, complemented
10#20298657C211yesmaximal, characteristic, complemented
11#493×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2211yescharacteristic
13C2×D4×D113C2211yescharacteristic
14C2×#14268635C2212yescomplemented
15C2×#14268632C2212yes—
16#16813618C2211yescharacteristic
17#16813614C2211yescharacteristic, complemented
18#16813610C2211yescharacteristic
19#16813609C2211yescharacteristic
20#16813603—22no—
21#16813594—22no—
22#16813594—22no—
23#16813593C2212yes—
24#16813590—22no—
25D4×Dic113C2212yescomplemented
26#16813579C2211yescharacteristic
27#16813551C2212yescomplemented
28#16813547C2212yescomplemented
29#16813544C2212yes—
30#16813543C2212yes—
31#16813543C2212yescomplemented
32#16813534C2212yes—
33#16813533C2211yescharacteristic, complemented
34C2×D8×C113C2212yes—
35C2×D8×C113C2212yescomplemented
36#127×C113C2211yescharacteristic
37#127×C113C2211yescharacteristic, complemented
38C4×C8×C113C2211yescharacteristic, complemented
39C23×D113—21no—
40#14268646—42no—
41C2×Dic226C2311yescharacteristic
42C2×D452C2311yescharacteristic
43C2×C22⋊D113—21no—
44C2×C22⋊D113—22no—
45C2×C22⋊D113—21no—
46C2×C22⋊D113—22no—
47D4×D113—42no—
48C22×Dic113—21no—
49C22×Dic113—22no—
50C2×C4×D113C2311yescharacteristic
51#14268635—42no—
52#14268632—42no—
53C2×#11744751C2312yes—
54C4⋊Dic113C2312yes—
55#14268626—22no—
56#14268626D412yes—
57C22⋊Dic113—22no—
58C22⋊Dic113—22no—
59C22⋊Dic113—22no—
60#14268624—22no—
61#14268624D412yes—
62C4×Dic113C2311yescharacteristic
63C2×D4×C113—22no—
64C2×D4×C113—22no—
65C2×D4×C113C2312yes—
66C2×D4×C113C2311yescharacteristic
67C2×D4×C113C2311yescharacteristic
68D8×C113—42no—
69D8×C113—42no—
70C2×C8×C113C2312yes—
71C42×C113C2311yescharacteristic
72C23×C113—22no—
73C23×C113—21no—
74C23×C113—21no—
75C22×D113—21no—
76C22×D113—42no—
77C22×D113—82no—
78C22×D113C2×D411yescharacteristic
79D4×C113—22no—
80D4×C113—22no—
81D4×C113—22no—
82D4×C113—22no—
83D4×C113—82no—
84D4×C113—82no—
85C2×C4×C113C2×D412yes—
86C2×C4×C113C2411yescharacteristic
87C22⋊D113—42no—
88C22⋊D113—42no—
89C22⋊D113—82no—
90C22⋊D113—82no—
91C2×Dic113—21no—
92C2×Dic113—22no—
93C2×Dic113—42no—
94C2×Dic113—82no—
95C2×Dic113C2×D412yes—
96C2×Dic113C2×D411yescharacteristic
97D452—22no—
98C4×D113—22no—
99Dic226—22no—
100C8×C113—22no—
101#11744751—22no—
102C22×C113—41no—
103C22×C113—41no—
104C22×C113—42no—
105C22×C113—42no—
106C22×C113—42no—
107C22×C113—42no—
108C22×C113—42no—
109C22×C113C22×D411yescharacteristic
110C2×D113—21no—
111C2×D113—22no—
112C2×D113—41no—
113C2×D113—42no—
114C2×D113—84no—
115C4×C113—22no—
116C4×C113H(5,𝔽2)12yes—
117Dic113—21no—
118Dic113—22no—
119Dic113—41no—
120Dic113—42no—
121C2×C113—81no—
122C2×C113—81no—
123C2×C113—82no—
124C2×C113#53511yescharacteristic
125C2×C113#57612yes—
126D113—41no—
127D113—81no—
128#3220—1131nomaximal, Sylow
129C113#322011yescharacteristic, complemented, Sylow
130#540—1131no—
131#535—1131no—
132#496—1131no—
133#493D11311yescharacteristic, complemented
134#490—1131no—
135#488—1131no—
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×D8C2×D11312yes—
146C2×D8C2×D11312yescomplemented
147#127—1131no—
148#127C2×D11311yescharacteristic
149#127C2×D11311yescharacteristic, complemented
150#125—1131no—
151#124—1131no—
152#124—1131no—
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#103—1132no—
162#102—1132no—
163#102—1132no—
164#102—1132no—
165C22⋊C8—1132no—
166#97—1131no—
167C4×C8C2×D11311yescharacteristic, complemented
168C24—2261no—
169#41—4522no—
170C2×Q8—1131no—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4—1131no—
174C2×D4—4522no—
175C2×D4—2262no—
176C2×D4—2261no—
177C2×D4—2262no—
178C2×D4—2261no—
179C2×D4C22×D11311yescharacteristic
180C2×D4C22×D11311yescharacteristic
181C2×D4C22×D11312yes—
182C22×C4—1131no—
183C22×C4—2262no—
184C22×C4—2261no—
185SD16—4522no—
186D8—42no—
187D8—42no—
188D8—4522no—
189C2×C8—1132no—
190C2×C8C22×D11312yes—
191C4⋊C4—1132no—
192C4⋊C4—1132no—
193C4⋊C4—2262no—
194C22⋊C4—1132no—
195C22⋊C4—2262no—
196C22⋊C4—2262no—
197C22⋊C4—2262no—
198C22⋊C4—2262no—
199C42—1131no—
200C42C22×D11311yescharacteristic
201C23—22no—
202C23—21no—
203C23—21no—
204C23—1131no—
205C23—9042no—
206C23—4522no—
207C23—2261no—
208Q8—2262no—
209D4—22no—
210D4—22no—
211D4—22no—
212D4—22no—
213D4—82no—
214D4—82no—
215D4—9042no—
216D4—9042no—
217D4—4522no—
218D4—4522no—
219D4—2262no—
220C2×C4—1132no—
221C2×C4—1131no—
222C2×C4—9042no—
223C2×C4—4522no—
224C2×C4—2261no—
225C2×C4—2262no—
226C2×C4—2262no—
227C2×C4D4×D11312yes—
228C2×C4C23×D11311yescharacteristic
229C8—22no—
230C8—2262no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—42no—
235C22—41no—
236C22—41no—
237C22—42no—
238C22—9044no—
239C22—4522no—
240C22—4521no—
241C22—2262no—
242C22—2261no—
243C22C2×D4×D11311yescharacteristic
244C4—22no—
245C4—4522no—
246C4—4521no—
247C4—2262no—
248C4—2261no—
249C4#1681366712yes—
250C2—81no—
251C2—82no—
252C2—81no—
253C2—9041no—
254C2—4521no—
255C2#2029916111yescharacteristic
256C2#2029939912yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#493×C113C2
socleC22×C113C22×D4
hypercenter#493D113
hypocenterC113#3220
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #20299202C2semidirect
2. #20299161C2semidirect
3. #20298985C2semidirect
4. #20298962C2semidirect
5. #20298953C2semidirect
6. #20298811C2semidirect
7. #20298791C2semidirect
8. #20298740C2semidirect
9. #20298730C2semidirect
10. #20298657C2semidirect
11. #493×C113C2semidirect
14. C2×#14268635C22semidirect
17. #16813614C22semidirect
25. D4×Dic113C22semidirect
27. #16813551C22semidirect
28. #16813547C22semidirect
31. #16813543C22semidirect
33. #16813533C22semidirect
35. C2×D8×C113C22semidirect
37. #127×C113C22semidirect
38. C4×C8×C113C22semidirect
129. C113#3220semidirect
133. #493D113semidirect
146. C2×D8C2×D113semidirect
149. #127C2×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
#202992022
#202991612
#202989852
#202989622
#202989532
#202988112
#202987912
#202987402
#202987302
#202986572
#493×C1132
#3220113