Finite Group Databasebeta

← #28401640

Subgroups — #28401640

Order 14464.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299167C211yesmaximal, characteristic
2#20298990C211yesmaximal, characteristic, complemented
3#20298972C211yesmaximal, characteristic, complemented
4#20298964C211yesmaximal, characteristic, complemented
5#20298955C211yesmaximal, characteristic, complemented
6#20298820C212yesmaximal, complemented
7#20298798C212yesmaximal, complemented
8#20298758C212yesmaximal, complemented
9#20298748C212yesmaximal, complemented
10#20298659C211yesmaximal, characteristic, complemented
11#541×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×D452C2211yescharacteristic
14C2×#14268637C2212yescomplemented
15C2×#14268634C2212yes—
16C2×#14268634C2212yes—
17C2×#14268634C2212yescomplemented
18#16813619C2211yescharacteristic
19#16813619C2211yescharacteristic
20#16813610C2211yescharacteristic
21#16813610C2211yescharacteristic
22#16813597—22no—
23#16813592—22no—
24C4⋊#11744751C2212yescomplemented
25#16813545C2212yescomplemented
26#16813542C2212yes—
27#16813542C2212yes—
28#16813542C2212yescomplemented
29C22⋊#11744751C2212yes—
30#16813533C2211yescharacteristic, complemented
31C4×#11744751C2211yescharacteristic, complemented
32C4⋊Q8×C113C2211yescharacteristic, complemented
33#126×C113—22no—
34#125×C113—22no—
35#125×C113C2211yescharacteristic, complemented
36C22⋊Q8×C113C2212yes—
37C4×Q8×C113C2212yescomplemented
38#117×C113C2211yescharacteristic
39C23×D113—21no—
40#14268647—42no—
41C2×Dic226C2311yescharacteristic
42C2×D452—21no—
43C2×D452—22no—
44C2×D452—22no—
45C2×D452—42no—
46C2×D452C2311yescharacteristic
47C2×D452C2311yescharacteristic
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—21no—
50C2×C4×D113—21no—
51#14268637—42no—
52#14268634—42no—
53#14268634—42no—
54#14268634—42no—
55C2×#11744751C2312yes—
56C2×#11744751C2312yes—
57#14268624—22no—
58#14268624—22no—
59C2×Q8×C113C2312yes—
60C22×C4×C113C2311yescharacteristic
61C4⋊C4×C113—22no—
62C4⋊C4×C113—22no—
63C4⋊C4×C113—22no—
64C4⋊C4×C113—22no—
65C4⋊C4×C113D412yes—
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C22⋊C4×C113D412yes—
69C42×C113—22no—
70C42×C113C2311yescharacteristic
71C42×C113C2311yescharacteristic
72C23×C113C2×D411yescharacteristic
73C22×D113—21no—
74C22×D113—21no—
75C22×D113—21no—
76C22×D113—42no—
77C22×D113—82no—
78Q8×C113—22no—
79Q8×C113—22no—
80C2×C4×C113—22no—
81C2×C4×C113—22no—
82C2×C4×C113—22no—
83C2×C4×C113C2×D412yes—
84C2×C4×C113C2×D412yes—
85C2×C4×C113C2×D411yescharacteristic
86C2×C4×C113C2411yescharacteristic
87C22⋊D113—42no—
88C2×Dic113—21no—
89D452—22no—
90D452—22no—
91D452—22no—
92D452—42no—
93D452—82no—
94D452—82no—
95C4×D113—42no—
96Dic226—22no—
97#11744751—22no—
98#11744751—22no—
99C22×C113—21no—
100C22×C113—22no—
101C22×C113C22×D411yescharacteristic
102C2×D113—41no—
103C2×D113—41no—
104C2×D113—41no—
105C2×D113—42no—
106C2×D113—42no—
107C2×D113—42no—
108C2×D113—84no—
109C4×C113—21no—
110C4×C113—22no—
111C4×C113—22no—
112C4×C113—42no—
113C4×C113—42no—
114C4×C113H(5,𝔽2)12yes—
115Dic113—41no—
116C2×C113—41no—
117C2×C113#53511yescharacteristic
118C2×C113#57712yes—
119D113—81no—
120D113—81no—
121D113—81no—
122#3222—1131nomaximal, Sylow
123C113#322211yescharacteristic, complemented, Sylow
124#541D11311yescharacteristic, complemented
125#535—1131no—
126#497—1131no—
127#492—1131no—
128#490—1131no—
129#488—1131no—
130#464—1132no—
131#460—1132no—
132#452—1132no—
133#450—1132no—
134#433—1131no—
135C2×#41—1131no—
136C22×D4—1131no—
137C2×Q16—1132no—
138C2×SD16—1132no—
139C2×SD16—1132no—
140C2×SD16—1132no—
141C4⋊Q8C2×D11311yescharacteristic, complemented
142#127—1131no—
143#127—1131no—
144#126—22no—
145#125—22no—
146#125C2×D11311yescharacteristic, complemented
147#124—1131no—
148#124—1131no—
149C22⋊Q8C2×D11312yes—
150#121—2262no—
151#120—2262no—
152C4×Q8C2×D11312yescomplemented
153#117C2×D11311yescharacteristic
154C4⋊C8—1132no—
155#103—1132no—
156#102—1132no—
157#102—1132no—
158#102—1132no—
159C22⋊C8—1132no—
160#97—1131no—
161C4×C8—1131no—
162C24—2261no—
163#41—4522no—
164C2×Q8—1131no—
165C2×Q8C22×D11312yes—
166C2×D4—1131no—
167C2×D4—1131no—
168C2×D4—1131no—
169C2×D4—4522no—
170C2×D4—2261no—
171C2×D4—2262no—
172C2×D4—2262no—
173C2×D4—2261no—
174C22×C4—2261no—
175C22×C4C22×D11311yescharacteristic
176Q16—4522no—
177SD16—4522no—
178SD16—4522no—
179SD16—4522no—
180C2×C8—1132no—
181C2×C8—1132no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4C22⋊D11312yes—
187C4⋊C4C22×D11312yes—
188C22⋊C4—22no—
189C22⋊C4—2262no—
190C22⋊C4—2262no—
191C22⋊C4C22⋊D11312yes—
192C42—22no—
193C42C22×D11311yescharacteristic
194C42C22×D11311yescharacteristic
195C23—9042no—
196C23—4522no—
197C23—2261no—
198C23—2261no—
199C23—2261no—
200C23C2×C22⋊D11311yescharacteristic
201Q8—22no—
202Q8—22no—
203Q8—2262no—
204D4—9042no—
205D4—9042no—
206D4—4522no—
207D4—4522no—
208D4—2262no—
209D4—2262no—
210D4—2262no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—4522no—
215C2×C4—2261no—
216C2×C4C2×C22⋊D11312yes—
217C2×C4C2×C22⋊D11312yes—
218C2×C4C2×C22⋊D11311yescharacteristic
219C2×C4C23×D11311yescharacteristic
220C8—2262no—
221C8—2262no—
222C22—22no—
223C22—21no—
224C22—9044no—
225C22—4522no—
226C22—4522no—
227C22—4522no—
228C22—4521no—
229C22—4521no—
230C22—4521no—
231C22C22×C22⋊D11311yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—42no—
236C4—42no—
237C4—4521no—
238C4#1681366812yes—
239C2—41no—
240C2—9041no—
241C2—9041no—
242C2—9041no—
243C2#2029916211yescharacteristic
244C2#2029940612yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#541×C113C2
socleC22×C113C22×D4
prime radical#20299167C2
hypercenter#541D113
hypocenterC113#3222
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #20298990C2semidirect
3. #20298972C2semidirect
4. #20298964C2semidirect
5. #20298955C2semidirect
6. #20298820C2semidirect
7. #20298798C2semidirect
8. #20298758C2semidirect
9. #20298748C2semidirect
10. #20298659C2semidirect
11. #541×C113C2semidirect
14. C2×#14268637C22semidirect
17. C2×#14268634C22semidirect
24. C4⋊#11744751C22semidirect
25. #16813545C22semidirect
28. #16813542C22semidirect
30. #16813533C22semidirect
31. C4×#11744751C22semidirect
32. C4⋊Q8×C113C22semidirect
35. #125×C113C22semidirect
37. C4×Q8×C113C22semidirect
123. C113#3222semidirect
124. #541D113semidirect
141. C4⋊Q8C2×D113semidirect
146. #125C2×D113semidirect
152. C4×Q8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991672
#202989902
#202989722
#202989642
#202989552
#202988202
#202987982
#202987582
#202987482
#202986592
#541×C1132
#3222113