Finite Group Databasebeta

← #28401166

Subgroups — #28401166

Order 14464.

408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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#20299146C211yesmaximal, characteristic, complemented
2#20299127C211yesmaximal, characteristic, complemented
3#20299007C211yesmaximal, characteristic, complemented
4#20298962C211yesmaximal, characteristic, complemented
5#20298957C211yesmaximal, characteristic, complemented
6#20298848C212yesmaximal, complemented
7#20298841C212yesmaximal, complemented
8SD16×Dic113C212yesmaximal, complemented
9D8×Dic113C212yesmaximal, complemented
10#20298550C211yesmaximal, characteristic, complemented
11#496×C113C211yesmaximal, characteristic, complemented
12C2×#14268646—21no—
13C2×#14268630C2212yes—
14#16813622C2211yescharacteristic
15#16813615—21no—
16#16813614C2211yescharacteristic
17#16813609—21no—
18#16813604—21no—
19#16813598C2211yescharacteristic
20#16813593—21no—
21#16813593C2212yes—
22#16813593C2211yescharacteristic
23Q8×Dic113C2211yescharacteristic
24D4×Dic113—21no—
25D4×Dic113C2211yescharacteristic
26D4×Dic113C2212yes—
27#16813582—21no—
28#16813578—21no—
29C42×D113C2211yescharacteristic
30#16813556C2212yes—
31#16813554C2212yes—
32#16813546C2212yes—
33#16813543C2212yes—
34#16813543C2212yes—
35#16813543C2212yes—
36#16813533C2211yescharacteristic
37C8×Dic113C2212yes—
38C2×SD16×C113C2212yes—
39C2×D8×C113C2212yes—
40#127×C113C2211yescharacteristic
41#124×C113C2211yescharacteristic
42#97×C113C2211yescharacteristic
43#14268646—44no—
44C2×Dic226—21no—
45C2×C22⋊D113—21no—
46C2×C22⋊D113—22no—
47C22×Dic113—21no—
48C22×Dic113—22no—
49C2×C4×D113D411yescharacteristic
50C2×C4×D113D411yescharacteristic
51C2×C4×D113C2311yescharacteristic
52#14268630—24no—
53C2×#11744751C2312yes—
54C4⋊Dic113—21no—
55C4⋊Dic113—21no—
56C4⋊Dic113C2312yes—
57C4⋊Dic113C2311yescharacteristic
58C4⋊Dic113C2311yescharacteristic
59#14268626—21no—
60#14268626—21no—
61#14268626—21no—
62C22⋊Dic113—21no—
63C22⋊Dic113—22no—
64C22⋊Dic113—22no—
65C22⋊Dic113—21no—
66#14268624—21no—
67C4×Dic113—21no—
68C4×Dic113D411yescharacteristic
69C4×Dic113D411yescharacteristic
70C4×Dic113C2311yescharacteristic
71C2×Q8×C113C2311yescharacteristic
72C2×D4×C113—21no—
73C2×D4×C113—21no—
74C2×D4×C113C2311yescharacteristic
75C2×D4×C113C2312yes—
76SD16×C113—24no—
77D8×C113—24no—
78C2×C8×C113C2312yes—
79C22⋊C4×C113—21no—
80C22⋊C4×C113—21no—
81C42×C113C2311yescharacteristic
82C23×C113—21no—
83C23×C113—22no—
84C22×D113C2×D411yescharacteristic
85Q8×C113—22no—
86D4×C113—22no—
87D4×C113—22no—
88D4×C113—22no—
89D4×C113—42no—
90D4×C113—42no—
91C2×C4×C113—21no—
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2411yescharacteristic
95C22⋊D113—42no—
96C22⋊D113—44no—
97C2×Dic113—21no—
98C2×Dic113—21no—
99C2×Dic113—22no—
100C2×Dic113—42no—
101C2×Dic113—44no—
102C2×Dic113C2×D411yescharacteristic
103C2×Dic113C2×D411yescharacteristic
104C2×Dic113C2×D411yescharacteristic
105C4×D113—22no—
106C4×D113—22no—
107C4×D113—41no—
108Dic226—42no—
109C8×C113#4114yescomplemented
110#11744751—22no—
111C22×C113—41no—
112C22×C113—42no—
113C22×C113—42no—
114C22×C113—41no—
115C22×C113—41no—
116C22×C113—42no—
117C22×C113C22×D411yescharacteristic
118C2×D113—21no—
119C2×D113—21no—
120C2×D113—21no—
121C4×C113—21no—
122C4×C113—21no—
123C4×C113—41no—
124C4×C113C2×#4112yes—
125Dic113—21no—
126Dic113—21no—
127Dic113—42no—
128Dic113—41no—
129Dic113—41no—
130Dic113AGL(1,ℤ/8)12yes—
131C2×C113—82no—
132C2×C113—81no—
133C2×C113#53211yescharacteristic
134C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
135C2×C113#57511yescharacteristic
136D113—41no—
137#3171—1131nomaximal, Sylow
138C113#317111yescharacteristic, complemented, Sylow
139#532—1131no—
140#529—1131no—
141#501—1131no—
142#496D11311yescharacteristic, complemented
143#490—1131no—
144#489—1131no—
145#469—1132no—
146#468—1132no—
147C4×SD16—1132no—
148C4×D8—1132no—
149C4×M16—1131no—
150C2×#41—2261no—
151C2×SD16C2×D11312yes—
152C2×D8C2×D11312yes—
153C2×M16—1132no—
154C4⋊Q8—1131no—
155#127C2×D11311yescharacteristic
156#126—2261no—
157#125—1131no—
158#124—2261no—
159#124C2×D11311yescharacteristic
160#123—2261no—
161C22⋊Q8—1131no—
162#121—1131no—
163#121—1132no—
164#121—2261no—
165C4×Q8—1131no—
166C4×D4—1131no—
167C4×D4—1132no—
168C4×D4—2261no—
169C4×D4—2261no—
170#117—2261no—
171C2×C42—1131no—
172#107—1132no—
173#106—1132no—
174#103—1132no—
175#102—1132no—
176#102—1132no—
177#102—1132no—
178#97—1131no—
179#97C2×D11311yescharacteristic
180C4×C8—1132no—
181#41—4524no—
182C2×Q8—2261no—
183C2×Q8C22×D11311yescharacteristic
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—2261no—
187C2×D4—2262no—
188C2×D4C22×D11311yescharacteristic
189C2×D4C22×D11312yes—
190C22×C4—1131no—
191C22×C4—1131no—
192C22×C4—1131no—
193C22×C4—2261no—
194C22×C4—2262no—
195SD16—24no—
196D8—24no—
197M16—2264no—
198C2×C8—1132no—
199C2×C8C22×D11312yes—
200C4⋊C4—1131no—
201C4⋊C4—1131no—
202C4⋊C4—1132no—
203C4⋊C4—2261no—
204C4⋊C4—2261no—
205C4⋊C4—2261no—
206C4⋊C4—2261no—
207C4⋊C4—2261no—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—2261no—
211C22⋊C4—2261no—
212C22⋊C4—2262no—
213C22⋊C4—2261no—
214C22⋊C4—2262no—
215C42—1131no—
216C42—1131no—
217C42—1131no—
218C42—2261no—
219C42C22×D11311yescharacteristic
220C23—21no—
221C23—22no—
222C23—1131no—
223Q8—22no—
224Q8—4522no—
225D4—22no—
226D4—22no—
227D4—22no—
228D4—42no—
229D4—42no—
230D4—4524no—
231D4—4522no—
232C2×C4—21no—
233C2×C4—1131no—
234C2×C4—1131no—
235C2×C4—1131no—
236C2×C4—4521no—
237C2×C4—4524no—
238C2×C4—4522no—
239C2×C4—2262no—
240C2×C4—2261no—
241C2×C4—2261no—
242C2×C4—2262no—
243C2×C4—2262no—
244C2×C4D4×D11311yescharacteristic
245C2×C4D4×D11311yescharacteristic
246C2×C4C23×D11311yescharacteristic
247C8—2262no—
248C8#1426864614yescomplemented
249C22—42no—
250C22—41no—
251C22—42no—
252C22—41no—
253C22—41no—
254C22—42no—
255C22—2261no—
256C22—2261no—
257C22—2261no—
258C22C2×D4×D11311yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—1132no—
263C4—4522no—
264C4—4521no—
265C4—4521no—
266C4—2261no—
267C4—2261no—
268C4C2×#1426864612yes—
269C2—82no—
270C2—81no—
271C2—4521no—
272C2#2029914611yescharacteristic
273C2AGL(1,ℤ/8)×D11311yescharacteristic
274C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#496×C113C2
socleC22×C113C22×D4
hypercenter#496D113
hypocenterC113#3171
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #20299146C2semidirect
2. #20299127C2semidirect
3. #20299007C2semidirect
4. #20298962C2semidirect
5. #20298957C2semidirect
6. #20298848C2semidirect
7. #20298841C2semidirect
8. SD16×Dic113C2semidirect
9. D8×Dic113C2semidirect
10. #20298550C2semidirect
11. #496×C113C2semidirect
109. C8×C113#41semidirect
138. C113#3171semidirect
142. #496D113semidirect
248. C8#14268646semidirect

Maximal subgroups

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

subgroupindex
#202991462
#202991272
#202990072
#202989622
#202989572
#202988482
#202988412
SD16×Dic1132
D8×Dic1132
#202985502
#496×C1132
#3171113