Finite Group Databasebeta

← #497×D113 #28401010

Subgroups — #497×D113 #28401010

Order 14464.

564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×Q16×D113C212yesmaximal, complemented
2C2×SD16×D113C212yesmaximal
3C4⋊Q8×D113C211yesmaximal, characteristic, complemented
4#124×D113C211yesmaximal, characteristic
5#20298993C211yesmaximal, characteristic, complemented
6#20298992C211yesmaximal, characteristic, complemented
7#20298991C212yesmaximal, complemented
8#20298990C211yesmaximal, characteristic, complemented
9#20298989C212yesmaximal, complemented
10#97×D113C211yesmaximal, characteristic, complemented
11#497×C113C211yesmaximal, characteristic, complemented
12C2×Q8×D113C2211yescharacteristic
13C2×Q8×D113C2212yes—
14C2×D4×D113C2211yescharacteristic
15C2×Dic452C2212yescomplemented
16C2×#14268637C2212yescomplemented
17C2×#14268637C2212yescomplemented
18Q16×D113—28no—
19C2×#14268636C2212yes—
20C2×#14268635C2212yes—
21C2×#14268634C2212yes—
22SD16×D113—28no—
23C2×C8×D113C2212yes—
24#16813622C2211yescharacteristic, complemented
25#16813621—22no—
26#16813620C2212yescomplemented
27#16813611C2211yescharacteristic
28#16813610C2211yescharacteristic
29#16813609C2211yescharacteristic
30#16813608—22no—
31C4⋊C4×D113—22no—
32C22⋊C4×D113—22no—
33C42×D113C2211yescharacteristic
34#16813533C2211yescharacteristic, complemented
35#16813532C2212yescomplemented
36C2×Q16×C113C2212yescomplemented
37C2×SD16×C113C2212yes—
38C4⋊Q8×C113C2211yescharacteristic, complemented
39#124×C113C2211yescharacteristic
40#97×C113C2211yescharacteristic, complemented
41C23×D113—21no—
42C2×Dic226—21no—
43C2×Dic226—22no—
44C2×Dic226C2311yescharacteristic
45C2×Dic226C2312yes—
46Q8×D113—24no—
47Q8×D113—24no—
48Q8×D113—24no—
49C2×D452C2311yescharacteristic
50C2×C22⋊D113—21no—
51D4×D113—24no—
52C2×C4×D113—21no—
53C2×C4×D113—22no—
54C2×C4×D113D412yes—
55C2×C4×D113C2311yescharacteristic
56Dic452—24no—
57#14268637—24no—
58#14268637—24no—
59#14268636—24no—
60#14268635—24no—
61#14268634—24no—
62C2×#11744751C2312yes—
63C8×D113D418yes—
64C4⋊Dic113—22no—
65#14268626—24no—
66C22⋊Dic113—22no—
67#14268624—22no—
68#14268624—22no—
69C4×Dic113D412yes—
70C4×Dic113C2311yescharacteristic
71C2×Q8×C113C2311yescharacteristic
72C2×Q8×C113C2312yes—
73C2×D4×C113C2311yescharacteristic
74Q16×C113—24no—
75SD16×C113—24no—
76C2×C8×C113C2312yes—
77C4⋊C4×C113—22no—
78C22⋊C4×C113—22no—
79C42×C113C2311yescharacteristic
80C23×C113—21no—
81C22×D113—21no—
82C22×D113—42no—
83C22×D113—44no—
84C22×D113C2×D411yescharacteristic
85Q8×C113—22no—
86Q8×C113—22no—
87Q8×C113—22no—
88D4×C113—22no—
89C2×C4×C113—21no—
90C2×C4×C113—22no—
91C2×C4×C113C2×D412yes—
92C2×C4×C113C2411yescharacteristic
93C22⋊D113—42no—
94C2×Dic113—21no—
95C2×Dic113—22no—
96C2×Dic113C2×D412yes—
97C2×Dic113C2×D411yescharacteristic
98D452—22no—
99C4×D113—24no—
100C4×D113—42no—
101C4×D113—44no—
102C4×D113C2×D414yes—
103Dic226—22no—
104Dic226—22no—
105Dic226—22no—
106Dic226—44no—
107Dic226—42no—
108C8×C113C2×D414yes—
109#11744751C2×D414yes—
110C22×C113—41no—
111C22×C113—42no—
112C22×C113C22×D411yescharacteristic
113C2×D113—41no—
114C2×D113—42no—
115C2×D113—84no—
116C2×D113#12712yes—
117C2×D113#13714yes—
118C4×C113—22no—
119C4×C113—41no—
120C4×C113—42no—
121C4×C113C22×D412yes—
122Dic113—22no—
123Dic113—42no—
124Dic113—41no—
125Dic113#12712yes—
126C2×C113—81no—
127C2×C113C2×#12711yescharacteristic
128C2×C113C2×#13712yes—
129D113—81no—
130D113#49714yesdirect product factor
131C2×#497—1131nomaximal, Sylow
132C113C2×#49711yescharacteristic, complemented, Sylow
133C22×Q16—1132no—
134C22×SD16—1132no—
135C2×C4⋊Q8—1131no—
136C2×#124—1131no—
137#497—1132no—
138#497—1132no—
139#497—1131no—
140#497—1131no—
141#497—1131no—
142#497D11311yescharacteristic, direct product factor
143C2×#97—1131no—
144C22×Q8—1131no—
145C22×Q8—1132no—
146C22×D4—1131no—
147C2×Q16—1132no—
148C2×Q16—1132no—
149C2×Q16—1132no—
150C2×Q16—2268no—
151C2×Q16C2×D11312yescomplemented
152C2×SD16—1132no—
153C2×SD16—1132no—
154C2×SD16—1132no—
155C2×SD16—2268no—
156C2×SD16C2×D11312yes—
157C22×C8—1132no—
158C4⋊Q8—1132no—
159C4⋊Q8—1131no—
160C4⋊Q8—2262no—
161C4⋊Q8C2×D11311yescharacteristic, complemented
162#124—1131no—
163#124—1131no—
164#124—1131no—
165#124—2262no—
166#124C2×D11311yescharacteristic
167C2×C4⋊C4—2262no—
168C2×C22⋊C4—2262no—
169C2×C42—1131no—
170#97—1132no—
171#97—1131no—
172#97C2×D11311yescharacteristic, complemented
173C24—2261no—
174C2×Q8—1131no—
175C2×Q8—1132no—
176C2×Q8—2261no—
177C2×Q8—2262no—
178C2×Q8—2264no—
179C2×Q8—2264no—
180C2×Q8—2264no—
181C2×Q8C22×D11311yescharacteristic
182C2×Q8C22×D11312yes—
183C2×D4—1131no—
184C2×D4—2264no—
185C2×D4—2261no—
186C2×D4C22×D11311yescharacteristic
187C22×C4—1131no—
188C22×C4—1132no—
189C22×C4—2261no—
190C22×C4—2262no—
191Q16—24no—
192Q16—2264no—
193Q16—2264no—
194Q16—2264no—
195SD16—24no—
196SD16—2264no—
197SD16—2264no—
198SD16—2264no—
199C2×C8—1132no—
200C2×C8—1138no—
201C2×C8C22×D11312yes—
202C4⋊C4—22no—
203C4⋊C4—2264no—
204C4⋊C4—2262no—
205C22⋊C4—22no—
206C22⋊C4—2262no—
207C22⋊C4—2262no—
208C22⋊C4—2262no—
209C42—1132no—
210C42—1131no—
211C42C22×D11311yescharacteristic
212C23—21no—
213C23—1131no—
214C23—4522no—
215C23—4524no—
216C23—2261no—
217Q8—22no—
218Q8—22no—
219Q8—22no—
220Q8—4522no—
221Q8—4524no—
222Q8—2262no—
223Q8—2262no—
224Q8—2262no—
225D4—22no—
226D4—4522no—
227D4—2262no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—1131no—
231C2×C4—1134no—
232C2×C4—1132no—
233C2×C4—4522no—
234C2×C4—4524no—
235C2×C4—2264no—
236C2×C4—2261no—
237C2×C4—2262no—
238C2×C4D4×D11312yes—
239C2×C4C23×D11311yescharacteristic
240C8—1134no—
241C8D4×D11314yes—
242C22—42no—
243C22—41no—
244C22—1134no—
245C22—1132no—
246C22—9044no—
247C22—4522no—
248C22—4521no—
249C22C2×D4×D11311yescharacteristic
250C4—22no—
251C4—41no—
252C4—42no—
253C4—1132no—
254C4—4521no—
255C4—4522no—
256C4—2262no—
257C4C2×D4×D11312yes—
258C2—81no—
259C2—1134no—
260C2—9041no—
261C2#127×D11311yescharacteristic
262C2#137×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#497×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#497D113
hypocenterC113C2×#497
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D113C2semidirect
3. C4⋊Q8×D113C2semidirect
5. #20298993C2semidirect
6. #20298992C2semidirect
7. #20298991C2semidirect
8. #20298990C2semidirect
9. #20298989C2semidirect
10. #97×D113C2semidirect
11. #497×C113C2semidirect
15. C2×Dic452C22semidirect
16. C2×#14268637C22semidirect
17. C2×#14268637C22semidirect
24. #16813622C22semidirect
26. #16813620C22semidirect
34. #16813533C22semidirect
35. #16813532C22semidirect
36. C2×Q16×C113C22semidirect
38. C4⋊Q8×C113C22semidirect
40. #97×C113C22semidirect
130. D113#497direct (N × H)
132. C113C2×#497semidirect
142. #497D113direct (N × H)
151. C2×Q16C2×D113semidirect
161. C4⋊Q8C2×D113semidirect
172. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D1132
C2×SD16×D1132
C4⋊Q8×D1132
#124×D1132
#202989932
#202989922
#202989912
#202989902
#202989892
#97×D1132
#497×C1132
C2×#497113