Finite Group Databasebeta

← #28401054

Subgroups — #28401054

Order 14464.

596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16813646C212yesmaximal, complemented
2C2×#16813641C211yesmaximal, characteristic, complemented
3C2×D8×D113C211yesmaximal, characteristic, complemented
4#20299161C212yesmaximal, complemented
5#20298986C212yesmaximal, complemented
6#20298985C212yesmaximal, complemented
7#20298982C211yesmaximal, characteristic, complemented
8#20298981C211yesmaximal, characteristic, complemented
9#20298973C211yesmaximal, characteristic, complemented
10#20298552C211yesmaximal, characteristic, complemented
11#493×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2212yes—
13C2×D4×D113C2212yes—
14#16813646—28no—
15#16813641—24no—
16C2×Dic452C2211yescharacteristic, complemented
17C2×#14268636C2212yescomplemented
18C2×#14268635C2212yescomplemented
19C2×#14268635C2212yescomplemented
20C2×D904C2211yescharacteristic
21C2×#14268632C2212yes—
22C2×#14268632C2212yescomplemented
23D8×D113—24no—
24C2×#14268630C2211yescharacteristic
25C2×C8×D113C2211yescharacteristic
26#16813618C2212yescomplemented
27#16813610C2212yescomplemented
28#16813609C2212yescomplemented
29#16813594—24no—
30#16813590—24no—
31#16813579C2211yescharacteristic
32#16813533C2211yescharacteristic, complemented
33#16813532C2211yescharacteristic, complemented
34C8×Dic113C2211yescharacteristic, complemented
35C2×D8×C113C2211yescharacteristic
36C2×D8×C113C2211yescharacteristic, complemented
37C2×D8×C113C2212yescomplemented
38#127×C113C2212yescomplemented
39C4×C8×C113C2211yescharacteristic, complemented
40C23×D113—22no—
41#14268646—24no—
42#14268646—24no—
43C2×Dic226C2312yes—
44C2×D452C2312yes—
45C2×C22⋊D113—22no—
46C2×C22⋊D113—22no—
47C2×C22⋊D113—24no—
48D4×D113—24no—
49D4×D113—24no—
50C22×Dic113—22no—
51C2×C4×D113C2311yescharacteristic
52Dic452—22no—
53#14268636—24no—
54#14268635—24no—
55#14268635—24no—
56D904—22no—
57#14268632—24no—
58#14268632—24no—
59#14268630D414yescomplemented
60C2×#11744751C2311yescharacteristic
61C2×#11744751C2311yescharacteristic
62C8×D113D414yescomplemented
63#14268626D412yes—
64C22⋊Dic113—24no—
65#14268624—24no—
66#14268624D412yes—
67C4×Dic113C2311yescharacteristic
68C2×D4×C113—24no—
69C2×D4×C113C2312yes—
70C2×D4×C113C2312yes—
71D8×C113—22no—
72D8×C113—22no—
73D8×C113—24no—
74C2×C8×C113C2311yescharacteristic
75C2×C8×C113C2311yescharacteristic
76C42×C113C2311yescharacteristic
77C23×C113—22no—
78C23×C113—22no—
79C22×D113—22no—
80C22×D113—44no—
81C22×D113—84no—
82C22×D113C2×D411yescharacteristic
83D4×C113—22no—
84D4×C113—22no—
85D4×C113—22no—
86D4×C113—22no—
87D4×C113—84no—
88C2×C4×C113C2×D412yes—
89C2×C4×C113C2411yescharacteristic
90C22⋊D113—44no—
91C22⋊D113—44no—
92C22⋊D113—84no—
93C2×Dic113—22no—
94C2×Dic113—44no—
95C2×Dic113C2×D412yes—
96C2×Dic113C2×D411yescharacteristic
97D452—22no—
98D452—22no—
99C4×D113C2×D412yes—
100C4×D113C2×D412yes—
101Dic226—22no—
102Dic226—22no—
103C8×C113C2×D412yes—
104C8×C113C2×D412yes—
105#11744751C2×D412yes—
106#11744751C2×D412yes—
107C22×C113—42no—
108C22×C113—42no—
109C22×C113—44no—
110C22×C113—44no—
111C22×C113C22×D411yescharacteristic
112C2×D113—22no—
113C2×D113—42no—
114C2×D113—44no—
115C2×D113—88no—
116C2×D113#12712yes—
117C4×C113—22no—
118C4×C113C22×D411yescharacteristic
119C4×C113C22×D411yescharacteristic
120Dic113—22no—
121Dic113—42no—
122Dic113#12712yes—
123C2×C113—82no—
124C2×C113—82no—
125C2×C113C2×#12711yescharacteristic
126C2×C113#57612yes—
127D113—22no—
128D113—82no—
129#3155—1131nomaximal, Sylow
130C113#315511yescharacteristic, complemented, Sylow
131C2×AGL(1,ℤ/8)—1132no—
132C2×#135—1131no—
133C22×D8—1131no—
134#535—1132no—
135#496—1132no—
136#496—1132no—
137#495—1131no—
138#495—1131no—
139#493—1131no—
140#493D11311yescharacteristic, complemented
141#405—1131no—
142C2×#41—1132no—
143C22×D4—1132no—
144AGL(1,ℤ/8)—2268no—
145#135—2264no—
146C2×Q16—1131no—
147C2×SD16—1132no—
148C2×SD16—1132no—
149C2×SD16—1132no—
150C2×D8—1132no—
151C2×D8—1132no—
152C2×D8—1131no—
153C2×D8—2264no—
154C2×D8C2×D11311yescharacteristic
155C2×D8C2×D11311yescharacteristic, complemented
156C2×D8C2×D11312yescomplemented
157C2×M16—1131no—
158C22×C8—1131no—
159#127—1132no—
160#127C2×D11312yescomplemented
161#124—1132no—
162#124—1132no—
163#121—2264no—
164#120—2264no—
165#117—1131no—
166#97—1131no—
167#97—1131no—
168C4×C8—1131no—
169C4×C8C2×D11311yescharacteristic, complemented
170C24—2262no—
171#41—2264no—
172#41—2264no—
173C2×Q8—1132no—
174C2×D4—24no—
175C2×D4—1132no—
176C2×D4—2264no—
177C2×D4—2264no—
178C2×D4—2264no—
179C2×D4—2262no—
180C2×D4—2262no—
181C2×D4C22×D11312yes—
182C2×D4C22×D11312yes—
183C22×C4—1131no—
184C22×C4—2262no—
185Q16—2262no—
186SD16—2264no—
187SD16—2264no—
188SD16—2264no—
189D8—22no—
190D8—22no—
191D8—24no—
192D8—2264no—
193D8—2264no—
194D8—2262no—
195M16—1134no—
196C2×C8—1131no—
197C2×C8—1131no—
198C2×C8—1134no—
199C2×C8C22×D11311yescharacteristic
200C2×C8C22×D11311yescharacteristic
201C4⋊C4—1132no—
202C22⋊C4—1132no—
203C22⋊C4—2264no—
204C22⋊C4—2264no—
205C42—1131no—
206C42C22×D11311yescharacteristic
207C23—22no—
208C23—22no—
209C23—1131no—
210C23—9044no—
211C23—4524no—
212C23—2262no—
213Q8—2262no—
214Q8—2262no—
215D4—22no—
216D4—22no—
217D4—22no—
218D4—22no—
219D4—84no—
220D4—9044no—
221D4—4524no—
222D4—4524no—
223D4—2262no—
224D4—2262no—
225C2×C4—1131no—
226C2×C4—1132no—
227C2×C4—1132no—
228C2×C4—1132no—
229C2×C4—4524no—
230C2×C4—2262no—
231C2×C4D4×D11312yes—
232C2×C4C23×D11311yescharacteristic
233C8—1132no—
234C8—1132no—
235C8D4×D11312yes—
236C8D4×D11312yes—
237C22—42no—
238C22—42no—
239C22—44no—
240C22—44no—
241C22—1132no—
242C22—9048no—
243C22—4522no—
244C22—4524no—
245C22—2262no—
246C22C2×D4×D11311yescharacteristic
247C4—22no—
248C4—1132no—
249C4—4522no—
250C4—2262no—
251C4C2×D4×D11311yescharacteristic
252C4C2×D4×D11311yescharacteristic
253C2—82no—
254C2—82no—
255C2—9042no—
256C2—2262no—
257C2#127×D11311yescharacteristic
258C2#2029939912yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#493×C113C2
socleC22×C113C22×D4
hypercenter#493D113
hypocenterC113#3155
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. C2×#16813646C2semidirect
2. C2×#16813641C2semidirect
3. C2×D8×D113C2semidirect
4. #20299161C2semidirect
5. #20298986C2semidirect
6. #20298985C2semidirect
7. #20298982C2semidirect
8. #20298981C2semidirect
9. #20298973C2semidirect
10. #20298552C2semidirect
11. #493×C113C2semidirect
16. C2×Dic452C22semidirect
17. C2×#14268636C22semidirect
18. C2×#14268635C22semidirect
19. C2×#14268635C22semidirect
22. C2×#14268632C22semidirect
26. #16813618C22semidirect
27. #16813610C22semidirect
28. #16813609C22semidirect
32. #16813533C22semidirect
33. #16813532C22semidirect
34. C8×Dic113C22semidirect
36. C2×D8×C113C22semidirect
37. C2×D8×C113C22semidirect
38. #127×C113C22semidirect
39. C4×C8×C113C22semidirect
59. #14268630D4semidirect
62. C8×D113D4semidirect
130. C113#3155semidirect
140. #493D113semidirect
155. C2×D8C2×D113semidirect
156. C2×D8C2×D113semidirect
160. #127C2×D113semidirect
169. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
C2×#168136412
C2×D8×D1132
#202991612
#202989862
#202989852
#202989822
#202989812
#202989732
#202985522
#493×C1132
#3155113