Finite Group Databasebeta

← #28402388

Subgroups — #28402388

Order 14464.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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#20299252C211yesmaximal, characteristic, complemented
2D4×D452C211yesmaximal, characteristic, complemented
3#20298945C211yesmaximal, characteristic, complemented
4#20298912C212yesmaximal, complemented
5#20298879C211yesmaximal, characteristic, complemented
6#20298834C212yesmaximal, complemented
7#20298794C211yesmaximal, characteristic, complemented
8#20298734C212yesmaximal, complemented
9C4×D904C211yesmaximal, characteristic, complemented
10C2×#16813544C212yesmaximal, complemented
11C8×D4×C113C211yesmaximal, characteristic, complemented
12C2×#14268646—21no—
13C22×D452C2212yes—
14C2×D4×D113—21no—
15C2×D904C2211yescharacteristic
16C2×D904C2212yescomplemented
17#16813622C2211yescharacteristic, complemented
18#16813619C2211yescharacteristic
19#16813606—22no—
20#16813602—21no—
21#16813597—21no—
22#16813596C2212yes—
23#16813596C2212yescomplemented
24#16813592—22no—
25C4×D452C2211yescharacteristic
26C4×D452C2211yescharacteristic, complemented
27C2×C4⋊Dic113C2212yescomplemented
28#16813556C2212yescomplemented
29#16813556C2211yescharacteristic, complemented
30#16813544C2211yescharacteristic
31#16813544C2212yes—
32#16813544C2212yescomplemented
33#16813544C2211yescharacteristic, complemented
34#16813544C2212yescomplemented
35#16813544C2212yescomplemented
36C22×C8×C113C2212yescomplemented
37C4×D4×C113C2211yescharacteristic
38C4⋊C8×C113C2211yescharacteristic, complemented
39C22⋊C8×C113C2212yescomplemented
40C4×C8×C113C2211yescharacteristic, complemented
41C23×D113—22no—
42#14268646—44no—
43C2×Dic226—21no—
44C2×D452—24no—
45C2×D452—22no—
46C2×D452—21no—
47C2×D452—21no—
48C2×D452—42no—
49C2×D452C2311yescharacteristic
50C2×D452C2312yes—
51C2×D452C2311yescharacteristic
52C2×C22⋊D113—22no—
53C2×C22⋊D113—22no—
54D4×D113—44no—
55C22×Dic113—22no—
56C2×C4×D113—21no—
57C2×C4×D113—21no—
58D904—22no—
59D904—42no—
60C4⋊Dic113—22no—
61C4⋊Dic113—21no—
62C4⋊Dic113C2311yescharacteristic
63C4⋊Dic113C2312yes—
64C4⋊Dic113C2311yescharacteristic
65#14268624—21no—
66#14268624—21no—
67#14268624—22no—
68#14268624—22no—
69C2×D4×C113D411yescharacteristic
70C22×C4×C113C2312yes—
71C2×C8×C113—42no—
72C2×C8×C113C2311yescharacteristic
73C2×C8×C113C2312yes—
74C2×C8×C113C2311yescharacteristic
75C4⋊C4×C113D411yescharacteristic
76C22⋊C4×C113D412yes—
77C42×C113C2311yescharacteristic
78C23×C113C2×D412yes—
79C22×D113—21no—
80C22×D113—21no—
81C22×D113—22no—
82C22×D113—44no—
83C22×D113—44no—
84C22×D113—82no—
85D4×C113D814yescomplemented
86C2×C4×C113—22no—
87C2×C4×C113—22no—
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113C2×D412yes—
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113C2411yescharacteristic
92C22⋊D113—44no—
93C22⋊D113—44no—
94C2×Dic113—21no—
95C2×Dic113—21no—
96C2×Dic113—22no—
97C2×Dic113—44no—
98D452—21no—
99D452—22no—
100D452—21no—
101D452—21no—
102D452—22no—
103D452—44no—
104D452—42no—
105D452—81no—
106D452#4112yescomplemented
107C4×D113—42no—
108C4×D113—42no—
109Dic226—42no—
110C8×C113—21no—
111C8×C113—21no—
112C8×C113—22no—
113C22×C113—22no—
114C22×C113—22no—
115C22×C113C2×D814yes—
116C22×C113C22×D411yescharacteristic
117C2×D113—22no—
118C2×D113—41no—
119C2×D113—41no—
120C2×D113—42no—
121C2×D113—41no—
122C2×D113—41no—
123C2×D113—42no—
124C2×D113—42no—
125C2×D113—41no—
126C2×D113—88no—
127C4×C113—22no—
128C4×C113—21no—
129C4×C113C2×D812yes—
130C4×C113C2×#4111yescharacteristic
131C4×C113H(5,𝔽2)11yescharacteristic
132Dic113—42no—
133Dic113—41no—
134Dic113—41no—
135C2×C113—24no—
136C2×C113#54611yescharacteristic
137C2×C113C22×D811yescharacteristic
138C2×C113#57711yescharacteristic
139D113—42no—
140D113—81no—
141D113—82no—
142#3294—1131nomaximal, Sylow
143C113#329411yescharacteristic, complemented, Sylow
144#547—1131no—
145D42—1131no—
146#486—1131no—
147#480—1132no—
148#474—1131no—
149#466—1132no—
150#459—1131no—
151#447—1132no—
152C4×D8—1131no—
153C8×D4D11311yescharacteristic, complemented
154C2×#102—1132no—
155C2×#41—2261no—
156C22×D4—1132no—
157C22×D4—2261no—
158C2×D8—1132no—
159C2×D8—1131no—
160C22×C8C2×D11312yescomplemented
161C4⋊Q8—1131no—
162#127—1131no—
163#123—2262no—
164C22⋊Q8—2261no—
165#121—1132no—
166#121—1132no—
167#121—2261no—
168#120—2262no—
169C4×D4—1131no—
170C4×D4—1131no—
171C4×D4C2×D11311yescharacteristic
172C2×C4⋊C4—1132no—
173#107—1131no—
174#107—1132no—
175C4⋊C8C2×D11311yescharacteristic, complemented
176#102—1131no—
177#102—1132no—
178#102—1132no—
179#102—1132no—
180#102—1131no—
181#102—1132no—
182C22⋊C8C2×D11312yescomplemented
183C4×C8C2×D11311yescharacteristic, complemented
184C24—2262no—
185#41—4524no—
186C2×Q8—2261no—
187C2×D4—1131no—
188C2×D4—1132no—
189C2×D4—1131no—
190C2×D4—4522no—
191C2×D4—4524no—
192C2×D4—2264no—
193C2×D4—2262no—
194C2×D4—2262no—
195C2×D4—2261no—
196C2×D4—2262no—
197C2×D4—2261no—
198C2×D4D45211yescharacteristic
199C22×C4—2262no—
200C22×C4—2261no—
201C22×C4—2261no—
202C22×C4C22×D11312yes—
203D8—4522no—
204D8—2262no—
205C2×C8—42no—
206C2×C8C22×D11311yescharacteristic
207C2×C8C22×D11311yescharacteristic
208C2×C8C22×D11312yes—
209C4⋊C4—1131no—
210C4⋊C4—1132no—
211C4⋊C4—1131no—
212C4⋊C4—2262no—
213C4⋊C4—2261no—
214C4⋊C4D45211yescharacteristic
215C22⋊C4—2261no—
216C22⋊C4—2261no—
217C22⋊C4—2262no—
218C22⋊C4—2262no—
219C22⋊C4D45212yes—
220C42C22×D11311yescharacteristic
221C23—9042no—
222C23—4524no—
223C23—4524no—
224C23—2261no—
225C23—2262no—
226C23—2261no—
227C23C2×D45212yes—
228Q8—4522no—
229D4—1132no—
230D4—9041no—
231D4—4524no—
232D4—4524no—
233D4—4524no—
234D4—4522no—
235D4—2261no—
236D4—2262no—
237D4—2261no—
238D4—2262no—
239D4—2261no—
240D4D90414yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—4524no—
244C2×C4—4522no—
245C2×C4—4522no—
246C2×C4—2261no—
247C2×C4—2261no—
248C2×C4—2262no—
249C2×C4C2×D45211yescharacteristic
250C2×C4C2×D45212yes—
251C2×C4C2×D45211yescharacteristic
252C2×C4C23×D11311yescharacteristic
253C8—21no—
254C8—21no—
255C8—22no—
256C22—22no—
257C22—22no—
258C22—9048no—
259C22—4521no—
260C22—4522no—
261C22—4522no—
262C22—4521no—
263C22—4522no—
264C22—4521no—
265C22—4521no—
266C22—4521no—
267C22—2262no—
268C22C2×D90414yes—
269C22C22×D45211yescharacteristic
270C4—21no—
271C4—22no—
272C4—4521no—
273C4—4521no—
274C4—4522no—
275C4C2×D90412yes—
276C4#41×D11311yescharacteristic
277C4#1681366711yescharacteristic
278C2—24no—
279C2—9042no—
280C2—9041no—
281C2—4522no—
282C2#2029924311yescharacteristic
283C2C22×D90411yescharacteristic
284C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC8×D4×C113C2
socleC22×C113C22×D4
hypercenterC8×D4D113
hypocenterC113#3294
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #20299252C2semidirect
2. D4×D452C2semidirect
3. #20298945C2semidirect
4. #20298912C2semidirect
5. #20298879C2semidirect
6. #20298834C2semidirect
7. #20298794C2semidirect
8. #20298734C2semidirect
9. C4×D904C2semidirect
10. C2×#16813544C2semidirect
11. C8×D4×C113C2semidirect
16. C2×D904C22semidirect
17. #16813622C22semidirect
23. #16813596C22semidirect
26. C4×D452C22semidirect
27. C2×C4⋊Dic113C22semidirect
28. #16813556C22semidirect
29. #16813556C22semidirect
32. #16813544C22semidirect
33. #16813544C22semidirect
34. #16813544C22semidirect
35. #16813544C22semidirect
36. C22×C8×C113C22semidirect
38. C4⋊C8×C113C22semidirect
39. C22⋊C8×C113C22semidirect
40. C4×C8×C113C22semidirect
85. D4×C113D8semidirect
106. D452#41semidirect
143. C113#3294semidirect
153. C8×D4D113semidirect
160. C22×C8C2×D113semidirect
175. C4⋊C8C2×D113semidirect
182. C22⋊C8C2×D113semidirect
183. C4×C8C2×D113semidirect
240. D4D904semidirect

Maximal subgroups

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

subgroupindex
#202992522
D4×D4522
#202989452
#202989122
#202988792
#202988342
#202987942
#202987342
C4×D9042
C2×#168135442
C8×D4×C1132
#3294113