Finite Group Databasebeta

← #28402389

Subgroups — #28402389

Order 14464.

494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299253C211yesmaximal, characteristic, complemented
2D4×D452C211yesmaximal, characteristic, complemented
3#20298945C211yesmaximal, characteristic, complemented
4#20298913C212yesmaximal, complemented
5#20298878C211yesmaximal, characteristic, complemented
6#20298833C212yesmaximal, complemented
7#20298793C211yesmaximal, characteristic, complemented
8#20298730C212yesmaximal, complemented
9C8×D452C211yesmaximal, characteristic, complemented
10#102×D113C212yesmaximal, complemented
11C4×D8×C113C211yesmaximal, characteristic, complemented
12C2×#14268647—21no—
13C22×D452—21no—
14C2×D4×D113C2212yes—
15C2×#14268632C2212yescomplemented
16C2×C8×D113C2212yescomplemented
17#16813622C2211yescharacteristic, complemented
18#16813619C2211yescharacteristic
19#16813604—22no—
20#16813601—21no—
21#16813597C2212yes—
22#16813596—21no—
23#16813593C2212yescomplemented
24#16813592—22no—
25C4×D452C2211yescharacteristic
26C4⋊C4×D113C2212yescomplemented
27#16813555C2212yescomplemented
28C4⋊#11744751C2211yescharacteristic, complemented
29#16813544C2212yescomplemented
30#16813544C2212yescomplemented
31#16813543C2212yes—
32#16813542C2212yescomplemented
33#16813534C2212yescomplemented
34C2×D8×C113C2211yescharacteristic
35C4×D4×C113C2211yescharacteristic
36C4×D4×C113C2211yescharacteristic, complemented
37#107×C113C2211yescharacteristic, complemented
38#102×C113C2211yescharacteristic
39#102×C113C2211yescharacteristic, complemented
40C4×C8×C113C2211yescharacteristic, complemented
41C23×D113—22no—
42#14268647—44no—
43C2×Dic226—21no—
44C2×D452—22no—
45C2×D452—21no—
46C2×D452—21no—
47C2×D452—44no—
48C2×D452D411yescharacteristic
49C2×D452C2312yes—
50C2×C22⋊D113—22no—
51C2×C22⋊D113—22no—
52D4×D113—24no—
53D4×D113—42no—
54C2×C4×D113—22no—
55C2×C4×D113C2312yes—
56#14268632—42no—
57C2×#11744751C2312yes—
58C8×D113—42no—
59C4⋊Dic113—21no—
60C4⋊Dic113D411yescharacteristic
61C4⋊Dic113C2312yes—
62#14268626—22no—
63C22⋊Dic113—22no—
64#14268624—22no—
65#14268624D412yes—
66C2×D4×C113C2311yescharacteristic
67C2×D4×C113C2311yescharacteristic
68C22×C4×C113—21no—
69C22×C4×C113—21no—
70D8×C113—22no—
71C2×C8×C113C2311yescharacteristic
72C2×C8×C113C2311yescharacteristic
73C4⋊C4×C113C2311yescharacteristic
74C4⋊C4×C113C2311yescharacteristic
75C22⋊C4×C113—21no—
76C22⋊C4×C113—21no—
77C42×C113C2311yescharacteristic
78C23×C113—21no—
79C23×C113—21no—
80C22×D113—22no—
81C22×D113—44no—
82C22×D113—44no—
83C22×D113—82no—
84C22×D113C2×D412yes—
85D4×C113—21no—
86D4×C113—21no—
87D4×C113—21no—
88D4×C113#4112yescomplemented
89C2×C4×C113—21no—
90C2×C4×C113—21no—
91C2×C4×C113—42no—
92C2×C4×C113—42no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2411yescharacteristic
96C22⋊D113—44no—
97C22⋊D113—44no—
98C2×Dic113—22no—
99C2×Dic113C2×D412yes—
100D452—22no—
101D452—22no—
102D452—44no—
103D452—42no—
104D452—81no—
105D452D814yescomplemented
106C4×D113—22no—
107C4×D113—22no—
108C4×D113—44no—
109Dic226—42no—
110C8×C113—21no—
111C8×C113—21no—
112#11744751—22no—
113C22×C113—22no—
114C22×C113—41no—
115C22×C113—41no—
116C22×C113—41no—
117C22×C113—41no—
118C22×C113—41no—
119C22×C113C22×D411yescharacteristic
120C2×D113—22no—
121C2×D113—22no—
122C2×D113—42no—
123C2×D113—42no—
124C2×D113—42no—
125C2×D113—88no—
126C2×D113C2×D814yes—
127C4×C113—21no—
128C4×C113—41no—
129C4×C113—41no—
130C4×C113C2×D812yes—
131C4×C113C2×#4111yescharacteristic
132C4×C113H(5,𝔽2)11yescharacteristic
133Dic113—22no—
134Dic113—42no—
135C2×C113—42no—
136C2×C113—81no—
137C2×C113#54611yescharacteristic
138C2×C113C22×D811yescharacteristic
139C2×C113#57711yescharacteristic
140D113—24no—
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×D8D11311yescharacteristic, complemented
153C8×D4—1131no—
154C2×#102—1132no—
155C2×#41—2261no—
156C22×D4—1132no—
157C22×D4—2261no—
158C2×D8—1132no—
159C2×D8C2×D11311yescharacteristic
160C22×C8—1132no—
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×D4C2×D11311yescharacteristic
171C4×D4C2×D11311yescharacteristic, complemented
172C2×C4⋊C4—1132no—
173#107—1132no—
174#107C2×D11311yescharacteristic, complemented
175C4⋊C8—1131no—
176#102—1132no—
177#102—1132no—
178#102—1132no—
179#102—1132no—
180#102C2×D11311yescharacteristic
181#102C2×D11311yescharacteristic, complemented
182C22⋊C8—1132no—
183C4×C8C2×D11311yescharacteristic, complemented
184C24—2262no—
185#41—4524no—
186C2×Q8—2261no—
187C2×D4—1131no—
188C2×D4—1132no—
189C2×D4—4524no—
190C2×D4—4522no—
191C2×D4—2262no—
192C2×D4—2262no—
193C2×D4—2262no—
194C2×D4—2264no—
195C2×D4—2261no—
196C2×D4—2261no—
197C2×D4C22×D11311yescharacteristic
198C2×D4C22×D11311yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—1132no—
202C22×C4—2262no—
203D8—22no—
204D8—4522no—
205C2×C8—1132no—
206C2×C8—4522no—
207C2×C8C22×D11311yescharacteristic
208C2×C8C22×D11311yescharacteristic
209C4⋊C4—1131no—
210C4⋊C4—1132no—
211C4⋊C4—2262no—
212C4⋊C4—2261no—
213C4⋊C4C22×D11311yescharacteristic
214C4⋊C4C22×D11311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—1132no—
218C22⋊C4—2262no—
219C22⋊C4—2262no—
220C42C22×D11311yescharacteristic
221C23—21no—
222C23—21no—
223C23—1132no—
224C23—9042no—
225C23—4524no—
226C23—4524no—
227C23—2262no—
228Q8—4522no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—1134no—
233D4—9041no—
234D4—4524no—
235D4—4524no—
236D4—4524no—
237D4—4522no—
238D4—2262no—
239D4—2262no—
240D4#1426864712yescomplemented
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—1132no—
246C2×C4—4524no—
247C2×C4—2262no—
248C2×C4—2262no—
249C2×C4—2262no—
250C2×C4D4×D11311yescharacteristic
251C2×C4D4×D11311yescharacteristic
252C2×C4C23×D11311yescharacteristic
253C8—21no—
254C8—21no—
255C8—2262no—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—1134no—
263C22—9048no—
264C22—4522no—
265C22—4522no—
266C22—4522no—
267C22—2262no—
268C22—2262no—
269C22C2×D4×D11311yescharacteristic
270C4—21no—
271C4—41no—
272C4—41no—
273C4—4522no—
274C4—2262no—
275C4D8×D11312yes—
276C4C2×#1426864711yescharacteristic
277C4#1681366811yescharacteristic
278C2—42no—
279C2—81no—
280C2—9042no—
281C2—2264no—
282C2#2029924411yescharacteristic
283C2C2×D8×D11311yescharacteristic
284C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×D8×C113C2
socleC22×C113C22×D4
hypercenterC4×D8D113
hypocenterC113#3294
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20299253C2semidirect
2. D4×D452C2semidirect
3. #20298945C2semidirect
4. #20298913C2semidirect
5. #20298878C2semidirect
6. #20298833C2semidirect
7. #20298793C2semidirect
8. #20298730C2semidirect
9. C8×D452C2semidirect
10. #102×D113C2semidirect
11. C4×D8×C113C2semidirect
15. C2×#14268632C22semidirect
16. C2×C8×D113C22semidirect
17. #16813622C22semidirect
23. #16813593C22semidirect
26. C4⋊C4×D113C22semidirect
27. #16813555C22semidirect
28. C4⋊#11744751C22semidirect
29. #16813544C22semidirect
30. #16813544C22semidirect
32. #16813542C22semidirect
33. #16813534C22semidirect
36. C4×D4×C113C22semidirect
37. #107×C113C22semidirect
39. #102×C113C22semidirect
40. C4×C8×C113C22semidirect
88. D4×C113#41semidirect
105. D452D8semidirect
143. C113#3294semidirect
152. C4×D8D113semidirect
171. C4×D4C2×D113semidirect
174. #107C2×D113semidirect
181. #102C2×D113semidirect
183. C4×C8C2×D113semidirect
240. D4#14268647semidirect

Maximal subgroups

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

subgroupindex
#202992532
D4×D4522
#202989452
#202989132
#202988782
#202988332
#202987932
#202987302
C8×D4522
#102×D1132
C4×D8×C1132
#3294113