Finite Group Databasebeta

← #28402269

Subgroups — #28402269

Order 14464.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×SD16×D113C212yesmaximal, complemented
2#20299263C211yesmaximal, characteristic, complemented
3#20299233C211yesmaximal, characteristic
4#20298824C212yesmaximal, complemented
5#20298800C211yesmaximal, characteristic, complemented
6#20298795C211yesmaximal, characteristic, complemented
7#20298747C212yesmaximal, complemented
8#20298735C212yesmaximal, complemented
9C4×#14268636C211yesmaximal, characteristic, complemented
10C8×D452C211yesmaximal, characteristic, complemented
11#492×C113C211yesmaximal, characteristic, complemented
12C2×Q8×D113C2212yescomplemented
13C2×D4×D113—21no—
14C2×D4×D113C2212yes—
15C2×#14268636C2211yescharacteristic
16C2×#14268635C2212yescomplemented
17C2×#14268634C2212yes—
18SD16×D113—28no—
19C2×C8×D113C2212yescomplemented
20#16813621—21no—
21#16813600—22no—
22#16813598C2212yescomplemented
23#16813593—21no—
24#16813593C2212yes—
25#16813590—22no—
26C4×Dic226C2211yescharacteristic, complemented
27C4×D452C2211yescharacteristic
28C4×D452C2211yescharacteristic
29#16813584—21no—
30#16813554C2211yescharacteristic, complemented
31C4⋊#11744751C2211yescharacteristic, complemented
32#16813547C2211yescharacteristic, complemented
33#16813546C2212yescomplemented
34#16813544C2211yescharacteristic
35#16813543C2212yescomplemented
36#16813534C2212yescomplemented
37C2×SD16×C113C2212yescomplemented
38C2×SD16×C113C2212yescomplemented
39C4⋊Q8×C113C2211yescharacteristic, complemented
40#127×C113C2211yescharacteristic
41C4×C8×C113C2211yescharacteristic, complemented
42C23×D113—22no—
43C2×Dic226—22no—
44C2×Dic226C2311yescharacteristic
45Q8×D113—24no—
46Q8×D113—42no—
47C2×D452D411yescharacteristic
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—22no—
50C2×C22⋊D113—22no—
51D4×D113—24no—
52D4×D113—42no—
53D4×D113—44no—
54C2×C4×D113—22no—
55C2×C4×D113—21no—
56C2×C4×D113C2312yes—
57#14268636D414yescomplemented
58#14268635—24no—
59#14268634—24no—
60C2×#11744751C2312yes—
61C8×D113—24no—
62C4⋊Dic113D411yescharacteristic
63C4⋊Dic113C2311yescharacteristic
64C4⋊Dic113C2311yescharacteristic
65#14268626—21no—
66#14268626—22no—
67C22⋊Dic113—22no—
68#14268624—22no—
69#14268624—21no—
70#14268624D412yes—
71C4×Dic113—21no—
72C2×Q8×C113C2312yes—
73C2×D4×C113—21no—
74C2×D4×C113—21no—
75C2×D4×C113C2312yes—
76SD16×C113—24no—
77SD16×C113—42no—
78C2×C8×C113C2311yescharacteristic
79C2×C8×C113C2311yescharacteristic
80C4⋊C4×C113—21no—
81C4⋊C4×C113—21no—
82C42×C113C2311yescharacteristic
83C23×C113—22no—
84C22×D113—21no—
85C22×D113—44no—
86C22×D113—44no—
87C22×D113—82no—
88C22×D113C2×D412yes—
89Q8×C113—22no—
90Q8×C113—22no—
91D4×C113—22no—
92D4×C113—22no—
93D4×C113—42no—
94D4×C113—81no—
95C2×C4×C113—22no—
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2411yescharacteristic
99C22⋊D113—44no—
100C22⋊D113—44no—
101C2×Dic113—21no—
102C2×Dic113—21no—
103C2×Dic113—21no—
104C2×Dic113C2×D412yes—
105D452—21no—
106D452SD1614yescomplemented
107D452C2×D412yes—
108C4×D113—22no—
109C4×D113—22no—
110C4×D113—44no—
111C4×D113—42no—
112Dic226—21no—
113Dic226—44no—
114Dic226C2×D412yescomplemented
115C8×C113—21no—
116C8×C113C2×D412yescomplemented
117#11744751—22no—
118C22×C113—42no—
119C22×C113—42no—
120C22×C113—42no—
121C22×C113C22×D411yescharacteristic
122C2×D113—22no—
123C2×D113—22no—
124C2×D113—22no—
125C2×D113—41no—
126C2×D113—41no—
127C2×D113—88no—
128C2×D113C2×SD1614yescomplemented
129C4×C113—21no—
130C4×C113—42no—
131C4×C113C2×SD1612yescomplemented
132C4×C113C22×D411yescharacteristic
133C4×C113H(5,𝔽2)11yescharacteristic
134Dic113—22no—
135Dic113—22no—
136Dic113—41no—
137Dic113—41no—
138C2×C113—82no—
139C2×C113D4211yescharacteristic
140C2×C113C22×SD1611yescharacteristic
141C2×C113#57711yescharacteristic
142D113—24no—
143D113—42no—
144D4×SD16—1131nomaximal, Sylow
145C113D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—1132no—
147D4×Q8—1131no—
148D42—1131no—
149#492D11311yescharacteristic, complemented
150#465—1132no—
151#461—1131no—
152#460—1131no—
153#450—1132no—
154#448—1132no—
155C4×SD16—1131no—
156C8×D4—1131no—
157C22×Q8—1132no—
158C22×D4—1132no—
159C22×D4—2261no—
160C2×SD16—1132no—
161C2×SD16—1132no—
162C2×SD16—1131no—
163C2×SD16—2268no—
164C2×SD16C2×D11312yescomplemented
165C2×SD16C2×D11312yescomplemented
166C22×C8—1132no—
167C4⋊Q8—2261no—
168C4⋊Q8C2×D11311yescharacteristic, complemented
169#127C2×D11311yescharacteristic
170C22⋊Q8—1132no—
171C22⋊Q8—2262no—
172#121—1132no—
173#121—2261no—
174#120—2262no—
175C4×Q8—1131no—
176C4×D4—1131no—
177C4×D4—1131no—
178C4×D4—2261no—
179#106—1131no—
180C4⋊C8—1131no—
181#103—1132no—
182#103—1131no—
183#102—1132no—
184#102—1131no—
185C22⋊C8—1132no—
186C4×C8C2×D11311yescharacteristic, complemented
187C24—2262no—
188C2×Q8—1131no—
189C2×Q8—4522no—
190C2×Q8—2262no—
191C2×Q8—2264no—
192C2×Q8C22×D11312yes—
193C2×D4—21no—
194C2×D4—21no—
195C2×D4—1131no—
196C2×D4—1131no—
197C2×D4—4524no—
198C2×D4—4522no—
199C2×D4—2262no—
200C2×D4—2264no—
201C2×D4—2262no—
202C2×D4C22×D11312yes—
203C22×C4—1132no—
204C22×C4—2262no—
205C22×C4—2261no—
206SD16—24no—
207SD16—42no—
208SD16—1134no—
209SD16—2264no—
210SD16—2264no—
211C2×C8—1132no—
212C2×C8—2264no—
213C2×C8C22×D11311yescharacteristic
214C2×C8C22×D11311yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—1131no—
218C4⋊C4—1131no—
219C4⋊C4—1131no—
220C4⋊C4—2262no—
221C4⋊C4—2261no—
222C22⋊C4—1132no—
223C22⋊C4—2262no—
224C22⋊C4—2262no—
225C22⋊C4—2261no—
226C42—2261no—
227C42C22×D11311yescharacteristic
228C23—22no—
229C23—1132no—
230C23—9042no—
231C23—4524no—
232C23—4524no—
233C23—2261no—
234Q8—22no—
235Q8—22no—
236Q8—1132no—
237Q8—4524no—
238Q8—2261no—
239D4—22no—
240D4—22no—
241D4—42no—
242D4—81no—
243D4—1134no—
244D4—1132no—
245D4—4524no—
246D4—4524no—
247D4—2261no—
248C2×C4—22no—
249C2×C4—1132no—
250C2×C4—4524no—
251C2×C4—4522no—
252C2×C4—2261no—
253C2×C4—2261no—
254C2×C4—2261no—
255C2×C4—2262no—
256C2×C4—2262no—
257C2×C4D4×D11311yescharacteristic
258C2×C4D4×D11311yescharacteristic
259C2×C4C23×D11311yescharacteristic
260C8—21no—
261C8—2262no—
262C8D4×D11312yescomplemented
263C22—42no—
264C22—42no—
265C22—42no—
266C22—1134no—
267C22—9048no—
268C22—4521no—
269C22—4521no—
270C22—2262no—
271C22—2262no—
272C22—2262no—
273C22C2×D4×D11311yescharacteristic
274C4—21no—
275C4—42no—
276C4—4521no—
277C4—4521no—
278C4—2262no—
279C4—2262no—
280C4SD16×D11312yescomplemented
281C4C2×D4×D11311yescharacteristic
282C4#1681366711yescharacteristic
283C2—82no—
284C2—4522no—
285C2—2264no—
286C2#2029923311yescharacteristic
287C2C2×SD16×D11311yescharacteristic
288C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#492×C113C2
socleC22×C113C22×D4
prime radical#20299233C2
hypercenter#492D113
hypocenterC113D4×SD16
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D113C2semidirect
2. #20299263C2semidirect
4. #20298824C2semidirect
5. #20298800C2semidirect
6. #20298795C2semidirect
7. #20298747C2semidirect
8. #20298735C2semidirect
9. C4×#14268636C2semidirect
10. C8×D452C2semidirect
11. #492×C113C2semidirect
12. C2×Q8×D113C22semidirect
16. C2×#14268635C22semidirect
19. C2×C8×D113C22semidirect
22. #16813598C22semidirect
26. C4×Dic226C22semidirect
30. #16813554C22semidirect
31. C4⋊#11744751C22semidirect
32. #16813547C22semidirect
33. #16813546C22semidirect
35. #16813543C22semidirect
36. #16813534C22semidirect
37. C2×SD16×C113C22semidirect
38. C2×SD16×C113C22semidirect
39. C4⋊Q8×C113C22semidirect
41. C4×C8×C113C22semidirect
57. #14268636D4semidirect
106. D452SD16semidirect
114. Dic226C2×D4semidirect
116. C8×C113C2×D4semidirect
128. C2×D113C2×SD16semidirect
131. C4×C113C2×SD16semidirect
145. C113D4×SD16semidirect
149. #492D113semidirect
164. C2×SD16C2×D113semidirect
165. C2×SD16C2×D113semidirect
168. C4⋊Q8C2×D113semidirect
186. C4×C8C2×D113semidirect
262. C8D4×D113semidirect
280. C4SD16×D113semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1132
#202992632
#202992332
#202988242
#202988002
#202987952
#202987472
#202987352
C4×#142686362
C8×D4522
#492×C1132
D4×SD16113