Finite Group Databasebeta

← #489×D113 #28400900

Subgroups — #489×D113 #28400900

Order 14464.

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

normal subgroups only

This group has 436 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
1C4⋊Q8×D113C211yesmaximal, characteristic, complemented
2#124×D113C211yesmaximal, characteristic
3#20298960C211yesmaximal, characteristic, complemented
4#20298959C212yesmaximal, complemented
5#20298958C211yesmaximal, characteristic, complemented
6#20298957C211yesmaximal, characteristic, complemented
7#20298956C212yesmaximal, complemented
8#103×D113C212yesmaximal, complemented
9#102×D113C212yesmaximal
10#97×D113C211yesmaximal, characteristic, complemented
11#489×C113C211yesmaximal, characteristic, complemented
12C2×Q8×D113—21no—
13C2×Q8×D113C2211yescharacteristic
14C2×D4×D113C2211yescharacteristic
15C2×C8×D113C2212yes—
16#16813622C2211yescharacteristic, complemented
17#16813621—21no—
18#16813621C2212yescomplemented
19#16813620—21no—
20#16813611C2211yescharacteristic
21#16813610C2211yescharacteristic
22#16813609C2211yescharacteristic
23#16813608—21no—
24#16813608—21no—
25C4⋊C4×D113—21no—
26C4⋊C4×D113C2212yes—
27C22⋊C4×D113—21no—
28C22⋊C4×D113—21no—
29C42×D113C2211yescharacteristic
30#16813547C2212yescomplemented
31#16813546C2212yescomplemented
32#16813545C2212yescomplemented
33#16813544C2212yes—
34#16813543C2212yes—
35#16813542C2212yes—
36#16813533C2211yescharacteristic, complemented
37#16813532C2212yescomplemented
38C4⋊Q8×C113C2211yescharacteristic, complemented
39#124×C113C2211yescharacteristic
40#103×C113C2212yescomplemented
41#102×C113C2212yes—
42#97×C113C2211yescharacteristic, complemented
43C23×D113—21no—
44C2×Dic226—21no—
45C2×Dic226—21no—
46C2×Dic226—22no—
47C2×Dic226C2311yescharacteristic
48Q8×D113—24no—
49Q8×D113—44no—
50C2×D452C2311yescharacteristic
51C2×C22⋊D113—21no—
52D4×D113—24no—
53C2×C4×D113—21no—
54C2×C4×D113—22no—
55C2×C4×D113D411yescharacteristic
56C2×C4×D113D411yescharacteristic
57C2×C4×D113C2311yescharacteristic
58C2×#11744751C2312yes—
59C8×D113—24no—
60C4⋊Dic113—21no—
61C4⋊Dic113C2312yes—
62#14268626—22no—
63#14268626—22no—
64C22⋊Dic113—21no—
65C22⋊Dic113—21no—
66#14268624—21no—
67#14268624—21no—
68#14268624—21no—
69#14268624—21no—
70C4×Dic113D411yescharacteristic
71C4×Dic113D411yescharacteristic
72C4×Dic113C2311yescharacteristic
73C2×Q8×C113—21no—
74C2×Q8×C113C2311yescharacteristic
75C2×D4×C113C2311yescharacteristic
76C2×C8×C113C2312yes—
77C4⋊C4×C113—21no—
78C4⋊C4×C113C2312yes—
79C22⋊C4×C113—21no—
80C22⋊C4×C113—21no—
81C42×C113C2311yescharacteristic
82C23×C113—21no—
83C22×D113—21no—
84C22×D113—42no—
85C22×D113—42no—
86C22×D113—42no—
87C22×D113C2×D411yescharacteristic
88Q8×C113—22no—
89Q8×C113—42no—
90D4×C113—22no—
91C2×C4×C113—21no—
92C2×C4×C113—22no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2411yescharacteristic
96C22⋊D113—42no—
97C2×Dic113—21no—
98C2×Dic113—22no—
99C2×Dic113C2×D411yescharacteristic
100C2×Dic113C2×D411yescharacteristic
101C2×Dic113C2×D411yescharacteristic
102D452—22no—
103C4×D113—22no—
104C4×D113—22no—
105C4×D113—42no—
106C4×D113—44no—
107C4×D113#4114yes—
108Dic226—22no—
109Dic226—44no—
110Dic226—42no—
111Dic226—42no—
112C8×C113—22no—
113#11744751—22no—
114C22×C113—41no—
115C22×C113—41no—
116C22×C113—41no—
117C22×C113C22×D411yescharacteristic
118C2×D113—41no—
119C2×D113—41no—
120C2×D113—41no—
121C2×D113—84no—
122C2×D113#12412yes—
123C2×D113AGL(1,ℤ/8)12yes—
124C2×D113#13712yes—
125C4×C113—21no—
126C4×C113—21no—
127C4×C113—41no—
128C4×C113—42no—
129C4×C113C2×#4112yes—
130Dic113—21no—
131Dic113—21no—
132Dic113—41no—
133Dic113—42no—
134Dic113#12412yes—
135C2×C113—81no—
136C2×C113C2×#12411yescharacteristic
137C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C113C2×#13711yescharacteristic
139D113—81no—
140D113#48914yesdirect product factor
141C2×#489—1131nomaximal, Sylow
142C113C2×#48911yescharacteristic, complemented, Sylow
143C2×C4⋊Q8—1131no—
144C2×#124—1131no—
145#489—1131no—
146#489—1131no—
147#489—1132no—
148#489—1132no—
149#489—1131no—
150#489D11311yescharacteristic, direct product factor
151C2×#103—1132no—
152C2×#102—1132no—
153C2×#97—1131no—
154C22×Q8—1131no—
155C22×Q8—2261no—
156C22×D4—1131no—
157C22×C8—1132no—
158C4⋊Q8—1132no—
159C4⋊Q8—1131no—
160C4⋊Q8—2261no—
161C4⋊Q8—2261no—
162C4⋊Q8C2×D11311yescharacteristic, complemented
163#124—1131no—
164#124—1131no—
165#124—1131no—
166#124—2261no—
167#124—2261no—
168#124C2×D11311yescharacteristic
169C2×C4⋊C4—1132no—
170C2×C4⋊C4—2261no—
171C2×C22⋊C4—2261no—
172C2×C22⋊C4—2261no—
173C2×C42—1131no—
174#103—1132no—
175#103—1132no—
176#103—1132no—
177#103C2×D11312yescomplemented
178#102—1132no—
179#102—1132no—
180#102—1132no—
181#102C2×D11312yes—
182#97—1132no—
183#97—1131no—
184#97C2×D11311yescharacteristic, complemented
185C24—2261no—
186C2×Q8—21no—
187C2×Q8—1131no—
188C2×Q8—4524no—
189C2×Q8—2261no—
190C2×Q8—2262no—
191C2×Q8—2264no—
192C2×Q8—2261no—
193C2×Q8C22×D11311yescharacteristic
194C2×D4—1131no—
195C2×D4—2264no—
196C2×D4—2261no—
197C2×D4C22×D11311yescharacteristic
198C22×C4—1131no—
199C22×C4—1131no—
200C22×C4—1131no—
201C22×C4—2261no—
202C22×C4—2262no—
203C2×C8—1132no—
204C2×C8—2264no—
205C2×C8C22×D11312yes—
206C4⋊C4—21no—
207C4⋊C4—1132no—
208C4⋊C4—2262no—
209C4⋊C4—2262no—
210C4⋊C4—2261no—
211C4⋊C4C22×D11312yes—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—2261no—
215C22⋊C4—2261no—
216C22⋊C4—2261no—
217C22⋊C4—2261no—
218C22⋊C4—2261no—
219C22⋊C4—2261no—
220C42—1131no—
221C42—1131no—
222C42—1131no—
223C42C22×D11311yescharacteristic
224C23—21no—
225C23—1131no—
226C23—4522no—
227C23—4522no—
228C23—4522no—
229C23—2261no—
230Q8—22no—
231Q8—42no—
232Q8—4522no—
233Q8—4522no—
234Q8—4524no—
235Q8—2262no—
236D4—22no—
237D4—4522no—
238D4—2262no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—1131no—
242C2×C4—1134no—
243C2×C4—1131no—
244C2×C4—1131no—
245C2×C4—4524no—
246C2×C4—4522no—
247C2×C4—2262no—
248C2×C4—2262no—
249C2×C4—2261no—
250C2×C4—2262no—
251C2×C4D4×D11311yescharacteristic
252C2×C4D4×D11311yescharacteristic
253C2×C4C23×D11311yescharacteristic
254C8—22no—
255C8—2262no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—1132no—
260C22—1132no—
261C22—1132no—
262C22—9044no—
263C22—4521no—
264C22—4521no—
265C22—4521no—
266C22C2×D4×D11311yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—42no—
271C4—1132no—
272C4—4521no—
273C4—4522no—
274C4—2261no—
275C4—2261no—
276C4#41×D11312yes—
277C2—81no—
278C2—1134no—
279C2—9041no—
280C2#124×D11311yescharacteristic
281C2AGL(1,ℤ/8)×D11311yescharacteristic
282C2#137×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#489×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#489D113
hypocenterC113C2×#489
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D113C2semidirect
3. #20298960C2semidirect
4. #20298959C2semidirect
5. #20298958C2semidirect
6. #20298957C2semidirect
7. #20298956C2semidirect
8. #103×D113C2semidirect
10. #97×D113C2semidirect
11. #489×C113C2semidirect
16. #16813622C22semidirect
18. #16813621C22semidirect
30. #16813547C22semidirect
31. #16813546C22semidirect
32. #16813545C22semidirect
36. #16813533C22semidirect
37. #16813532C22semidirect
38. C4⋊Q8×C113C22semidirect
40. #103×C113C22semidirect
42. #97×C113C22semidirect
140. D113#489direct (N × H)
142. C113C2×#489semidirect
150. #489D113direct (N × H)
162. C4⋊Q8C2×D113semidirect
177. #103C2×D113semidirect
184. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1132
#124×D1132
#202989602
#202989592
#202989582
#202989572
#202989562
#103×D1132
#102×D1132
#97×D1132
#489×C1132
C2×#489113