Finite Group Databasebeta

← #470×D113 #28400172

Subgroups — #470×D113 #28400172

Order 14464.

492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 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×Q16×D113C211yesmaximal, characteristic, complemented
2C2×M16×D113C211yesmaximal, characteristic
3C22⋊Q8×D113C212yesmaximal
4#20298857C211yesmaximal, characteristic, complemented
5#20298856C211yesmaximal, characteristic, complemented
6#20298855C212yesmaximal, complemented
7#20298854C212yesmaximal, complemented
8#20298853C211yesmaximal, characteristic, complemented
9#106×D113C211yesmaximal, characteristic, complemented
10#103×D113C212yesmaximal, complemented
11#470×C113C211yesmaximal, characteristic, complemented
12C2×Q8×D113C2212yes—
13C22×C4×D113C2211yescharacteristic
14C2×Dic452C2211yescharacteristic, complemented
15C2×#14268637C2212yescomplemented
16Q16×D113—24no—
17C2×#14268631C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19C2×#14268630C2211yescharacteristic
20M16×D113—24no—
21C2×C8×D113C2211yescharacteristic
22C2×C8×D113C2211yescharacteristic
23#16813602C2212yes—
24#16813601C2212yes—
25#16813600—22no—
26#16813599—22no—
27#16813598C2212yes—
28C4⋊C4×D113—22no—
29C4⋊C4×D113C2212yes—
30C22⋊C4×D113—22no—
31#16813554C2211yescharacteristic, complemented
32#16813553C2212yescomplemented
33#16813547C2212yescomplemented
34#16813546C2212yescomplemented
35#16813545C2212yescomplemented
36C2×Q16×C113C2211yescharacteristic, complemented
37C2×M16×C113C2211yescharacteristic
38C22⋊Q8×C113C2212yes—
39#106×C113C2211yescharacteristic, complemented
40#103×C113C2212yescomplemented
41C23×D113D411yescharacteristic
42C2×Dic226—22no—
43C2×Dic226C2312yes—
44Q8×D113—24no—
45Q8×D113—24no—
46C22×Dic113D411yescharacteristic
47C2×C4×D113—22no—
48C2×C4×D113—22no—
49C2×C4×D113—22no—
50C2×C4×D113—22no—
51C2×C4×D113D411yescharacteristic
52C2×C4×D113D411yescharacteristic
53C2×C4×D113C2311yescharacteristic
54C2×C4×D113C2311yescharacteristic
55Dic452—22no—
56#14268637—24no—
57#14268631—22no—
58#14268630—22no—
59#14268630—22no—
60C2×#11744751C2311yescharacteristic
61C2×#11744751C2311yescharacteristic
62C8×D113—22no—
63C8×D113D414yes—
64C4⋊Dic113—22no—
65C4⋊Dic113C2312yes—
66#14268626—22no—
67#14268626—22no—
68#14268626—22no—
69C22⋊Dic113—22no—
70#14268624—22no—
71#14268624—22no—
72C2×Q8×C113C2312yes—
73C22×C4×C113C2311yescharacteristic
74Q16×C113—22no—
75M16×C113—22no—
76C2×C8×C113C2311yescharacteristic
77C2×C8×C113C2311yescharacteristic
78C4⋊C4×C113—22no—
79C4⋊C4×C113C2312yes—
80C22⋊C4×C113—22no—
81C23×C113C2×D411yescharacteristic
82C22×D113—22no—
83C22×D113—24no—
84C22×D113C2×D411yescharacteristic
85C22×D113C2×D411yescharacteristic
86Q8×C113—22no—
87Q8×C113—22no—
88C2×C4×C113—21no—
89C2×C4×C113—21no—
90C2×C4×C113—22no—
91C2×C4×C113—22no—
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2411yescharacteristic
94C2×Dic113—22no—
95C2×Dic113—22no—
96C2×Dic113—22no—
97C2×Dic113C2×D411yescharacteristic
98C2×Dic113C2×D411yescharacteristic
99C4×D113—22no—
100C4×D113—21no—
101C4×D113—21no—
102C4×D113—22no—
103C4×D113—44no—
104C4×D113—44no—
105C4×D113C2×D412yes—
106C4×D113#4112yes—
107Dic226—22no—
108Dic226—22no—
109Dic226—44no—
110C8×C113—21no—
111C8×C113C2×D412yes—
112#11744751—21no—
113#11744751C2×D412yes—
114C22×C113—21no—
115C22×C113—22no—
116C22×C113C22×D411yescharacteristic
117C2×D113—21no—
118C2×D113—22no—
119C2×D113—44no—
120C2×D113#12112yes—
121C2×D113#13714yes—
122C4×C113—21no—
123C4×C113—42no—
124C4×C113—42no—
125C4×C113C22×D411yescharacteristic
126C4×C113C2×#4111yescharacteristic
127Dic113—21no—
128Dic113—42no—
129Dic113—42no—
130Dic113#12112yes—
131C2×C113—41no—
132C2×C113C2×#12111yescharacteristic
133C2×C113C2×#13712yes—
134D113—41no—
135D113#47014yesdirect product factor
136C2×#470—1131nomaximal, Sylow
137C113C2×#47011yescharacteristic, complemented, Sylow
138C22×Q16—1131no—
139C22×M16—1131no—
140C2×C22⋊Q8—1132no—
141#470—1131no—
142#470—1131no—
143#470—1132no—
144#470—1131no—
145#470—1132no—
146#470D11311yescharacteristic, direct product factor
147C2×#106—1131no—
148C2×#103—1132no—
149C22×Q8—1132no—
150C23×C4—1131no—
151C2×Q16—1132no—
152C2×Q16—1131no—
153C2×Q16—2264no—
154C2×Q16C2×D11311yescharacteristic, complemented
155C2×M16—1131no—
156C2×M16—1131no—
157C2×M16—1131no—
158C2×M16—2264no—
159C2×M16C2×D11311yescharacteristic
160C22×C8—1131no—
161C22×C8—1131no—
162C22⋊Q8—1132no—
163C22⋊Q8—1132no—
164C22⋊Q8—1132no—
165C22⋊Q8—2262no—
166C22⋊Q8—2262no—
167C22⋊Q8C2×D11312yes—
168C2×C4⋊C4—1132no—
169C2×C4⋊C4—2262no—
170C2×C22⋊C4—2262no—
171#106—1131no—
172#106—1132no—
173#106C2×D11311yescharacteristic, complemented
174#103—1132no—
175#103—1132no—
176#103—1132no—
177#103C2×D11312yescomplemented
178C24—1131no—
179C2×Q8—1132no—
180C2×Q8—2262no—
181C2×Q8—2264no—
182C2×Q8—2264no—
183C2×Q8C22×D11312yes—
184C22×C4—1131no—
185C22×C4—1131no—
186C22×C4—1131no—
187C22×C4—1131no—
188C22×C4—1131no—
189C22×C4—2262no—
190C22×C4—2262no—
191C22×C4—2262no—
192C22×C4—2262no—
193C22×C4C22×D11311yescharacteristic
194Q16—22no—
195Q16—2264no—
196Q16—2262no—
197M16—22no—
198M16—2262no—
199M16—2262no—
200M16—2262no—
201C2×C8—1131no—
202C2×C8—1134no—
203C2×C8—1131no—
204C2×C8—2262no—
205C2×C8C22×D11311yescharacteristic
206C2×C8C22×D11311yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—1132no—
209C4⋊C4—2262no—
210C4⋊C4—2262no—
211C4⋊C4—2262no—
212C4⋊C4—2262no—
213C4⋊C4C22×D11312yes—
214C22⋊C4—22no—
215C22⋊C4—2262no—
216C22⋊C4—2262no—
217C22⋊C4—2262no—
218C23—1131no—
219C23—1131no—
220C23—2262no—
221C23—2264no—
222C23D4×D11311yescharacteristic
223Q8—22no—
224Q8—22no—
225Q8—4524no—
226Q8—2262no—
227Q8—2262no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—1131no—
233C2×C4—1132no—
234C2×C4—1132no—
235C2×C4—1131no—
236C2×C4—4524no—
237C2×C4—4524no—
238C2×C4—2262no—
239C2×C4—2262no—
240C2×C4—2262no—
241C2×C4—2262no—
242C2×C4—2262no—
243C2×C4—2261no—
244C2×C4—2261no—
245C2×C4D4×D11311yescharacteristic
246C2×C4C23×D11311yescharacteristic
247C8—21no—
248C8—1132no—
249C8—2261no—
250C8D4×D11312yes—
251C22—21no—
252C22—22no—
253C22—1132no—
254C22—1134no—
255C22—4524no—
256C22—2261no—
257C22—2262no—
258C22C2×D4×D11311yescharacteristic
259C4—21no—
260C4—42no—
261C4—42no—
262C4—1132no—
263C4—4522no—
264C4—4522no—
265C4—2261no—
266C4C2×D4×D11311yescharacteristic
267C4#41×D11311yescharacteristic
268C2—41no—
269C2—1134no—
270C2—4521no—
271C2#121×D11311yescharacteristic
272C2#137×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#470×C113C2
socleC22×C113C22×D4
prime radicalC23×D113D4
hypercenter#470D113
hypocenterC113C2×#470
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D113C2semidirect
4. #20298857C2semidirect
5. #20298856C2semidirect
6. #20298855C2semidirect
7. #20298854C2semidirect
8. #20298853C2semidirect
9. #106×D113C2semidirect
10. #103×D113C2semidirect
11. #470×C113C2semidirect
14. C2×Dic452C22semidirect
15. C2×#14268637C22semidirect
31. #16813554C22semidirect
32. #16813553C22semidirect
33. #16813547C22semidirect
34. #16813546C22semidirect
35. #16813545C22semidirect
36. C2×Q16×C113C22semidirect
39. #106×C113C22semidirect
40. #103×C113C22semidirect
135. D113#470direct (N × H)
137. C113C2×#470semidirect
146. #470D113direct (N × H)
154. C2×Q16C2×D113semidirect
173. #106C2×D113semidirect
177. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D1132
C2×M16×D1132
C22⋊Q8×D1132
#202988572
#202988562
#202988552
#202988542
#202988532
#106×D1132
#103×D1132
#470×C1132
C2×#470113