Finite Group Databasebeta

← #28400220

Subgroups — #28400220

Order 14464.

524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D113C211yesmaximal, characteristic, complemented
2C2×#16813630C211yesmaximal, characteristic, complemented
3#20299164C212yesmaximal, complemented
4#20298852C211yesmaximal, characteristic, complemented
5#20298851C211yesmaximal, characteristic, complemented
6#20298848C211yesmaximal, characteristic, complemented
7#20298833C212yesmaximal, complemented
8#20298832C212yesmaximal, complemented
9#20298633C211yesmaximal, characteristic, complemented
10#20298601C212yesmaximal, complemented
11#469×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C2×D4×D113C2212yes—
14C2×D904C2211yescharacteristic
15C2×#14268632C2212yes—
16D8×D113—24no—
17#16813630—24no—
18C2×#14268630C2211yescharacteristic
19C2×#14268630C2211yescharacteristic, complemented
20C22×#11744751C2211yescharacteristic, complemented
21C2×C8×D113C2211yescharacteristic
22C2×C8×D113C2211yescharacteristic, complemented
23#16813618—22no—
24#16813608—22no—
25#16813597C2212yescomplemented
26#16813596C2212yescomplemented
27#16813593C2212yescomplemented
28#16813592—22no—
29#16813590—22no—
30#16813580C2212yes—
31#16813555C2212yescomplemented
32#16813554C2211yescharacteristic, complemented
33#16813544C2212yescomplemented
34#16813543C2212yescomplemented
35#16813542C2212yescomplemented
36C2×D8×C113C2211yescharacteristic
37C2×M16×C113C2211yescharacteristic, complemented
38#121×C113C2212yescomplemented
39#106×C113C2211yescharacteristic, complemented
40#102×C113C2212yescomplemented
41C23×D113—22no—
42#14268647—22no—
43#14268647—22no—
44C2×Dic226D411yescharacteristic
45C2×D452—22no—
46C2×D452D411yescharacteristic
47C2×D452C2312yes—
48C2×C22⋊D113—22no—
49C2×C22⋊D113—22no—
50C2×C22⋊D113—22no—
51C2×C22⋊D113D411yescharacteristic
52C2×C22⋊D113D411yescharacteristic
53D4×D113—24no—
54D4×D113—24no—
55C2×C4×D113C2311yescharacteristic
56C2×C4×D113C2311yescharacteristic
57D904—22no—
58#14268632—24no—
59#14268630—22no—
60#14268630—22no—
61C2×#11744751—22no—
62C2×#11744751C2311yescharacteristic
63C2×#11744751C2311yescharacteristic
64C8×D113—22no—
65C8×D113D414yescomplemented
66C4⋊Dic113C2312yes—
67C22⋊Dic113—22no—
68#14268624—22no—
69#14268624—22no—
70#14268624—22no—
71C4×Dic113—22no—
72C2×D4×C113—22no—
73C2×D4×C113C2312yes—
74C22×C4×C113C2311yescharacteristic
75D8×C113—22no—
76M16×C113—22no—
77C2×C8×C113C2311yescharacteristic
78C2×C8×C113C2311yescharacteristic
79C4⋊C4×C113C2312yes—
80C22⋊C4×C113—22no—
81C23×C113—22no—
82C23×C113C2×D411yescharacteristic
83C22×D113—22no—
84C22×D113—44no—
85C22×D113—82no—
86C22×D113—82no—
87C22×D113C2×D411yescharacteristic
88C22×D113C2×D411yescharacteristic
89D4×C113—22no—
90D4×C113—22no—
91D4×C113—82no—
92C2×C4×C113—21no—
93C2×C4×C113—21no—
94C2×C4×C113—22no—
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2411yescharacteristic
97C22⋊D113—22no—
98C22⋊D113—22no—
99C22⋊D113—44no—
100C22⋊D113—82no—
101C22⋊D113—82no—
102C2×Dic113—22no—
103C2×Dic113C2×D411yescharacteristic
104C2×Dic113C2×D411yescharacteristic
105D452—22no—
106D452—22no—
107D452—22no—
108D452—82no—
109C4×D113—21no—
110C4×D113—21no—
111C4×D113C2×D412yes—
112C4×D113#4112yes—
113Dic226—22no—
114C8×C113—21no—
115C8×C113C2×D412yes—
116#11744751—21no—
117#11744751C2×D412yes—
118C22×C113—21no—
119C22×C113—22no—
120C22×C113—42no—
121C22×C113—42no—
122C22×C113—42no—
123C22×C113C22×D411yescharacteristic
124C2×D113—22no—
125C2×D113—21no—
126C2×D113—22no—
127C2×D113—42no—
128C2×D113—42no—
129C2×D113—42no—
130C2×D113—88no—
131C2×D113#12112yes—
132C4×C113—21no—
133C4×C113—42no—
134C4×C113C22×D411yescharacteristic
135C4×C113C2×#4111yescharacteristic
136Dic113—21no—
137Dic113—42no—
138Dic113#12112yes—
139C2×C113—41no—
140C2×C113—82no—
141C2×C113C2×#12111yescharacteristic
142C2×C113#57612yes—
143D113—22no—
144D113—41no—
145D113—82no—
146#3058—1131nomaximal, Sylow
147C113#305811yescharacteristic, complemented, Sylow
148C22×D8—1131no—
149C2×#131—1131no—
150#535—1132no—
151#469—1131no—
152#469—1131no—
153#469—1131no—
154#469D11311yescharacteristic, complemented
155#466—1132no—
156#466—1132no—
157#427—1131no—
158#418—1132no—
159C2×#41—1131no—
160C22×D4—1132no—
161C2×D8—1132no—
162C2×D8—1131no—
163C2×D8—2264no—
164C2×D8C2×D11311yescharacteristic
165#131—2264no—
166C2×M16—1131no—
167C2×M16—1131no—
168C2×M16C2×D11311yescharacteristic, complemented
169C22×C8—1131no—
170C22×C8—1131no—
171C22×C8—1131no—
172#127—2262no—
173#124—2262no—
174#121—1132no—
175#121—1132no—
176#121—1132no—
177#121C2×D11312yescomplemented
178#120—2262no—
179#120—2262no—
180#117—1132no—
181#107—1132no—
182#106—1131no—
183#106C2×D11311yescharacteristic, complemented
184#102—1132no—
185#102—1132no—
186#102—1132no—
187#102C2×D11312yescomplemented
188C24—2262no—
189#41—2262no—
190#41—2262no—
191C2×Q8—1131no—
192C2×D4—22no—
193C2×D4—1131no—
194C2×D4—1131no—
195C2×D4—1131no—
196C2×D4—1132no—
197C2×D4—2262no—
198C2×D4—2264no—
199C2×D4—2264no—
200C2×D4—2262no—
201C2×D4—2262no—
202C2×D4—2262no—
203C2×D4C22×D11312yes—
204C22×C4—1131no—
205C22×C4—1131no—
206C22×C4C22×D11311yescharacteristic
207D8—22no—
208D8—2264no—
209D8—2262no—
210M16—22no—
211M16—2262no—
212M16—2262no—
213C2×C8—1131no—
214C2×C8—1134no—
215C2×C8—1131no—
216C2×C8—2262no—
217C2×C8—2262no—
218C2×C8C22×D11311yescharacteristic
219C2×C8C22×D11311yescharacteristic
220C4⋊C4—1132no—
221C4⋊C4C22×D11312yes—
222C22⋊C4—22no—
223C22⋊C4—2262no—
224C22⋊C4—2262no—
225C22⋊C4—2262no—
226C22⋊C4—2262no—
227C42—2262no—
228C23—22no—
229C23—1131no—
230C23—1131no—
231C23—9042no—
232C23—9042no—
233C23—4524no—
234C23—2262no—
235C23D4×D11311yescharacteristic
236Q8—2262no—
237D4—22no—
238D4—22no—
239D4—82no—
240D4—9042no—
241D4—9042no—
242D4—9042no—
243D4—4524no—
244D4—2262no—
245D4—2262no—
246D4—2262no—
247D4—2262no—
248D4—2262no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—1131no—
253C2×C4—1132no—
254C2×C4—1132no—
255C2×C4—1131no—
256C2×C4—2262no—
257C2×C4—2261no—
258C2×C4—2261no—
259C2×C4D4×D11311yescharacteristic
260C2×C4C23×D11311yescharacteristic
261C8—21no—
262C8—1132no—
263C8—2261no—
264C8D4×D11312yes—
265C22—21no—
266C22—22no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—1132no—
271C22—9048no—
272C22—4522no—
273C22—4522no—
274C22—4522no—
275C22—2261no—
276C22—2262no—
277C22—2262no—
278C22C2×D4×D11311yescharacteristic
279C4—21no—
280C4—42no—
281C4—1132no—
282C4—4522no—
283C4—2261no—
284C4C2×D4×D11311yescharacteristic
285C4#41×D11311yescharacteristic
286C2—41no—
287C2—82no—
288C2—9042no—
289C2—4521no—
290C2—2262no—
291C2#121×D11311yescharacteristic
292C2#2029940212yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#469×C113C2
socleC22×C113C22×D4
hypercenter#469D113
hypocenterC113#3058
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D113C2semidirect
2. C2×#16813630C2semidirect
3. #20299164C2semidirect
4. #20298852C2semidirect
5. #20298851C2semidirect
6. #20298848C2semidirect
7. #20298833C2semidirect
8. #20298832C2semidirect
9. #20298633C2semidirect
10. #20298601C2semidirect
11. #469×C113C2semidirect
19. C2×#14268630C22semidirect
20. C22×#11744751C22semidirect
22. C2×C8×D113C22semidirect
25. #16813597C22semidirect
26. #16813596C22semidirect
27. #16813593C22semidirect
31. #16813555C22semidirect
32. #16813554C22semidirect
33. #16813544C22semidirect
34. #16813543C22semidirect
35. #16813542C22semidirect
37. C2×M16×C113C22semidirect
38. #121×C113C22semidirect
39. #106×C113C22semidirect
40. #102×C113C22semidirect
65. C8×D113D4semidirect
147. C113#3058semidirect
154. #469D113semidirect
168. C2×M16C2×D113semidirect
177. #121C2×D113semidirect
183. #106C2×D113semidirect
187. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1132
C2×#168136302
#202991642
#202988522
#202988512
#202988482
#202988332
#202988322
#202986332
#202986012
#469×C1132
#3058113