Finite Group Databasebeta

← #28401591

Subgroups — #28401591

Order 14464.

490 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 115 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#127×D113C211yesmaximal, characteristic, complemented
2#20299130C211yesmaximal, characteristic, complemented
3#20298986C212yesmaximal, complemented
4#20298961C212yesmaximal, complemented
5#20298799C211yesmaximal, characteristic, complemented
6#20298795C211yesmaximal, characteristic, complemented
7#20298793C211yesmaximal, characteristic, complemented
8#20298750C212yesmaximal, complemented
9#20298730C212yesmaximal, complemented
10#20298654C211yesmaximal, characteristic, complemented
11#459×C113C211yesmaximal, characteristic, complemented
12C2×D4×D113—21no—
13C2×D4×D113—21no—
14C2×D4×D113C2212yes—
15C2×#14268636C2212yescomplemented
16C2×#14268635C2212yescomplemented
17C2×#14268632C2212yescomplemented
18#16813619C2211yescharacteristic
19#16813618—21no—
20#16813618—21no—
21#16813618C2212yes—
22#16813615—21no—
23#16813613C2211yescharacteristic, complemented
24#16813609C2211yescharacteristic, complemented
25#16813604—21no—
26#16813602C2211yescharacteristic
27#16813593C2211yescharacteristic
28C4×Dic226C2211yescharacteristic, complemented
29C4×C22⋊D113—21no—
30#16813581—21no—
31C42×D113C2211yescharacteristic
32C4⋊#11744751C2211yescharacteristic, complemented
33#16813544C2212yescomplemented
34#16813543C2212yescomplemented
35#16813542C2212yescomplemented
36#16813534C2212yes—
37#16813532C2212yescomplemented
38C2×D8×C113C2212yescomplemented
39#127×C113C2211yescharacteristic
40C4×D4×C113C2211yescharacteristic, complemented
41C4⋊C8×C113C2211yescharacteristic, complemented
42#102×C113C2212yescomplemented
43C23×D113—22no—
44C2×Dic226C2311yescharacteristic
45C2×D452—21no—
46C2×D452—21no—
47C2×D452C2312yes—
48C2×C22⋊D113—21no—
49C2×C22⋊D113—22no—
50C2×C22⋊D113—22no—
51C2×C22⋊D113—22no—
52D4×D113—42no—
53D4×D113—42no—
54D4×D113—44no—
55D4×D113—44no—
56C2×C4×D113D411yescharacteristic
57C2×C4×D113D411yescharacteristic
58C2×C4×D113C2311yescharacteristic
59#14268636—42no—
60#14268635—42no—
61#14268632—42no—
62C2×#11744751C2312yes—
63C4⋊Dic113—21no—
64C4⋊Dic113—21no—
65C4⋊Dic113C2311yescharacteristic
66#14268626—21no—
67#14268626—21no—
68C22⋊Dic113—21no—
69C22⋊Dic113—21no—
70C22⋊Dic113—21no—
71#14268624—21no—
72C4×Dic113—21no—
73C4×Dic113D411yescharacteristic
74C4×Dic113D411yescharacteristic
75C4×Dic113C2311yescharacteristic
76C2×D4×C113—21no—
77C2×D4×C113—21no—
78C2×D4×C113C2311yescharacteristic
79C2×D4×C113C2312yes—
80C22×C4×C113—21no—
81D8×C113—42no—
82C2×C8×C113C2312yes—
83C4⋊C4×C113C2311yescharacteristic
84C22⋊C4×C113—21no—
85C42×C113C2311yescharacteristic
86C23×C113—21no—
87C23×C113—22no—
88C22×D113—22no—
89C22×D113—44no—
90C22×D113—44no—
91C22×D113—44no—
92C22×D113C2×D411yescharacteristic
93D4×C113—21no—
94D4×C113—22no—
95D4×C113—21no—
96D4×C113—22no—
97D4×C113—42no—
98D4×C113—42no—
99C2×C4×C113—21no—
100C2×C4×C113—42no—
101C2×C4×C113C2×D411yescharacteristic
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113C2411yescharacteristic
104C22⋊D113—44no—
105C22⋊D113—44no—
106C22⋊D113—44no—
107C22⋊D113—42no—
108C2×Dic113—21no—
109C2×Dic113—21no—
110C2×Dic113C2×D411yescharacteristic
111C2×Dic113C2×D411yescharacteristic
112C2×Dic113C2×D411yescharacteristic
113D452—22no—
114D452—22no—
115D452—42no—
116D452—42no—
117C4×D113—22no—
118C4×D113—22no—
119C4×D113—21no—
120C4×D113—21no—
121Dic226—21no—
122Dic226—21no—
123C8×C113—22no—
124#11744751—22no—
125C22×C113—42no—
126C22×C113—41no—
127C22×C113—42no—
128C22×C113—42no—
129C22×C113—41no—
130C22×C113—41no—
131C22×C113C22×D411yescharacteristic
132C2×D113—21no—
133C2×D113—21no—
134C2×D113—42no—
135C2×D113—42no—
136C2×D113—42no—
137C2×D113—88no—
138C2×D113AGL(1,ℤ/8)12yes—
139C4×C113—21no—
140C4×C113—41no—
141C4×C113AGL(1,ℤ/8)12yes—
142C4×C113H(5,𝔽2)11yescharacteristic
143C4×C113H(5,𝔽2)11yescharacteristic
144Dic113—21no—
145Dic113—21no—
146Dic113—21no—
147Dic113—41no—
148Dic113—41no—
149C2×C113—82no—
150C2×C113—81no—
151C2×C113#53511yescharacteristic
152C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
154D113—22no—
155D113—82no—
156#3217—1131nomaximal, Sylow
157C113#321711yescharacteristic, complemented, Sylow
158C2×#127—1131no—
159#529—1131no—
160#496—1132no—
161#490—1132no—
162#460—1131no—
163#460—1131no—
164#459—1131no—
165#459D11311yescharacteristic, complemented
166#450—1132no—
167#447—1132no—
168#432—1131no—
169C22×D4—1132no—
170C22×D4—2261no—
171C22×D4—2261no—
172C2×SD16—1132no—
173C2×SD16—1132no—
174C2×D8—1132no—
175C2×D8C2×D11312yescomplemented
176#127—1132no—
177#127—1131no—
178#127—2261no—
179#127—2261no—
180#127C2×D11311yescharacteristic
181#126—2261no—
182#125—1131no—
183#124—1131no—
184#123—2261no—
185C22⋊Q8—1131no—
186#121—1131no—
187C4×Q8—1131no—
188C4×D4—2261no—
189C4×D4C2×D11311yescharacteristic, complemented
190#117—2261no—
191C2×C42—1131no—
192C4⋊C8—1131no—
193C4⋊C8C2×D11311yescharacteristic, complemented
194#102—1132no—
195#102—1132no—
196#102—1132no—
197#102C2×D11312yescomplemented
198C22⋊C8—1132no—
199#97—1132no—
200C24—2262no—
201C2×Q8—1131no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—1132no—
205C2×D4—4522no—
206C2×D4—4522no—
207C2×D4—4524no—
208C2×D4—4524no—
209C2×D4—2262no—
210C2×D4—2262no—
211C2×D4—2262no—
212C2×D4—2261no—
213C2×D4—2261no—
214C2×D4—2261no—
215C2×D4C22×D11312yes—
216C2×D4C22×D11311yescharacteristic
217C22×C4—21no—
218C22×C4—1131no—
219C22×C4—1131no—
220C22×C4—1131no—
221SD16—4522no—
222SD16—4522no—
223D8—42no—
224D8—4522no—
225C2×C8—1132no—
226C2×C8C22×D11312yes—
227C4⋊C4—1131no—
228C4⋊C4—2261no—
229C4⋊C4—2261no—
230C4⋊C4—2261no—
231C4⋊C4—2261no—
232C4⋊C4C22×D11311yescharacteristic
233C22⋊C4—21no—
234C22⋊C4—2261no—
235C22⋊C4—2261no—
236C22⋊C4—2261no—
237C22⋊C4—2261no—
238C42—1131no—
239C42—1131no—
240C42—1131no—
241C42—2261no—
242C42C22×D11311yescharacteristic
243C23—21no—
244C23—22no—
245C23—1131no—
246C23—4524no—
247C23—4524no—
248C23—4524no—
249C23—2262no—
250Q8—2261no—
251Q8—2261no—
252D4—21no—
253D4—22no—
254D4—21no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—4522no—
259D4—4522no—
260D4—4524no—
261D4—4524no—
262D4—4524no—
263D4—4522no—
264D4—2262no—
265D4—2262no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—1131no—
269C2×C4—1131no—
270C2×C4—1131no—
271C2×C4—2262no—
272C2×C4—2261no—
273C2×C4—2261no—
274C2×C4—2262no—
275C2×C4—2261no—
276C2×C4—2261no—
277C2×C4D4×D11311yescharacteristic
278C2×C4D4×D11311yescharacteristic
279C2×C4C23×D11311yescharacteristic
280C8—22no—
281C8—2262no—
282C22—42no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—1132no—
289C22—9048no—
290C22—4522no—
291C22—4522no—
292C22—4522no—
293C22—2261no—
294C22—2261no—
295C22C2×D4×D11311yescharacteristic
296C4—21no—
297C4—41no—
298C4—4521no—
299C4—4521no—
300C4—2261no—
301C4—2261no—
302C4—2261no—
303C4#1681364612yes—
304C4#1681366711yescharacteristic
305C4#1681366811yescharacteristic
306C2—82no—
307C2—81no—
308C2—9042no—
309C2—2262no—
310C2#2029916411yescharacteristic
311C2AGL(1,ℤ/8)×D11311yescharacteristic
312C2C2×#1681364611yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3217
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #127×D113C2semidirect
2. #20299130C2semidirect
3. #20298986C2semidirect
4. #20298961C2semidirect
5. #20298799C2semidirect
6. #20298795C2semidirect
7. #20298793C2semidirect
8. #20298750C2semidirect
9. #20298730C2semidirect
10. #20298654C2semidirect
11. #459×C113C2semidirect
15. C2×#14268636C22semidirect
16. C2×#14268635C22semidirect
17. C2×#14268632C22semidirect
23. #16813613C22semidirect
24. #16813609C22semidirect
28. C4×Dic226C22semidirect
32. C4⋊#11744751C22semidirect
33. #16813544C22semidirect
34. #16813543C22semidirect
35. #16813542C22semidirect
37. #16813532C22semidirect
38. C2×D8×C113C22semidirect
40. C4×D4×C113C22semidirect
41. C4⋊C8×C113C22semidirect
42. #102×C113C22semidirect
157. C113#3217semidirect
165. #459D113semidirect
175. C2×D8C2×D113semidirect
189. C4×D4C2×D113semidirect
193. C4⋊C8C2×D113semidirect
197. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#127×D1132
#202991302
#202989862
#202989612
#202987992
#202987952
#202987932
#202987502
#202987302
#202986542
#459×C1132
#3217113