Finite Group Databasebeta

← #28401595

Subgroups — #28401595

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
1C2×#16813618C211yesmaximal, characteristic, complemented
2#20299134C211yesmaximal, characteristic, complemented
3#20298984C212yesmaximal, complemented
4#20298961C212yesmaximal, complemented
5#20298796C212yesmaximal, complemented
6#20298792C212yesmaximal, complemented
7#20298748C211yesmaximal, characteristic, complemented
8#20298734C211yesmaximal, characteristic, complemented
9#20298732C211yesmaximal, characteristic, complemented
10#20298652C211yesmaximal, characteristic, complemented
11#450×C113C211yesmaximal, characteristic, complemented
12C22×D452C2211yescharacteristic
13C22×C22⋊D113—21no—
14C22×C22⋊D113—21no—
15C2×#14268634C2212yescomplemented
16C2×D904C2212yescomplemented
17C2×#14268632C2212yescomplemented
18#16813618—21no—
19#16813618—21no—
20#16813618C2212yes—
21#16813618C2212yes—
22#16813617—21no—
23#16813613C2211yescharacteristic, complemented
24#16813611C2211yescharacteristic, complemented
25#16813606—21no—
26#16813596C2211yescharacteristic
27Q8×Dic113C2211yescharacteristic, complemented
28#16813584C2211yescharacteristic, complemented
29#16813582—21no—
30#16813580—21no—
31C2×C4×Dic113C2211yescharacteristic
32#16813551C2212yescomplemented
33#16813544C2212yescomplemented
34#16813543C2212yescomplemented
35#16813542C2212yescomplemented
36C22⋊#11744751C2211yescharacteristic
37#16813532C2212yescomplemented
38C22×D4×C113C2211yescharacteristic
39C2×SD16×C113C2212yescomplemented
40C22⋊Q8×C113C2211yescharacteristic
41#102×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113—21no—
44C2×D452—21no—
45C2×D452—42no—
46C2×D452C2311yescharacteristic
47C2×D452C2312yes—
48C2×C22⋊D113—21no—
49C2×C22⋊D113—22no—
50C2×C22⋊D113—22no—
51C2×C22⋊D113—22no—
52C2×C22⋊D113—22no—
53C2×C22⋊D113—44no—
54C2×C22⋊D113—44no—
55C22×Dic113D411yescharacteristic
56C22×Dic113D411yescharacteristic
57C2×C4×D113—21no—
58#14268634—42no—
59D904—42no—
60#14268632—42no—
61C2×#11744751C2312yes—
62C4⋊Dic113—21no—
63C4⋊Dic113—21no—
64C4⋊Dic113C2311yescharacteristic
65#14268626—21no—
66#14268624—21no—
67#14268624—21no—
68#14268624—21no—
69#14268624—21no—
70C4×Dic113—21no—
71C4×Dic113D411yescharacteristic
72C4×Dic113D411yescharacteristic
73C4×Dic113C2311yescharacteristic
74C4×Dic113C2311yescharacteristic
75C24×C113—21no—
76C2×Q8×C113C2311yescharacteristic
77C2×D4×C113—21no—
78C2×D4×C113—42no—
79C2×D4×C113C2312yes—
80C22×C4×C113C2311yescharacteristic
81SD16×C113—42no—
82C2×C8×C113C2312yes—
83C4⋊C4×C113—21no—
84C4⋊C4×C113C2311yescharacteristic
85C22⋊C4×C113—21no—
86C23×C113—22no—
87C23×C113—42no—
88C23×C113—42no—
89C23×C113—42no—
90C23×C113C2×D411yescharacteristic
91C22×D113—21no—
92C22×D113—22no—
93C22×D113—42no—
94C22×D113—42no—
95C22×D113—42no—
96Q8×C113—22no—
97D4×C113—22no—
98D4×C113—22no—
99D4×C113—42no—
100C2×C4×C113—22no—
101C2×C4×C113—21no—
102C2×C4×C113—21no—
103C2×C4×C113C2×D411yescharacteristic
104C2×C4×C113C2411yescharacteristic
105C22⋊D113—44no—
106C22⋊D113—44no—
107C22⋊D113—44no—
108C22⋊D113—42no—
109C22⋊D113—44no—
110C2×Dic113—22no—
111C2×Dic113—22no—
112C2×Dic113—21no—
113C2×Dic113C2×D411yescharacteristic
114C2×Dic113C2×D411yescharacteristic
115C2×Dic113C2×D411yescharacteristic
116C2×Dic113C2×D411yescharacteristic
117D452—22no—
118D452—22no—
119D452—22no—
120D452—42no—
121C4×D113—42no—
122C8×C113—22no—
123#11744751—22no—
124C22×C113—21no—
125C22×C113—21no—
126C22×C113—42no—
127C22×C113—42no—
128C22×C113—42no—
129C22×C113—84no—
130C22×C113AGL(1,ℤ/8)12yes—
131C22×C113C22×D411yescharacteristic
132C2×D113—42no—
133C2×D113—41no—
134C2×D113—41no—
135C2×D113—42no—
136C2×D113—42no—
137C2×D113—41no—
138C2×D113—84no—
139C4×C113—21no—
140C4×C113—41no—
141C4×C113—41no—
142C4×C113H(5,𝔽2)12yes—
143Dic113—21no—
144Dic113—21no—
145Dic113—21no—
146Dic113—41no—
147Dic113AGL(1,ℤ/8)12yes—
148C2×C113—22no—
149C2×C113—82no—
150C2×C113#53511yescharacteristic
151C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
152C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
153D113—81no—
154D113—82no—
155#3217—1131nomaximal, Sylow
156C113#321711yescharacteristic, complemented, Sylow
157C2×#127—1131no—
158#529—1131no—
159#496—1132no—
160#490—1132no—
161#460—1132no—
162#459—1132no—
163#450—1131no—
164#450D11311yescharacteristic, complemented
165#447—1131no—
166#447—1131no—
167#432—1131no—
168C22×D4—1131no—
169C22×D4—2261no—
170C22×D4—2261no—
171C22×D4C2×D11311yescharacteristic
172C2×SD16—1132no—
173C2×SD16C2×D11312yescomplemented
174C2×D8—1132no—
175C2×D8—1132no—
176#127—1132no—
177#127—1132no—
178#127—2261no—
179#127—2261no—
180#126—2261no—
181#125—1131no—
182#124—1131no—
183#123—2261no—
184C22⋊Q8C2×D11311yescharacteristic
185#121—1131no—
186C4×Q8—1131no—
187C4×D4—1131no—
188C4×D4—2261no—
189#117—2261no—
190C2×C42—1131no—
191C4⋊C8—1132no—
192#102—1132no—
193#102—1132no—
194#102—1132no—
195#102C2×D11312yescomplemented
196C22⋊C8—1131no—
197C22⋊C8C2×D11311yescharacteristic
198#97—1132no—
199C24—21no—
200C24—2261no—
201C2×Q8C22×D11311yescharacteristic
202C2×D4—21no—
203C2×D4—42no—
204C2×D4—1132no—
205C2×D4—1131no—
206C2×D4—4522no—
207C2×D4—4524no—
208C2×D4—4524no—
209C2×D4—2262no—
210C2×D4—2262no—
211C2×D4—2262no—
212C2×D4—2262no—
213C2×D4—2261no—
214C2×D4—2261no—
215C2×D4C22×D11312yes—
216C22×C4—1131no—
217C22×C4—1131no—
218C22×C4—2261no—
219C22×C4C22×D11311yescharacteristic
220SD16—42no—
221SD16—4522no—
222D8—4522no—
223D8—4522no—
224C2×C8—1132no—
225C2×C8C22×D11312yes—
226C4⋊C4—21no—
227C4⋊C4—1131no—
228C4⋊C4—2261no—
229C4⋊C4—2261no—
230C4⋊C4—2261no—
231C4⋊C4C22×D11311yescharacteristic
232C22⋊C4—21no—
233C22⋊C4—2261no—
234C22⋊C4—2261no—
235C22⋊C4—2261no—
236C22⋊C4—2261no—
237C42—1131no—
238C42—1131no—
239C42—1131no—
240C42—1131no—
241C42—2261no—
242C23—22no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—4522no—
247C23—4522no—
248C23—4522no—
249C23—2261no—
250C23—2262no—
251C23D4×D11311yescharacteristic
252Q8—22no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—4522no—
257D4—4524no—
258D4—4522no—
259D4—4524no—
260D4—4524no—
261D4—4524no—
262D4—2262no—
263D4—2262no—
264D4—2262no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—1131no—
269C2×C4—1131no—
270C2×C4—1131no—
271C2×C4—1131no—
272C2×C4—4522no—
273C2×C4—2262no—
274C2×C4—2261no—
275C2×C4—2262no—
276C2×C4D4×D11311yescharacteristic
277C2×C4C23×D11311yescharacteristic
278C8—22no—
279C8—2262no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—9044no—
287C22—4521no—
288C22—4522no—
289C22—4522no—
290C22—4521no—
291C22—4522no—
292C22—4521no—
293C22#1681364912yes—
294C22C2×D4×D11311yescharacteristic
295C4—21no—
296C4—41no—
297C4—41no—
298C4—1132no—
299C4—4521no—
300C4—2261no—
301C4—2261no—
302C4—2261no—
303C4#1681366712yes—
304C2—22no—
305C2—82no—
306C2—9042no—
307C2—9041no—
308C2#2029916311yescharacteristic
309C2AGL(1,ℤ/8)×D11311yescharacteristic
310C2C2×#1681364911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
hypercenter#450D113
hypocenterC113#3217
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#16813618C2semidirect
2. #20299134C2semidirect
3. #20298984C2semidirect
4. #20298961C2semidirect
5. #20298796C2semidirect
6. #20298792C2semidirect
7. #20298748C2semidirect
8. #20298734C2semidirect
9. #20298732C2semidirect
10. #20298652C2semidirect
11. #450×C113C2semidirect
15. C2×#14268634C22semidirect
16. C2×D904C22semidirect
17. C2×#14268632C22semidirect
23. #16813613C22semidirect
24. #16813611C22semidirect
27. Q8×Dic113C22semidirect
28. #16813584C22semidirect
32. #16813551C22semidirect
33. #16813544C22semidirect
34. #16813543C22semidirect
35. #16813542C22semidirect
37. #16813532C22semidirect
39. C2×SD16×C113C22semidirect
41. #102×C113C22semidirect
156. C113#3217semidirect
164. #450D113semidirect
173. C2×SD16C2×D113semidirect
195. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136182
#202991342
#202989842
#202989612
#202987962
#202987922
#202987482
#202987342
#202987322
#202986522
#450×C1132
#3217113