Finite Group Databasebeta

← #28400049

Subgroups — #28400049

Order 14464.

584 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16813646C212yesmaximal, complemented
2#127×D113C211yesmaximal, characteristic, complemented
3C4×#14268646C211yesmaximal, characteristic, complemented
4#20298799C211yesmaximal, characteristic, complemented
5#20298797C212yesmaximal, complemented
6#20298795C211yesmaximal, characteristic, complemented
7#20298793C211yesmaximal, characteristic, complemented
8#20298791C212yesmaximal, complemented
9#20298620C211yesmaximal, characteristic, complemented
10#20298601C212yesmaximal, complemented
11#459×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2211yescharacteristic
13C2×D4×D113—21no—
14C2×D4×D113—21no—
15C2×D4×D113C2212yes—
16#16813646—28no—
17C2×#14268636C2212yescomplemented
18C2×#14268635C2212yescomplemented
19C2×#14268632C2212yescomplemented
20C2×#14268630C2212yes—
21#16813619C2211yescharacteristic
22#16813618—21no—
23#16813618—21no—
24#16813618C2212yes—
25C4×Dic226C2211yescharacteristic, complemented
26#16813587C2211yescharacteristic, complemented
27D4×Dic113C2211yescharacteristic, complemented
28C4×C22⋊D113—21no—
29#16813582—21no—
30#16813580C2211yescharacteristic
31#16813578—21no—
32C2×C4×Dic113—21no—
33C42×D113C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic, complemented
35#16813551C2212yescomplemented
36#16813544C2212yescomplemented
37#16813543C2212yescomplemented
38#16813542C2212yescomplemented
39C2×D8×C113C2212yescomplemented
40#127×C113C2211yescharacteristic
41C4×D4×C113C2211yescharacteristic, complemented
42C4⋊C8×C113C2211yescharacteristic, complemented
43#102×C113C2212yescomplemented
44C23×D113—22no—
45#14268646—22no—
46#14268646D414yescomplemented
47C2×Dic226C2311yescharacteristic
48C2×D452—21no—
49C2×D452—21no—
50C2×D452C2312yes—
51C2×C22⋊D113—21no—
52C2×C22⋊D113—22no—
53C2×C22⋊D113—22no—
54C2×C22⋊D113—22no—
55D4×D113—24no—
56D4×D113—24no—
57D4×D113—44no—
58D4×D113—44no—
59C22×Dic113—21no—
60C22×Dic113—21no—
61C2×C4×D113D411yescharacteristic
62C2×C4×D113D411yescharacteristic
63C2×C4×D113C2311yescharacteristic
64#14268636—24no—
65#14268635—24no—
66#14268632—24no—
67#14268630—24no—
68C2×#11744751C2312yes—
69C4⋊Dic113C2311yescharacteristic
70#14268626—21no—
71#14268626—21no—
72C22⋊Dic113—21no—
73#14268624—21no—
74C4×Dic113—21no—
75C4×Dic113—21no—
76C4×Dic113—21no—
77C4×Dic113D411yescharacteristic
78C4×Dic113D411yescharacteristic
79C4×Dic113C2311yescharacteristic
80C2×D4×C113—21no—
81C2×D4×C113—21no—
82C2×D4×C113C2312yes—
83C2×D4×C113C2311yescharacteristic
84C22×C4×C113—21no—
85D8×C113—24no—
86C2×C8×C113C2312yes—
87C4⋊C4×C113C2311yescharacteristic
88C22⋊C4×C113—21no—
89C42×C113C2311yescharacteristic
90C23×C113—21no—
91C23×C113—22no—
92C22×D113—22no—
93C22×D113—44no—
94C22×D113—44no—
95C22×D113—44no—
96C22×D113C2×D411yescharacteristic
97D4×C113—22no—
98D4×C113—21no—
99D4×C113—22no—
100D4×C113—42no—
101D4×C113—42no—
102D4×C113C2×D412yescomplemented
103C2×C4×C113—21no—
104C2×C4×C113—42no—
105C2×C4×C113C2×D411yescharacteristic
106C2×C4×C113C2×D411yescharacteristic
107C2×C4×C113C2411yescharacteristic
108C22⋊D113—24no—
109C22⋊D113—44no—
110C22⋊D113—44no—
111C22⋊D113—44no—
112C2×Dic113—21no—
113C2×Dic113—24no—
114C2×Dic113—21no—
115C2×Dic113—42no—
116C2×Dic113C2×D411yescharacteristic
117C2×Dic113C2×D411yescharacteristic
118C2×Dic113C2×D411yescharacteristic
119D452—22no—
120D452—22no—
121D452—42no—
122D452—42no—
123C4×D113—22no—
124C4×D113—22no—
125C4×D113C2×D412yes—
126C4×D113#4112yes—
127Dic226—21no—
128Dic226C2×D412yescomplemented
129C8×C113—22no—
130#11744751—22no—
131C22×C113—22no—
132C22×C113—41no—
133C22×C113—41no—
134C22×C113—42no—
135C22×C113—42no—
136C22×C113—42no—
137C22×C113C22×D411yescharacteristic
138C2×D113—21no—
139C2×D113—21no—
140C2×D113—42no—
141C2×D113—42no—
142C2×D113—42no—
143C2×D113—88no—
144C2×D113#12112yes—
145C4×C113—21no—
146C4×C113—41no—
147C4×C113AGL(1,ℤ/8)12yescomplemented
148C4×C113C22×D411yescharacteristic
149C4×C113C2×#4111yescharacteristic
150Dic113—22no—
151Dic113—21no—
152Dic113—41no—
153Dic113#12112yes—
154Dic113AGL(1,ℤ/8)12yescomplemented
155C2×C113—42no—
156C2×C113—82no—
157C2×C113C2×#12111yescharacteristic
158C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
159C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
160D113—22no—
161D113—82no—
162#3038—1131nomaximal, Sylow
163C113#303811yescharacteristic, complemented, Sylow
164C2×AGL(1,ℤ/8)—1132no—
165C2×#127—1131no—
166C4×#41—1131no—
167#460—1131no—
168#460—1131no—
169#460—1132no—
170#459—1132no—
171#459—1131no—
172#459D11311yescharacteristic, complemented
173#423—1131no—
174#418—1132no—
175C2×#41—1131no—
176C22×D4—1132no—
177C22×D4—2261no—
178C22×D4—2261no—
179AGL(1,ℤ/8)—2268no—
180C2×SD16—1132no—
181C2×SD16—1132no—
182C2×D8—1132no—
183C2×D8C2×D11312yescomplemented
184C2×M16—1132no—
185#127—1132no—
186#127—1131no—
187#127—2261no—
188#127—2261no—
189#127C2×D11311yescharacteristic
190C4×Q8—1131no—
191C4×Q8—1131no—
192C4×D4—1131no—
193C4×D4—2261no—
194C4×D4—2261no—
195C4×D4C2×D11311yescharacteristic, complemented
196#117—1131no—
197#117—2261no—
198C2×C42—1131no—
199C2×C42—2261no—
200C4⋊C8—1132no—
201C4⋊C8—1131no—
202C4⋊C8C2×D11311yescharacteristic, complemented
203#102—1132no—
204#102—1132no—
205#102—1132no—
206#102C2×D11312yescomplemented
207C24—2262no—
208#41—1134no—
209#41—2262no—
210C2×Q8—1131no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—1132no—
214C2×D4—4524no—
215C2×D4—4524no—
216C2×D4—2264no—
217C2×D4—2264no—
218C2×D4—2262no—
219C2×D4—2262no—
220C2×D4—2262no—
221C2×D4—2261no—
222C2×D4—2261no—
223C2×D4—2261no—
224C2×D4C22×D11312yes—
225C2×D4C22×D11311yescharacteristic
226C22×C4—21no—
227C22×C4—1131no—
228C22×C4—1131no—
229C22×C4—1131no—
230C22×C4—2261no—
231C22×C4—2261no—
232SD16—2264no—
233SD16—2264no—
234D8—24no—
235D8—2264no—
236M16—2264no—
237C2×C8—1132no—
238C2×C8C22×D11312yes—
239C4⋊C4—1131no—
240C4⋊C4—2261no—
241C4⋊C4—2261no—
242C4⋊C4C22×D11311yescharacteristic
243C22⋊C4—21no—
244C22⋊C4—2261no—
245C22⋊C4—2261no—
246C42—1131no—
247C42—1131no—
248C42—1131no—
249C42—2261no—
250C42—2261no—
251C42—2261no—
252C42C22×D11311yescharacteristic
253C23—21no—
254C23—22no—
255C23—1131no—
256C23—4524no—
257C23—4524no—
258C23—4524no—
259C23—2262no—
260Q8—1132no—
261Q8—2261no—
262D4—22no—
263D4—21no—
264D4—22no—
265D4—42no—
266D4—42no—
267D4—4522no—
268D4—4524no—
269D4—4524no—
270D4—4524no—
271D4—4522no—
272D4—2264no—
273D4—2262no—
274D4—2262no—
275D4D4×D11312yescomplemented
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—1131no—
279C2×C4—1131no—
280C2×C4—1132no—
281C2×C4—1132no—
282C2×C4—1131no—
283C2×C4—4522no—
284C2×C4—2262no—
285C2×C4—2264no—
286C2×C4—2261no—
287C2×C4—2261no—
288C2×C4—2262no—
289C2×C4D4×D11311yescharacteristic
290C2×C4D4×D11311yescharacteristic
291C2×C4C23×D11311yescharacteristic
292C8—22no—
293C8—2262no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—1132no—
301C22—9048no—
302C22—4522no—
303C22—4522no—
304C22—4522no—
305C22—2261no—
306C22—2261no—
307C22C2×D4×D11311yescharacteristic
308C4—21no—
309C4—41no—
310C4—1132no—
311C4—1132no—
312C4—4521no—
313C4—2262no—
314C4—2261no—
315C4#1681364612yescomplemented
316C4C2×D4×D11311yescharacteristic
317C4#41×D11311yescharacteristic
318C2—42no—
319C2—82no—
320C2—9042no—
321C2—2262no—
322C2#121×D11311yescharacteristic
323C2AGL(1,ℤ/8)×D11311yescharacteristic
324C2C2×#1681364611yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3038
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. C2×#16813646C2semidirect
2. #127×D113C2semidirect
3. C4×#14268646C2semidirect
4. #20298799C2semidirect
5. #20298797C2semidirect
6. #20298795C2semidirect
7. #20298793C2semidirect
8. #20298791C2semidirect
9. #20298620C2semidirect
10. #20298601C2semidirect
11. #459×C113C2semidirect
17. C2×#14268636C22semidirect
18. C2×#14268635C22semidirect
19. C2×#14268632C22semidirect
25. C4×Dic226C22semidirect
26. #16813587C22semidirect
27. D4×Dic113C22semidirect
34. C4⋊#11744751C22semidirect
35. #16813551C22semidirect
36. #16813544C22semidirect
37. #16813543C22semidirect
38. #16813542C22semidirect
39. C2×D8×C113C22semidirect
41. C4×D4×C113C22semidirect
42. C4⋊C8×C113C22semidirect
43. #102×C113C22semidirect
46. #14268646D4semidirect
102. D4×C113C2×D4semidirect
128. Dic226C2×D4semidirect
147. C4×C113AGL(1,ℤ/8)semidirect
154. Dic113AGL(1,ℤ/8)semidirect
163. C113#3038semidirect
172. #459D113semidirect
183. C2×D8C2×D113semidirect
195. C4×D4C2×D113semidirect
202. C4⋊C8C2×D113semidirect
206. #102C2×D113semidirect
275. D4D4×D113semidirect
315. C4#16813646semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
#127×D1132
C4×#142686462
#202987992
#202987972
#202987952
#202987932
#202987912
#202986202
#202986012
#459×C1132
#3038113