Finite Group Databasebeta

← #28400217

Subgroups — #28400217

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×#16813628C211yesmaximal, characteristic, complemented
3#20299164C212yesmaximal, complemented
4#20298850C212yesmaximal, complemented
5#20298849C212yesmaximal, complemented
6#20298835C211yesmaximal, characteristic, complemented
7#20298834C211yesmaximal, characteristic, complemented
8#20298831C211yesmaximal, characteristic, complemented
9#20298635C211yesmaximal, characteristic, complemented
10#20298601C212yesmaximal, complemented
11#466×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C2×D4×D113C2212yes—
14C2×D904C2211yescharacteristic
15C2×#14268632C2212yes—
16D8×D113—24no—
17#16813628—24no—
18C2×#14268631C2211yescharacteristic, complemented
19C2×#14268630C2211yescharacteristic
20C2×#14268630C2211yescharacteristic, 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#16813556C2211yescharacteristic, complemented
32#16813553C2212yescomplemented
33#16813544C2212yescomplemented
34#16813543C2212yescomplemented
35#16813542C2212yescomplemented
36C2×D8×C113C2211yescharacteristic
37C22×C8×C113C2211yescharacteristic, complemented
38#121×C113C2212yescomplemented
39#107×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#14268631—22no—
60#14268630—22no—
61#14268630—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—
76C2×C8×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—21no—
120C22×C113—21no—
121C22×C113—42no—
122C22×C113—42no—
123C22×C113—42no—
124C22×C113C22×D411yescharacteristic
125C2×D113—21no—
126C2×D113—21no—
127C2×D113—21no—
128C2×D113—21no—
129C2×D113—21no—
130C2×D113—42no—
131C2×D113—42no—
132C2×D113—42no—
133C2×D113—88no—
134C2×D113#12112yes—
135C4×C113—21no—
136C4×C113—42no—
137C4×C113C22×D411yescharacteristic
138C4×C113C2×#4111yescharacteristic
139Dic113—21no—
140Dic113—42no—
141Dic113#12112yes—
142C2×C113—41no—
143C2×C113—82no—
144C2×C113C2×#12111yescharacteristic
145C2×C113#57611yescharacteristic
146C2×C113#57611yescharacteristic
147D113—22no—
148D113—41no—
149D113—82no—
150#3058—1131nomaximal, Sylow
151C113#305811yescharacteristic, complemented, Sylow
152C22×D8—1131no—
153C2×#131—1131no—
154#535—1132no—
155#469—1132no—
156#469—1132no—
157#466—1131no—
158#466—1131no—
159#466—1131no—
160#466D11311yescharacteristic, complemented
161#427—1131no—
162#418—1132no—
163C2×#41—1131no—
164C22×D4—1132no—
165C2×D8—1132no—
166C2×D8—1131no—
167C2×D8—2264no—
168C2×D8C2×D11311yescharacteristic
169#131—2264no—
170C2×M16—1131no—
171C2×M16—1131no—
172C2×M16—1131no—
173C22×C8—1131no—
174C22×C8—1131no—
175C22×C8C2×D11311yescharacteristic, complemented
176#127—2262no—
177#124—2262no—
178#121—1132no—
179#121—1132no—
180#121—1132no—
181#121C2×D11312yescomplemented
182#120—2262no—
183#120—2262no—
184#117—1132no—
185#107—1131no—
186#107C2×D11311yescharacteristic, complemented
187#106—1132no—
188#102—1132no—
189#102—1132no—
190#102—1132no—
191#102C2×D11312yescomplemented
192C24—2262no—
193#41—2262no—
194#41—2262no—
195C2×Q8—1131no—
196C2×D4—22no—
197C2×D4—1131no—
198C2×D4—1131no—
199C2×D4—1131no—
200C2×D4—1132no—
201C2×D4—2262no—
202C2×D4—2264no—
203C2×D4—2264no—
204C2×D4—2262no—
205C2×D4—2262no—
206C2×D4—2262no—
207C2×D4C22×D11312yes—
208C22×C4—1131no—
209C22×C4—1131no—
210C22×C4C22×D11311yescharacteristic
211D8—22no—
212D8—2264no—
213D8—2262no—
214M16—2262no—
215M16—2262no—
216M16—2262no—
217C2×C8—22no—
218C2×C8—1131no—
219C2×C8—1134no—
220C2×C8—1131no—
221C2×C8—2262no—
222C2×C8C22×D11311yescharacteristic
223C2×C8C22×D11311yescharacteristic
224C4⋊C4—1132no—
225C4⋊C4C22×D11312yes—
226C22⋊C4—22no—
227C22⋊C4—2262no—
228C22⋊C4—2262no—
229C22⋊C4—2262no—
230C22⋊C4—2262no—
231C42—2262no—
232C23—22no—
233C23—1131no—
234C23—1131no—
235C23—9042no—
236C23—9042no—
237C23—4524no—
238C23—2262no—
239C23D4×D11311yescharacteristic
240Q8—2262no—
241D4—22no—
242D4—22no—
243D4—82no—
244D4—9042no—
245D4—9042no—
246D4—9042no—
247D4—4524no—
248D4—2262no—
249D4—2262no—
250D4—2262no—
251D4—2262no—
252D4—2262no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—1131no—
257C2×C4—1132no—
258C2×C4—1132no—
259C2×C4—1131no—
260C2×C4—2262no—
261C2×C4—2261no—
262C2×C4—2261no—
263C2×C4D4×D11311yescharacteristic
264C2×C4C23×D11311yescharacteristic
265C8—21no—
266C8—1132no—
267C8—2261no—
268C8D4×D11312yes—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—1132no—
276C22—9048no—
277C22—4522no—
278C22—4522no—
279C22—4522no—
280C22—2261no—
281C22—2261no—
282C22—2261no—
283C22—2261no—
284C22—2261no—
285C22C2×D4×D11311yescharacteristic
286C4—21no—
287C4—42no—
288C4—1132no—
289C4—4522no—
290C4—2261no—
291C4C2×D4×D11311yescharacteristic
292C4#41×D11311yescharacteristic
293C2—41no—
294C2—82no—
295C2—9042no—
296C2—4521no—
297C2—2262no—
298C2#121×D11311yescharacteristic
299C2#2029939911yescharacteristic
300C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#466×C113C2
socleC22×C113C22×D4
hypercenter#466D113
hypocenterC113#3058
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×D8×D113C2semidirect
2. C2×#16813628C2semidirect
3. #20299164C2semidirect
4. #20298850C2semidirect
5. #20298849C2semidirect
6. #20298835C2semidirect
7. #20298834C2semidirect
8. #20298831C2semidirect
9. #20298635C2semidirect
10. #20298601C2semidirect
11. #466×C113C2semidirect
18. C2×#14268631C22semidirect
20. C2×#14268630C22semidirect
22. C2×C8×D113C22semidirect
25. #16813597C22semidirect
26. #16813596C22semidirect
27. #16813593C22semidirect
31. #16813556C22semidirect
32. #16813553C22semidirect
33. #16813544C22semidirect
34. #16813543C22semidirect
35. #16813542C22semidirect
37. C22×C8×C113C22semidirect
38. #121×C113C22semidirect
39. #107×C113C22semidirect
40. #102×C113C22semidirect
65. C8×D113D4semidirect
151. C113#3058semidirect
160. #466D113semidirect
175. C22×C8C2×D113semidirect
181. #121C2×D113semidirect
186. #107C2×D113semidirect
191. #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×#168136282
#202991642
#202988502
#202988492
#202988352
#202988342
#202988312
#202986352
#202986012
#466×C1132
#3058113