Finite Group Databasebeta

← #28402390

Subgroups — #28402390

Order 14464.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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#20299253C211yesmaximal, characteristic, complemented
2#20299233C211yesmaximal, characteristic, complemented
3#20298944C211yesmaximal, characteristic, complemented
4#20298910C212yesmaximal, complemented
5#20298879C211yesmaximal, characteristic, complemented
6#20298831C212yesmaximal, complemented
7#20298730C212yesmaximal, complemented
8C4×#14268632C211yesmaximal, characteristic, complemented
9#20298663C211yesmaximal, characteristic, complemented
10#102×D113C212yesmaximal, complemented
11#459×C113C211yesmaximal, characteristic, complemented
12C2×#14268647—21no—
13C2×D4×D113—21no—
14C2×D4×D113C2212yes—
15C2×#14268632C2211yescharacteristic
16C2×C8×D113C2212yescomplemented
17#16813622C2211yescharacteristic, complemented
18#16813604—22no—
19#16813601—21no—
20#16813593—21no—
21#16813593C2212yes—
22#16813593C2212yescomplemented
23#16813590—22no—
24C4×D452C2211yescharacteristic
25C4×D452C2211yescharacteristic
26C4⋊C4×D113C2212yescomplemented
27#16813556C2212yescomplemented
28#16813555C2211yescharacteristic, complemented
29#16813544C2212yes—
30#16813543C2211yescharacteristic, complemented
31#16813543C2212yescomplemented
32#16813543C2212yescomplemented
33#16813542C2211yescharacteristic
34#16813534C2212yescomplemented
35C4×#11744751C2211yescharacteristic, complemented
36C2×D8×C113C2212yescomplemented
37#127×C113C2211yescharacteristic
38C4×D4×C113C2211yescharacteristic, complemented
39C4⋊C8×C113C2211yescharacteristic, complemented
40#102×C113C2212yescomplemented
41C23×D113—22no—
42#14268647—44no—
43C2×Dic226—21no—
44C2×D452D411yescharacteristic
45C2×D452C2311yescharacteristic
46C2×C22⋊D113—22no—
47C2×C22⋊D113—22no—
48C2×C22⋊D113—22no—
49D4×D113—24no—
50D4×D113—42no—
51D4×D113—44no—
52C2×C4×D113—22no—
53C2×C4×D113—21no—
54C2×C4×D113C2312yes—
55#14268632—22no—
56C2×#11744751C2311yescharacteristic
57C2×#11744751C2311yescharacteristic
58C8×D113—42no—
59C4⋊Dic113—21no—
60C4⋊Dic113D411yescharacteristic
61C4⋊Dic113C2312yes—
62C4⋊Dic113C2311yescharacteristic
63#14268626—22no—
64C22⋊Dic113—22no—
65C22⋊Dic113—22no—
66#14268624—21no—
67#14268624D412yes—
68C2×D4×C113—21no—
69C2×D4×C113—21no—
70C2×D4×C113C2312yes—
71C2×D4×C113C2311yescharacteristic
72C22×C4×C113—21no—
73D8×C113—42no—
74C2×C8×C113C2312yes—
75C4⋊C4×C113C2311yescharacteristic
76C22⋊C4×C113—21no—
77C42×C113C2311yescharacteristic
78C23×C113—21no—
79C23×C113—22no—
80C22×D113—21no—
81C22×D113—44no—
82C22×D113—44no—
83C22×D113—82no—
84C22×D113C2×D412yes—
85D4×C113—21no—
86D4×C113—22no—
87D4×C113—21no—
88D4×C113—22no—
89D4×C113—42no—
90D4×C113—81no—
91C2×C4×C113—21no—
92C2×C4×C113—42no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2411yescharacteristic
96C22⋊D113—44no—
97C22⋊D113—44no—
98C22⋊D113—44no—
99C2×Dic113—21no—
100C2×Dic113—22no—
101C2×Dic113C2×D412yes—
102D452—21no—
103D452D814yescomplemented
104D452#4112yescomplemented
105C4×D113—22no—
106C4×D113—22no—
107C4×D113—44no—
108C4×D113—42no—
109Dic226—42no—
110C8×C113—22no—
111#11744751—21no—
112#11744751—21no—
113C22×C113—42no—
114C22×C113—41no—
115C22×C113—41no—
116C22×C113—42no—
117C22×C113—42no—
118C22×C113—41no—
119C22×C113C22×D411yescharacteristic
120C2×D113—22no—
121C2×D113—22no—
122C2×D113—22no—
123C2×D113—41no—
124C2×D113—41no—
125C2×D113—88no—
126C2×D113C2×D814yes—
127C4×C113—21no—
128C4×C113—41no—
129C4×C113C2×D812yes—
130C4×C113C2×#4111yescharacteristic
131C4×C113H(5,𝔽2)11yescharacteristic
132Dic113—22no—
133Dic113—42no—
134Dic113—41no—
135C2×C113—82no—
136C2×C113—81no—
137C2×C113#54611yescharacteristic
138C2×C113C22×D811yescharacteristic
139C2×C113#57711yescharacteristic
140D113—24no—
141D113—42no—
142#3294—1131nomaximal, Sylow
143C113#329411yescharacteristic, complemented, Sylow
144#547—1131no—
145D42—1131no—
146#486—1131no—
147#480—1132no—
148#474—1131no—
149#466—1132no—
150#459D11311yescharacteristic, complemented
151#447—1132no—
152C4×D8—1131no—
153C8×D4—1131no—
154C2×#102—1132no—
155C2×#41—2261no—
156C22×D4—1132no—
157C22×D4—2261no—
158C2×D8—1131no—
159C2×D8C2×D11312yescomplemented
160C22×C8—1132no—
161C4⋊Q8—1131no—
162#127C2×D11311yescharacteristic
163#123—2262no—
164C22⋊Q8—2261no—
165#121—1132no—
166#121—1132no—
167#121—2261no—
168#120—2262no—
169C4×D4—1131no—
170C4×D4—1131no—
171C4×D4C2×D11311yescharacteristic, complemented
172C2×C4⋊C4—1132no—
173#107—1132no—
174#107—1131no—
175C4⋊C8C2×D11311yescharacteristic, complemented
176#102—1132no—
177#102—1131no—
178#102—1132no—
179#102—1132no—
180#102—1131no—
181#102C2×D11312yescomplemented
182C22⋊C8—1132no—
183C4×C8—1131no—
184C24—2262no—
185#41—4524no—
186C2×Q8—2261no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—1131no—
190C2×D4—1131no—
191C2×D4—4524no—
192C2×D4—4522no—
193C2×D4—2262no—
194C2×D4—2264no—
195C2×D4—2262no—
196C2×D4—2262no—
197C2×D4C22×D11312yes—
198C2×D4C22×D11311yescharacteristic
199C22×C4—21no—
200C22×C4—1132no—
201C22×C4—2262no—
202C22×C4—2261no—
203D8—42no—
204D8—2262no—
205C2×C8—1131no—
206C2×C8—1131no—
207C2×C8—4522no—
208C2×C8C22×D11312yes—
209C4⋊C4—1131no—
210C4⋊C4—1132no—
211C4⋊C4—1131no—
212C4⋊C4—2262no—
213C4⋊C4—2261no—
214C4⋊C4C22×D11311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—1132no—
217C22⋊C4—2262no—
218C22⋊C4—2262no—
219C22⋊C4—2261no—
220C42C22×D11311yescharacteristic
221C23—21no—
222C23—22no—
223C23—1132no—
224C23—9042no—
225C23—4524no—
226C23—4524no—
227C23—2261no—
228Q8—4522no—
229D4—21no—
230D4—22no—
231D4—21no—
232D4—22no—
233D4—42no—
234D4—81no—
235D4—1134no—
236D4—1132no—
237D4—4524no—
238D4—4524no—
239D4—4524no—
240D4—2261no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—1132no—
244C2×C4—4524no—
245C2×C4—4522no—
246C2×C4—2261no—
247C2×C4—2262no—
248C2×C4—2262no—
249C2×C4—2262no—
250C2×C4D4×D11311yescharacteristic
251C2×C4D4×D11311yescharacteristic
252C2×C4C23×D11311yescharacteristic
253C8—22no—
254C8—2261no—
255C8—2261no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—41no—
262C22—1134no—
263C22—9048no—
264C22—4521no—
265C22—4521no—
266C22—2262no—
267C22—2262no—
268C22—2262no—
269C22C2×D4×D11311yescharacteristic
270C4—21no—
271C4—41no—
272C4—4521no—
273C4—4522no—
274C4—2262no—
275C4D8×D11312yes—
276C4#41×D11311yescharacteristic
277C4#1681366711yescharacteristic
278C2—82no—
279C2—81no—
280C2—4522no—
281C2—2264no—
282C2#2029924511yescharacteristic
283C2C2×D8×D11311yescharacteristic
284C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3294
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. #20299253C2semidirect
2. #20299233C2semidirect
3. #20298944C2semidirect
4. #20298910C2semidirect
5. #20298879C2semidirect
6. #20298831C2semidirect
7. #20298730C2semidirect
8. C4×#14268632C2semidirect
9. #20298663C2semidirect
10. #102×D113C2semidirect
11. #459×C113C2semidirect
16. C2×C8×D113C22semidirect
17. #16813622C22semidirect
22. #16813593C22semidirect
26. C4⋊C4×D113C22semidirect
27. #16813556C22semidirect
28. #16813555C22semidirect
30. #16813543C22semidirect
31. #16813543C22semidirect
32. #16813543C22semidirect
34. #16813534C22semidirect
35. C4×#11744751C22semidirect
36. C2×D8×C113C22semidirect
38. C4×D4×C113C22semidirect
39. C4⋊C8×C113C22semidirect
40. #102×C113C22semidirect
103. D452D8semidirect
104. D452#41semidirect
143. C113#3294semidirect
150. #459D113semidirect
159. C2×D8C2×D113semidirect
171. C4×D4C2×D113semidirect
175. C4⋊C8C2×D113semidirect
181. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992532
#202992332
#202989442
#202989102
#202988792
#202988312
#202987302
C4×#142686322
#202986632
#102×D1132
#459×C1132
#3294113