Finite Group Databasebeta

← #28402807

Subgroups — #28402807

Order 14464.

448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299321C211yesmaximal, characteristic, complemented
2D4×D452C211yesmaximal, characteristic
3#20298945C211yesmaximal, characteristic, complemented
4#20298924C212yesmaximal, complemented
5#20298878C211yesmaximal, characteristic, complemented
6#20298847C212yesmaximal, complemented
7#20298798C211yesmaximal, characteristic, complemented
8#20298747C212yesmaximal, complemented
9#20298677C211yesmaximal, characteristic, complemented
10#20298601C212yesmaximal, complemented
11C4×SD16×C113C211yesmaximal, characteristic, complemented
12C22×D452—21no—
13C2×D4×D113C2212yes—
14C2×#14268634C2212yescomplemented
15C2×#14268630C2212yescomplemented
16#16813622C2211yescharacteristic, complemented
17#16813619C2211yescharacteristic
18#16813617—22no—
19#16813610—21no—
20#16813598C2212yescomplemented
21#16813597C2212yes—
22#16813596—21no—
23#16813592—22no—
24C4×Dic226—21no—
25C4×D452C2211yescharacteristic
26#16813580C2212yescomplemented
27#16813555C2212yescomplemented
28C4⋊#11744751C2211yescharacteristic, complemented
29#16813544C2212yescomplemented
30#16813544C2212yescomplemented
31#16813543C2212yes—
32#16813542C2212yescomplemented
33#16813534C2212yescomplemented
34C2×SD16×C113C2211yescharacteristic
35C4×Q8×C113C2211yescharacteristic, complemented
36C4×D4×C113C2211yescharacteristic
37#106×C113C2211yescharacteristic, complemented
38#103×C113C2211yescharacteristic, complemented
39#102×C113C2211yescharacteristic
40C4×C8×C113C2211yescharacteristic, complemented
41C23×D113—22no—
42C2×Dic226—21no—
43C2×D452—22no—
44C2×D452—21no—
45C2×D452—21no—
46C2×D452—44no—
47C2×D452D411yescharacteristic
48C2×D452C2312yes—
49C2×C22⋊D113—22no—
50D4×D113—24no—
51D4×D113—42no—
52C2×C4×D113C2312yes—
53#14268634—42no—
54#14268630—42no—
55C2×#11744751C2312yes—
56C4⋊Dic113—21no—
57C4⋊Dic113D411yescharacteristic
58C4⋊Dic113C2312yes—
59#14268626—22no—
60#14268624—22no—
61#14268624—22no—
62#14268624—22no—
63#14268624D412yes—
64C4×Dic113—22no—
65C2×Q8×C113C2311yescharacteristic
66C2×D4×C113C2311yescharacteristic
67C22×C4×C113—21no—
68SD16×C113—22no—
69C2×C8×C113C2311yescharacteristic
70C2×C8×C113C2311yescharacteristic
71C4⋊C4×C113—21no—
72C4⋊C4×C113C2311yescharacteristic
73C4⋊C4×C113C2311yescharacteristic
74C22⋊C4×C113—21no—
75C42×C113—21no—
76C42×C113C2311yescharacteristic
77C23×C113—21no—
78C22×D113—22no—
79C22×D113—44no—
80C22×D113—44no—
81C22×D113—82no—
82C22×D113C2×D412yes—
83Q8×C113—21no—
84Q8×C113—21no—
85D4×C113—21no—
86D4×C113#4112yes—
87C2×C4×C113—21no—
88C2×C4×C113—21no—
89C2×C4×C113—21no—
90C2×C4×C113—42no—
91C2×C4×C113C2×D411yescharacteristic
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2411yescharacteristic
94C22⋊D113—44no—
95C2×Dic113—22no—
96C2×Dic113C2×D412yes—
97D452—22no—
98D452—22no—
99D452—22no—
100D452—44no—
101D452—42no—
102D452—81no—
103C4×D113—22no—
104C4×D113—22no—
105Dic226—42no—
106C8×C113—21no—
107C8×C113—21no—
108#11744751—22no—
109C22×C113—22no—
110C22×C113—41no—
111C22×C113—41no—
112C22×C113C22×D411yescharacteristic
113C2×D113—22no—
114C2×D113—22no—
115C2×D113—22no—
116C2×D113—42no—
117C2×D113—42no—
118C2×D113—42no—
119C2×D113—88no—
120C4×C113—21no—
121C4×C113—41no—
122C4×C113—41no—
123C4×C113—41no—
124C4×C113AGL(1,ℤ/8)12yes—
125C4×C113C2×#4111yescharacteristic
126C4×C113H(5,𝔽2)11yescharacteristic
127Dic113—22no—
128Dic113—42no—
129C2×C113—42no—
130C2×C113#54611yescharacteristic
131C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C113#57711yescharacteristic
133D113—42no—
134D113—82no—
135#3324—1131nomaximal, Sylow
136C113#332411yescharacteristic, complemented, Sylow
137#556—1131no—
138D42—1131no—
139#486—1131no—
140#482—1132no—
141#474—1131no—
142#468—1132no—
143#460—1131no—
144#450—1132no—
145C4×SD16D11311yescharacteristic, complemented
146#436—1131no—
147#418—1132no—
148C22×D4—1132no—
149C22×D4—2261no—
150C2×SD16—1132no—
151C2×SD16C2×D11311yescharacteristic
152C2×M16—1132no—
153C4⋊Q8—1131no—
154#127—1131no—
155#126—2262no—
156#124—2261no—
157C22⋊Q8—1132no—
158#121—1132no—
159#121—2261no—
160#120—2262no—
161C4×Q8—2261no—
162C4×Q8C2×D11311yescharacteristic, complemented
163C4×D4—1131no—
164C4×D4C2×D11311yescharacteristic
165#117—1132no—
166#107—1132no—
167#106C2×D11311yescharacteristic, complemented
168C4⋊C8—1131no—
169#103C2×D11311yescharacteristic, complemented
170#102—1132no—
171#102—1132no—
172#102—1132no—
173#102—1132no—
174#102C2×D11311yescharacteristic
175C22⋊C8—1132no—
176C4×C8C2×D11311yescharacteristic, complemented
177C24—2262no—
178C2×Q8—2261no—
179C2×Q8C22×D11311yescharacteristic
180C2×D4—1131no—
181C2×D4—1132no—
182C2×D4—4524no—
183C2×D4—4522no—
184C2×D4—2262no—
185C2×D4—2262no—
186C2×D4—2264no—
187C2×D4—2261no—
188C2×D4—2261no—
189C2×D4C22×D11311yescharacteristic
190C22×C4—21no—
191C22×C4—1132no—
192SD16—22no—
193SD16—4522no—
194M16—4522no—
195C2×C8—1132no—
196C2×C8C22×D11311yescharacteristic
197C2×C8C22×D11311yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—1131no—
200C4⋊C4—1132no—
201C4⋊C4—2262no—
202C4⋊C4—2261no—
203C4⋊C4C22×D11311yescharacteristic
204C4⋊C4C22×D11311yescharacteristic
205C22⋊C4—21no—
206C22⋊C4—1132no—
207C22⋊C4—2262no—
208C22⋊C4—2262no—
209C22⋊C4—2262no—
210C42—21no—
211C42—2262no—
212C42C22×D11311yescharacteristic
213C23—21no—
214C23—1132no—
215C23—9042no—
216C23—4524no—
217C23—4524no—
218C23—2262no—
219Q8—21no—
220Q8—21no—
221Q8—4522no—
222D4—21no—
223D4—9041no—
224D4—4524no—
225D4—4524no—
226D4—4522no—
227D4—2262no—
228D4—2262no—
229D4—2262no—
230D4#1426864712yes—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—1132no—
236C2×C4—2262no—
237C2×C4—2262no—
238C2×C4—2262no—
239C2×C4D4×D11311yescharacteristic
240C2×C4D4×D11311yescharacteristic
241C2×C4C23×D11311yescharacteristic
242C8—21no—
243C8—21no—
244C8—2262no—
245C22—22no—
246C22—41no—
247C22—41no—
248C22—9048no—
249C22—4522no—
250C22—4522no—
251C22—4522no—
252C22—2262no—
253C22—2262no—
254C22—2262no—
255C22C2×D4×D11311yescharacteristic
256C4—21no—
257C4—41no—
258C4—41no—
259C4—41no—
260C4—4522no—
261C4—2262no—
262C4#1681364912yes—
263C4C2×#1426864711yescharacteristic
264C4#1681366811yescharacteristic
265C2—42no—
266C2—9042no—
267C2—4522no—
268C2#2029924411yescharacteristic
269C2C2×#1681364911yescharacteristic
270C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×SD16×C113C2
socleC22×C113C22×D4
prime radicalD4×D452C2
hypercenterC4×SD16D113
hypocenterC113#3324
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #20299321C2semidirect
3. #20298945C2semidirect
4. #20298924C2semidirect
5. #20298878C2semidirect
6. #20298847C2semidirect
7. #20298798C2semidirect
8. #20298747C2semidirect
9. #20298677C2semidirect
10. #20298601C2semidirect
11. C4×SD16×C113C2semidirect
14. C2×#14268634C22semidirect
15. C2×#14268630C22semidirect
16. #16813622C22semidirect
20. #16813598C22semidirect
26. #16813580C22semidirect
27. #16813555C22semidirect
28. C4⋊#11744751C22semidirect
29. #16813544C22semidirect
30. #16813544C22semidirect
32. #16813542C22semidirect
33. #16813534C22semidirect
35. C4×Q8×C113C22semidirect
37. #106×C113C22semidirect
38. #103×C113C22semidirect
40. C4×C8×C113C22semidirect
136. C113#3324semidirect
145. C4×SD16D113semidirect
162. C4×Q8C2×D113semidirect
167. #106C2×D113semidirect
169. #103C2×D113semidirect
176. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993212
D4×D4522
#202989452
#202989242
#202988782
#202988472
#202987982
#202987472
#202986772
#202986012
C4×SD16×C1132
#3324113