Finite Group Databasebeta

← #28402808

Subgroups — #28402808

Order 14464.

448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 448 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
1#20299321C211yesmaximal, characteristic, complemented
2#20299233C211yesmaximal, characteristic
3#20298944C211yesmaximal, characteristic, complemented
4#20298920C212yesmaximal, complemented
5#20298879C211yesmaximal, characteristic, complemented
6#20298841C212yesmaximal, complemented
7#20298747C212yesmaximal, complemented
8C4×#14268634C211yesmaximal, characteristic, complemented
9#20298675C211yesmaximal, characteristic, complemented
10#20298601C212yesmaximal, complemented
11#460×C113C211yesmaximal, characteristic, complemented
12C2×D4×D113—21no—
13C2×D4×D113C2212yes—
14C2×#14268634C2211yescharacteristic
15C2×#14268630C2212yescomplemented
16#16813622C2211yescharacteristic, complemented
17#16813617—22no—
18#16813610—21no—
19#16813598C2212yescomplemented
20#16813593—21no—
21#16813593C2212yes—
22#16813590—22no—
23C4×Dic226—21no—
24C4×D452C2211yescharacteristic
25C4×D452C2211yescharacteristic
26#16813580C2212yescomplemented
27#16813556C2212yescomplemented
28#16813553C2211yescharacteristic, complemented
29#16813546C2211yescharacteristic, complemented
30#16813544C2212yes—
31#16813543C2212yescomplemented
32#16813543C2212yescomplemented
33#16813542C2211yescharacteristic
34#16813534C2212yescomplemented
35C4×#11744751C2211yescharacteristic, complemented
36C2×SD16×C113C2212yescomplemented
37#127×C113C2211yescharacteristic
38C4×Q8×C113C2211yescharacteristic, complemented
39C4⋊C8×C113C2211yescharacteristic, complemented
40#102×C113C2212yescomplemented
41C23×D113—22no—
42C2×Dic226—21no—
43C2×D452D411yescharacteristic
44C2×D452C2311yescharacteristic
45C2×C22⋊D113—22no—
46C2×C22⋊D113—22no—
47D4×D113—24no—
48D4×D113—42no—
49D4×D113—44no—
50C2×C4×D113—21no—
51C2×C4×D113C2312yes—
52#14268634—22no—
53#14268630—42no—
54C2×#11744751C2311yescharacteristic
55C2×#11744751C2311yescharacteristic
56C4⋊Dic113—21no—
57C4⋊Dic113D411yescharacteristic
58C4⋊Dic113C2312yes—
59C4⋊Dic113C2311yescharacteristic
60#14268626—22no—
61C22⋊Dic113—22no—
62#14268624—22no—
63#14268624—22no—
64#14268624—21no—
65#14268624D412yes—
66C4×Dic113—22no—
67C2×Q8×C113C2311yescharacteristic
68C2×D4×C113—21no—
69C2×D4×C113—21no—
70C2×D4×C113C2312yes—
71SD16×C113—42no—
72C2×C8×C113C2312yes—
73C4⋊C4×C113—21no—
74C4⋊C4×C113C2311yescharacteristic
75C42×C113—21no—
76C42×C113C2311yescharacteristic
77C23×C113—22no—
78C22×D113—21no—
79C22×D113—44no—
80C22×D113—44no—
81C22×D113—82no—
82C22×D113C2×D412yes—
83Q8×C113—21no—
84Q8×C113—21no—
85D4×C113—22no—
86D4×C113—22no—
87D4×C113—42no—
88D4×C113—81no—
89C2×C4×C113—21no—
90C2×C4×C113—21no—
91C2×C4×C113C2×D411yescharacteristic
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2411yescharacteristic
94C22⋊D113—44no—
95C22⋊D113—44no—
96C2×Dic113—22no—
97C2×Dic113—21no—
98C2×Dic113C2×D412yes—
99D452—22no—
100D452—21no—
101D452#4112yes—
102C4×D113—22no—
103C4×D113—22no—
104C4×D113—42no—
105Dic226—42no—
106C8×C113—22no—
107#11744751—21no—
108#11744751—21no—
109C22×C113—42no—
110C22×C113—42no—
111C22×C113—42no—
112C22×C113C22×D411yescharacteristic
113C2×D113—22no—
114C2×D113—22no—
115C2×D113—22no—
116C2×D113—22no—
117C2×D113—41no—
118C2×D113—41no—
119C2×D113—88no—
120C4×C113—21no—
121C4×C113—41no—
122C4×C113—41no—
123C4×C113AGL(1,ℤ/8)12yes—
124C4×C113C2×#4111yescharacteristic
125C4×C113H(5,𝔽2)11yescharacteristic
126Dic113—22no—
127Dic113—42no—
128Dic113—41no—
129C2×C113—82no—
130C2×C113#54611yescharacteristic
131C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C113#57711yescharacteristic
133D113—42no—
134D113—42no—
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#460D11311yescharacteristic, complemented
144#450—1132no—
145C4×SD16—1131no—
146#436—1131no—
147#418—1132no—
148C22×D4—1132no—
149C22×D4—2261no—
150C2×SD16—1131no—
151C2×SD16C2×D11312yescomplemented
152C2×M16—1132no—
153C4⋊Q8—1131no—
154#127C2×D11311yescharacteristic
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×D4—1131no—
165#117—1132no—
166#107—1132no—
167#106—1131no—
168C4⋊C8C2×D11311yescharacteristic, complemented
169#103—1131no—
170#102—1132no—
171#102—1132no—
172#102—1132no—
173#102—1131no—
174#102C2×D11312yescomplemented
175C22⋊C8—1132no—
176C4×C8—1131no—
177C24—2262no—
178C2×Q8—2261no—
179C2×Q8C22×D11311yescharacteristic
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—1131no—
183C2×D4—1131no—
184C2×D4—4524no—
185C2×D4—4522no—
186C2×D4—2262no—
187C2×D4—2264no—
188C2×D4—2262no—
189C2×D4C22×D11312yes—
190C22×C4—1132no—
191C22×C4—2261no—
192SD16—42no—
193SD16—2262no—
194M16—4522no—
195C2×C8—1131no—
196C2×C8—1131no—
197C2×C8C22×D11312yes—
198C4⋊C4—21no—
199C4⋊C4—1131no—
200C4⋊C4—1132no—
201C4⋊C4—1131no—
202C4⋊C4—2262no—
203C4⋊C4—2261no—
204C4⋊C4C22×D11311yescharacteristic
205C22⋊C4—1132no—
206C22⋊C4—2262no—
207C22⋊C4—2262no—
208C22⋊C4—2262no—
209C22⋊C4—2261no—
210C42—21no—
211C42—2262no—
212C42C22×D11311yescharacteristic
213C23—22no—
214C23—1132no—
215C23—9042no—
216C23—4524no—
217C23—4524no—
218C23—2261no—
219Q8—21no—
220Q8—21no—
221Q8—4522no—
222D4—22no—
223D4—22no—
224D4—42no—
225D4—81no—
226D4—1132no—
227D4—4524no—
228D4—4524no—
229D4—2262no—
230D4—2261no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—1132no—
234C2×C4—4522no—
235C2×C4—2262no—
236C2×C4—2261no—
237C2×C4—2262no—
238C2×C4—2262no—
239C2×C4D4×D11311yescharacteristic
240C2×C4D4×D11311yescharacteristic
241C2×C4C23×D11311yescharacteristic
242C8—22no—
243C8—2261no—
244C8—2261no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—9048no—
249C22—4521no—
250C22—4521no—
251C22—2262no—
252C22—2262no—
253C22—2262no—
254C22—2262no—
255C22C2×D4×D11311yescharacteristic
256C4—21no—
257C4—41no—
258C4—41no—
259C4—4521no—
260C4—4522no—
261C4—2262no—
262C4#1681364912yes—
263C4#41×D11311yescharacteristic
264C4#1681366711yescharacteristic
265C2—82no—
266C2—4522no—
267C2—4522no—
268C2#2029924511yescharacteristic
269C2C2×#1681364911yescharacteristic
270C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#460×C113C2
socleC22×C113C22×D4
prime radical#20299233C2
hypercenter#460D113
hypocenterC113#3324
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #20299321C2semidirect
3. #20298944C2semidirect
4. #20298920C2semidirect
5. #20298879C2semidirect
6. #20298841C2semidirect
7. #20298747C2semidirect
8. C4×#14268634C2semidirect
9. #20298675C2semidirect
10. #20298601C2semidirect
11. #460×C113C2semidirect
15. C2×#14268630C22semidirect
16. #16813622C22semidirect
19. #16813598C22semidirect
26. #16813580C22semidirect
27. #16813556C22semidirect
28. #16813553C22semidirect
29. #16813546C22semidirect
31. #16813543C22semidirect
32. #16813543C22semidirect
34. #16813534C22semidirect
35. C4×#11744751C22semidirect
36. C2×SD16×C113C22semidirect
38. C4×Q8×C113C22semidirect
39. C4⋊C8×C113C22semidirect
40. #102×C113C22semidirect
136. C113#3324semidirect
143. #460D113semidirect
151. C2×SD16C2×D113semidirect
162. C4×Q8C2×D113semidirect
168. C4⋊C8C2×D113semidirect
174. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993212
#202992332
#202989442
#202989202
#202988792
#202988412
#202987472
C4×#142686342
#202986752
#202986012
#460×C1132
#3324113