Finite Group Databasebeta

← #28402904

Subgroups — #28402904

Order 14464.

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

normal subgroups only

This group has 430 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#20299268C211yesmaximal, characteristic, complemented
2#20299253C211yesmaximal, characteristic, complemented
3#20298944C211yesmaximal, characteristic, complemented
4#20298915C212yesmaximal, complemented
5#20298884C211yesmaximal, characteristic, complemented
6#20298848C212yesmaximal, complemented
7#20298740C212yesmaximal, complemented
8C4×#14268635C211yesmaximal, characteristic, complemented
9#20298675C211yesmaximal, characteristic, complemented
10#20298596C212yesmaximal, complemented
11#459×C113C211yesmaximal, characteristic, complemented
12C2×#14268647—21no—
13C2×#14268646C2212yes—
14C2×#14268635C2211yescharacteristic
15C2×#14268630C2212yes—
16#16813622C2211yescharacteristic
17#16813618—21no—
18#16813604—22no—
19#16813601—21no—
20#16813594—22no—
21#16813593C2212yes—
22#16813593C2212yes—
23C4×Dic226C2211yescharacteristic
24C4×D452C2211yescharacteristic
25D4×Dic113—21no—
26C4⋊C4×D113C2212yes—
27#16813554C2212yes—
28#16813553C2211yescharacteristic
29#16813547C2212yes—
30#16813545C2211yescharacteristic
31#16813543C2211yescharacteristic
32#16813543C2212yes—
33#16813543C2212yes—
34#16813534C2212yes—
35C4×#11744751C2211yescharacteristic
36C2×D8×C113C2212yes—
37#127×C113C2211yescharacteristic
38C4×D4×C113C2211yescharacteristic
39C4⋊C8×C113C2211yescharacteristic
40#102×C113C2212yes—
41#14268647—44no—
42#14268646—24no—
43#14268646—42no—
44C2×Dic226—21no—
45C2×Dic226C2311yescharacteristic
46C2×D452D411yescharacteristic
47C2×C22⋊D113—22no—
48C2×C22⋊D113—22no—
49C2×C22⋊D113—22no—
50C22×Dic113—22no—
51C2×C4×D113—22no—
52C2×C4×D113C2312yes—
53#14268635—22no—
54#14268630—42no—
55C2×#11744751C2311yescharacteristic
56C2×#11744751C2311yescharacteristic
57C4⋊Dic113—21no—
58C4⋊Dic113D411yescharacteristic
59C4⋊Dic113C2312yes—
60C4⋊Dic113C2311yescharacteristic
61#14268626—21no—
62#14268626—22no—
63C22⋊Dic113—22no—
64C22⋊Dic113—22no—
65#14268624D412yes—
66C4×Dic113—21no—
67C2×D4×C113—21no—
68C2×D4×C113—21no—
69C2×D4×C113C2311yescharacteristic
70C2×D4×C113C2312yes—
71C22×C4×C113—21no—
72D8×C113—42no—
73C2×C8×C113C2312yes—
74C4⋊C4×C113C2311yescharacteristic
75C22⋊C4×C113—21no—
76C42×C113C2311yescharacteristic
77C23×C113—21no—
78C23×C113—22no—
79C22×D113C2×D412yes—
80D4×C113—21no—
81D4×C113—22no—
82D4×C113—21no—
83D4×C113—22no—
84D4×C113—42no—
85D4×C113—81no—
86C2×C4×C113—21no—
87C2×C4×C113—42no—
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2411yescharacteristic
91C22⋊D113—44no—
92C22⋊D113—44no—
93C22⋊D113—82no—
94C2×Dic113—21no—
95C2×Dic113—21no—
96C2×Dic113—22no—
97C2×Dic113—44no—
98C2×Dic113C2×D412yes—
99D452—22no—
100C4×D113—22no—
101C4×D113—22no—
102C4×D113—44no—
103Dic226—21no—
104Dic226—42no—
105Dic226#4112yescomplemented
106C8×C113—22no—
107#11744751—21no—
108#11744751—21no—
109C22×C113—42no—
110C22×C113—41no—
111C22×C113—41no—
112C22×C113—42no—
113C22×C113—42no—
114C22×C113—41no—
115C22×C113C22×D411yescharacteristic
116C2×D113—22no—
117C2×D113—22no—
118C2×D113—22no—
119C4×C113—21no—
120C4×C113—41no—
121C4×C113AGL(1,ℤ/8)12yes—
122C4×C113C2×#4111yescharacteristic
123C4×C113H(5,𝔽2)11yescharacteristic
124Dic113—22no—
125Dic113—22no—
126Dic113—42no—
127Dic113—41no—
128C2×C113—82no—
129C2×C113—81no—
130C2×C113#54611yescharacteristic
131C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C113#57711yescharacteristic
133D113—42no—
134#3332—1131nomaximal, Sylow
135C113#333211yescharacteristic, complemented, Sylow
136#550—1131no—
137#547—1131no—
138#486—1131no—
139#481—1132no—
140#475—1131no—
141#469—1132no—
142#459D11311yescharacteristic, complemented
143#449—1132no—
144C4×SD16—1131no—
145#436—1131no—
146#417—1132no—
147C2×#41—1132no—
148C2×#41—2261no—
149C2×SD16—1131no—
150C2×D8C2×D11312yes—
151C2×M16—1132no—
152C4⋊Q8—1131no—
153#127—2261no—
154#127C2×D11311yescharacteristic
155#123—2262no—
156C22⋊Q8—2261no—
157#121—1132no—
158#121—1132no—
159#121—2262no—
160C4×Q8—1131no—
161C4×D4—1131no—
162C4×D4—2261no—
163C4×D4C2×D11311yescharacteristic
164C2×C4⋊C4—1132no—
165#106—1132no—
166#106—1131no—
167C4⋊C8C2×D11311yescharacteristic
168#103—1132no—
169#103—1131no—
170#102—1132no—
171#102—1131no—
172#102—1132no—
173#102C2×D11312yes—
174C22⋊C8—1132no—
175C4×C8—1131no—
176#41—4524no—
177#41—4522no—
178#41—2264no—
179C2×Q8—1131no—
180C2×Q8—2261no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—1131no—
184C2×D4—2262no—
185C2×D4—2262no—
186C2×D4—2262no—
187C2×D4C22×D11312yes—
188C2×D4C22×D11311yescharacteristic
189C22×C4—21no—
190C22×C4—1132no—
191C22×C4—2262no—
192C22×C4—2262no—
193SD16—2262no—
194D8—42no—
195M16—4522no—
196C2×C8—1131no—
197C2×C8—1131no—
198C2×C8C22×D11312yes—
199C4⋊C4—1131no—
200C4⋊C4—1132no—
201C4⋊C4—1131no—
202C4⋊C4—2262no—
203C4⋊C4—2261no—
204C4⋊C4—2261no—
205C4⋊C4C22×D11311yescharacteristic
206C22⋊C4—21no—
207C22⋊C4—1132no—
208C22⋊C4—2262no—
209C22⋊C4—2262no—
210C42—2261no—
211C42C22×D11311yescharacteristic
212C23—21no—
213C23—22no—
214C23—1132no—
215Q8—1132no—
216Q8—4522no—
217Q8—2261no—
218D4—21no—
219D4—22no—
220D4—21no—
221D4—22no—
222D4—42no—
223D4—81no—
224D4—9042no—
225D4—4524no—
226D4—4524no—
227D4—2262no—
228C2×C4—21no—
229C2×C4—42no—
230C2×C4—1132no—
231C2×C4—4524no—
232C2×C4—4524no—
233C2×C4—2261no—
234C2×C4—2262no—
235C2×C4—2261no—
236C2×C4—2262no—
237C2×C4—2262no—
238C2×C4D4×D11311yescharacteristic
239C2×C4D4×D11311yescharacteristic
240C2×C4C23×D11311yescharacteristic
241C8—22no—
242C8—2261no—
243C8—2261no—
244C22—41no—
245C22—42no—
246C22—42no—
247C22—41no—
248C22—42no—
249C22—41no—
250C22—2262no—
251C22—2262no—
252C22—2262no—
253C22C2×D4×D11311yescharacteristic
254C4—21no—
255C4—41no—
256C4—4522no—
257C4—4521no—
258C4—2262no—
259C4—2262no—
260C4#1681364612yes—
261C4#41×D11311yescharacteristic
262C4#1681366711yescharacteristic
263C2—81no—
264C2—82no—
265C2—4522no—
266C2#2029924511yescharacteristic
267C2C2×#1681364611yescharacteristic
268C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3332
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. #20299268C2semidirect
2. #20299253C2semidirect
3. #20298944C2semidirect
4. #20298915C2semidirect
5. #20298884C2semidirect
6. #20298848C2semidirect
7. #20298740C2semidirect
8. C4×#14268635C2semidirect
9. #20298675C2semidirect
10. #20298596C2semidirect
11. #459×C113C2semidirect
105. Dic226#41semidirect
135. C113#3332semidirect
142. #459D113semidirect

Maximal subgroups

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

subgroupindex
#202992682
#202992532
#202989442
#202989152
#202988842
#202988482
#202987402
C4×#142686352
#202986752
#202985962
#459×C1132
#3332113