Finite Group Databasebeta

← #28399977

Subgroups — #28399977

Order 14464.

772 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 145 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#20299434C211yesmaximal, characteristic, complemented
2#20299167C212yesmaximal, complemented
3#20299162C211yesmaximal, characteristic, complemented
4#20298786C218yesmaximal, complemented
5#20298571C212yesmaximal, complemented
6#410×C113C211yesmaximal, characteristic, complemented
7#16813670—21no—
8#16813669—22no—
9#16813668—22no—
10#16813667—21no—
11#16813667C2214yes—
12C2×#14268647—22no—
13C2×#14268647C2212yes—
14#41×D113—24no—
15C22×D452C2211yescharacteristic, complemented
16#16813619—22no—
17#16813618—21no—
18#16813611—21no—
19#16813610—22no—
20#16813597—24no—
21#16813596—22no—
22#16813592C2218yescomplemented
23#16813590C2214yescomplemented
24#16813581C2211yescharacteristic, complemented
25#16813536C2218yescomplemented
26C2×#41×C113C2211yescharacteristic
27#117×C113C2212yescomplemented
28#99×C113C2214yescomplemented
29C23×D113C2312yes—
30#14268648—24no—
31#14268647—24no—
32#14268647—24no—
33#14268647—22no—
34#14268647—22no—
35#14268647—24no—
36#14268647—22no—
37#14268647—22no—
38#14268646—24no—
39#14268646—28no—
40C2×Dic226—22no—
41C2×Dic226D412yescomplemented
42Q8×D113—24no—
43C2×D452—22no—
44C2×D452—21no—
45C2×D452—22no—
46C2×D452—22no—
47C2×D452—21no—
48C2×D452—28no—
49C2×D452D412yescomplemented
50C2×C22⋊D113—24no—
51C2×C22⋊D113—24no—
52C2×C22⋊D113C2314yes—
53D4×D113—24no—
54D4×D113—28no—
55C2×C4×D113—24no—
56C2×C4×D113D414yescomplemented
57C4⋊Dic113—21no—
58C22⋊Dic113C2312yes—
59#14268624—24no—
60#14268624—28no—
61C4×Dic113—21no—
62#41×C113—22no—
63#41×C113—22no—
64C2×Q8×C113D411yescharacteristic, complemented
65C2×D4×C113D411yescharacteristic, complemented
66C2×D4×C113C2312yes—
67C22×C4×C113D412yescomplemented
68C22×C4×C113C2311yescharacteristic
69C4⋊C4×C113—22no—
70C22⋊C4×C113C2314yes—
71C42×C113—22no—
72C23×C113C2×D412yes—
73C23×C113C2411yescharacteristic
74C22×D113—24no—
75C22×D113—22no—
76C22×D113—24no—
77C22×D113—82no—
78C22×D113C2×D414yes—
79Q8×C113—22no—
80D4×C113—24no—
81D4×C113—22no—
82C2×C4×C113—22no—
83C2×C4×C113—22no—
84C2×C4×C113—24no—
85C2×C4×C113C2×D412yes—
86C2×C4×C113C2×D412yes—
87C2×C4×C113C2×D412yes—
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113C2×D411yescharacteristic
90C22⋊D113—28no—
91C22⋊D113—24no—
92C22⋊D113—24no—
93C22⋊D113—84no—
94C2×Dic113—24no—
95C2×Dic113—22no—
96C2×Dic113C2×D414yes—
97D452—24no—
98D452—22no—
99D452—22no—
100D452—41no—
101D452—42no—
102D452—41no—
103D452—88no—
104C4×D113—28no—
105C4×D113—24no—
106C4×D113—24no—
107Dic226—24no—
108Dic226—22no—
109Dic226—22no—
110C22×C113—22no—
111C22×C113—41no—
112C22×C113—42no—
113C22×C113C22×D412yes—
114C22×C113C22×D411yescharacteristic
115C2×D113—24no—
116C2×D113—44no—
117C2×D113—48no—
118C2×D113—44no—
119C2×D113—42no—
120C2×D113—84no—
121C4×C113—22no—
122C4×C113—44no—
123C4×C113#12011yescharacteristic
124C4×C113#12012yes—
125C4×C113#12011yescharacteristic
126Dic113—24no—
127Dic113—42no—
128C2×C113—21no—
129C2×C113—22no—
130C2×C113—42no—
131C2×C113C2×#12011yescharacteristic
132D113—44no—
133D113—82no—
134#3027—1131nomaximal, Sylow
135C113#302711yescharacteristic, complemented, Sylow
136#585—1131no—
137#535—1131no—
138#535—1132no—
139B(4,𝔽2)—1138no—
140#410—1132no—
141#410D11311yescharacteristic, complemented
1422−1+4—2262no—
1432−1+4—2261no—
144H(5,𝔽2)—1134no—
145H(5,𝔽2)—2262no—
146H(5,𝔽2)—2261no—
147C2×#41—1132no—
148C2×#41—2264no—
149C2×#41—2262no—
150C2×#41C2×D11311yescharacteristic
151C22×D4—1131no—
152#127—2262no—
153#127—2261no—
154#124—2262no—
155#124—2261no—
156#121—2264no—
157#121—2262no—
158#120—1134no—
159#120—1138no—
160#117—1131no—
161#117C2×D11312yescomplemented
162#99—1138no—
163#99C2×D11314yescomplemented
164C24—1132no—
165#41—22no—
166#41—22no—
167#41—2264no—
168#41—2264no—
169#41—2268no—
170#41—2264no—
171#41—2264no—
172#41—2262no—
173#41—2262no—
174#41—2262no—
175#41—2262no—
176#41—2264no—
177C2×Q8—1132no—
178C2×Q8—2262no—
179C2×Q8—2264no—
180C2×Q8D45211yescharacteristic, complemented
181C2×D4—1134no—
182C2×D4—1132no—
183C2×D4—2268no—
184C2×D4—2262no—
185C2×D4—2268no—
186C2×D4—2264no—
187C2×D4—2264no—
188C2×D4—2264no—
189C2×D4—2262no—
190C2×D4—2262no—
191C2×D4—2261no—
192C2×D4—2261no—
193C2×D4D45211yescharacteristic, complemented
194C2×D4C22×D11312yes—
195C22×C4—1134no—
196C22×C4—2264no—
197C22×C4D45212yescomplemented
198C22×C4C22×D11311yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—2261no—
201C22⋊C4—1132no—
202C22⋊C4—2268no—
203C22⋊C4—2264no—
204C22⋊C4C22×D11314yes—
205C42—22no—
206C42—2261no—
207C23—1134no—
208C23—9042no—
209C23—2264no—
210C23—2264no—
211C23—2262no—
212C23C2×D45212yes—
213C23C23×D11311yescharacteristic
214Q8—22no—
215Q8—2264no—
216Q8—2262no—
217Q8—2262no—
218D4—24no—
219D4—22no—
220D4—9048no—
221D4—9044no—
222D4—4521no—
223D4—4521no—
224D4—4522no—
225D4—2264no—
226D4—2268no—
227D4—2264no—
228D4—2264no—
229D4—2262no—
230D4—2262no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—1134no—
235C2×C4—2268no—
236C2×C4—2262no—
237C2×C4—2264no—
238C2×C4—2264no—
239C2×C4—2264no—
240C2×C4D4×D11312yes—
241C2×C4D4×D11312yes—
242C2×C4C2×D45212yes—
243C2×C4C2×D45211yescharacteristic
244C2×C4C2×D45211yescharacteristic
245C22—22no—
246C22—41no—
247C22—42no—
248C22—9044no—
249C22—4528no—
250C22—4524no—
251C22—4524no—
252C22—4522no—
253C22—2264no—
254C22C2×D4×D11312yes—
255C22C22×D45211yescharacteristic
256C4—22no—
257C4—44no—
258C4—4522no—
259C4—2264no—
260C4#1681359211yescharacteristic
261C4#1681359211yescharacteristic
262C4#1681359212yes—
263C2—22no—
264C2—21no—
265C2—42no—
266C2—9042no—
267C2—4524no—
268C2C2×#1681359211yescharacteristic
subgroupG/H
centerC2C2×#16813592
commutator, cosocleC23×C113C24
FrattiniC23C23×D113
Fitting#410×C113C2
socleC2×C113C2×#120
hypercenter#410D113
hypocenterC113#3027
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #20299434C2semidirect
2. #20299167C2semidirect
3. #20299162C2semidirect
4. #20298786C2semidirect
5. #20298571C2semidirect
6. #410×C113C2semidirect
15. C22×D452C22semidirect
22. #16813592C22semidirect
23. #16813590C22semidirect
24. #16813581C22semidirect
25. #16813536C22semidirect
27. #117×C113C22semidirect
28. #99×C113C22semidirect
41. C2×Dic226D4semidirect
49. C2×D452D4semidirect
56. C2×C4×D113D4semidirect
64. C2×Q8×C113D4semidirect
65. C2×D4×C113D4semidirect
67. C22×C4×C113D4semidirect
135. C113#3027semidirect
141. #410D113semidirect
161. #117C2×D113semidirect
163. #99C2×D113semidirect
180. C2×Q8D452semidirect
193. C2×D4D452semidirect
197. C22×C4D452semidirect

Maximal subgroups

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

subgroupindex
#202994342
#202991672
#202991622
#202987862
#202985712
#410×C1132
#3027113