Finite Group Databasebeta

← #28400532

Subgroups — #28400532

Order 14464.

418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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#20299162C211yesmaximal, characteristic
2#20298922C212yesmaximal, complemented
3#20298922C212yesmaximal, complemented
4#20298916C212yesmaximal, complemented
5#20298911C212yesmaximal, complemented
6#20298638C211yesmaximal, characteristic, complemented
7#20298634C211yesmaximal, characteristic, complemented
8#20298602C211yesmaximal, characteristic, complemented
9C2×#16813542C211yesmaximal, characteristic, complemented
10#20298565C211yesmaximal, characteristic, complemented
11#520×C113C211yesmaximal, characteristic, complemented
12C22×D452C2211yescharacteristic
13C2×#14268631C2211yescharacteristic
14C22×#11744751C2211yescharacteristic
15#16813618—21no—
16#16813611—21no—
17#16813596C2212yes—
18#16813596C2212yes—
19#16813590—22no—
20#16813581C2211yescharacteristic
21#16813555C2211yescharacteristic, complemented
22#16813555C2211yescharacteristic, complemented
23#16813555C2212yescomplemented
24#16813553C2211yescharacteristic, complemented
25#16813553C2211yescharacteristic, complemented
26#16813553C2212yescomplemented
27#16813542C2212yes—
28#16813542C2212yes—
29#16813542C2212yes—
30#16813542C2212yes—
31C22⋊#11744751C2212yescomplemented
32C22⋊#11744751C2212yescomplemented
33C2×#41×C113C2211yescharacteristic
34C4×Q8×C113—21no—
35C4×D4×C113—21no—
36C4×D4×C113—22no—
37#117×C113C2211yescharacteristic
38#117×C113C2212yescomplemented
39C2×C4⋊C4×C113C2211yescharacteristic
40C2×C4⋊C4×C113C2212yescomplemented
41C23×D113—21no—
42C2×D452—22no—
43C2×D452—22no—
44C2×D452—21no—
45C2×D452C2312yes—
46C2×C22⋊D113—22no—
47C2×C22⋊D113—22no—
48#14268631—22no—
49C2×#11744751—22no—
50C2×#11744751C2311yescharacteristic
51C2×#11744751C2311yescharacteristic
52C2×#11744751C2312yes—
53C4⋊Dic113C2311yescharacteristic
54C4⋊Dic113C2311yescharacteristic
55C22⋊Dic113—21no—
56#14268624—22no—
57#14268624—22no—
58C4×Dic113—21no—
59#41×C113—22no—
60#41×C113—22no—
61C2×Q8×C113D411yescharacteristic
62C2×D4×C113D412yes—
63C2×D4×C113D411yescharacteristic
64C22×C4×C113—21no—
65C22×C4×C113—22no—
66C22×C4×C113C2312yes—
67C22×C4×C113C2311yescharacteristic
68C4⋊C4×C113—21no—
69C4⋊C4×C113—22no—
70C4⋊C4×C113C2312yes—
71C4⋊C4×C113C2311yescharacteristic
72C4⋊C4×C113C2311yescharacteristic
73C22⋊C4×C113—21no—
74C22⋊C4×C113—22no—
75C42×C113—21no—
76C42×C113—22no—
77C23×C113C2×D412yes—
78C23×C113C2×D411yescharacteristic
79C22×D113—22no—
80C22×D113—42no—
81C22×D113—81no—
82C22×D113—81no—
83Q8×C113—22no—
84D4×C113—24no—
85D4×C113—22no—
86C2×C4×C113—22no—
87C2×C4×C113—22no—
88C2×C4×C113—21no—
89C2×C4×C113—21no—
90C2×C4×C113—22no—
91C2×C4×C113—81no—
92C2×C4×C113—82no—
93C2×C4×C113C2×D412yes—
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113#4112yes—
96C2×C4×C113#4112yes—
97C2×C4×C113C2411yescharacteristic
98C22⋊D113—82no—
99C22⋊D113—82no—
100C2×Dic113—21no—
101C2×Dic113—21no—
102D452—22no—
103D452—22no—
104D452—42no—
105#11744751—21no—
106#11744751—21no—
107#11744751—22no—
108C22×C113—21no—
109C22×C113—21no—
110C22×C113—22no—
111C22×C113—22no—
112C22×C113—22no—
113C22×C113#12312yes—
114C22×C113C22×D411yescharacteristic
115C2×D113—42no—
116C2×D113—42no—
117C2×D113—42no—
118C2×D113—84no—
119C4×C113—22no—
120C4×C113—41no—
121C4×C113—42no—
122C4×C113—41no—
123C4×C113#12312yes—
124C4×C113C2×#4111yescharacteristic
125C4×C113C2×#4111yescharacteristic
126Dic113—41no—
127Dic113—41no—
128C2×C113—22no—
129C2×C113—42no—
130C2×C113C2×#12311yescharacteristic
131C2×C113#57611yescharacteristic
132C2×C113#57711yescharacteristic
133D113—82no—
134#3096—1131nomaximal, Sylow
135C113#309611yescharacteristic, complemented, Sylow
136#535—1131no—
137#520D11311yescharacteristic, complemented
138#482—1132no—
139#482—1132no—
140#481—1132no—
141#480—1132no—
142#428—1131no—
143#427—1131no—
144#418—1131no—
145C2×#102—1131no—
146#408—1131no—
147C2×#41C2×D11311yescharacteristic
148C22×D4—1131no—
149C2×M16—1131no—
150C22×C8—1131no—
151#127—2261no—
152#124—2261no—
153#121—1132no—
154#121—1132no—
155#120—2262no—
156C4×Q8—21no—
157C4×D4—21no—
158C4×D4—22no—
159#117—1131no—
160#117C2×D11311yescharacteristic
161#117C2×D11312yescomplemented
162C2×C4⋊C4C2×D11311yescharacteristic
163C2×C4⋊C4C2×D11312yescomplemented
164#107—1131no—
165#107—1131no—
166#107—1132no—
167#106—1131no—
168#106—1131no—
169#106—1132no—
170#102—1132no—
171#102—1132no—
172#102—1132no—
173#102—1132no—
174C22⋊C8—1132no—
175C22⋊C8—1132no—
176C24—2261no—
177#41—22no—
178#41—22no—
179C2×Q8C22⋊D11311yescharacteristic
180C2×D4—1132no—
181C2×D4—2262no—
182C2×D4—2262no—
183C2×D4—2261no—
184C2×D4—2262no—
185C2×D4—2262no—
186C2×D4C22⋊D11312yes—
187C2×D4C22⋊D11311yescharacteristic
188C22×C4—21no—
189C22×C4—22no—
190C22×C4C22×D11312yes—
191C22×C4C22×D11311yescharacteristic
192M16—2262no—
193C2×C8—1131no—
194C2×C8—1132no—
195C2×C8—1131no—
196C2×C8—2262no—
197C4⋊C4—21no—
198C4⋊C4—22no—
199C4⋊C4—1131no—
200C4⋊C4—1131no—
201C4⋊C4C22×D11312yes—
202C4⋊C4C22×D11311yescharacteristic
203C4⋊C4C22×D11311yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—22no—
206C22⋊C4—2261no—
207C22⋊C4—2262no—
208C22⋊C4—2262no—
209C42—21no—
210C42—22no—
211C42—2261no—
212C23—9041no—
213C23—9041no—
214C23—4522no—
215C23—2262no—
216C23C2×C22⋊D11312yes—
217C23C2×C22⋊D11311yescharacteristic
218Q8—22no—
219D4—24no—
220D4—22no—
221D4—9042no—
222D4—9042no—
223D4—4522no—
224D4—2262no—
225D4—2262no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4—2261no—
234C2×C4—2261no—
235C2×C4C2×C22⋊D11312yes—
236C2×C4C2×C22⋊D11311yescharacteristic
237C2×C4#1426864712yes—
238C2×C4#1426864712yes—
239C2×C4C23×D11311yescharacteristic
240C8—2261no—
241C8—2261no—
242C8—2262no—
243C22—21no—
244C22—21no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—9044no—
249C22—4522no—
250C22—4522no—
251C22—4522no—
252C22#1681360512yes—
253C22C22×C22⋊D11311yescharacteristic
254C4—22no—
255C4—41no—
256C4—42no—
257C4—41no—
258C4—4521no—
259C4—4521no—
260C4#1681360512yes—
261C4C2×#1426864711yescharacteristic
262C4C2×#1426864711yescharacteristic
263C2—22no—
264C2—42no—
265C2—9042no—
266C2C2×#1681360511yescharacteristic
267C2#2029940111yescharacteristic
268C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#520×C113C2
socleC22×C113C22×D4
prime radical#20299162C2
hypercenter#520D113
hypocenterC113#3096
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #520

Complements

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

NH ≅ G/Ntype
2. #20298922C2semidirect
3. #20298922C2semidirect
4. #20298916C2semidirect
5. #20298911C2semidirect
6. #20298638C2semidirect
7. #20298634C2semidirect
8. #20298602C2semidirect
9. C2×#16813542C2semidirect
10. #20298565C2semidirect
11. #520×C113C2semidirect
21. #16813555C22semidirect
22. #16813555C22semidirect
23. #16813555C22semidirect
24. #16813553C22semidirect
25. #16813553C22semidirect
26. #16813553C22semidirect
31. C22⋊#11744751C22semidirect
32. C22⋊#11744751C22semidirect
38. #117×C113C22semidirect
40. C2×C4⋊C4×C113C22semidirect
135. C113#3096semidirect
137. #520D113semidirect
161. #117C2×D113semidirect
163. C2×C4⋊C4C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991622
#202989222
#202989162
#202989112
#202986382
#202986342
#202986022
C2×#168135422
#202985652
#520×C1132
#3096113