Finite Group Databasebeta

← #28400528

Subgroups — #28400528

Order 14464.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299165C211yesmaximal, characteristic
2#20299079C211yesmaximal, characteristic, complemented
3#20298921C212yesmaximal, complemented
4#20298920C212yesmaximal, complemented
5#20298915C212yesmaximal, complemented
6#20298910C212yesmaximal, complemented
7#20298638C211yesmaximal, characteristic, complemented
8#20298636C211yesmaximal, characteristic, complemented
9#20298603C211yesmaximal, characteristic, complemented
10#20298564C211yesmaximal, characteristic, complemented
11C2×#102×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C2×#14268631C2211yescharacteristic
14#16813618—21no—
15#16813609—21no—
16#16813593C2212yes—
17#16813593C2212yes—
18#16813591—22no—
19#16813587—21no—
20#16813584—21no—
21C4×C22⋊D113—22no—
22#16813581C2211yescharacteristic
23#16813581C2211yescharacteristic
24#16813580C2212yescomplemented
25C4⋊C4×D113C2212yescomplemented
26#16813556C2211yescharacteristic, complemented
27#16813556C2211yescharacteristic, complemented
28#16813555C2212yescomplemented
29#16813554C2211yescharacteristic, complemented
30#16813554C2211yescharacteristic, complemented
31#16813553C2212yescomplemented
32#16813543C2212yes—
33#16813543C2212yes—
34#16813534C2212yescomplemented
35#16813534C2212yescomplemented
36C22×D4×C113C2211yescharacteristic
37C22×C8×C113C2211yescharacteristic
38C2×C4⋊C4×C113C2211yescharacteristic
39#102×C113C2212yes—
40#102×C113C2212yes—
41#14268647—22no—
42#14268647—22no—
43C2×Dic226D411yescharacteristic
44C2×D452D411yescharacteristic
45C2×C22⋊D113—22no—
46C2×C22⋊D113—22no—
47C2×C22⋊D113D412yes—
48C2×C4×D113—22no—
49C2×C4×D113C2312yes—
50#14268631—22no—
51C2×#11744751C2312yes—
52C4⋊Dic113C2311yescharacteristic
53C4⋊Dic113C2311yescharacteristic
54C4⋊Dic113C2311yescharacteristic
55C4⋊Dic113C2311yescharacteristic
56#14268626—22no—
57C22⋊Dic113—21no—
58C22⋊Dic113—21no—
59C22⋊Dic113—22no—
60C22⋊Dic113—22no—
61#14268624—22no—
62C4×Dic113—21no—
63C4×Dic113—21no—
64C4×Dic113—22no—
65C24×C113—21no—
66C2×D4×C113—21no—
67C2×D4×C113—22no—
68C2×D4×C113—22no—
69C2×D4×C113C2312yes—
70C22×C4×C113—21no—
71C22×C4×C113C2311yescharacteristic
72C2×C8×C113—22no—
73C2×C8×C113C2311yescharacteristic
74C2×C8×C113C2311yescharacteristic
75C4⋊C4×C113—21no—
76C4⋊C4×C113C2312yes—
77C23×C113—22no—
78C23×C113—42no—
79C23×C113—81no—
80C23×C113—81no—
81C23×C113C2×D411yescharacteristic
82C22×D113C2×D412yes—
83D4×C113—22no—
84D4×C113—22no—
85D4×C113—42no—
86C2×C4×C113—22no—
87C2×C4×C113—81no—
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113#4112yes—
90C2×C4×C113#4112yes—
91C2×C4×C113C2411yescharacteristic
92C22⋊D113—24no—
93C22⋊D113—82no—
94C22⋊D113—82no—
95C2×Dic113—21no—
96C2×Dic113—21no—
97C2×Dic113—21no—
98C2×Dic113—21no—
99C2×Dic113C2×D412yes—
100D452—22no—
101C4×D113—22no—
102C4×D113—22no—
103C4×D113—82no—
104Dic226—22no—
105C8×C113—21no—
106C8×C113—21no—
107#11744751—22no—
108C22×C113—21no—
109C22×C113—21no—
110C22×C113—42no—
111C22×C113—42no—
112C22×C113—42no—
113C22×C113—84no—
114C22×C113#12312yes—
115C22×C113C22×D411yescharacteristic
116C2×D113—22no—
117C2×D113—22no—
118C2×D113—22no—
119C4×C113—42no—
120C4×C113#12312yes—
121C4×C113C2×#4111yescharacteristic
122C4×C113C2×#4111yescharacteristic
123Dic113—22no—
124Dic113—41no—
125Dic113—41no—
126Dic113—41no—
127Dic113—41no—
128C2×C113—22no—
129C2×C113—82no—
130C2×C113C2×#12311yescharacteristic
131C2×C113#57611yescharacteristic
132C2×C113#57711yescharacteristic
133D113—42no—
134#3096—1131nomaximal, Sylow
135C113#309611yescharacteristic, complemented, Sylow
136#535—1131no—
137#520—1131no—
138#482—1132no—
139#482—1132no—
140#481—1132no—
141#480—1132no—
142#428—1131no—
143#427—1131no—
144#418—1131no—
145C2×#102D11311yescharacteristic, complemented
146#408—1131no—
147C2×#41—1131no—
148C22×D4C2×D11311yescharacteristic
149C2×M16—1131no—
150C22×C8C2×D11311yescharacteristic
151#127—2261no—
152#124—2261no—
153#121—1132no—
154#121—1132no—
155#120—2262no—
156C4×Q8—2261no—
157C4×D4—2261no—
158C4×D4—2262no—
159#117—1131no—
160#117—1131no—
161#117—1132no—
162C2×C4⋊C4—1132no—
163C2×C4⋊C4C2×D11311yescharacteristic
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#102C2×D11312yes—
173#102C2×D11312yes—
174C22⋊C8—1132no—
175C22⋊C8—1132no—
176C24—21no—
177#41—2262no—
178#41—2262no—
179C2×Q8—1131no—
180C2×D4—21no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—1132no—
184C2×D4—1131no—
185C2×D4—2262no—
186C2×D4—2262no—
187C2×D4C22×D11312yes—
188C22×C4—21no—
189C22×C4—1132no—
190C22×C4—2262no—
191C22×C4C22×D11311yescharacteristic
192M16—2262no—
193C2×C8—22no—
194C2×C8—1132no—
195C2×C8C22×D11311yescharacteristic
196C2×C8C22×D11311yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—1131no—
199C4⋊C4—1131no—
200C4⋊C4—1131no—
201C4⋊C4—1131no—
202C4⋊C4—2262no—
203C4⋊C4C22×D11312yes—
204C22⋊C4—2262no—
205C22⋊C4—2262no—
206C22⋊C4—2262no—
207C22⋊C4—2261no—
208C22⋊C4—2261no—
209C42—2262no—
210C42—2261no—
211C42—2261no—
212C23—22no—
213C23—42no—
214C23—81no—
215C23—81no—
216C23—1132no—
217C23D4×D11311yescharacteristic
218Q8—2262no—
219D4—22no—
220D4—22no—
221D4—42no—
222D4—9042no—
223D4—9042no—
224D4—2264no—
225D4—2262no—
226C2×C4—22no—
227C2×C4—81no—
228C2×C4—1132no—
229C2×C4—9042no—
230C2×C4—2261no—
231C2×C4—2261no—
232C2×C4—2261no—
233C2×C4—2261no—
234C2×C4—2262no—
235C2×C4—2262no—
236C2×C4D4×D11311yescharacteristic
237C2×C4#1426864612yes—
238C2×C4#1426864712yes—
239C2×C4C23×D11311yescharacteristic
240C8—21no—
241C8—21no—
242C8—2262no—
243C22—21no—
244C22—21no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—84no—
249C22—2262no—
250C22—2262no—
251C22—2262no—
252C22#1681360412yes—
253C22C2×D4×D11311yescharacteristic
254C4—42no—
255C4—4521no—
256C4—4521no—
257C4—4521no—
258C4—4521no—
259C4—2262no—
260C4#1681360412yes—
261C4C2×#1426864611yescharacteristic
262C4C2×#1426864711yescharacteristic
263C2—22no—
264C2—82no—
265C2—4522no—
266C2C2×#1681360411yescharacteristic
267C2#2029939911yescharacteristic
268C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#102×C113C2
socleC22×C113C22×D4
prime radical#20299165C2
hypercenterC2×#102D113
hypocenterC113#3096
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. #20299079C2semidirect
3. #20298921C2semidirect
4. #20298920C2semidirect
5. #20298915C2semidirect
6. #20298910C2semidirect
7. #20298638C2semidirect
8. #20298636C2semidirect
9. #20298603C2semidirect
10. #20298564C2semidirect
11. C2×#102×C113C2semidirect
24. #16813580C22semidirect
25. C4⋊C4×D113C22semidirect
26. #16813556C22semidirect
27. #16813556C22semidirect
28. #16813555C22semidirect
29. #16813554C22semidirect
30. #16813554C22semidirect
31. #16813553C22semidirect
34. #16813534C22semidirect
35. #16813534C22semidirect
135. C113#3096semidirect
145. C2×#102D113semidirect

Maximal subgroups

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

subgroupindex
#202991652
#202990792
#202989212
#202989202
#202989152
#202989102
#202986382
#202986362
#202986032
#202985642
C2×#102×C1132
#3096113