Finite Group Databasebeta

← #28400533

Subgroups — #28400533

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#20299081C211yesmaximal, characteristic, complemented
3#20298923C212yesmaximal, complemented
4#20298923C212yesmaximal, complemented
5#20298917C212yesmaximal, complemented
6#20298912C212yesmaximal, complemented
7#20298640C211yesmaximal, characteristic, complemented
8#20298636C211yesmaximal, characteristic, complemented
9#20298604C211yesmaximal, characteristic, complemented
10C2×#16813544C211yesmaximal, characteristic, complemented
11#408×C113C211yesmaximal, characteristic, complemented
12C22×D452C2211yescharacteristic
13#16813618—21no—
14#16813611—21no—
15#16813596C2212yes—
16#16813596C2212yes—
17#16813590—22no—
18Q8×Dic113—21no—
19D4×Dic113—22no—
20D4×Dic113—21no—
21#16813581C2211yescharacteristic
22#16813581C2211yescharacteristic
23#16813581C2212yescomplemented
24C2×C4⋊Dic113C2211yescharacteristic
25C2×C4⋊Dic113C2212yescomplemented
26#16813556C2211yescharacteristic, complemented
27#16813556C2211yescharacteristic, complemented
28#16813556C2212yescomplemented
29#16813554C2211yescharacteristic, complemented
30#16813554C2211yescharacteristic, complemented
31#16813554C2212yescomplemented
32#16813544C2212yes—
33#16813544C2212yes—
34#16813544C2212yes—
35#16813544C2212yes—
36C2×#41×C113C2211yescharacteristic
37C2×M16×C113C2211yescharacteristic
38C22×C8×C113C2211yescharacteristic
39C22⋊C8×C113C2212yescomplemented
40C22⋊C8×C113C2212yescomplemented
41C23×D113—21no—
42C2×D452—22no—
43C2×D452—22no—
44C2×D452—21no—
45C2×D452C2312yes—
46C2×C22⋊D113—22no—
47C2×C22⋊D113—22no—
48C22×Dic113—21no—
49C22×Dic113—22no—
50C4⋊Dic113—21no—
51C4⋊Dic113—22no—
52C4⋊Dic113C2312yes—
53C4⋊Dic113C2311yescharacteristic
54C4⋊Dic113C2311yescharacteristic
55C4⋊Dic113C2311yescharacteristic
56C4⋊Dic113C2311yescharacteristic
57C22⋊Dic113—21no—
58C22⋊Dic113—21no—
59C22⋊Dic113—22no—
60#14268624—22no—
61#14268624—22no—
62C4×Dic113—21no—
63C4×Dic113—21no—
64C4×Dic113—22no—
65#41×C113—22no—
66#41×C113—22no—
67C2×Q8×C113D411yescharacteristic
68C2×D4×C113D412yes—
69C2×D4×C113D411yescharacteristic
70C22×C4×C113C2312yes—
71C22×C4×C113C2311yescharacteristic
72M16×C113—22no—
73C2×C8×C113—22no—
74C2×C8×C113C2311yescharacteristic
75C2×C8×C113C2311yescharacteristic
76C2×C8×C113C2312yes—
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×C113C2×D412yes—
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113#4112yes—
91C2×C4×C113#4112yes—
92C2×C4×C113C2411yescharacteristic
93C22⋊D113—82no—
94C22⋊D113—82no—
95C2×Dic113—21no—
96C2×Dic113—21no—
97C2×Dic113—21no—
98C2×Dic113—21no—
99C2×Dic113—22no—
100C2×Dic113—81no—
101C2×Dic113—82no—
102D452—22no—
103D452—22no—
104D452—42no—
105C8×C113—21no—
106C8×C113—21no—
107C8×C113—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#12312yes—
121C4×C113C2×#4111yescharacteristic
122C4×C113C2×#4111yescharacteristic
123Dic113—41no—
124Dic113—42no—
125Dic113—41no—
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#520—1131no—
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#408D11311yescharacteristic, complemented
147C2×#41C2×D11311yescharacteristic
148C22×D4—1131no—
149C2×M16C2×D11311yescharacteristic
150C22×C8C2×D11311yescharacteristic
151#127—2261no—
152#124—2261no—
153#121—1132no—
154#121—1132no—
155#120—2262no—
156C4×Q8—2261no—
157C4×D4—2262no—
158C4×D4—2261no—
159#117—1131no—
160#117—1132no—
161#117—1131no—
162C2×C4⋊C4—1131no—
163C2×C4⋊C4—1132no—
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⋊C8C2×D11312yescomplemented
175C22⋊C8C2×D11312yescomplemented
176C24—2261no—
177#41—22no—
178#41—22no—
179C2×Q8D45211yescharacteristic
180C2×D4—1132no—
181C2×D4—2262no—
182C2×D4—2262no—
183C2×D4—2261no—
184C2×D4—2262no—
185C2×D4—2262no—
186C2×D4D45212yes—
187C2×D4D45211yescharacteristic
188C22×C4—2262no—
189C22×C4—2261no—
190C22×C4C22×D11312yes—
191C22×C4C22×D11311yescharacteristic
192M16—22no—
193C2×C8—22no—
194C2×C8C22×D11311yescharacteristic
195C2×C8C22×D11312yes—
196C2×C8C22×D11311yescharacteristic
197C4⋊C4—1132no—
198C4⋊C4—1131no—
199C4⋊C4—1131no—
200C4⋊C4—1131no—
201C4⋊C4—1131no—
202C4⋊C4—2262no—
203C4⋊C4—2261no—
204C22⋊C4—2262no—
205C22⋊C4—2261no—
206C22⋊C4—2261no—
207C22⋊C4—2262no—
208C22⋊C4—2262no—
209C42—2262no—
210C42—2261no—
211C42—2261no—
212C23—9041no—
213C23—9041no—
214C23—4522no—
215C23—2262no—
216C23C2×D45212yes—
217C23C2×D45211yescharacteristic
218Q8—22no—
219D4—24no—
220D4—22no—
221D4—9042no—
222D4—9042no—
223D4—4522no—
224D4—2262no—
225D4—2262no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—9041no—
229C2×C4—9042no—
230C2×C4—2261no—
231C2×C4—2261no—
232C2×C4—2261no—
233C2×C4—2262no—
234C2×C4—2261no—
235C2×C4C2×D45212yes—
236C2×C4C2×D45211yescharacteristic
237C2×C4#1426864612yes—
238C2×C4#1426864612yes—
239C2×C4C23×D11311yescharacteristic
240C8—21no—
241C8—21no—
242C8—22no—
243C22—21no—
244C22—21no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—9044no—
249C22—4522no—
250C22—4522no—
251C22—4522no—
252C22#1681360612yes—
253C22C22×D45211yescharacteristic
254C4—22no—
255C4—4522no—
256C4—4521no—
257C4—4521no—
258C4—4521no—
259C4—4521no—
260C4#1681360612yes—
261C4C2×#1426864611yescharacteristic
262C4C2×#1426864611yescharacteristic
263C2—22no—
264C2—42no—
265C2—9042no—
266C2C2×#1681360611yescharacteristic
267C2#2029940311yescharacteristic
268C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#408×C113C2
socleC22×C113C22×D4
prime radical#20299162C2
hypercenter#408D113
hypocenterC113#3096
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #20299081C2semidirect
3. #20298923C2semidirect
4. #20298923C2semidirect
5. #20298917C2semidirect
6. #20298912C2semidirect
7. #20298640C2semidirect
8. #20298636C2semidirect
9. #20298604C2semidirect
10. C2×#16813544C2semidirect
11. #408×C113C2semidirect
23. #16813581C22semidirect
25. C2×C4⋊Dic113C22semidirect
26. #16813556C22semidirect
27. #16813556C22semidirect
28. #16813556C22semidirect
29. #16813554C22semidirect
30. #16813554C22semidirect
31. #16813554C22semidirect
39. C22⋊C8×C113C22semidirect
40. C22⋊C8×C113C22semidirect
135. C113#3096semidirect
146. #408D113semidirect
174. C22⋊C8C2×D113semidirect
175. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991622
#202990812
#202989232
#202989172
#202989122
#202986402
#202986362
#202986042
C2×#168135442
#408×C1132
#3096113