Finite Group Databasebeta

← #13124796

Subgroups — #13124796

Order 1664.

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#11719230C211yesmaximal, characteristic
2#11719209C211yesmaximal, characteristic, complemented
3C13×#428C211yesmaximal, characteristic, complemented
4#11718792C211yesmaximal, characteristic, complemented
5#11718790C211yesmaximal, characteristic, complemented
6#11718659C211yesmaximal, characteristic, complemented
7C2×#88049C211yesmaximal, characteristic, complemented
8#11718546C212yesmaximal, complemented
9#11718543C212yesmaximal, complemented
10#11718527C212yesmaximal, complemented
11#11718524C212yesmaximal, complemented
12C2×#6127C2211yescharacteristic
13C22×D52C2211yescharacteristic
14C2×C13×M16C2211yescharacteristic
15C13×#117C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C4×C22⋊D13—22no—
18#88180C2211yescharacteristic
19C22×#1055C2211yescharacteristic
20#88149C2212yes—
21#88149C2212yes—
22#88147—21no—
23#88146C2212yescomplemented
24C4⋊C4×D13C2212yescomplemented
25#88141—21no—
26#88136—22no—
27#88129—21no—
28#88128—21no—
29C13×#107C2212yescomplemented
30C13×#106C2212yescomplemented
31#88061C2212yes—
32#88061C2212yes—
33#88060C2212yescomplemented
34#88060C2212yescomplemented
35#88049C2212yes—
36#88049C2212yes—
37#88048C2211yescharacteristic, complemented
38#88048C2211yescharacteristic, complemented
39#88047C2211yescharacteristic, complemented
40#88047C2211yescharacteristic, complemented
41C23×D13—21no—
42C22×C4×C13—21no—
43C22×C4×C13C2311yescharacteristic
44C2×C22⋊D13D412yes—
45#6127—22no—
46#6127—22no—
47C2×D52—22no—
48C2×D52—22no—
49C2×D52—21no—
50C2×D52—22no—
51C2×D52—22no—
52C2×D52D411yescharacteristic
53C2×D52C2312yes—
54C2×C4×D13—22no—
55C2×C4×D13C2312yes—
56C2×Dic26D411yescharacteristic
57C13×M16—22no—
58C2×C8×C13C2312yes—
59C13×C4⋊C4—21no—
60C13×C4⋊C4C2311yescharacteristic
61C13×C4⋊C4C2312yes—
62C13×C4⋊C4C2311yescharacteristic
63C13×C22⋊C4—21no—
64C42×C13—21no—
65C22⋊Dic13—21no—
66#6103—22no—
67#6103—22no—
68#6103—22no—
69C4⋊Dic13C2311yescharacteristic
70C4⋊Dic13C2311yescharacteristic
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13—22no—
74C2×#1055—22no—
75C2×#1055C2311yescharacteristic
76C2×#1055C2311yescharacteristic
77#3096—131nomaximal, Sylow
78C23×C13C2×D411yescharacteristic
79C22×D13—22no—
80C22×D13—42no—
81C22×D13—81no—
82C22×D13—81no—
83C22×D13C2×D412yes—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—81no—
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13#4112yes—
90C2×C4×C13#4112yes—
91C2×C4×C13C2411yescharacteristic
92C22⋊D13—24no—
93C2×Dic13—21no—
94C2×Dic13—21no—
95C2×Dic13C2×D412yes—
96D52—22no—
97D52—22no—
98D52—22no—
99D52—42no—
100D52—82no—
101D52—82no—
102C4×D13—22no—
103C4×D13—22no—
104C4×D13—82no—
105Dic26—22no—
106C8×C13—22no—
107#1055—21no—
108#1055—21no—
109#535—131no—
110#520—131no—
111#482—132no—
112#482—132no—
113#481—132no—
114#480—132no—
115#428D1311yescharacteristic, complemented
116#427—131no—
117#418—131no—
118C2×#102—131no—
119#408—131no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13#12312yes—
123C22×C13C22×D411yescharacteristic
124C2×D13—22no—
125C2×D13—22no—
126C2×D13—22no—
127C2×D13—42no—
128C2×D13—42no—
129C2×D13—42no—
130C2×D13—84no—
131C4×C13—42no—
132C4×C13—41no—
133C4×C13—41no—
134C4×C13#12312yes—
135C4×C13C2×#4111yescharacteristic
136C4×C13C2×#4111yescharacteristic
137Dic13—22no—
138Dic13—41no—
139Dic13—41no—
140C2×#41—131no—
141C22×D4—131no—
142C2×M16C2×D1311yescharacteristic
143C22×C8—131no—
144#127—261no—
145#124—261no—
146#121—132no—
147#121—132no—
148#120—262no—
149C4×Q8—261no—
150C4×D4—261no—
151C4×D4—262no—
152#117—131no—
153#117—132no—
154#117C2×D1311yescharacteristic
155C2×C4⋊C4—132no—
156C2×C4⋊C4C2×D1311yescharacteristic
157#107—131no—
158#107—131no—
159#107C2×D1312yescomplemented
160#106—131no—
161#106—131no—
162#106C2×D1312yescomplemented
163#102—132no—
164#102—132no—
165#102—132no—
166#102—132no—
167C22⋊C8—132no—
168C22⋊C8—132no—
169C2×C13—22no—
170C2×C13C2×#12311yescharacteristic
171C2×C13#57611yescharacteristic
172C2×C13#57711yescharacteristic
173D13—42no—
174D13—82no—
175C24—261no—
176#41—262no—
177#41—262no—
178C2×Q8—131no—
179C2×D4—132no—
180C2×D4—131no—
181C2×D4—132no—
182C2×D4—262no—
183C2×D4—262no—
184C2×D4—262no—
185C2×D4—261no—
186C2×D4—262no—
187C22×C4—21no—
188C22×C4—132no—
189C22×C4—262no—
190C22×C4C22×D1311yescharacteristic
191M16—22no—
192C2×C8—131no—
193C2×C8—131no—
194C2×C8—262no—
195C2×C8C22×D1312yes—
196C4⋊C4—21no—
197C4⋊C4—131no—
198C4⋊C4—131no—
199C4⋊C4—262no—
200C4⋊C4C22×D1312yes—
201C4⋊C4C22×D1311yescharacteristic
202C4⋊C4C22×D1311yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—262no—
205C22⋊C4—262no—
206C22⋊C4—262no—
207C22⋊C4—261no—
208C42—21no—
209C42—262no—
210C42—261no—
211C13#309611yescharacteristic, complemented, Sylow
212C23—132no—
213C23—262no—
214C23—522no—
215C23—1041no—
216C23—1041no—
217C23D4×D1311yescharacteristic
218Q8—262no—
219D4—264no—
220D4—262no—
221D4—262no—
222D4—262no—
223D4—522no—
224D4—1042no—
225D4—1042no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—81no—
230C2×C4—132no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—1042no—
236C2×C4#612712yes—
237C2×C4D4×D1311yescharacteristic
238C2×C4#613112yes—
239C2×C4C23×D1311yescharacteristic
240C8—22no—
241C8—261no—
242C8—261no—
243C22—21no—
244C22—21no—
245C22—262no—
246C22—262no—
247C22—262no—
248C22—522no—
249C22—522no—
250C22—522no—
251C22—1044no—
252C22#8814812yes—
253C22C2×D4×D1311yescharacteristic
254C4—42no—
255C4—41no—
256C4—41no—
257C4—262no—
258C4—521no—
259C4—521no—
260C4#8814812yes—
261C4C2×#612711yescharacteristic
262C4C2×#613111yescharacteristic
263C2—22no—
264C2—522no—
265C2—1042no—
266C2C2×#8814811yescharacteristic
267C2#1171947911yescharacteristic
268C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
prime radical#11719230C2
hypercenter#428D13
hypocenterC13#3096
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #11719209C2semidirect
3. C13×#428C2semidirect
4. #11718792C2semidirect
5. #11718790C2semidirect
6. #11718659C2semidirect
7. C2×#88049C2semidirect
8. #11718546C2semidirect
9. #11718543C2semidirect
10. #11718527C2semidirect
11. #11718524C2semidirect
23. #88146C22semidirect
24. C4⋊C4×D13C22semidirect
29. C13×#107C22semidirect
30. C13×#106C22semidirect
33. #88060C22semidirect
34. #88060C22semidirect
37. #88048C22semidirect
38. #88048C22semidirect
39. #88047C22semidirect
40. #88047C22semidirect
115. #428D13semidirect
159. #107C2×D13semidirect
162. #106C2×D13semidirect
211. C13#3096semidirect

Maximal subgroups

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

subgroupindex
#117192302
#117192092
C13×#4282
#117187922
#117187902
#117186592
C2×#880492
#117185462
#117185432
#117185272
#117185242
#309613