Finite Group Databasebeta

← #13124751

Subgroups — #13124751

Order 1664.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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#11719496C211yesmaximal, characteristic
2C2×#88180C211yesmaximal, characteristic, complemented
3C2×C13×C22⋊C8C211yesmaximal, characteristic, complemented
4#11718774C212yesmaximal, complemented
5#11718767C212yesmaximal, complemented
6#11718398C212yesmaximal, complemented
7#11718397C211yesmaximal, characteristic, complemented
8#11718396C211yesmaximal, characteristic, complemented
9#11718384C212yesmaximal, complemented
10#11718383C211yesmaximal, characteristic, complemented
11#11718382C211yesmaximal, characteristic, complemented
12C23×C4×C13C2211yescharacteristic
13C2×#6127C2211yescharacteristic
14C22×C8×C13C2212yes—
15#88207—21no—
16C2×C22⋊Dic13—21no—
17#88184C2211yescharacteristic
18#88184C2211yescharacteristic
19#88183—21no—
20C4×C22⋊D13—21no—
21C4×C22⋊D13—21no—
22#88180—21no—
23#88180—21no—
24#88180C2212yes—
25#88180C2212yes—
26#88180C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29#88178C2211yescharacteristic
30#88178C2211yescharacteristic
31C2×C4×Dic13—21no—
32C13×C22⋊C8C2211yescharacteristic
33C13×C22⋊C8C2211yescharacteristic
34C13×C22⋊C8C2212yes—
35#88061C2212yescomplemented
36#88061C2212yescomplemented
37#88058C2212yescomplemented
38#88058C2212yescomplemented
39#88057C2212yescomplemented
40#88057C2212yescomplemented
41#88056C2212yescomplemented
42#88056C2212yescomplemented
43C24×C13D411yescharacteristic
44C22×C4×C13—24no—
45C22×C4×C13D411yescharacteristic
46C22×C4×C13D411yescharacteristic
47C22×C4×C13D411yescharacteristic
48C22×C4×C13C2311yescharacteristic
49C22×C4×C13C2311yescharacteristic
50C22×C4×C13C2311yescharacteristic
51C2×C22⋊D13—21no—
52C2×C22⋊D13—21no—
53C2×C22⋊D13—21no—
54C22×Dic13—21no—
55C22×Dic13—21no—
56#6127—24no—
57C2×D52C2311yescharacteristic
58C2×C4×D13—21no—
59C2×Dic26C2311yescharacteristic
60C2×C8×C13—24no—
61C2×C8×C13C2312yes—
62C2×C8×C13C2312yes—
63C22⋊Dic13—21no—
64C22⋊Dic13—21no—
65C22⋊Dic13—22no—
66C22⋊Dic13—22no—
67C22⋊Dic13—21no—
68#6103—21no—
69#6103—21no—
70C4⋊Dic13—21no—
71C4⋊Dic13—21no—
72C4⋊Dic13C2311yescharacteristic
73C4⋊Dic13C2311yescharacteristic
74C4⋊Dic13C2312yes—
75C4⋊Dic13C2312yes—
76#6101—21no—
77#6101—21no—
78C4×Dic13—22no—
79C4×Dic13—22no—
80C4×Dic13—21no—
81#3091—131nomaximal, Sylow
82C23×C13—22no—
83C23×C13—22no—
84C23×C13—41no—
85C23×C13C2×D411yescharacteristic
86C23×C13C2×D411yescharacteristic
87C23×C13C2×D411yescharacteristic
88C22×D13—21no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13#4114yes—
98C2×C4×C13C2411yescharacteristic
99C22⋊D13—42no—
100C22⋊D13—42no—
101C22⋊D13—42no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109D52—22no—
110C4×D13—42no—
111Dic26—22no—
112C8×C13—22no—
113C8×C13—22no—
114#525—131no—
115C2×#117—131no—
116#485—132no—
117#484—131no—
118#483—131no—
119#482—132no—
120#481—131no—
121#480—131no—
122#427—132no—
123#416—132no—
124C2×C22⋊C8D1311yescharacteristic, complemented
125C22×C13—21no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13—44no—
133C22×C13#12312yes—
134C22×C13#13512yes—
135C22×C13C22×D411yescharacteristic
136C2×D13—41no—
137C2×D13—41no—
138C2×D13—41no—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13#12312yes—
142C4×C13C2×#4112yes—
143Dic13—41no—
144Dic13—42no—
145Dic13—41no—
146Dic13—42no—
147Dic13—41no—
148C2×#41—131no—
149C23×C4C2×D1311yescharacteristic
150C22×C8C2×D1312yes—
151#123—261no—
152C22⋊Q8—131no—
153C22⋊Q8—131no—
154#121—131no—
155#121—131no—
156#120—261no—
157C4×D4—261no—
158C4×D4—261no—
159#117—132no—
160#117—132no—
161#117—131no—
162#117—261no—
163#117—261no—
164C2×C4⋊C4—131no—
165C2×C4⋊C4—131no—
166C2×C22⋊C4—261no—
167C2×C42—261no—
168#107—132no—
169#107—132no—
170#106—132no—
171#106—132no—
172#103—132no—
173#103—132no—
174#102—132no—
175#102—132no—
176C22⋊C8C2×D1311yescharacteristic
177C22⋊C8C2×D1311yescharacteristic
178C22⋊C8C2×D1312yes—
179C2×C13—22no—
180C2×C13—22no—
181C2×C13—41no—
182C2×C13C2×#12311yescharacteristic
183C2×C13C2×#13511yescharacteristic
184C2×C13#57511yescharacteristic
185D13—81no—
186C24D5211yescharacteristic
187#41—264no—
188C2×Q8—131no—
189C2×D4—131no—
190C2×D4—261no—
191C2×D4—261no—
192C2×D4—261no—
193C22×C4—24no—
194C22×C4—261no—
195C22×C4—261no—
196C22×C4—261no—
197C22×C4D5211yescharacteristic
198C22×C4D5211yescharacteristic
199C22×C4D5211yescharacteristic
200C22×C4C22×D1311yescharacteristic
201C22×C4C22×D1311yescharacteristic
202C22×C4C22×D1311yescharacteristic
203C2×C8—24no—
204C2×C8C22×D1312yes—
205C2×C8C22×D1312yes—
206C4⋊C4—132no—
207C4⋊C4—132no—
208C4⋊C4—131no—
209C4⋊C4—131no—
210C4⋊C4—261no—
211C4⋊C4—261no—
212C4⋊C4—261no—
213C4⋊C4—261no—
214C22⋊C4—262no—
215C22⋊C4—262no—
216C22⋊C4—261no—
217C22⋊C4—261no—
218C22⋊C4—261no—
219C22⋊C4—261no—
220C22⋊C4—261no—
221C42—262no—
222C42—262no—
223C42—261no—
224C13#309111yescharacteristic, complemented, Sylow
225C23—22no—
226C23—22no—
227C23—41no—
228C23—261no—
229C23C2×D5211yescharacteristic
230C23C2×D5211yescharacteristic
231C23C2×D5211yescharacteristic
232Q8—262no—
233D4—262no—
234D4—522no—
235D4—522no—
236D4—522no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—261no—
245C2×C4—261no—
246C2×C4—261no—
247C2×C4—522no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4C2×D5211yescharacteristic
251C2×C4C2×D5211yescharacteristic
252C2×C4C2×D5211yescharacteristic
253C2×C4#612914yes—
254C2×C4C23×D1311yescharacteristic
255C8—22no—
256C8—22no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—521no—
266C22—521no—
267C22—521no—
268C22#8814012yes—
269C22#8815812yes—
270C22C22×D5211yescharacteristic
271C4—21no—
272C4—21no—
273C4—522no—
274C4—521no—
275C4—521no—
276C4—522no—
277C4—521no—
278C4#8814012yes—
279C4C2×#612912yes—
280C2—22no—
281C2—22no—
282C2—41no—
283C2—1041no—
284C2C2×#8814011yescharacteristic
285C2C2×#8815811yescharacteristic
286C2#1171945311yescharacteristic
subgroupG/H
centerC2×C4C2×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×C22⋊C8C2
socleC22×C13C22×D4
prime radical#11719496C2
hypercenterC2×C22⋊C8D13
hypocenterC13#3091
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#88180C2semidirect
3. C2×C13×C22⋊C8C2semidirect
4. #11718774C2semidirect
5. #11718767C2semidirect
6. #11718398C2semidirect
7. #11718397C2semidirect
8. #11718396C2semidirect
9. #11718384C2semidirect
10. #11718383C2semidirect
11. #11718382C2semidirect
35. #88061C22semidirect
36. #88061C22semidirect
37. #88058C22semidirect
38. #88058C22semidirect
39. #88057C22semidirect
40. #88057C22semidirect
41. #88056C22semidirect
42. #88056C22semidirect
124. C2×C22⋊C8D13semidirect
224. C13#3091semidirect

Maximal subgroups

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

subgroupindex
#117194962
C2×#881802
C2×C13×C22⋊C82
#117187742
#117187672
#117183982
#117183972
#117183962
#117183842
#117183832
#117183822
#309113