Finite Group Databasebeta

← #13125801

Subgroups — #13125801

Order 1664.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×C13×#124C211yesmaximal, characteristic, complemented
2#11719184C211yesmaximal, characteristic, complemented
3#11718889C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic, complemented
5#11718879C211yesmaximal, characteristic, complemented
6#11718878C211yesmaximal, characteristic
7#11718720C212yesmaximal, complemented
8#11718718C212yesmaximal, complemented
9#11718717C212yesmaximal, complemented
10#11718715C212yesmaximal, complemented
11#11718586C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×D4×C13C2211yescharacteristic
14C13×#124—21no—
15C13×#124—21no—
16C13×#124C2212yes—
17C13×#124C2212yes—
18C2×C13×C22⋊C4—21no—
19C2×C13×C22⋊C4—21no—
20C2×C42×C13C2211yescharacteristic
21C2×#6107C2212yescomplemented
22C2×#6106C2212yescomplemented
23C2×#6105C2212yes—
24C2×#6104C2212yes—
25#88184C2211yescharacteristic
26#88183—21no—
27C4×C22⋊D13—21no—
28#88178C2211yescharacteristic
29#88130—21no—
30#88129C2211yescharacteristic, complemented
31C4×D52C2211yescharacteristic, complemented
32#88126—21no—
33#88124C2211yescharacteristic, complemented
34C4×Dic26C2211yescharacteristic, complemented
35#88075C2212yescomplemented
36#88075C2212yescomplemented
37#88072C2212yes—
38#88072C2212yes—
39C22⋊#1055C2211yescharacteristic
40C22⋊#1055C2211yescharacteristic
41C4⋊#1055C2212yescomplemented
42C4×#1055C2212yescomplemented
43C24×C13—21no—
44C2×Q8×C13—21no—
45C2×Q8×C13—42no—
46C2×Q8×C13C2312yes—
47C2×D4×C13—21no—
48C2×D4×C13—42no—
49C2×D4×C13C2312yes—
50C22×C4×C13—21no—
51C22×C4×C13D411yescharacteristic
52C22×C4×C13D411yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C2×C22⋊D13—21no—
55C2×D52C2311yescharacteristic
56C2×C4×D13—21no—
57C2×Dic26C2311yescharacteristic
58C13×C22⋊C4—22no—
59C13×C22⋊C4—22no—
60C13×C22⋊C4—22no—
61C13×C22⋊C4—22no—
62C42×C13D411yescharacteristic
63C42×C13D411yescharacteristic
64C42×C13C2311yescharacteristic
65C42×C13C2311yescharacteristic
66C22⋊Dic13—21no—
67#6107—42no—
68#6106—42no—
69#6105—42no—
70#6104—42no—
71#6103—21no—
72#6103—21no—
73#6103—21no—
74#6103—21no—
75C4⋊Dic13C2311yescharacteristic
76C4⋊Dic13C2311yescharacteristic
77#6101—21no—
78#6101—21no—
79#6101—21no—
80#6101—21no—
81C4×Dic13—21no—
82C2×#1055C2312yes—
83C2×#1055C2312yes—
84#3211—131nomaximal, Sylow
85C23×C13—22no—
86C23×C13—42no—
87C23×C13—42no—
88C23×C13—42no—
89C23×C13C2×D411yescharacteristic
90C22×D13—21no—
91Q8×C13—22no—
92Q8×C13—22no—
93Q8×C13—42no—
94D4×C13—22no—
95D4×C13—22no—
96D4×C13—42no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13C2×D411yescharacteristic
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2×D411yescharacteristic
105C2×C4×C13C2×D411yescharacteristic
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2411yescharacteristic
108C22⋊D13—42no—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112D52—22no—
113C4×D13—42no—
114Dic26—22no—
115#1055—22no—
116#1055—22no—
117#529—131no—
118C2×#124D1311yescharacteristic, complemented
119#495—132no—
120#488—132no—
121#464—132no—
122#463—132no—
123#451—131no—
124#450—131no—
125#448—131no—
126#447—131no—
127#431—131no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—84no—
134C22×C13#13512yes—
135C22×C13C22×D411yescharacteristic
136C2×D13—41no—
137C2×D13—41no—
138C2×D13—41no—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—21no—
144C4×C13—42no—
145C4×C13H(5,𝔽2)12yes—
146Dic13—41no—
147Dic13—41no—
148Dic13—41no—
149C22×Q8C2×D1311yescharacteristic
150C22×D4C2×D1311yescharacteristic
151C2×Q16—132no—
152C2×SD16—132no—
153C2×SD16—132no—
154C2×D8—132no—
155#126—261no—
156#125—131no—
157#124—21no—
158#124—21no—
159#124—131no—
160#124C2×D1312yes—
161#124C2×D1312yes—
162#123—261no—
163C22⋊Q8—131no—
164#121—131no—
165C4×Q8—131no—
166C4×D4—131no—
167C4×D4—261no—
168#117—261no—
169C2×C22⋊C4—21no—
170C2×C22⋊C4—21no—
171C2×C42C2×D1311yescharacteristic
172C4⋊C8—132no—
173#103—132no—
174#103—132no—
175#102—132no—
176#102—132no—
177C22⋊C8—131no—
178C22⋊C8—131no—
179C4×C8—132no—
180C2×C13—22no—
181C2×C13—82no—
182C2×C13#53511yescharacteristic
183C2×C13C2×#13511yescharacteristic
184C2×C13#57511yescharacteristic
185D13—81no—
186C24—21no—
187C2×Q8—21no—
188C2×Q8—42no—
189C2×Q8—131no—
190C2×Q8C22×D1312yes—
191C2×D4—21no—
192C2×D4—42no—
193C2×D4—131no—
194C2×D4—261no—
195C2×D4C22×D1312yes—
196C22×C4—21no—
197C22×C4—261no—
198C22×C4C22⋊D1311yescharacteristic
199C22×C4C22⋊D1311yescharacteristic
200C22×C4C22×D1311yescharacteristic
201Q16—522no—
202SD16—522no—
203SD16—522no—
204D8—522no—
205C2×C8—132no—
206C2×C8—132no—
207C4⋊C4—131no—
208C4⋊C4—131no—
209C4⋊C4—261no—
210C4⋊C4—261no—
211C4⋊C4—261no—
212C4⋊C4—261no—
213C22⋊C4—22no—
214C22⋊C4—22no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—261no—
218C22⋊C4—261no—
219C22⋊C4—261no—
220C22⋊C4—261no—
221C22⋊C4—261no—
222C42—261no—
223C42C22⋊D1311yescharacteristic
224C42C22⋊D1311yescharacteristic
225C42C22×D1311yescharacteristic
226C42C22×D1311yescharacteristic
227C13#321111yescharacteristic, complemented, Sylow
228C23—22no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—261no—
233C23C2×C22⋊D1311yescharacteristic
234Q8—22no—
235Q8—22no—
236Q8—42no—
237Q8—262no—
238D4—22no—
239D4—22no—
240D4—42no—
241D4—262no—
242D4—522no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—261no—
249C2×C4—261no—
250C2×C4—261no—
251C2×C4—522no—
252C2×C4C2×C22⋊D1311yescharacteristic
253C2×C4C2×C22⋊D1311yescharacteristic
254C2×C4C2×C22⋊D1311yescharacteristic
255C2×C4C2×C22⋊D1311yescharacteristic
256C2×C4C2×C22⋊D1311yescharacteristic
257C2×C4C23×D1311yescharacteristic
258C8—262no—
259C8—262no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—521no—
267C22—521no—
268C22—521no—
269C22#8820412yes—
270C22C22×C22⋊D1311yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—42no—
277C4—521no—
278C4—521no—
279C4—521no—
280C4#8825112yes—
281C2—22no—
282C2—82no—
283C2—1041no—
284C2#1171951011yescharacteristic
285C2C2×#8820411yescharacteristic
286C2#1171952711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#124C2
socleC22×C13C22×D4
prime radical#11718878C2
hypercenterC2×#124D13
hypocenterC13#3211
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C13×#124C2semidirect
2. #11719184C2semidirect
3. #11718889C2semidirect
4. #11718888C2semidirect
5. #11718879C2semidirect
7. #11718720C2semidirect
8. #11718718C2semidirect
9. #11718717C2semidirect
10. #11718715C2semidirect
11. #11718586C2semidirect
21. C2×#6107C22semidirect
22. C2×#6106C22semidirect
30. #88129C22semidirect
31. C4×D52C22semidirect
33. #88124C22semidirect
34. C4×Dic26C22semidirect
35. #88075C22semidirect
36. #88075C22semidirect
41. C4⋊#1055C22semidirect
42. C4×#1055C22semidirect
118. C2×#124D13semidirect
227. C13#3211semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1242
#117191842
#117188892
#117188882
#117188792
#117188782
#117187202
#117187182
#117187172
#117187152
#117185862
#321113