Finite Group Databasebeta

← #13125195

Subgroups — #13125195

Order 1664.

404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 404 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
1C13×#544C211yesmaximal, characteristic, complemented
2#11719230C211yesmaximal, characteristic
3#11718750C212yesmaximal, complemented
4#11718749C212yesmaximal, complemented
5#11718729C212yesmaximal, complemented
6#11718728C212yesmaximal, complemented
7#11718663C211yesmaximal, characteristic, complemented
8#11718662C211yesmaximal, characteristic, complemented
9#11718658C211yesmaximal, characteristic, complemented
10#11718627C211yesmaximal, characteristic, complemented
11C2×#88049C211yesmaximal, characteristic, complemented
12C2×#6127C2211yescharacteristic
13C22×D52C2211yescharacteristic
14C13×C4⋊Q8—21no—
15C13×C4⋊Q8C2212yescomplemented
16C13×#125—21no—
17C13×#125C2212yescomplemented
18C13×C22⋊Q8—22no—
19C13×#117C2211yescharacteristic
20C13×#117C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×#6099C2211yescharacteristic
23C22×#1055C2211yescharacteristic
24#88149—21no—
25#88149—21no—
26#88136—22no—
27#88129C2212yes—
28#88128C2212yes—
29#88050C2211yescharacteristic, complemented
30#88050C2211yescharacteristic, complemented
31#88050C2212yescomplemented
32#88049C2212yes—
33#88049C2212yes—
34#88049C2212yes—
35#88049C2212yes—
36#88049C2211yescharacteristic, complemented
37#88049C2211yescharacteristic, complemented
38#88049C2212yescomplemented
39#88043C2212yescomplemented
40C4×#1055C2212yescomplemented
41C23×D13—21no—
42C2×Q8×C13—22no—
43C22×C4×C13—21no—
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—21no—
46#6127—22no—
47#6127—22no—
48C2×D52—22no—
49C2×D52—22no—
50C2×D52—21no—
51C2×D52—22no—
52C2×D52—22no—
53C2×D52C2311yescharacteristic
54C2×D52C2312yes—
55C2×C4×D13—21no—
56C2×Dic26C2311yescharacteristic
57C13×C4⋊C4—21no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4—22no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4D411yescharacteristic
62C13×C4⋊C4D411yescharacteristic
63C13×C4⋊C4C2312yes—
64C13×C4⋊C4C2311yescharacteristic
65C13×C4⋊C4C2311yescharacteristic
66C13×C22⋊C4—21no—
67C13×C22⋊C4D412yes—
68C42×C13—21no—
69C42×C13C2312yes—
70#6103—22no—
71#6103—22no—
72#6099—22no—
73C2×#1055—22no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2311yescharacteristic
76C2×#1055C2312yes—
77#3136—131nomaximal, Sylow
78C23×C13C2×D411yescharacteristic
79C22×D13—22no—
80C22×D13—21no—
81C22×D13—42no—
82C22×D13—81no—
83C22×D13—81no—
84Q8×C13—82no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—81no—
89C2×C4×C13C2×D412yes—
90C2×C4×C13C2×D412yes—
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13#4112yes—
93C2×C4×C13#4112yes—
94C2×C4×C13C2411yescharacteristic
95C22⋊D13—42no—
96C2×Dic13—21no—
97D52—22no—
98D52—22no—
99D52—21no—
100D52—21no—
101D52—42no—
102D52—82no—
103D52—82no—
104C4×D13—42no—
105Dic26—21no—
106Dic26—21no—
107#1055—21no—
108#1055—21no—
109#1055—22no—
110#544D1311yescharacteristic, complemented
111#535—131no—
112#490—132no—
113#489—132no—
114#488—132no—
115#486—132no—
116#418—131no—
117#417—131no—
118#416—131no—
119C2×#102—131no—
120#405—131no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#12412yes—
124C22×C13C22×D411yescharacteristic
125C2×D13—41no—
126C2×D13—42no—
127C2×D13—41no—
128C2×D13—42no—
129C2×D13—41no—
130C2×D13—42no—
131C2×D13—84no—
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—42no—
135C4×C13—41no—
136C4×C13—41no—
137C4×C13#12412yes—
138C4×C13C2×#4111yescharacteristic
139C4×C13C2×#4111yescharacteristic
140Dic13—41no—
141C2×#41—131no—
142C22×D4—131no—
143C2×M16—131no—
144C22×C8—131no—
145C4⋊Q8—21no—
146C4⋊Q8C2×D1312yescomplemented
147#127—132no—
148#125—21no—
149#125C2×D1312yescomplemented
150#124—132no—
151C22⋊Q8—22no—
152#121—261no—
153#121—261no—
154#120—262no—
155#117C2×D1311yescharacteristic
156#117C2×D1311yescharacteristic
157C2×C4⋊C4C2×D1311yescharacteristic
158#103—131no—
159#103—131no—
160#103—132no—
161#102—132no—
162#102—132no—
163#102—131no—
164#102—131no—
165#102—132no—
166#102—132no—
167#102—132no—
168#97—132no—
169C4×C8—132no—
170C2×C13—22no—
171C2×C13C2×#12411yescharacteristic
172C2×C13#57611yescharacteristic
173C2×C13#57711yescharacteristic
174D13—81no—
175D13—82no—
176C24—261no—
177#41—262no—
178#41—262no—
179C2×Q8—22no—
180C2×Q8—131no—
181C2×D4—132no—
182C2×D4—131no—
183C2×D4—261no—
184C2×D4—262no—
185C2×D4—262no—
186C2×D4—261no—
187C2×D4—262no—
188C2×D4—262no—
189C22×C4—21no—
190C22×C4—261no—
191C22×C4C22×D1311yescharacteristic
192M16—262no—
193C2×C8—131no—
194C2×C8—132no—
195C2×C8—131no—
196C2×C8—262no—
197C4⋊C4—21no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4C22⋊D1311yescharacteristic
202C4⋊C4C22⋊D1311yescharacteristic
203C4⋊C4C22×D1312yes—
204C4⋊C4C22×D1311yescharacteristic
205C4⋊C4C22×D1311yescharacteristic
206C22⋊C4—21no—
207C22⋊C4—262no—
208C22⋊C4—262no—
209C22⋊C4C22⋊D1312yes—
210C42—21no—
211C42C22×D1312yes—
212C13#313611yescharacteristic, complemented, Sylow
213C23—262no—
214C23—261no—
215C23—522no—
216C23—1041no—
217C23—1041no—
218C23C2×C22⋊D1311yescharacteristic
219Q8—82no—
220Q8—261no—
221Q8—261no—
222D4—262no—
223D4—262no—
224D4—261no—
225D4—261no—
226D4—522no—
227D4—522no—
228D4—1042no—
229D4—1042no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—81no—
234C2×C4—261no—
235C2×C4—522no—
236C2×C4#613112yes—
237C2×C4#613112yes—
238C2×C4C2×C22⋊D1312yes—
239C2×C4C2×C22⋊D1312yes—
240C2×C4C2×C22⋊D1311yescharacteristic
241C2×C4C23×D1311yescharacteristic
242C8—261no—
243C8—261no—
244C8—262no—
245C22—21no—
246C22—21no—
247C22—521no—
248C22—522no—
249C22—521no—
250C22—522no—
251C22—521no—
252C22—522no—
253C22—1044no—
254C22#8820112yes—
255C22C22×C22⋊D1311yescharacteristic
256C4—22no—
257C4—22no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—521no—
262C4#8820112yes—
263C4C2×#613111yescharacteristic
264C4C2×#613111yescharacteristic
265C2—22no—
266C2—1042no—
267C2—1041no—
268C2C2×#8820111yescharacteristic
269C2#1171954011yescharacteristic
270C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#544C2
socleC22×C13C22×D4
prime radical#11719230C2
hypercenter#544D13
hypocenterC13#3136
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
1. C13×#544C2semidirect
3. #11718750C2semidirect
4. #11718749C2semidirect
5. #11718729C2semidirect
6. #11718728C2semidirect
7. #11718663C2semidirect
8. #11718662C2semidirect
9. #11718658C2semidirect
10. #11718627C2semidirect
11. C2×#88049C2semidirect
15. C13×C4⋊Q8C22semidirect
17. C13×#125C22semidirect
29. #88050C22semidirect
30. #88050C22semidirect
31. #88050C22semidirect
36. #88049C22semidirect
37. #88049C22semidirect
38. #88049C22semidirect
39. #88043C22semidirect
40. C4×#1055C22semidirect
110. #544D13semidirect
146. C4⋊Q8C2×D13semidirect
149. #125C2×D13semidirect
212. C13#3136semidirect

Maximal subgroups

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

subgroupindex
C13×#5442
#117192302
#117187502
#117187492
#117187292
#117187282
#117186632
#117186622
#117186582
#117186272
C2×#880492
#313613