Finite Group Databasebeta

← #13125188

Subgroups — #13125188

Order 1664.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 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#11719510C211yesmaximal, characteristic
2#11719205C211yesmaximal, characteristic, complemented
3C2×C13×#102C211yesmaximal, characteristic, complemented
4#11718876C211yesmaximal, characteristic, complemented
5#11718774C211yesmaximal, characteristic, complemented
6#11718762C211yesmaximal, characteristic, complemented
7#11718627C211yesmaximal, characteristic, complemented
8#11718429C212yesmaximal, complemented
9#11718426C212yesmaximal, complemented
10#11718425C212yesmaximal, complemented
11#11718421C212yesmaximal, complemented
12C22×D4×C13C2211yescharacteristic
13C2×#6127C2211yescharacteristic
14C22×C8×C13C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16#88207—22no—
17#88194C2212yes—
18#88192—21no—
19#88192—21no—
20#88190C2212yes—
21#88180C2211yescharacteristic
22#88180C2211yescharacteristic
23#88178—22no—
24C2×#6099C2211yescharacteristic
25#88144—21no—
26#88144C2212yescomplemented
27#88142—21no—
28#88142C2212yescomplemented
29C13×#102C2212yes—
30C13×#102C2212yes—
31#88072C2212yes—
32#88072C2212yes—
33#88061C2211yescharacteristic, complemented
34#88061C2211yescharacteristic, complemented
35#88056C2211yescharacteristic, complemented
36#88056C2211yescharacteristic, complemented
37#88055C2212yescomplemented
38C8×Dic13C2212yescomplemented
39#88050C2212yescomplemented
40#88049C2212yescomplemented
41C24×C13—21no—
42C2×D4×C13—21no—
43C2×D4×C13—22no—
44C2×D4×C13—22no—
45C2×D4×C13C2312yes—
46C22×C4×C13—21no—
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—21no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51#6127—22no—
52#6127—22no—
53C2×D52C2311yescharacteristic
54C2×C4×D13—21no—
55C2×Dic26—22no—
56C2×Dic26C2311yescharacteristic
57C2×C8×C13—22no—
58C2×C8×C13C2311yescharacteristic
59C2×C8×C13C2311yescharacteristic
60C13×C4⋊C4—21no—
61C13×C4⋊C4C2312yes—
62C22⋊Dic13—21no—
63C22⋊Dic13—22no—
64C22⋊Dic13—22no—
65C22⋊Dic13D412yes—
66C4⋊Dic13—22no—
67C4⋊Dic13D411yescharacteristic
68C4⋊Dic13D411yescharacteristic
69C4⋊Dic13C2311yescharacteristic
70C4⋊Dic13C2311yescharacteristic
71#6101—22no—
72#6101—22no—
73C4×Dic13—21no—
74C4×Dic13C2312yes—
75#6099—22no—
76C2×#1055C2312yes—
77#3136—131nomaximal, Sylow
78C23×C13—22no—
79C23×C13—42no—
80C23×C13—81no—
81C23×C13—81no—
82C23×C13C2×D411yescharacteristic
83C22×D13—21no—
84D4×C13—22no—
85D4×C13—22no—
86D4×C13—42no—
87C2×C4×C13—22no—
88C2×C4×C13—81no—
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13#4112yes—
91C2×C4×C13#4112yes—
92C2×C4×C13C2411yescharacteristic
93C22⋊D13—42no—
94C22⋊D13—82no—
95C22⋊D13—82no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13C2×D412yes—
100C2×Dic13C2×D412yes—
101D52—21no—
102D52—21no—
103C4×D13—42no—
104Dic26—21no—
105Dic26—21no—
106Dic26—82no—
107C8×C13—21no—
108C8×C13—21no—
109#1055—22no—
110#544—131no—
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×#102D1311yescharacteristic, complemented
120#405—131no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—84no—
127C22×C13#12412yes—
128C22×C13C22×D411yescharacteristic
129C2×D13—41no—
130C2×D13—41no—
131C2×D13—41no—
132C4×C13—42no—
133C4×C13#12412yes—
134C4×C13C2×#4111yescharacteristic
135C4×C13C2×#4111yescharacteristic
136Dic13—22no—
137Dic13—22no—
138Dic13—41no—
139Dic13—41no—
140Dic13—41no—
141C2×#41—131no—
142C22×D4C2×D1311yescharacteristic
143C2×M16—131no—
144C22×C8C2×D1311yescharacteristic
145C4⋊Q8—132no—
146C4⋊Q8—261no—
147#127—132no—
148#125—132no—
149#125—261no—
150#124—132no—
151C22⋊Q8—262no—
152#121—261no—
153#121—261no—
154#120—262no—
155#117—131no—
156#117—131no—
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#102C2×D1312yes—
167#102C2×D1312yes—
168#97—132no—
169C4×C8—132no—
170C2×C13—22no—
171C2×C13—82no—
172C2×C13C2×#12411yescharacteristic
173C2×C13#57611yescharacteristic
174C2×C13#57711yescharacteristic
175D13—81no—
176C24—21no—
177#41—262no—
178#41—262no—
179C2×Q8—131no—
180C2×Q8—262no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—131no—
185C2×D4—262no—
186C2×D4—262no—
187C2×D4—261no—
188C2×D4C22×D1312yes—
189C22×C4—21no—
190C22×C4—261no—
191C22×C4C22×D1311yescharacteristic
192M16—262no—
193C2×C8—22no—
194C2×C8—132no—
195C2×C8C22×D1311yescharacteristic
196C2×C8C22×D1311yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—131no—
199C4⋊C4—131no—
200C4⋊C4—131no—
201C4⋊C4—131no—
202C4⋊C4—262no—
203C4⋊C4—262no—
204C4⋊C4—262no—
205C4⋊C4C22×D1312yes—
206C22⋊C4—132no—
207C22⋊C4—262no—
208C22⋊C4—262no—
209C22⋊C4—261no—
210C42—132no—
211C42—261no—
212C13#313611yescharacteristic, complemented, Sylow
213C23—22no—
214C23—42no—
215C23—81no—
216C23—81no—
217C23—261no—
218C23D4×D1311yescharacteristic
219Q8—261no—
220Q8—261no—
221Q8—1042no—
222D4—22no—
223D4—22no—
224D4—42no—
225D4—261no—
226D4—261no—
227D4—522no—
228D4—1042no—
229D4—1042no—
230C2×C4—22no—
231C2×C4—81no—
232C2×C4—132no—
233C2×C4—132no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—261no—
237C2×C4—522no—
238C2×C4#612712yes—
239C2×C4D4×D1311yescharacteristic
240C2×C4#612912yes—
241C2×C4C23×D1311yescharacteristic
242C8—21no—
243C8—21no—
244C8—262no—
245C22—21no—
246C22—21no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—84no—
251C22—521no—
252C22—521no—
253C22—521no—
254C22#8813912yes—
255C22C2×D4×D1311yescharacteristic
256C4—42no—
257C4—262no—
258C4—262no—
259C4—521no—
260C4—521no—
261C4—521no—
262C4#8813912yes—
263C4C2×#612711yescharacteristic
264C4C2×#612911yescharacteristic
265C2—22no—
266C2—82no—
267C2—1041no—
268C2C2×#8813911yescharacteristic
269C2#1171946211yescharacteristic
270C2#1171946711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#102C2
socleC22×C13C22×D4
prime radical#11719510C2
hypercenterC2×#102D13
hypocenterC13#3136
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. #11719205C2semidirect
3. C2×C13×#102C2semidirect
4. #11718876C2semidirect
5. #11718774C2semidirect
6. #11718762C2semidirect
7. #11718627C2semidirect
8. #11718429C2semidirect
9. #11718426C2semidirect
10. #11718425C2semidirect
11. #11718421C2semidirect
26. #88144C22semidirect
28. #88142C22semidirect
33. #88061C22semidirect
34. #88061C22semidirect
35. #88056C22semidirect
36. #88056C22semidirect
37. #88055C22semidirect
38. C8×Dic13C22semidirect
39. #88050C22semidirect
40. #88049C22semidirect
119. C2×#102D13semidirect
212. C13#3136semidirect

Maximal subgroups

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

subgroupindex
#117195102
#117192052
C2×C13×#1022
#117188762
#117187742
#117187622
#117186272
#117184292
#117184262
#117184252
#117184212
#313613