Finite Group Databasebeta

← #13124932

Subgroups — #13124932

Order 1664.

444 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 119 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#11719327C211yesmaximal, characteristic, complemented
2C2×#88147C211yesmaximal, characteristic
3C13×#484C211yesmaximal, characteristic, complemented
4#11718707C211yesmaximal, characteristic
5#11718631C211yesmaximal, characteristic, complemented
6#11718551C212yesmaximal, complemented
7#11718550C212yesmaximal, complemented
8#11718479C212yesmaximal, complemented
9#11718478C212yesmaximal, complemented
10#11718392C211yesmaximal, characteristic
11#11718380C211yesmaximal, characteristic, complemented
12C22×D52C2211yescharacteristic
13C22×C4×D13—21no—
14C13×C22⋊Q8C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16Q8×Dic13C2211yescharacteristic, complemented
17#88198C2211yescharacteristic, complemented
18C2×#6106C2212yes—
19C2×#6103—21no—
20#88178C2211yescharacteristic
21C2×C4×Dic13C2211yescharacteristic
22C2×#6095C2212yes—
23#88147—21no—
24#88147—21no—
25#88147C2212yes—
26#88147C2212yes—
27#88143—21no—
28#88142C2211yescharacteristic, complemented
29#88141—21no—
30#88141C2211yescharacteristic, complemented
31#88132—21no—
32#88131—21no—
33C13×#107C2212yescomplemented
34C13×#103C2212yescomplemented
35C13×C22⋊C8C2211yescharacteristic
36C22⋊#1055C2211yescharacteristic
37#88061C2212yes—
38#88055C2212yescomplemented
39#88054C2212yescomplemented
40#88050C2212yescomplemented
41#88049C2212yes—
42#88047C2212yescomplemented
43C23×D13—21no—
44C2×Q8×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C22×Dic13D411yescharacteristic
48C22×Dic13D411yescharacteristic
49C2×D52—21no—
50C2×D52—24no—
51C2×D52C2312yes—
52C2×C4×D13—22no—
53C2×C4×D13—22no—
54C2×C4×D13—44no—
55C2×Dic26—21no—
56C2×Dic26C2311yescharacteristic
57C2×C8×C13C2312yes—
58C13×C4⋊C4—21no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4C2312yes—
61C13×C4⋊C4C2311yescharacteristic
62C13×C22⋊C4—21no—
63C22⋊Dic13—21no—
64#6106—24no—
65#6103—22no—
66#6103—22no—
67C4⋊Dic13—21no—
68C4⋊Dic13C2311yescharacteristic
69#6101—21no—
70#6101—21no—
71#6101—21no—
72#6101—21no—
73#6101—21no—
74C4×Dic13—21no—
75C4×Dic13—21no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C4×Dic13C2311yescharacteristic
80C2×#1055C2312yes—
81#6095—24no—
82#3110—131nomaximal, Sylow
83C23×C13C2×D411yescharacteristic
84C22×D13—24no—
85C22×D13—22no—
86C22×D13—42no—
87C22×D13—42no—
88Q8×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—42no—
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2411yescharacteristic
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13C2×D411yescharacteristic
101C2×Dic13C2×D411yescharacteristic
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104D52—24no—
105D52—22no—
106D52#4114yes—
107C4×D13—44no—
108C4×D13—44no—
109Dic26—22no—
110Dic26—42no—
111C8×C13—22no—
112#1055—22no—
113#533—131no—
114C2×C4×D4—131no—
115#484—131no—
116#484D1311yescharacteristic, complemented
117#474—132no—
118#461—132no—
119#450—131no—
120#450—131no—
121#440—132no—
122#440—132no—
123#432—131no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13#13712yes—
127C22×C13C22×D411yescharacteristic
128C2×D13—24no—
129C2×D13—48no—
130C2×D13—42no—
131C2×D13—42no—
132C4×C13—21no—
133C4×C13—41no—
134C4×C13—41no—
135C4×C13—42no—
136C4×C13C2×#4112yes—
137Dic13—21no—
138Dic13—21no—
139Dic13—21no—
140Dic13—41no—
141Dic13—41no—
142Dic13AGL(1,ℤ/8)12yes—
143C22×D4—131no—
144C23×C4—261no—
145C2×SD16—132no—
146C2×SD16—132no—
147C4⋊Q8—131no—
148C4⋊Q8—131no—
149#125—261no—
150C22⋊Q8—131no—
151C22⋊Q8—261no—
152C22⋊Q8C2×D1311yescharacteristic
153C4×Q8—131no—
154C4×Q8—131no—
155C4×Q8—261no—
156C4×D4—132no—
157C4×D4—132no—
158C4×D4—261no—
159C4×D4—261no—
160#117—261no—
161C2×C4⋊C4C2×D1311yescharacteristic
162C2×C22⋊C4—261no—
163C2×C42—131no—
164#107—132no—
165#107C2×D1312yescomplemented
166C4⋊C8—132no—
167#103—132no—
168#103C2×D1312yescomplemented
169#102—132no—
170#102—132no—
171C22⋊C8—131no—
172C22⋊C8C2×D1311yescharacteristic
173#97—132no—
174C2×C13—22no—
175C2×C13#52511yescharacteristic
176C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C13C2×#13711yescharacteristic
178D13—44no—
179C24—261no—
180C2×Q8—131no—
181C2×Q8—261no—
182C2×Q8C22×D1311yescharacteristic
183C2×D4—132no—
184C2×D4—264no—
185C2×D4—261no—
186C22×C4—21no—
187C22×C4—131no—
188C22×C4—131no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4—524no—
192C22×C4C22×D1311yescharacteristic
193SD16—264no—
194SD16—264no—
195C2×C8—132no—
196C2×C8C22×D1312yes—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—131no—
200C4⋊C4—261no—
201C4⋊C4—261no—
202C4⋊C4—261no—
203C4⋊C4—261no—
204C4⋊C4—261no—
205C4⋊C4—261no—
206C4⋊C4C22×D1311yescharacteristic
207C4⋊C4C22×D1312yes—
208C22⋊C4—21no—
209C22⋊C4—262no—
210C22⋊C4—262no—
211C22⋊C4—261no—
212C42—131no—
213C42—131no—
214C42—131no—
215C42—131no—
216C42—261no—
217C42—261no—
218C13#311011yescharacteristic, complemented, Sylow
219C23—264no—
220C23—262no—
221C23—522no—
222C23—522no—
223C23D4×D1311yescharacteristic
224Q8—22no—
225Q8—262no—
226Q8—522no—
227D4—134no—
228D4—264no—
229D4—262no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—131no—
236C2×C4—131no—
237C2×C4—131no—
238C2×C4—131no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—261no—
242C2×C4—261no—
243C2×C4—524no—
244C2×C4—524no—
245C2×C4D4×D1311yescharacteristic
246C2×C4C23×D1311yescharacteristic
247C8—22no—
248C8—262no—
249C22—21no—
250C22—21no—
251C22—264no—
252C22—528no—
253C22—522no—
254C22—522no—
255C22#8817212yes—
256C22C2×D4×D1311yescharacteristic
257C4—21no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—132no—
262C4—261no—
263C4—261no—
264C4—261no—
265C4—521no—
266C4—521no—
267C4#41×D1312yes—
268C2—22no—
269C2—524no—
270C2#1171936111yescharacteristic
271C2C2×#8817211yescharacteristic
272C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#484C2
socleC22×C13C22×D4
prime radicalC22×D52C22
hypercenter#484D13
hypocenterC13#3110
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #11719327C2semidirect
3. C13×#484C2semidirect
5. #11718631C2semidirect
6. #11718551C2semidirect
7. #11718550C2semidirect
8. #11718479C2semidirect
9. #11718478C2semidirect
11. #11718380C2semidirect
16. Q8×Dic13C22semidirect
17. #88198C22semidirect
28. #88142C22semidirect
30. #88141C22semidirect
33. C13×#107C22semidirect
34. C13×#103C22semidirect
38. #88055C22semidirect
39. #88054C22semidirect
40. #88050C22semidirect
42. #88047C22semidirect
116. #484D13semidirect
165. #107C2×D13semidirect
168. #103C2×D13semidirect
218. C13#3110semidirect

Maximal subgroups

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

subgroupindex
#117193272
C2×#881472
C13×#4842
#117187072
#117186312
#117185512
#117185502
#117184792
#117184782
#117183922
#117183802
#311013