Finite Group Databasebeta

← #13125859

Subgroups — #13125859

Order 1664.

386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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
1D13×C4⋊Q8C211yesmaximal, characteristic, complemented
2#11719385C211yesmaximal, characteristic
3C13×#497C211yesmaximal, characteristic, complemented
4#11718847C212yesmaximal, complemented
5#11718843C212yesmaximal, complemented
6#11718831C212yesmaximal
7#11718823C212yesmaximal, complemented
8#11718743C211yesmaximal, characteristic, complemented
9#11718721C211yesmaximal, characteristic, complemented
10#11718366C211yesmaximal, characteristic, complemented
11#11718364C211yesmaximal, characteristic, complemented
12C2×Q8×D13C2212yes—
13C2×C13×Q16C2212yes—
14C2×C13×SD16C2212yes—
15C13×C4⋊Q8C2211yescharacteristic
16C13×#124C2211yescharacteristic
17#88200C2211yescharacteristic
18Q8×Dic13C2211yescharacteristic
19#88198C2212yes—
20C2×#6107C2212yes—
21#88192C2211yescharacteristic
22D4×Dic13C2211yescharacteristic
23C2×#6105C2212yes—
24C4⋊C4×D13—21no—
25C4⋊C4×D13—21no—
26#88142—21no—
27#88142—21no—
28#88137—21no—
29#88135—21no—
30#88133—21no—
31#88131—21no—
32C42×D13C2211yescharacteristic
33#88124C2211yescharacteristic
34#88123C2211yescharacteristic
35C13×#97C2211yescharacteristic
36#88075C2212yes—
37#88075C2212yes—
38#88060C2212yes—
39#88056C2212yes—
40#88056C2212yes—
41#88054C2212yes—
42#88043C2211yescharacteristic
43C2×Q8×C13C2312yes—
44C2×Q8×C13C2311yescharacteristic
45C2×D4×C13C2311yescharacteristic
46C2×C22⋊D13—21no—
47C22×Dic13—21no—
48Q8×D13—42no—
49Q8×D13—42no—
50C2×C4×D13—22no—
51C2×C4×D13D411yescharacteristic
52C2×C4×D13D411yescharacteristic
53C2×C4×D13C2311yescharacteristic
54C2×Dic26—22no—
55C2×Dic26C2312yes—
56C13×Q16—42no—
57C13×SD16—42no—
58C2×C8×C13C2312yes—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—21no—
61C13×C22⋊C4—21no—
62C13×C22⋊C4—21no—
63C42×C13C2311yescharacteristic
64C22⋊Dic13—21no—
65C22⋊Dic13—21no—
66#6107—42no—
67#6105—42no—
68#6103—21no—
69C4⋊Dic13—21no—
70C4⋊Dic13—21no—
71C4⋊Dic13—21no—
72C4⋊Dic13C2311yescharacteristic
73C4⋊Dic13C2311yescharacteristic
74#6101—21no—
75#6101—21no—
76#6101—21no—
77#6101—22no—
78#6101—22no—
79C4×Dic13—21no—
80C4×Dic13D411yescharacteristic
81C4×Dic13D411yescharacteristic
82C4×Dic13C2311yescharacteristic
83C2×#1055C2312yes—
84#3218—131nomaximal, Sylow
85C23×C13—21no—
86C22×D13C2×D411yescharacteristic
87Q8×C13—22no—
88Q8×C13—22no—
89Q8×C13—22no—
90D4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2411yescharacteristic
96C22⋊D13—42no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—22no—
100C2×Dic13—42no—
101C2×Dic13C2×D411yescharacteristic
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104C4×D13—22no—
105C4×D13—22no—
106C4×D13—22no—
107C4×D13—44no—
108Dic26—22no—
109Dic26—22no—
110Dic26—44no—
111C8×C13—22no—
112#1055—22no—
113C2×C4⋊Q8—131no—
114#529—131no—
115#497—131no—
116#497D1311yescharacteristic, complemented
117#491—131no—
118#491—131no—
119#462—132no—
120#461—132no—
121#451—132no—
122#448—132no—
123#432—131no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—41no—
127C22×C13C22×D411yescharacteristic
128C2×D13—21no—
129C2×D13—21no—
130C2×D13#13712yes—
131C4×C13—21no—
132C4×C13—21no—
133C4×C13—42no—
134C4×C13—41no—
135C4×C13H(5,𝔽2)12yes—
136Dic13—21no—
137Dic13—21no—
138Dic13—42no—
139Dic13—41no—
140Dic13—41no—
141Dic13#13712yes—
142C22×Q8—132no—
143C2×Q16—132no—
144C2×Q16C2×D1312yes—
145C2×SD16—132no—
146C2×SD16C2×D1312yes—
147C4⋊Q8—132no—
148C4⋊Q8—131no—
149C4⋊Q8—261no—
150C4⋊Q8—261no—
151C4⋊Q8C2×D1311yescharacteristic
152#126—261no—
153#125—131no—
154#124C2×D1311yescharacteristic
155#123—261no—
156C22⋊Q8—131no—
157#121—131no—
158C4×Q8—131no—
159C4×D4—131no—
160C4×D4—261no—
161#117—261no—
162C2×C4⋊C4—261no—
163C2×C4⋊C4—261no—
164C2×C42—131no—
165C4⋊C8—132no—
166#103—132no—
167#103—132no—
168#103—132no—
169#103—132no—
170C22⋊C8—132no—
171#97—131no—
172#97C2×D1311yescharacteristic
173C2×C13—81no—
174C2×C13#53511yescharacteristic
175C2×C13C2×#13711yescharacteristic
176C2×C13C2×#13711yescharacteristic
177D13—22no—
178C2×Q8—132no—
179C2×Q8—262no—
180C2×Q8—522no—
181C2×Q8—522no—
182C2×Q8C22×D1312yes—
183C2×Q8C22×D1311yescharacteristic
184C2×D4—261no—
185C2×D4C22×D1311yescharacteristic
186C22×C4—131no—
187C22×C4—131no—
188C22×C4—131no—
189C22×C4—262no—
190C22×C4—261no—
191Q16—42no—
192Q16—522no—
193SD16—42no—
194SD16—522no—
195C2×C8—132no—
196C2×C8C22×D1312yes—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—131no—
200C4⋊C4—131no—
201C4⋊C4—262no—
202C4⋊C4—262no—
203C4⋊C4—261no—
204C4⋊C4—261no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C4⋊C4—261no—
208C4⋊C4—261no—
209C22⋊C4—21no—
210C22⋊C4—21no—
211C22⋊C4—261no—
212C22⋊C4—261no—
213C22⋊C4—261no—
214C42—131no—
215C42—131no—
216C42—131no—
217C42—261no—
218C42C22×D1311yescharacteristic
219C13#321811yescharacteristic, complemented, Sylow
220C23—21no—
221C23—131no—
222Q8—22no—
223Q8—22no—
224Q8—22no—
225Q8—262no—
226Q8—262no—
227Q8—524no—
228D4—22no—
229D4—522no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—131no—
233C2×C4—131no—
234C2×C4—131no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—261no—
239C2×C4—261no—
240C2×C4—262no—
241C2×C4—524no—
242C2×C4—522no—
243C2×C4D4×D1311yescharacteristic
244C2×C4D4×D1311yescharacteristic
245C2×C4C23×D1311yescharacteristic
246C8—22no—
247C8—262no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—132no—
252C22—261no—
253C22—261no—
254C22C2×D4×D1311yescharacteristic
255C4—21no—
256C4—21no—
257C4—42no—
258C4—41no—
259C4—132no—
260C4—261no—
261C4—261no—
262C4—521no—
263C4—521no—
264C4—522no—
265C4#8825112yes—
266C2—81no—
267C2—262no—
268C2#1171942011yescharacteristic
269C2D13×#13711yescharacteristic
270C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#497C2
socleC22×C13C22×D4
prime radical#88192C22
hypercenter#497D13
hypocenterC13#3218
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. D13×C4⋊Q8C2semidirect
3. C13×#497C2semidirect
4. #11718847C2semidirect
5. #11718843C2semidirect
7. #11718823C2semidirect
8. #11718743C2semidirect
9. #11718721C2semidirect
10. #11718366C2semidirect
11. #11718364C2semidirect
116. #497D13semidirect
219. C13#3218semidirect

Maximal subgroups

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

subgroupindex
D13×C4⋊Q82
#117193852
C13×#4972
#117188472
#117188432
#117188312
#117188232
#117187432
#117187212
#117183662
#117183642
#321813