Finite Group Databasebeta

← #13127195

Subgroups — #13127195

Order 1664.

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

normal subgroups only

This group has 388 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#11719284C211yesmaximal, characteristic, complemented
2#11719256C211yesmaximal, characteristic
3C4×C13×SD16C211yesmaximal, characteristic, complemented
4#11718832C212yesmaximal, complemented
5#11718681C211yesmaximal, characteristic, complemented
6#11718669C211yesmaximal, characteristic, complemented
7D13×#106C212yesmaximal, complemented
8#11718466C212yesmaximal, complemented
9#11718438C212yesmaximal, complemented
10C8×D52C211yesmaximal, characteristic, complemented
11#11718341C211yesmaximal, characteristic, complemented
12C2×#6127—21no—
13C2×C13×SD16C2211yescharacteristic
14C4×Q8×C13C2211yescharacteristic
15C4×D4×C13C2211yescharacteristic
16#88200C2212yes—
17#88192C2212yes—
18#88178—21no—
19C2×C8×D13C2212yes—
20#88150—22no—
21C4⋊C4×D13C2212yes—
22C4⋊C4×D13C2212yes—
23#88137—22no—
24C4×D52—21no—
25C4×D52C2211yescharacteristic
26#88124—21no—
27#88123C2211yescharacteristic
28#88123C2211yescharacteristic
29C13×#106C2211yescharacteristic
30C13×#103C2211yescharacteristic
31C13×#102C2211yescharacteristic
32C4×C8×C13C2211yescharacteristic
33#88075C2212yes—
34#88072C2212yes—
35#88060C2212yes—
36#88057C2212yes—
37#88057C2212yes—
38#88048C2212yes—
39#88048C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13C2311yescharacteristic
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C2×C22⋊D13—22no—
45#6127—44no—
46C2×D52D411yescharacteristic
47C2×C4×D13—22no—
48C2×C4×D13—22no—
49C2×C4×D13C2312yes—
50C2×Dic26—21no—
51C2×Dic26—21no—
52C13×SD16—22no—
53C2×C8×C13C2311yescharacteristic
54C2×C8×C13C2311yescharacteristic
55C13×C4⋊C4—21no—
56C13×C4⋊C4C2311yescharacteristic
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—21no—
59C42×C13—21no—
60C42×C13C2311yescharacteristic
61C22⋊Dic13—22no—
62#6103—22no—
63#6103D412yes—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13D411yescharacteristic
67C4⋊Dic13C2312yes—
68C4⋊Dic13C2312yes—
69#6101—22no—
70#6101—22no—
71#6101—22no—
72C2×#1055C2312yes—
73C8×D13—24no—
74#3335—131nomaximal, Sylow
75C23×C13—21no—
76C22×D13C2×D412yes—
77Q8×C13—21no—
78Q8×C13—21no—
79D4×C13—21no—
80D4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—42no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2411yescharacteristic
88C22⋊D13—44no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13C2×D412yes—
92D52SD1614yescomplemented
93C4×D13—22no—
94C4×D13—22no—
95C4×D13—44no—
96C4×D13—82no—
97Dic26—42no—
98Dic26—81no—
99C8×C13—21no—
100C8×C13#4112yescomplemented
101#1055—22no—
102#554—131no—
103#547—131no—
104#498—131no—
105#483—132no—
106#481—132no—
107#476—131no—
108#475—131no—
109#465—132no—
110C4×SD16D1311yescharacteristic, complemented
111C8×D4—131no—
112C2×#106—132no—
113C22×C13—41no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13C22×D411yescharacteristic
117C2×D13—22no—
118C2×D13—22no—
119C2×D13C2×SD1614yes—
120C4×C13—21no—
121C4×C13—41no—
122C4×C13—41no—
123C4×C13—41no—
124C4×C13C2×SD1612yes—
125C4×C13C2×#4111yescharacteristic
126C4×C132−1+411yescharacteristic
127Dic13—22no—
128Dic13—42no—
129Dic13—42no—
130C2×#41—261no—
131C2×SD16C2×D1311yescharacteristic
132C22×C8—132no—
133C4⋊Q8—131no—
134C4⋊Q8—131no—
135#125—261no—
136#123—262no—
137C22⋊Q8—132no—
138C22⋊Q8—262no—
139C22⋊Q8—261no—
140#121—132no—
141C4×Q8C2×D1311yescharacteristic
142C4×D4—131no—
143C4×D4—261no—
144C4×D4C2×D1311yescharacteristic
145C2×C4⋊C4—132no—
146C2×C4⋊C4—132no—
147#106—132no—
148#106—132no—
149#106—132no—
150#106—132no—
151#106C2×D1311yescharacteristic
152C4⋊C8—131no—
153#103—132no—
154#103C2×D1311yescharacteristic
155#102—132no—
156#102C2×D1311yescharacteristic
157C22⋊C8—132no—
158C4×C8C2×D1311yescharacteristic
159C2×C13—81no—
160C2×C13#54711yescharacteristic
161C2×C13C22×SD1611yescharacteristic
162C2×C13#57711yescharacteristic
163D13—24no—
164#41—524no—
165C2×Q8—261no—
166C2×Q8—261no—
167C2×Q8C22×D1311yescharacteristic
168C2×D4—131no—
169C2×D4—262no—
170C2×D4C22×D1311yescharacteristic
171C22×C4—21no—
172C22×C4—132no—
173C22×C4—262no—
174C22×C4—262no—
175SD16—22no—
176C2×C8—132no—
177C2×C8—264no—
178C2×C8C22×D1311yescharacteristic
179C2×C8C22×D1311yescharacteristic
180C4⋊C4—21no—
181C4⋊C4—131no—
182C4⋊C4—132no—
183C4⋊C4—132no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4—262no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4C22×D1311yescharacteristic
190C4⋊C4C22×D1311yescharacteristic
191C22⋊C4—21no—
192C22⋊C4—132no—
193C22⋊C4—262no—
194C22⋊C4—262no—
195C42—21no—
196C42C22×D1311yescharacteristic
197C13#333511yescharacteristic, complemented, Sylow
198C23—21no—
199C23—132no—
200Q8—21no—
201Q8—21no—
202Q8—522no—
203Q8—1041no—
204D4—21no—
205D4—21no—
206D4—134no—
207D4—524no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—42no—
212C2×C4—132no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—524no—
218C2×C4—1042no—
219C2×C4D4×D1311yescharacteristic
220C2×C4D4×D1311yescharacteristic
221C2×C4C23×D1311yescharacteristic
222C8—21no—
223C8—262no—
224C8#612712yescomplemented
225C22—41no—
226C22—41no—
227C22—41no—
228C22—134no—
229C22—262no—
230C22—262no—
231C22C2×D4×D1311yescharacteristic
232C4—21no—
233C4—41no—
234C4—41no—
235C4—41no—
236C4—262no—
237C4—522no—
238C4—522no—
239C4SD16×D1312yes—
240C4C2×#612711yescharacteristic
241C4#8825711yescharacteristic
242C2—81no—
243C2—264no—
244C2#1171925611yescharacteristic
245C2C2×SD16×D1311yescharacteristic
246C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×SD16C2
socleC22×C13C22×D4
prime radical#11719256C2
hypercenterC4×SD16D13
hypocenterC13#3335
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #11719284C2semidirect
3. C4×C13×SD16C2semidirect
4. #11718832C2semidirect
5. #11718681C2semidirect
6. #11718669C2semidirect
7. D13×#106C2semidirect
8. #11718466C2semidirect
9. #11718438C2semidirect
10. C8×D52C2semidirect
11. #11718341C2semidirect
92. D52SD16semidirect
100. C8×C13#41semidirect
110. C4×SD16D13semidirect
197. C13#3335semidirect
224. C8#6127semidirect

Maximal subgroups

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

subgroupindex
#117192842
#117192562
C4×C13×SD162
#117188322
#117186812
#117186692
D13×#1062
#117184662
#117184382
C8×D522
#117183412
#333513