Finite Group Databasebeta

← #13127190

Subgroups — #13127190

Order 1664.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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#11719435C211yesmaximal, characteristic, complemented
2#11719256C211yesmaximal, characteristic
3C13×#476C211yesmaximal, characteristic, complemented
4#11718740C211yesmaximal, characteristic, complemented
5C4×#6105C211yesmaximal, characteristic, complemented
6#11718523C212yesmaximal, complemented
7D13×#106C212yesmaximal, complemented
8#11718512C211yesmaximal, characteristic, complemented
9#11718495C211yesmaximal, characteristic, complemented
10#11718439C212yesmaximal, complemented
11#11718438C212yesmaximal, complemented
12C2×#6127—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C4×D4×C13C2211yescharacteristic
15#88200—22no—
16#88192C2212yes—
17C2×#6105C2211yescharacteristic
18#88178—21no—
19C2×C8×D13C2212yes—
20#88151C2212yes—
21#88147—21no—
22C4⋊C4×D13C2212yes—
23C4⋊C4×D13C2212yes—
24#88144—21no—
25#88137—22no—
26C4×D52C2211yescharacteristic
27#88123C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#106C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#102C2212yes—
32#88072C2211yescharacteristic
33#88060C2212yes—
34#88057C2212yes—
35#88056C2212yes—
36#88050C2211yescharacteristic
37#88048C2211yescharacteristic
38#88048C2212yes—
39#88048C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
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×Dic26C2311yescharacteristic
52C2×C8×C13C2312yes—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2312yes—
55C13×C4⋊C4C2311yescharacteristic
56C13×C22⋊C4—21no—
57C42×C13C2311yescharacteristic
58C22⋊Dic13—22no—
59#6105—22no—
60#6103—22no—
61#6103D412yes—
62C4⋊Dic13—21no—
63C4⋊Dic13—22no—
64C4⋊Dic13D411yescharacteristic
65C4⋊Dic13C2311yescharacteristic
66C4⋊Dic13C2312yes—
67#6101—21no—
68#6101—22no—
69#6101—22no—
70C4×Dic13—21no—
71C2×#1055C2311yescharacteristic
72C2×#1055C2311yescharacteristic
73C8×D13—24no—
74#3335—131nomaximal, Sylow
75C23×C13—21no—
76C22×D13C2×D412yes—
77Q8×C13—81no—
78D4×C13—21no—
79D4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—42no—
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2411yescharacteristic
86C22⋊D13—44no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13C2×D412yes—
91D52SD1614yescomplemented
92C4×D13—22no—
93C4×D13—22no—
94C4×D13—44no—
95C4×D13—82no—
96Dic26—21no—
97Dic26—21no—
98Dic26—42no—
99C8×C13—22no—
100#1055—21no—
101#1055#4112yescomplemented
102#554—131no—
103#547—131no—
104#498—131no—
105#483—132no—
106#481—132no—
107#476D1311yescharacteristic, complemented
108#475—131no—
109#465—132no—
110C4×SD16—131no—
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—42no—
123C4×C13C2×SD1612yes—
124C4×C13C2×#4111yescharacteristic
125C4×C132−1+411yescharacteristic
126Dic13—22no—
127Dic13—41no—
128Dic13—42no—
129Dic13—41no—
130C2×#41—261no—
131C2×SD16—131no—
132C22×C8—132no—
133C4⋊Q8—131no—
134C4⋊Q8C2×D1311yescharacteristic
135#125—261no—
136#123—262no—
137C22⋊Q8—132no—
138C22⋊Q8—262no—
139C22⋊Q8—261no—
140#121—132no—
141C4×Q8—131no—
142C4×D4—131no—
143C4×D4—261no—
144C4×D4C2×D1311yescharacteristic
145C2×C4⋊C4—132no—
146C2×C4⋊C4—132no—
147#106—132no—
148#106—131no—
149#106—132no—
150#106—132no—
151#106C2×D1312yes—
152C4⋊C8C2×D1311yescharacteristic
153#103—132no—
154#103—131no—
155#102—131no—
156#102C2×D1312yes—
157C22⋊C8—132no—
158C4×C8—131no—
159C2×C13—81no—
160C2×C13#54711yescharacteristic
161C2×C13C22×SD1611yescharacteristic
162C2×C13#57711yescharacteristic
163D13—24no—
164#41—524no—
165C2×Q8—21no—
166C2×Q8—131no—
167C2×Q8—261no—
168C2×D4—131no—
169C2×D4—262no—
170C2×D4C22×D1311yescharacteristic
171C22×C4—21no—
172C22×C4—132no—
173C22×C4—262no—
174C22×C4—262no—
175SD16—262no—
176C2×C8—131no—
177C2×C8—131no—
178C2×C8—264no—
179C2×C8C22×D1312yes—
180C4⋊C4—21no—
181C4⋊C4—131no—
182C4⋊C4—131no—
183C4⋊C4—132no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4—262no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4C22×D1312yes—
190C4⋊C4C22×D1311yescharacteristic
191C22⋊C4—21no—
192C22⋊C4—132no—
193C22⋊C4—262no—
194C22⋊C4—262no—
195C42—261no—
196C42C22×D1311yescharacteristic
197C13#333511yescharacteristic, complemented, Sylow
198C23—21no—
199C23—132no—
200Q8—81no—
201Q8—261no—
202Q8—261no—
203Q8—522no—
204D4—21no—
205D4—21no—
206D4—134no—
207D4—524no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—132no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—261no—
215C2×C4—261no—
216C2×C4—262no—
217C2×C4—524no—
218C2×C4—1042no—
219C2×C4D4×D1311yescharacteristic
220C2×C4D4×D1311yescharacteristic
221C2×C4C23×D1311yescharacteristic
222C8—22no—
223C8—132no—
224C8—261no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—134no—
229C22—262no—
230C22—262no—
231C22C2×D4×D1311yescharacteristic
232C4—21no—
233C4—41no—
234C4—42no—
235C4—262no—
236C4—522no—
237C4—521no—
238C4—521no—
239C4SD16×D1312yes—
240C4#8825411yescharacteristic
241C4#41×D1311yescharacteristic
242C2—81no—
243C2—264no—
244C2#1171933611yescharacteristic
245C2C2×SD16×D1311yescharacteristic
246C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#476C2
socleC22×C13C22×D4
prime radical#11719256C2
hypercenter#476D13
hypocenterC13#3335
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #11719435C2semidirect
3. C13×#476C2semidirect
4. #11718740C2semidirect
5. C4×#6105C2semidirect
6. #11718523C2semidirect
7. D13×#106C2semidirect
8. #11718512C2semidirect
9. #11718495C2semidirect
10. #11718439C2semidirect
11. #11718438C2semidirect
91. D52SD16semidirect
101. #1055#41semidirect
107. #476D13semidirect
197. C13#3335semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117192562
C13×#4762
#117187402
C4×#61052
#117185232
D13×#1062
#117185122
#117184952
#117184392
#117184382
#333513