Finite Group Databasebeta

← #13126043

Subgroups — #13126043

Order 1664.

324 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 111 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#11719433C211yesmaximal, characteristic
2D13×#125C211yesmaximal, characteristic
3C13×#501C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718730C211yesmaximal, characteristic, complemented
6#11718545C212yesmaximal
7#11718538C212yesmaximal, complemented
8#11718523C212yesmaximal
9#11718518C212yesmaximal, complemented
10#11718366C211yesmaximal, characteristic
11#11718364C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×#125C2211yescharacteristic
14#88200—21no—
15Q8×Dic13—21no—
16#88151C2212yes—
17#88146—21no—
18C4⋊C4×D13—21no—
19C4⋊C4×D13—21no—
20C4⋊C4×D13C2211yescharacteristic
21C4⋊C4×D13C2211yescharacteristic
22#88144—21no—
23#88144C2211yescharacteristic
24#88144C2211yescharacteristic
25#88143—21no—
26#88143—21no—
27#88141C2212yes—
28C42×D13C2211yescharacteristic
29#88124C2211yescharacteristic
30#88123C2211yescharacteristic
31C13×#107C2212yes—
32C13×#106C2212yes—
33C13×#97C2211yescharacteristic
34#88060C2212yes—
35#88056C2212yes—
36#88056C2212yes—
37#88054C2212yes—
38#88050C2212yes—
39#88050C2212yes—
40#88048C2212yes—
41#88047C2212yes—
42#88043C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×C4×D13—21no—
45C2×C4×D13—21no—
46C2×C4×D13D411yescharacteristic
47C2×C4×D13D411yescharacteristic
48C2×C4×D13C2311yescharacteristic
49C2×Dic26C2312yes—
50C2×C8×C13C2312yes—
51C13×C4⋊C4—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2311yescharacteristic
55C13×C4⋊C4C2312yes—
56C13×C4⋊C4C2311yescharacteristic
57C42×C13C2311yescharacteristic
58#6103—22no—
59C4⋊Dic13—21no—
60C4⋊Dic13—21no—
61C4⋊Dic13—21no—
62C4⋊Dic13—21no—
63C4⋊Dic13—22no—
64C4⋊Dic13C2311yescharacteristic
65C4⋊Dic13C2311yescharacteristic
66#6101—21no—
67#6101—21no—
68#6101—22no—
69#6101—21no—
70#6101—21no—
71#6101—21no—
72#6101—21no—
73C4×Dic13—22no—
74C4×Dic13D411yescharacteristic
75C4×Dic13D411yescharacteristic
76C4×Dic13C2311yescharacteristic
77C2×#1055C2312yes—
78#3236—131nomaximal, Sylow
79C22×D13C2×D411yescharacteristic
80Q8×C13—42no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C2×Dic13—22no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13C2×D411yescharacteristic
91C2×Dic13C2×D411yescharacteristic
92C2×Dic13C2×D411yescharacteristic
93C4×D13—22no—
94C4×D13—22no—
95C4×D13—41no—
96C4×D13—42no—
97C4×D13—42no—
98Dic26—24no—
99C8×C13—22no—
100#1055—22no—
101#533—131no—
102C2×#125—131no—
103#501—131no—
104#501D1311yescharacteristic, complemented
105#491—131no—
106#491—131no—
107#484—132no—
108#483—132no—
109#479—132no—
110#479—132no—
111#432—131no—
112C22×C13C22×D411yescharacteristic
113C2×D13—21no—
114C2×D13—21no—
115C2×D13#13712yes—
116C4×C13—21no—
117C4×C13—21no—
118C4×C13—41no—
119C4×C13—41no—
120C4×C13—42no—
121C4×C132−1+412yes—
122Dic13—21no—
123Dic13—21no—
124Dic13—21no—
125Dic13—42no—
126Dic13—41no—
127Dic13—41no—
128C4⋊Q8—131no—
129C4⋊Q8C2×D1311yescharacteristic
130#125—131no—
131#125—131no—
132#125—131no—
133#125—261no—
134#125—261no—
135#125—261no—
136#125C2×D1311yescharacteristic
137C22⋊Q8—132no—
138C22⋊Q8—261no—
139C4×Q8—132no—
140C4×Q8—261no—
141#117—261no—
142C2×C4⋊C4—131no—
143C2×C4⋊C4—131no—
144C2×C4⋊C4—261no—
145C2×C4⋊C4—261no—
146C2×C42—131no—
147#107—132no—
148#107C2×D1312yes—
149#106—132no—
150#106C2×D1312yes—
151C4⋊C8—132no—
152#103—132no—
153#103—132no—
154#103—132no—
155#103—132no—
156C22⋊C8—132no—
157#97—131no—
158#97C2×D1311yescharacteristic
159C2×C13#53611yescharacteristic
160C2×C13C2×#13711yescharacteristic
161C2×C13#57511yescharacteristic
162D13—22no—
163C2×Q8—21no—
164C2×Q8—132no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—261no—
169C22×C4—261no—
170C2×C8—132no—
171C2×C8C22×D1312yes—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—131no—
176C4⋊C4—131no—
177C4⋊C4—261no—
178C4⋊C4—261no—
179C4⋊C4—261no—
180C4⋊C4—261no—
181C4⋊C4—261no—
182C4⋊C4—261no—
183C4⋊C4—262no—
184C4⋊C4—262no—
185C4⋊C4—261no—
186C4⋊C4—261no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4C22×D1311yescharacteristic
190C4⋊C4C22×D1311yescharacteristic
191C4⋊C4C22×D1312yes—
192C22⋊C4—262no—
193C42—131no—
194C42—131no—
195C42—131no—
196C42—262no—
197C42C22×D1311yescharacteristic
198C13#323611yescharacteristic, complemented, Sylow
199C23—131no—
200Q8—42no—
201Q8—264no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—131no—
206C2×C4—131no—
207C2×C4—131no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—261no—
212C2×C4—261no—
213C2×C4—521no—
214C2×C4—522no—
215C2×C4—522no—
216C2×C4D4×D1311yescharacteristic
217C2×C4D4×D1311yescharacteristic
218C2×C4C23×D1311yescharacteristic
219C8—22no—
220C8—262no—
221C22—132no—
222C22—261no—
223C22—261no—
224C22C2×D4×D1311yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—42no—
229C4—41no—
230C4—261no—
231C4—261no—
232C4—261no—
233C4—522no—
234C4—521no—
235C4—521no—
236C4#8825412yes—
237C2—262no—
238C2#1171942911yescharacteristic
239C2#1171947811yescharacteristic
240C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#501D13
hypocenterC13#3236
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. C13×#501C2semidirect
4. #11718741C2semidirect
5. #11718730C2semidirect
7. #11718538C2semidirect
9. #11718518C2semidirect
11. #11718364C2semidirect
104. #501D13semidirect
198. C13#3236semidirect

Maximal subgroups

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

subgroupindex
#117194332
D13×#1252
C13×#5012
#117187412
#117187302
#117185452
#117185382
#117185232
#117185182
#117183662
#117183642
#323613