Finite Group Databasebeta

← #13126049

Subgroups — #13126049

Order 1664.

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

normal subgroups only

This group has 322 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
1#11719433C211yesmaximal, characteristic
2#11719283C211yesmaximal, characteristic
3C13×#475C211yesmaximal, characteristic, complemented
4#11718755C211yesmaximal, characteristic, complemented
5#11718682C211yesmaximal, characteristic, complemented
6#11718528C212yesmaximal
7#11718517C212yesmaximal, complemented
8#11718511C211yesmaximal, characteristic, complemented
9#11718496C211yesmaximal, characteristic
10#11718475C212yesmaximal
11#11718458C212yesmaximal, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C4×Q8×C13C2211yescharacteristic
14#88200—21no—
15#88200C2211yescharacteristic
16Q8×Dic13—21no—
17#88198C2211yescharacteristic
18#88151—21no—
19#88151C2211yescharacteristic
20#88150—21no—
21#88146C2212yes—
22#88144C2212yes—
23#88143—21no—
24#88142C2211yescharacteristic
25#88141—21no—
26#88126—21no—
27C42×D13C2211yescharacteristic
28#88123C2211yescharacteristic
29C4×Dic26—21no—
30C4×Dic26C2211yescharacteristic
31C13×#106C2212yes—
32C13×C4⋊C8C2211yescharacteristic
33C13×#103C2212yes—
34#88075C2212yes—
35#88060C2212yes—
36#88058C2212yes—
37#88056C2212yes—
38#88055C2212yes—
39#88050C2212yes—
40#88048C2212yes—
41#88047C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×Q8×C13C2311yescharacteristic
45C2×C4×D13D411yescharacteristic
46C2×C4×D13D411yescharacteristic
47C2×C4×D13C2311yescharacteristic
48C2×Dic26—21no—
49C2×Dic26—21no—
50C2×Dic26C2311yescharacteristic
51C2×C8×C13C2312yes—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2312yes—
55C13×C4⋊C4C2311yescharacteristic
56C42×C13—21no—
57C42×C13C2311yescharacteristic
58#6103—21no—
59#6103—21no—
60#6103—22no—
61C4⋊Dic13—21no—
62C4⋊Dic13—21no—
63C4⋊Dic13—22no—
64C4⋊Dic13C2312yes—
65C4⋊Dic13C2311yescharacteristic
66#6101—21no—
67#6101—21no—
68#6101—21no—
69#6101—21no—
70#6101—21no—
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13—22no—
74C4×Dic13D411yescharacteristic
75C4×Dic13D411yescharacteristic
76C4×Dic13C2311yescharacteristic
77C2×#1055C2312yes—
78#3237—131nomaximal, Sylow
79C22×D13C2×D411yescharacteristic
80Q8×C13—21no—
81Q8×C13—21no—
82Q8×C13—42no—
83C2×C4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13C2×D411yescharacteristic
93C2×Dic13C2×D411yescharacteristic
94C2×Dic13C2×D411yescharacteristic
95C4×D13—22no—
96C4×D13—21no—
97C4×D13—21no—
98C4×D13—41no—
99Dic26—21no—
100Dic26—21no—
101Dic26—42no—
102Dic26—42no—
103C8×C13—22no—
104#1055—22no—
105#533—131no—
106#533—131no—
107#501—132no—
108#491—132no—
109#485—132no—
110#485—132no—
111#477—131no—
112#477—131no—
113#475—131no—
114#475D1311yescharacteristic, complemented
115#432—131no—
116C22×C13C22×D411yescharacteristic
117C2×D13—21no—
118C2×D13—21no—
119C2×D13—21no—
120C4×C13—21no—
121C4×C13—41no—
122C4×C13—42no—
123C4×C13—41no—
124C4×C13#13712yes—
125C4×C132−1+411yescharacteristic
126C4×C132−1+411yescharacteristic
127Dic13—21no—
128Dic13—21no—
129Dic13—21no—
130Dic13—41no—
131Dic13—41no—
132Dic13—42no—
133C4⋊Q8—131no—
134C4⋊Q8—131no—
135C4⋊Q8—131no—
136C4⋊Q8C2×D1311yescharacteristic
137#125—132no—
138#125—261no—
139C22⋊Q8—131no—
140C22⋊Q8—131no—
141C22⋊Q8—261no—
142C22⋊Q8—261no—
143C22⋊Q8—261no—
144C4×Q8—131no—
145C4×Q8—261no—
146C4×Q8—261no—
147C4×Q8—261no—
148C4×Q8C2×D1311yescharacteristic
149#117—132no—
150#117—261no—
151C2×C42—131no—
152#107—132no—
153#107—132no—
154#106—132no—
155#106C2×D1312yes—
156C4⋊C8—131no—
157C4⋊C8C2×D1311yescharacteristic
158#103—132no—
159#103—132no—
160#103—132no—
161#103C2×D1312yes—
162C22⋊C8—132no—
163#97—132no—
164C2×C13#53611yescharacteristic
165C2×C13C2×#13711yescharacteristic
166C2×C13#57511yescharacteristic
167D13—41no—
168C2×Q8—21no—
169C2×Q8—131no—
170C2×Q8—261no—
171C2×Q8—261no—
172C2×Q8C22×D1311yescharacteristic
173C22×C4—131no—
174C22×C4—131no—
175C22×C4—131no—
176C2×C8—132no—
177C2×C8C22×D1312yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—132no—
181C4⋊C4—131no—
182C4⋊C4—261no—
183C4⋊C4—261no—
184C4⋊C4—261no—
185C4⋊C4—261no—
186C4⋊C4—262no—
187C4⋊C4—262no—
188C4⋊C4—261no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C4⋊C4C22×D1312yes—
192C4⋊C4C22×D1311yescharacteristic
193C22⋊C4—262no—
194C22⋊C4—261no—
195C22⋊C4—261no—
196C42—21no—
197C42—131no—
198C42—131no—
199C42—131no—
200C42—262no—
201C42—261no—
202C42C22×D1311yescharacteristic
203C13#323711yescharacteristic, complemented, Sylow
204C23—131no—
205Q8—21no—
206Q8—21no—
207Q8—42no—
208Q8—261no—
209Q8—261no—
210Q8—522no—
211Q8—522no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—131no—
216C2×C4—131no—
217C2×C4—131no—
218C2×C4—262no—
219C2×C4—261no—
220C2×C4—261no—
221C2×C4—262no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—521no—
225C2×C4D4×D1311yescharacteristic
226C2×C4D4×D1311yescharacteristic
227C2×C4C23×D1311yescharacteristic
228C8—22no—
229C8—262no—
230C22—261no—
231C22—261no—
232C22—261no—
233C22C2×D4×D1311yescharacteristic
234C4—21no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4—261no—
239C4—261no—
240C4—261no—
241C4—522no—
242C4—521no—
243C4—521no—
244C4#8816912yes—
245C4#8825411yescharacteristic
246C4#8825711yescharacteristic
247C2—521no—
248C2#1171933311yescharacteristic
249C2C2×#8816911yescharacteristic
250C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#475D13
hypocenterC13#3237
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. C13×#475C2semidirect
4. #11718755C2semidirect
5. #11718682C2semidirect
7. #11718517C2semidirect
8. #11718511C2semidirect
11. #11718458C2semidirect
114. #475D13semidirect
203. C13#3237semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117192832
C13×#4752
#117187552
#117186822
#117185282
#117185172
#117185112
#117184962
#117184752
#117184582
#323713