Finite Group Databasebeta

← #13126167

Subgroups — #13126167

Order 1664.

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

normal subgroups only

This group has 354 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
1C13×#533C211yesmaximal, characteristic, complemented
2#11719184C211yesmaximal, characteristic
3#11718755C211yesmaximal, characteristic, complemented
4#11718751C211yesmaximal, characteristic, complemented
5#11718748C211yesmaximal, characteristic, complemented
6#11718744C211yesmaximal, characteristic, complemented
7#11718712C212yesmaximal, complemented
8#11718709C212yesmaximal
9#11718689C212yesmaximal, complemented
10#11718683C212yesmaximal, complemented
11C2×C4⋊#1055C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×C4⋊Q8C2211yescharacteristic
14C13×#125—21no—
15C13×C22⋊Q8—21no—
16C13×C22⋊Q8C2212yes—
17C4×Q8×C13—21no—
18C4×Q8×C13C2212yes—
19C13×#117—21no—
20C2×C42×C13C2211yescharacteristic
21C2×#6107C2212yes—
22C2×#6106C2212yes—
23#88184C2211yescharacteristic
24#88183—21no—
25C4×C22⋊D13—21no—
26#88178C2211yescharacteristic
27C22×#1055C2212yes—
28#88130—21no—
29#88129C2211yescharacteristic
30C4×D52C2211yescharacteristic
31#88126—21no—
32#88124C2211yescharacteristic
33C4×Dic26C2211yescharacteristic
34#88075C2212yes—
35#88075C2212yes—
36#88050C2212yes—
37#88049C2212yes—
38#88048C2212yes—
39#88047C2212yes—
40C4⋊#1055C2212yes—
41C4⋊#1055C2211yescharacteristic
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×Q8×C13C2312yes—
45C22×C4×C13D411yescharacteristic
46C22×C4×C13D411yescharacteristic
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—21no—
49C2×D52C2311yescharacteristic
50C2×C4×D13—21no—
51C2×Dic26C2311yescharacteristic
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4C2312yes—
58C13×C22⋊C4—22no—
59C42×C13—22no—
60C42×C13D411yescharacteristic
61C42×C13D411yescharacteristic
62C42×C13C2311yescharacteristic
63C42×C13C2311yescharacteristic
64C22⋊Dic13—21no—
65#6107—42no—
66#6106—42no—
67#6103—21no—
68#6103—21no—
69#6103—21no—
70#6103—21no—
71C4⋊Dic13C2311yescharacteristic
72C4⋊Dic13C2311yescharacteristic
73#6101—21no—
74#6101—21no—
75#6101—21no—
76#6101—21no—
77C4×Dic13—21no—
78C2×#1055—42no—
79C2×#1055C2312yes—
80C2×#1055C2312yes—
81#3248—131nomaximal, Sylow
82C23×C13C2×D411yescharacteristic
83C22×D13—21no—
84Q8×C13—22no—
85Q8×C13—22no—
86Q8×C13—42no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2411yescharacteristic
99C22⋊D13—42no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103D52—21no—
104D52—21no—
105C4×D13—42no—
106Dic26—21no—
107Dic26—21no—
108#1055—22no—
109#1055—22no—
110#533D1311yescharacteristic, complemented
111#529—131no—
112#479—132no—
113#475—131no—
114#474—131no—
115#467—132no—
116#465—132no—
117#464—132no—
118#462—131no—
119#461—131no—
120C2×C4⋊C8—131no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#13712yes—
124C22×C13C22×D411yescharacteristic
125C2×D13—41no—
126C2×D13—41no—
127C2×D13—41no—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—42no—
133C4×C13—42no—
134C4×C13#13512yes—
135C4×C13H(5,𝔽2)11yescharacteristic
136C4×C132−1+411yescharacteristic
137Dic13—41no—
138Dic13—41no—
139Dic13—41no—
140C2×Q16—132no—
141C2×SD16—132no—
142C22×C8—132no—
143C4⋊Q8C2×D1311yescharacteristic
144C4⋊Q8C2×D1311yescharacteristic
145#126—261no—
146#125—21no—
147#125—131no—
148#124—131no—
149#123—261no—
150C22⋊Q8—21no—
151C22⋊Q8—131no—
152C22⋊Q8C2×D1312yes—
153#121—131no—
154C4×Q8—21no—
155C4×Q8—131no—
156C4×Q8C2×D1312yes—
157C4×D4—131no—
158C4×D4—261no—
159#117—21no—
160#117—261no—
161C2×C42C2×D1311yescharacteristic
162#107—132no—
163#106—132no—
164C4⋊C8—131no—
165C4⋊C8—131no—
166C4⋊C8—132no—
167#103—132no—
168#103—132no—
169#103—132no—
170#102—132no—
171C2×C13—22no—
172C2×C13#53711yescharacteristic
173C2×C13C2×#13511yescharacteristic
174C2×C13C2×#13711yescharacteristic
175D13—81no—
176C2×Q8—21no—
177C2×Q8—131no—
178C2×Q8C22×D1312yes—
179C2×D4—131no—
180C2×D4—261no—
181C22×C4—261no—
182C22×C4C22⋊D1311yescharacteristic
183C22×C4C22⋊D1311yescharacteristic
184C22×C4C22×D1311yescharacteristic
185Q16—522no—
186SD16—522no—
187C2×C8—132no—
188C2×C8—132no—
189C2×C8—522no—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—131no—
196C4⋊C4—131no—
197C4⋊C4—261no—
198C4⋊C4—261no—
199C4⋊C4—261no—
200C4⋊C4—261no—
201C4⋊C4C22×D1312yes—
202C22⋊C4—22no—
203C22⋊C4—261no—
204C22⋊C4—261no—
205C22⋊C4—261no—
206C22⋊C4—261no—
207C22⋊C4—261no—
208C42—22no—
209C42—261no—
210C42C22⋊D1311yescharacteristic
211C42C22⋊D1311yescharacteristic
212C42C22×D1311yescharacteristic
213C42C22×D1311yescharacteristic
214C13#324811yescharacteristic, complemented, Sylow
215C23—261no—
216C23C2×C22⋊D1311yescharacteristic
217Q8—22no—
218Q8—22no—
219Q8—42no—
220Q8—261no—
221Q8—261no—
222D4—261no—
223D4—261no—
224D4—522no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—261no—
234C2×C4—522no—
235C2×C4C2×C22⋊D1311yescharacteristic
236C2×C4C2×C22⋊D1311yescharacteristic
237C2×C4C2×C22⋊D1311yescharacteristic
238C2×C4C2×C22⋊D1311yescharacteristic
239C2×C4C2×C22⋊D1311yescharacteristic
240C2×C4C23×D1311yescharacteristic
241C8—262no—
242C8—262no—
243C22—21no—
244C22—21no—
245C22—521no—
246C22—521no—
247C22—521no—
248C22#8819612yes—
249C22C22×C22⋊D1311yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—42no—
255C4—42no—
256C4—521no—
257C4—521no—
258C4—521no—
259C4#8820412yes—
260C4#8825611yescharacteristic
261C4#8825711yescharacteristic
262C2—22no—
263C2—1041no—
264C2C2×#8819611yescharacteristic
265C2C2×#8820411yescharacteristic
266C2#1171953811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#533C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#533D13
hypocenterC13#3248
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C13×#533C2semidirect
3. #11718755C2semidirect
4. #11718751C2semidirect
5. #11718748C2semidirect
6. #11718744C2semidirect
7. #11718712C2semidirect
9. #11718689C2semidirect
10. #11718683C2semidirect
11. C2×C4⋊#1055C2semidirect
110. #533D13semidirect
214. C13#3248semidirect

Maximal subgroups

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

subgroupindex
C13×#5332
#117191842
#117187552
#117187512
#117187482
#117187442
#117187122
#117187092
#117186892
#117186832
C2×C4⋊#10552
#324813