Finite Group Databasebeta

← #13125539

Subgroups — #13125539

Order 1664.

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

normal subgroups only

This group has 366 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#11718750C211yesmaximal, characteristic, complemented
4#11718747C211yesmaximal, characteristic, complemented
5#11718743C211yesmaximal, characteristic, complemented
6#11718741C211yesmaximal, characteristic, complemented
7#11718712C212yesmaximal, complemented
8#11718709C212yesmaximal
9#11718691C212yesmaximal, complemented
10#11718687C212yesmaximal, complemented
11C2×#88043C211yesmaximal, 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—
40#88043C2212yes—
41#88043C2211yescharacteristic
42#88043C2211yescharacteristic
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—24no—
66#6106—24no—
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—24no—
79C2×#1055C2312yes—
80C2×#1055C2312yes—
81#3181—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—22no—
90C2×C4×C13—22no—
91C2×C4×C13—41no—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2411yescharacteristic
98C22⋊D13—42no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102D52—22no—
103C4×D13—42no—
104Dic26—22no—
105#1055—22no—
106#1055#4114yes—
107#533D1311yescharacteristic, complemented
108#529—131no—
109#501—131no—
110#497—131no—
111#491—131no—
112#489—131no—
113#467—132no—
114#465—132no—
115#441—132no—
116#440—132no—
117C2×#97—131no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13#13712yes—
121C22×C13C22×D411yescharacteristic
122C2×D13—41no—
123C2×D13—41no—
124C2×D13—41no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—21no—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—42no—
131C4×C13—42no—
132C4×C13C2×#4112yes—
133Dic13—41no—
134Dic13—41no—
135Dic13—41no—
136C2×Q16—132no—
137C2×SD16—132no—
138C22×C8—132no—
139C4⋊Q8C2×D1311yescharacteristic
140C4⋊Q8C2×D1311yescharacteristic
141#126—261no—
142#125—21no—
143#125—131no—
144#124—131no—
145#123—261no—
146C22⋊Q8—21no—
147C22⋊Q8—131no—
148C22⋊Q8C2×D1312yes—
149#121—131no—
150C4×Q8—21no—
151C4×Q8—131no—
152C4×Q8C2×D1312yes—
153C4×D4—131no—
154C4×D4—261no—
155#117—21no—
156#117—261no—
157C2×C42C2×D1311yescharacteristic
158#107—132no—
159#106—132no—
160#103—132no—
161#103—132no—
162#103—132no—
163#102—132no—
164#97—132no—
165#97—131no—
166#97—131no—
167C2×C13—22no—
168C2×C13#53211yescharacteristic
169C2×C13C2×#13711yescharacteristic
170C2×C13#57511yescharacteristic
171D13—81no—
172C2×Q8—21no—
173C2×Q8—131no—
174C2×Q8C22×D1312yes—
175C2×D4—131no—
176C2×D4—261no—
177C22×C4—261no—
178C22×C4C22⋊D1311yescharacteristic
179C22×C4C22⋊D1311yescharacteristic
180C22×C4C22×D1311yescharacteristic
181Q16—264no—
182SD16—264no—
183C2×C8—132no—
184C2×C8—132no—
185C2×C8—264no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—131no—
192C4⋊C4—131no—
193C4⋊C4—261no—
194C4⋊C4—261no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4C22×D1312yes—
198C22⋊C4—22no—
199C22⋊C4—261no—
200C22⋊C4—261no—
201C22⋊C4—261no—
202C22⋊C4—261no—
203C22⋊C4—261no—
204C42—22no—
205C42—261no—
206C42C22⋊D1311yescharacteristic
207C42C22⋊D1311yescharacteristic
208C42C22×D1311yescharacteristic
209C42C22×D1311yescharacteristic
210C13#318111yescharacteristic, complemented, Sylow
211C23—261no—
212C23C2×C22⋊D1311yescharacteristic
213Q8—22no—
214Q8—22no—
215Q8—42no—
216Q8—262no—
217D4—262no—
218D4—522no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—522no—
228C2×C4C2×C22⋊D1311yescharacteristic
229C2×C4C2×C22⋊D1311yescharacteristic
230C2×C4C2×C22⋊D1311yescharacteristic
231C2×C4C2×C22⋊D1311yescharacteristic
232C2×C4C2×C22⋊D1311yescharacteristic
233C2×C4C23×D1311yescharacteristic
234C8—134no—
235C8—262no—
236C22—21no—
237C22—21no—
238C22—521no—
239C22—521no—
240C22—521no—
241C22#8819612yes—
242C22C22×C22⋊D1311yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—42no—
250C4—521no—
251C4—521no—
252C4—521no—
253C4#41×D1312yes—
254C2—22no—
255C2—1041no—
256C2C2×#8819611yescharacteristic
257C2#1171952711yescharacteristic
258C2#1171953711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#533C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#533D13
hypocenterC13#3181
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. #11718750C2semidirect
4. #11718747C2semidirect
5. #11718743C2semidirect
6. #11718741C2semidirect
7. #11718712C2semidirect
9. #11718691C2semidirect
10. #11718687C2semidirect
11. C2×#88043C2semidirect
107. #533D13semidirect
210. C13#3181semidirect

Maximal subgroups

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

subgroupindex
C13×#5332
#117191842
#117187502
#117187472
#117187432
#117187412
#117187122
#117187092
#117186912
#117186872
C2×#880432
#318113