Finite Group Databasebeta

← #13125467

Subgroups — #13125467

Order 1664.

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

normal subgroups only

This group has 362 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#11719436C211yesmaximal, characteristic, complemented
2#11719403C211yesmaximal, characteristic
3C13×#491C211yesmaximal, characteristic, complemented
4#11718746C211yesmaximal, characteristic, complemented
5#11718725C211yesmaximal, characteristic, complemented
6#11718478C212yesmaximal, complemented
7#11718473C212yesmaximal, complemented
8#11718468C212yesmaximal, complemented
9#11718449C212yesmaximal, complemented
10#11718374C211yesmaximal, characteristic, complemented
11#11718369C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×#125C2211yescharacteristic
14#88200C2212yes—
15Q8×Dic13C2212yes—
16C2×#6106C2212yes—
17C2×#6106C2212yes—
18C2×#6094C2211yescharacteristic
19C2×C8×D13C2211yescharacteristic
20#88152—22no—
21#88149—22no—
22#88149C2212yes—
23#88148—22no—
24#88147C2212yes—
25#88143—22no—
26#88128C2211yescharacteristic
27#88126C2211yescharacteristic
28#88124C2211yescharacteristic
29C13×#103C2212yes—
30C13×#103C2212yes—
31C13×#97C2211yescharacteristic
32#88061C2212yes—
33#88061C2212yes—
34#88055C2211yescharacteristic
35C8×Dic13C2211yescharacteristic
36#88048C2212yes—
37#88047C2212yes—
38C4×#1055C2211yescharacteristic
39C2×Q8×C13C2312yes—
40C2×D52—22no—
41C2×D52—22no—
42C2×D52C2312yes—
43C2×C4×D13—22no—
44C2×C4×D13C2311yescharacteristic
45C2×C8×C13C2311yescharacteristic
46C2×C8×C13C2311yescharacteristic
47C13×C4⋊C4—22no—
48C13×C4⋊C4—22no—
49C13×C4⋊C4C2312yes—
50C42×C13C2311yescharacteristic
51#6106—24no—
52#6106—24no—
53#6103—22no—
54#6103—22no—
55#6103—22no—
56#6103D412yes—
57C4⋊Dic13—22no—
58C4⋊Dic13C2312yes—
59#6101—22no—
60#6101—22no—
61#6101D412yes—
62C4×Dic13—22no—
63C4×Dic13C2311yescharacteristic
64C2×#1055C2311yescharacteristic
65C2×#1055C2311yescharacteristic
66#6094—22no—
67C8×D13—22no—
68#3174—131nomaximal, Sylow
69C22×D13—22no—
70C22×D13C2×D411yescharacteristic
71Q8×C13—22no—
72Q8×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13C2×D412yes—
76C2×C4×C13C2411yescharacteristic
77C2×Dic13—22no—
78C2×Dic13C2×D412yes—
79C2×Dic13C2×D411yescharacteristic
80D52—22no—
81D52—22no—
82D52—82no—
83D52—82no—
84C4×D13—21no—
85C4×D13—21no—
86C4×D13—82no—
87C8×C13—21no—
88C8×C13—21no—
89#1055#4112yes—
90#1055#4112yes—
91#541—131no—
92#540—131no—
93#499—131no—
94#492—131no—
95#491D1311yescharacteristic, complemented
96#490—131no—
97#468—132no—
98#465—132no—
99#440—132no—
100C4×SD16—132no—
101#405—131no—
102C22×C13C22×D411yescharacteristic
103C2×D13—21no—
104C2×D13—22no—
105C2×D13—42no—
106C2×D13—42no—
107C2×D13—42no—
108C4×C13—22no—
109C4×C13—42no—
110C4×C13—42no—
111C4×C13C2×#4111yescharacteristic
112C4×C13C2×#4111yescharacteristic
113Dic13—21no—
114Dic13—22no—
115Dic13—42no—
116C2×SD16—132no—
117C2×SD16—132no—
118C2×M16—131no—
119C22×C8—131no—
120C4⋊Q8C2×D1311yescharacteristic
121#127—131no—
122#126—262no—
123#125—131no—
124#125—262no—
125#125C2×D1311yescharacteristic
126#123—262no—
127C22⋊Q8—132no—
128#121—132no—
129#121—262no—
130C4×Q8—132no—
131C4×D4—132no—
132#117—131no—
133#107—132no—
134#106—132no—
135#103C2×D1312yes—
136#103C2×D1312yes—
137#102—132no—
138#102—132no—
139#97—131no—
140#97C2×D1311yescharacteristic
141C4×C8—131no—
142C4×C8—131no—
143C2×C13#53211yescharacteristic
144C2×C13#57712yes—
145D13—41no—
146D13—82no—
147C2×Q8C22×D1312yes—
148C2×D4—132no—
149C2×D4—262no—
150C2×D4—262no—
151C22×C4—131no—
152C22×C4—262no—
153SD16—264no—
154SD16—264no—
155M16—262no—
156C2×C8—131no—
157C2×C8—131no—
158C2×C8—262no—
159C2×C8C22×D1311yescharacteristic
160C2×C8C22×D1311yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—132no—
164C4⋊C4—132no—
165C4⋊C4—262no—
166C4⋊C4—262no—
167C4⋊C4—262no—
168C4⋊C4C22×D1312yes—
169C22⋊C4—132no—
170C22⋊C4—262no—
171C22⋊C4—262no—
172C22⋊C4—262no—
173C42—131no—
174C42—262no—
175C42C22×D1311yescharacteristic
176C13#317411yescharacteristic, complemented, Sylow
177C23—131no—
178C23—262no—
179Q8—22no—
180Q8—22no—
181D4—262no—
182D4—262no—
183D4—1042no—
184D4—1042no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—132no—
188C2×C4—131no—
189C2×C4—261no—
190C2×C4—261no—
191C2×C4—262no—
192C2×C4—1042no—
193C2×C4D4×D1312yes—
194C2×C4C23×D1311yescharacteristic
195C8—21no—
196C8—21no—
197C8—132no—
198C8—132no—
199C22—262no—
200C22—261no—
201C22—522no—
202C22—522no—
203C22—522no—
204C22C2×D4×D1311yescharacteristic
205C4—22no—
206C4—42no—
207C4—42no—
208C4—262no—
209C4—261no—
210C4—522no—
211C4#41×D1311yescharacteristic
212C4#41×D1311yescharacteristic
213C2—521no—
214C2—1042no—
215C2#1171937311yescharacteristic
216C2#1171948312yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#491C2
socleC22×C13C22×D4
prime radical#11719403C2
hypercenter#491D13
hypocenterC13#3174
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #11719436C2semidirect
3. C13×#491C2semidirect
4. #11718746C2semidirect
5. #11718725C2semidirect
6. #11718478C2semidirect
7. #11718473C2semidirect
8. #11718468C2semidirect
9. #11718449C2semidirect
10. #11718374C2semidirect
11. #11718369C2semidirect
95. #491D13semidirect
176. C13#3174semidirect

Maximal subgroups

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

subgroupindex
#117194362
#117194032
C13×#4912
#117187462
#117187252
#117184782
#117184732
#117184682
#117184492
#117183742
#117183692
#317413