Finite Group Databasebeta

← #13125083

Subgroups — #13125083

Order 1664.

394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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×#541C211yesmaximal, characteristic, complemented
2#11719226C211yesmaximal, characteristic
3#11718744C212yesmaximal, complemented
4#11718727C212yesmaximal, complemented
5#11718707C212yesmaximal
6#11718706C212yesmaximal, complemented
7#11718687C212yesmaximal, complemented
8C4×#6106C212yesmaximal, complemented
9#11718661C211yesmaximal, characteristic, complemented
10C22×D52C2211yescharacteristic
11C13×C4⋊Q8C2211yescharacteristic, complemented
12C13×#126—22no—
13C13×#125—22no—
14C13×#125C2211yescharacteristic, complemented
15C13×C22⋊Q8C2212yes—
16C4×Q8×C13C2212yescomplemented
17C13×#117C2211yescharacteristic
18C2×#6106C2212yes—
19C2×#6106C2212yes—
20#88180C2211yescharacteristic
21#88147—22no—
22C22⋊C4×D13—22no—
23C4×D52C2212yes—
24C4×D52C2212yes—
25#88075C2212yescomplemented
26#88075C2212yescomplemented
27C22⋊#1055C2212yes—
28#88049C2212yes—
29#88049C2212yes—
30#88048C2212yescomplemented
31#88047C2212yescomplemented
32C4⋊#1055C2212yescomplemented
33#88043C2211yescharacteristic, complemented
34C4×#1055C2211yescharacteristic, complemented
35C23×D13—21no—
36C2×Q8×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C2×D52—21no—
39C2×D52—24no—
40C2×D52C2312yes—
41C2×C4×D13—22no—
42C2×C4×D13—22no—
43C13×C4⋊C4—22no—
44C13×C4⋊C4—22no—
45C13×C4⋊C4—22no—
46C13×C4⋊C4—22no—
47C13×C4⋊C4D412yes—
48C13×C4⋊C4C2312yes—
49C13×C22⋊C4—22no—
50C13×C22⋊C4D412yes—
51C42×C13—22no—
52C42×C13C2311yescharacteristic
53C42×C13C2311yescharacteristic
54C22⋊Dic13—21no—
55#6106—24no—
56#6106—24no—
57#6103—22no—
58#6103—22no—
59C4⋊Dic13C2312yes—
60C4×Dic13—21no—
61C2×#1055C2312yes—
62C2×#1055C2312yes—
63#3123—131nomaximal, Sylow
64C23×C13C2×D411yescharacteristic
65C22×D13—22no—
66C22×D13—24no—
67C22×D13—82no—
68Q8×C13—22no—
69Q8×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D412yes—
75C2×C4×C13C2×D412yes—
76C2×C4×C13C2411yescharacteristic
77C2×Dic13—22no—
78D52—24no—
79D52—22no—
80D52#4114yes—
81C4×D13—82no—
82C4×D13—82no—
83#1055—22no—
84#1055—22no—
85#541D1311yescharacteristic, complemented
86#518—131no—
87#485—132no—
88#478—132no—
89#461—132no—
90#450—132no—
91#440—132no—
92C4×SD16—132no—
93#433—131no—
94C22×C13—21no—
95C22×C13—22no—
96C22×C13C22×D411yescharacteristic
97C2×D13—24no—
98C2×D13—42no—
99C2×D13—42no—
100C2×D13—84no—
101C4×C13—21no—
102C4×C13—22no—
103C4×C13—22no—
104C4×C13—42no—
105C4×C13—42no—
106C4×C13C2×#4112yes—
107Dic13—42no—
108C22×D4—131no—
109C2×SD16—132no—
110C2×SD16—132no—
111C4⋊Q8C2×D1311yescharacteristic, complemented
112#126—22no—
113#125—22no—
114#125C2×D1311yescharacteristic, complemented
115C22⋊Q8C2×D1312yes—
116C4×Q8C2×D1312yescomplemented
117C4×D4—132no—
118C4×D4—132no—
119C4×D4—262no—
120#117—131no—
121#117C2×D1311yescharacteristic
122C2×C22⋊C4—262no—
123#107—132no—
124#106—132no—
125C4⋊C8—132no—
126#103—132no—
127#103—132no—
128#102—132no—
129#102—132no—
130C22⋊C8—132no—
131#97—131no—
132C4×C8—131no—
133C2×C13—41no—
134C2×C13#52511yescharacteristic
135C2×C13#57712yes—
136D13—44no—
137C24—261no—
138C2×Q8C22×D1312yes—
139C2×D4—132no—
140C2×D4—264no—
141C2×D4—261no—
142C22×C4—262no—
143C22×C4—262no—
144C22×C4C22×D1311yescharacteristic
145SD16—264no—
146SD16—264no—
147C2×C8—132no—
148C2×C8—132no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—132no—
154C4⋊C4C22⋊D1312yes—
155C4⋊C4C22×D1312yes—
156C22⋊C4—22no—
157C22⋊C4—261no—
158C22⋊C4—262no—
159C22⋊C4—262no—
160C22⋊C4C22⋊D1312yes—
161C42—22no—
162C42—261no—
163C42C22×D1311yescharacteristic
164C42C22×D1311yescharacteristic
165C13#312311yescharacteristic, complemented, Sylow
166C23—264no—
167C23—262no—
168C23—1042no—
169C23C2×C22⋊D1311yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—134no—
173D4—264no—
174D4—262no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—262no—
179C2×C4—1042no—
180C2×C4—1042no—
181C2×C4C2×C22⋊D1312yes—
182C2×C4C2×C22⋊D1311yescharacteristic
183C2×C4C2×C22⋊D1312yes—
184C2×C4C23×D1311yescharacteristic
185C8—262no—
186C8—262no—
187C22—21no—
188C22—22no—
189C22—264no—
190C22—522no—
191C22—522no—
192C22—1044no—
193C22C22×C22⋊D1311yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—42no—
199C4—522no—
200C4#41×D1312yes—
201C2—41no—
202C2—524no—
203C2#1171953311yescharacteristic
204C2#1171954212yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#541C2
socleC22×C13C22×D4
prime radicalC22×D52C22
hypercenter#541D13
hypocenterC13#3123
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C13×#541C2semidirect
3. #11718744C2semidirect
4. #11718727C2semidirect
6. #11718706C2semidirect
7. #11718687C2semidirect
8. C4×#6106C2semidirect
9. #11718661C2semidirect
11. C13×C4⋊Q8C22semidirect
14. C13×#125C22semidirect
16. C4×Q8×C13C22semidirect
25. #88075C22semidirect
26. #88075C22semidirect
30. #88048C22semidirect
31. #88047C22semidirect
32. C4⋊#1055C22semidirect
33. #88043C22semidirect
34. C4×#1055C22semidirect
85. #541D13semidirect
111. C4⋊Q8C2×D13semidirect
114. #125C2×D13semidirect
116. C4×Q8C2×D13semidirect
165. C13#3123semidirect

Maximal subgroups

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

subgroupindex
C13×#5412
#117192262
#117187442
#117187272
#117187072
#117187062
#117186872
C4×#61062
#117186612
#312313