Finite Group Databasebeta

← #13125089

Subgroups — #13125089

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
1#11719226C211yesmaximal, characteristic
2#11719223C211yesmaximal, characteristic, complemented
3C13×#433C211yesmaximal, characteristic, complemented
4#11718508C212yesmaximal, complemented
5#11718502C212yesmaximal, complemented
6#11718392C212yesmaximal
7#11718384C212yesmaximal, complemented
8#11718371C212yesmaximal, complemented
9C4×#6095C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C13×#117C2211yescharacteristic
12#88180C2211yescharacteristic
13#88178C2212yes—
14C2×#6095C2212yes—
15C2×#6095C2212yes—
16#88147—22no—
17#88143—22no—
18C22⋊C4×D13—22no—
19#88133—22no—
20C4×D52C2212yes—
21C4×D52C2212yes—
22#88124C2211yescharacteristic, complemented
23#88123C2211yescharacteristic, complemented
24C4×Dic26C2212yescomplemented
25C13×C4⋊C8C2212yescomplemented
26C13×C22⋊C8C2212yes—
27C13×#97C2211yescharacteristic, complemented
28C4×C8×C13C2211yescharacteristic, complemented
29#88061C2212yes—
30#88061C2212yes—
31#88058C2212yescomplemented
32#88057C2212yescomplemented
33#88056C2212yescomplemented
34#88056C2212yescomplemented
35C23×D13—21no—
36C22×C4×C13C2311yescharacteristic
37C2×D52—21no—
38C2×D52—24no—
39C2×D52C2312yes—
40C2×C4×D13—22no—
41C2×C4×D13—22no—
42C2×Dic26C2312yes—
43C2×C8×C13C2312yes—
44C2×C8×C13C2312yes—
45C13×C4⋊C4D412yes—
46C13×C22⋊C4D412yes—
47C42×C13C2311yescharacteristic
48C42×C13C2311yescharacteristic
49C22⋊Dic13—22no—
50C22⋊Dic13—21no—
51#6103—22no—
52#6103—22no—
53C4⋊Dic13—22no—
54C4⋊Dic13C2312yes—
55C4⋊Dic13C2312yes—
56#6101—22no—
57#6101—22no—
58#6101—22no—
59C4×Dic13—22no—
60C4×Dic13—21no—
61#6095—24no—
62#6095—24no—
63#3123—131nomaximal, Sylow
64C23×C13C2×D411yescharacteristic
65C22×D13—22no—
66C22×D13—24no—
67C22×D13—82no—
68C2×C4×C13—22no—
69C2×C4×C13C2×D411yescharacteristic
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×D412yes—
72C2×C4×C13C2411yescharacteristic
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76D52—24no—
77D52—22no—
78D52#4114yes—
79C4×D13—82no—
80C4×D13—82no—
81Dic26—22no—
82Dic26—22no—
83C8×C13—22no—
84C8×C13—22no—
85#541—131no—
86#518—131no—
87#485—132no—
88#478—132no—
89#461—132no—
90#450—132no—
91#440—132no—
92C4×SD16—132no—
93#433D1311yescharacteristic, complemented
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×C13C2×#4112yes—
105Dic13—42no—
106Dic13—42no—
107Dic13—42no—
108C22×D4—131no—
109C2×SD16—132no—
110C2×SD16—132no—
111C4⋊Q8—131no—
112#126—262no—
113#125—131no—
114#125—262no—
115C22⋊Q8—132no—
116C4×Q8—132no—
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⋊C8C2×D1312yescomplemented
126#103—132no—
127#103—132no—
128#102—132no—
129#102—132no—
130C22⋊C8C2×D1312yes—
131#97C2×D1311yescharacteristic, complemented
132C4×C8C2×D1311yescharacteristic, complemented
133C2×C13—41no—
134C2×C13#52511yescharacteristic
135C2×C13#57712yes—
136D13—44no—
137C24—261no—
138C2×Q8—132no—
139C2×D4—132no—
140C2×D4—264no—
141C2×D4—261no—
142C22×C4—262no—
143C22×C4—262no—
144C22×C4C22×D1311yescharacteristic
145SD16—264no—
146SD16—264no—
147C2×C8C22×D1312yes—
148C2×C8C22×D1312yes—
149C4⋊C4—132no—
150C4⋊C4—132no—
151C4⋊C4—262no—
152C4⋊C4—262no—
153C4⋊C4—262no—
154C4⋊C4—262no—
155C4⋊C4D5212yes—
156C22⋊C4—261no—
157C22⋊C4—262no—
158C22⋊C4—262no—
159C22⋊C4—262no—
160C22⋊C4D5212yes—
161C42—261no—
162C42—262no—
163C42C22×D1311yescharacteristic
164C42C22×D1311yescharacteristic
165C13#312311yescharacteristic, complemented, Sylow
166C23—264no—
167C23—262no—
168C23—1042no—
169C23C2×D5211yescharacteristic
170Q8—262no—
171Q8—262no—
172D4—134no—
173D4—264no—
174D4—262no—
175C2×C4—22no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—1042no—
180C2×C4—1042no—
181C2×C4C2×D5212yes—
182C2×C4C2×D5211yescharacteristic
183C2×C4C2×D5212yes—
184C2×C4C23×D1311yescharacteristic
185C8—22no—
186C8—22no—
187C22—22no—
188C22—21no—
189C22—264no—
190C22—522no—
191C22—522no—
192C22—1044no—
193C22C22×D5211yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—522no—
198C4—522no—
199C4—522no—
200C4#41×D1312yes—
201C2—41no—
202C2—524no—
203C2#1171922911yescharacteristic
204C2#1171945612yes—
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#433C2
socleC22×C13C22×D4
prime radicalC22×D52C22
hypercenter#433D13
hypocenterC13#3123
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #11719223C2semidirect
3. C13×#433C2semidirect
4. #11718508C2semidirect
5. #11718502C2semidirect
7. #11718384C2semidirect
8. #11718371C2semidirect
9. C4×#6095C2semidirect
22. #88124C22semidirect
23. #88123C22semidirect
24. C4×Dic26C22semidirect
25. C13×C4⋊C8C22semidirect
27. C13×#97C22semidirect
28. C4×C8×C13C22semidirect
31. #88058C22semidirect
32. #88057C22semidirect
33. #88056C22semidirect
34. #88056C22semidirect
93. #433D13semidirect
125. C4⋊C8C2×D13semidirect
131. #97C2×D13semidirect
132. C4×C8C2×D13semidirect
165. C13#3123semidirect

Maximal subgroups

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

subgroupindex
#117192262
#117192232
C13×#4332
#117185082
#117185022
#117183922
#117183842
#117183712
C4×#60952
#312313