Finite Group Databasebeta

← #13115900

Subgroups — #13115900

Order 1664.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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×#575C211yesmaximal, characteristic, complemented
2#11719533C212yesmaximal, complemented
3#11718897C212yesmaximal, complemented
4#11718787C211yesmaximal, characteristic, complemented
5#11718149C211yesmaximal, characteristic, complemented
6C2×C13×#41C2212yes—
7C22×C4×D13C2211yescharacteristic
8C13×#137—22no—
9C13×AGL(1,ℤ/8)—22no—
10C13×#135—22no—
11C2×C13×M16C2211yescharacteristic
12#88200—22no—
13#88192—22no—
14#88191—22no—
15#88189—22no—
16C4×C22⋊D13—24no—
17#88180C2212yes—
18C2×#6099C2211yescharacteristic
19#88077—24no—
20#88060—22no—
21C23×D13D411yescharacteristic
22C13×#41—22no—
23C13×#41—22no—
24C13×#41—22no—
25C13×#41—22no—
26C2×Q8×C13D412yescomplemented
27C2×D4×C13—22no—
28C2×D4×C13D412yescomplemented
29C22×C4×C13—22no—
30C22×C4×C13C2311yescharacteristic
31C2×C22⋊D13—24no—
32C22×Dic13D411yescharacteristic
33C2×C4×D13—22no—
34C2×C4×D13—22no—
35C2×C4×D13—21no—
36C2×C4×D13—21no—
37C13×Q16—22no—
38C13×SD16—24no—
39C13×D8—22no—
40C13×M16—22no—
41C2×C8×C13D412yescomplemented
42C22⋊Dic13—24no—
43C22⋊Dic13—22no—
44#6103—24no—
45C4⋊Dic13—22no—
46#6101—24no—
47C4×Dic13D414yescomplemented
48#6099—22no—
49C2×#1055—21no—
50#2010—131nomaximal, Sylow
51C23×C13—22no—
52C23×C13C2×D411yescharacteristic
53C22×D13—22no—
54C22×D13—21no—
55C22×D13—42no—
56Q8×C13—22no—
57Q8×C13—22no—
58D4×C13—22no—
59D4×C13—22no—
60D4×C13—42no—
61D4×C13—42no—
62C2×C4×C13—22no—
63C2×C4×C13—42no—
64C2×C4×C13—42no—
65C2×C4×C13C2×D412yes—
66C2×C4×C13C2×D411yescharacteristic
67C2×C4×C13C2×D412yes—
68C2×C4×C13#4111yescharacteristic
69C22⋊D13—48no—
70C2×Dic13—24no—
71C2×Dic13—22no—
72C2×Dic13—21no—
73C4×D13—41no—
74C4×D13—42no—
75C4×D13—41no—
76C8×C13—22no—
77#1055—41no—
78#575D1311yescharacteristic, complemented
79#525—132no—
80#421—132no—
81#407—131no—
82H(3,ℤ/4)—131no—
83C22×C13—41no—
84C22×C13—44no—
85C22×C13—42no—
86C22×C13#12012yes—
87C22×C13#12111yescharacteristic
88C2×D13—24no—
89C2×D13—22no—
90C2×D13—42no—
91C2×D13—41no—
92C2×D13—41no—
93C4×C13—42no—
94C4×C13#12011yescharacteristic
95C4×C13#12112yes—
96C4×C13#12711yescharacteristic
97Dic13—44no—
98Dic13—41no—
99C2×#41C2×D1312yes—
100C23×C4—131no—
101#137—22no—
102AGL(1,ℤ/8)—22no—
103#135—22no—
104C2×M16—131no—
105C2×M16C2×D1311yescharacteristic
106#123—262no—
107C22⋊Q8—262no—
108#121—262no—
109#120—262no—
110C4×D4—264no—
111#117—132no—
112#104—264no—
113C22⋊C8—262no—
114C2×C13—22no—
115C2×C13—21no—
116C2×C13—82no—
117C2×C13#39211yescharacteristic
118D13—42no—
119C24—131no—
120#41—22no—
121#41—22no—
122#41—22no—
123#41—22no—
124C2×Q8C22⋊D1312yescomplemented
125C2×D4—22no—
126C2×D4—264no—
127C2×D4C22⋊D1312yescomplemented
128C22×C4—22no—
129C22×C4—131no—
130C22×C4—262no—
131C22×C4—261no—
132C22×C4—261no—
133C22×C4—262no—
134C22×C4C22×D1311yescharacteristic
135Q16—22no—
136SD16—24no—
137D8—22no—
138M16—22no—
139M16—262no—
140C2×C8—261no—
141C2×C8C22⋊D1312yescomplemented
142C4⋊C4—264no—
143C4⋊C4—262no—
144C22⋊C4—264no—
145C22⋊C4—264no—
146C22⋊C4—262no—
147C42—134no—
148C13#201011yescharacteristic, complemented, Sylow
149C23—22no—
150C23—262no—
151C23—261no—
152C23—522no—
153C23D4×D1311yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—528no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—264no—
165C2×C4—262no—
166C2×C4—261no—
167C2×C4—522no—
168C2×C4—521no—
169C2×C4—521no—
170C2×C4D4×D1312yes—
171C2×C4#612911yescharacteristic
172C2×C4C2×C22⋊D1312yes—
173C2×C4C2×C22⋊D1311yescharacteristic
174C8—22no—
175C8—521no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—264no—
180C22—262no—
181C22—522no—
182C22—521no—
183C22—521no—
184C22#8819112yes—
185C22#8819211yescharacteristic
186C4—42no—
187C4—524no—
188C4—521no—
189C4#8819312yes—
190C4#8819411yescharacteristic
191C4#8820711yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—522no—
196C2#1171888411yescharacteristic
subgroupG/H
centerC4#88194
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#575C2
socleC2×C13#392
hypercenter#575D13
hypocenterC13#2010
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C13×#575C2semidirect
2. #11719533C2semidirect
3. #11718897C2semidirect
4. #11718787C2semidirect
5. #11718149C2semidirect
26. C2×Q8×C13D4semidirect
28. C2×D4×C13D4semidirect
41. C2×C8×C13D4semidirect
47. C4×Dic13D4semidirect
78. #575D13semidirect
124. C2×Q8C22⋊D13semidirect
127. C2×D4C22⋊D13semidirect
141. C2×C8C22⋊D13semidirect
148. C13#2010semidirect

Maximal subgroups

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

subgroupindex
C13×#5752
#117195332
#117188972
#117187872
#117181492
#201013