Finite Group Databasebeta

← #13125238

Subgroups — #13125238

Order 1664.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719430C211yesmaximal, characteristic
2D13×#125C211yesmaximal, characteristic, complemented
3C13×#491C211yesmaximal, characteristic, complemented
4#11718743C211yesmaximal, characteristic, complemented
5#11718728C211yesmaximal, characteristic, complemented
6#11718464C214yesmaximal, complemented
7#11718461C214yesmaximal, complemented
8#11718374C211yesmaximal, characteristic, complemented
9#11718368C211yesmaximal, characteristic, complemented
10C2×#6131C2212yes—
11C13×C4⋊Q8C2211yescharacteristic
12C13×#125C2211yescharacteristic
13#88201C2212yes—
14C2×#6094C2212yes—
15#88149—22no—
16#88147—22no—
17C4⋊C4×D13—22no—
18C4⋊C4×D13C2212yes—
19#88144C2212yes—
20#88143—22no—
21#88128C2211yescharacteristic
22C42×D13C2211yescharacteristic
23#88124C2211yescharacteristic
24C13×#103C2214yes—
25C13×#97C2211yescharacteristic
26#88075C2214yes—
27#88061C2214yes—
28C8×Dic13C2212yes—
29#88049C2214yes—
30#88043C2211yescharacteristic
31C2×Q8×C13C2312yes—
32#6131—28no—
33C2×D52—22no—
34C2×D52—22no—
35C2×D52C2312yes—
36C2×C4×D13—22no—
37C2×C4×D13—22no—
38C2×C4×D13D412yes—
39C2×C4×D13C2311yescharacteristic
40C2×C8×C13C2312yes—
41C13×C4⋊C4—22no—
42C13×C4⋊C4—22no—
43C13×C4⋊C4C2312yes—
44C42×C13C2311yescharacteristic
45#6103—24no—
46C4⋊Dic13—22no—
47C4⋊Dic13C2312yes—
48#6101—22no—
49#6101—22no—
50#6101—22no—
51C4×Dic13D412yes—
52C4×Dic13C2311yescharacteristic
53C2×#1055C2312yes—
54#6094—24no—
55#3142—131nomaximal, Sylow
56C22×D13—22no—
57C22×D13C2×D411yescharacteristic
58Q8×C13—24no—
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13C2×D412yes—
62C2×C4×C13C2411yescharacteristic
63C2×Dic13—22no—
64C2×Dic13C2×D412yes—
65C2×Dic13C2×D411yescharacteristic
66D52—24no—
67D52—44no—
68D52—44no—
69C4×D13—42no—
70C4×D13—44no—
71C4×D13—44no—
72C4×D13#4114yes—
73C8×C13—22no—
74#1055—22no—
75#532—131no—
76C2×#125—131no—
77#491—131no—
78#491D1311yescharacteristic, complemented
79#490—131no—
80#490—131no—
81#488—134no—
82#417—134no—
83C4×M16—131no—
84C22×C13C22×D411yescharacteristic
85C2×D13—22no—
86C2×D13—42no—
87C2×D13—44no—
88C2×D13#12412yes—
89C4×C13—22no—
90C4×C13—42no—
91C4×C13—42no—
92C4×C13C2×#4112yes—
93Dic13—22no—
94Dic13—42no—
95Dic13#12412yes—
96C2×#41—132no—
97C2×M16—132no—
98C4⋊Q8C2×D1311yescharacteristic
99#127—131no—
100#125—132no—
101#125—131no—
102#125—262no—
103#125C2×D1311yescharacteristic
104#124—132no—
105#121—262no—
106C4×D4—262no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—262no—
109C2×C42—131no—
110#103—134no—
111#103C2×D1314yes—
112#102—134no—
113#102—134no—
114#97—131no—
115#97C2×D1311yescharacteristic
116C4×C8—132no—
117C2×C13C2×#12411yescharacteristic
118C2×C13#57512yes—
119D13—22no—
120D13—82no—
121#41—268no—
122C2×Q8C22×D1312yes—
123C2×D4—132no—
124C2×D4—262no—
125C2×D4—262no—
126C22×C4—131no—
127C22×C4—132no—
128C22×C4—262no—
129C22×C4—262no—
130M16—264no—
131C2×C8—132no—
132C2×C8C22×D1312yes—
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—132no—
136C4⋊C4—262no—
137C4⋊C4—262no—
138C4⋊C4—262no—
139C4⋊C4—262no—
140C4⋊C4C22×D1312yes—
141C22⋊C4—264no—
142C42—132no—
143C42—131no—
144C42C22×D1311yescharacteristic
145C13#314211yescharacteristic, complemented, Sylow
146C23—131no—
147C23—262no—
148Q8—24no—
149D4—264no—
150D4—524no—
151D4—524no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—131no—
155C2×C4—134no—
156C2×C4—132no—
157C2×C4—262no—
158C2×C4—522no—
159C2×C4—524no—
160C2×C4—524no—
161C2×C4D4×D1312yes—
162C2×C4C23×D1311yescharacteristic
163C8—22no—
164C8—262no—
165C22—132no—
166C22—262no—
167C22—524no—
168C22—522no—
169C22C2×D4×D1311yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—132no—
174C4—262no—
175C4—522no—
176C4#41×D1312yes—
177C2—262no—
178C2—1042no—
179C2D13×#12411yescharacteristic
180C2#1171948212yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#491C2
socleC22×C13C22×D4
prime radical#11719430C2
hypercenter#491D13
hypocenterC13#3142
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
2. D13×#125C2semidirect
3. C13×#491C2semidirect
4. #11718743C2semidirect
5. #11718728C2semidirect
6. #11718464C2semidirect
7. #11718461C2semidirect
8. #11718374C2semidirect
9. #11718368C2semidirect
78. #491D13semidirect
145. C13#3142semidirect

Maximal subgroups

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

subgroupindex
#117194302
D13×#1252
C13×#4912
#117187432
#117187282
#117184642
#117184612
#117183742
#117183682
#314213