Finite Group Databasebeta

← #15750460

Subgroups — #15750460

Order 3328.

178 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 41 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#13116254C211yesmaximal, characteristic
2#13112963C211yesmaximal, characteristic
3C13×#1319C211yesmaximal, characteristic
4C13×#391C2211yescharacteristic
5C2×#88076—21no—
6C2×#88075—21no—
7#11718597C411yescharacteristic
8C13×#324—21no—
9#11718121—21no—
10#11718116C411yescharacteristic
11C22×Q8×C13D411yescharacteristic
12C2×C13×C4⋊C4D411yescharacteristic
13C2×C42×C13C2×C411yescharacteristic
14C2×C4⋊Dic13—21no—
15C2×#6099—41no—
16C22×#1055—21no—
17C13×C22⋊C8—41no—
18C13×#95—41no—
19#88076—22no—
20#88076—41no—
21#88075—41no—
22#88075—41no—
23#88071—41no—
24#7413—131nomaximal, Sylow
25C2×Q8×C13—21no—
26C2×Q8×C13—41no—
27C2×Q8×C13—41no—
28C2×Q8×C13D811yescharacteristic
29C2×Q8×C13SD1611yescharacteristic
30C22×C4×C13—21no—
31C22×C4×C13—21no—
32C22×C4×C13—21no—
33C22×C4×C13C22⋊C411yescharacteristic
34C22×Dic13—41no—
35C2×C8×C13—81no—
36C13×C4⋊C4—41no—
37C42×C13—41no—
38C4⋊Dic13—41no—
39C4⋊Dic13—41no—
40#6099—42no—
41#6099—81no—
42C2×#1055—41no—
43C2×#1055—41no—
44C2×#1055—41no—
45C2×#1055—81no—
46#2074—131no—
47#1394—131no—
48#1319D1311yescharacteristic
49C23×C13#9911yescharacteristic
50Q8×C13—41no—
51Q8×C13—41no—
52Q8×C13—81no—
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—41no—
58C2×C4×C13—41no—
59C2×C4×C13—41no—
60C2×C4×C13—41no—
61C2×C4×C13—41no—
62C2×C4×C13—41no—
63C2×C4×C13—81no—
64C2×C4×C13#10211yescharacteristic
65C2×C4×C13#10411yescharacteristic
66C2×Dic13—81no—
67C2×Dic13—81no—
68C2×Dic13—81no—
69C8×C13—161no—
70#1055—81no—
71#1055—82no—
72C2×#103—261no—
73C2×#101—261no—
74#391C2×D1311yescharacteristic
75#382—131no—
76#340—261no—
77#336—131no—
78#324—21no—
79C22×C13—21no—
80C22×C13—21no—
81C22×C13#32711yescharacteristic
82C22×C13#35211yescharacteristic
83C22×C13#35411yescharacteristic
84C4×C13—21no—
85C4×C13—21no—
86C4×C13—41no—
87C4×C13—41no—
88C4×C13—81no—
89C4×C13—81no—
90Dic13—161no—
91C22×Q8D5211yescharacteristic
92C2×M16—521no—
93C22×C8—261no—
94C2×C4⋊C4—261no—
95C2×C4⋊C4C22⋊D1311yescharacteristic
96C2×C42C4×D1311yescharacteristic
97#103—521no—
98#103—521no—
99#101—262no—
100#101—521no—
101C22⋊C8—41no—
102#95—41no—
103#95—521no—
104C2×C13—21no—
105C2×C13—21no—
106C2×C13#134411yescharacteristic
107C2×C13#141311yescharacteristic
108C2×C13#141411yescharacteristic
109C2×Q8—21no—
110C2×Q8—41no—
111C2×Q8—41no—
112C2×Q8#609511yescharacteristic
113C2×Q8D10411yescharacteristic
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—521no—
118C22×C4#610311yescharacteristic
119M16—522no—
120M16—1041no—
121C2×C8—81no—
122C2×C8—521no—
123C2×C8—521no—
124C2×C8—521no—
125C2×C8—1041no—
126C4⋊C4—41no—
127C4⋊C4—521no—
128C4⋊C4—521no—
129C42—41no—
130C13#741311yescharacteristic, complemented, Sylow
131C23#8804611yescharacteristic
132Q8—41no—
133Q8—41no—
134Q8—81no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—81no—
146C2×C4—1041no—
147C2×C4—1041no—
148C2×C4—1041no—
149C2×C4#8806111yescharacteristic
150C2×C4#8806511yescharacteristic
151C8—161no—
152C8—1041no—
153C8—1042no—
154C22—21no—
155C22—21no—
156C22#1171806211yescharacteristic
157C22#1171806511yescharacteristic
158C22#1171806811yescharacteristic
159C4—21no—
160C4—21no—
161C4—41no—
162C4—41no—
163C4—81no—
164C4—81no—
165C4—2081no—
166C2—21no—
167C2—21no—
168C2#1311283711yescharacteristic
169C2#1311300811yescharacteristic
170C2#1311301011yescharacteristic
subgroupG/H
centerC22#11718065
commutatorC2×C42×C13C2×C4
Frattini#391C2×D13
FittingC13×#1319C2
socleC22×C13#354
prime radicalC23×C13#99
cosocleC13×#391C22
hypercenter#1319D13
hypocenterC13#7413
LCSG ▷ C2×C42×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1319

Complements

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

NH ≅ G/Ntype
130. C13#7413semidirect

Maximal subgroups

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

subgroupindex
#131162542
#131129632
C13×#13192
#741313