Finite Group Databasebeta

← #15750529

Subgroups — #15750529

Order 3328.

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

normal subgroups only

This group has 194 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#13116374C211yesmaximal, characteristic
2#13112963C211yesmaximal, characteristic
3C13×#1319C211yesmaximal, characteristic
4C13×#391C2211yescharacteristic
5C2×#88076—21no—
6C2×#88075—21no—
7C2×#88047—21no—
8#11718596C411yescharacteristic
9C13×#324—21no—
10#11718116C411yescharacteristic
11C22×Q8×C13D411yescharacteristic
12C2×C13×C4⋊C4D411yescharacteristic
13C2×C42×C13C2×C411yescharacteristic
14C2×C4⋊Dic13—21no—
15C2×C4⋊Dic13—41no—
16C2×#6099—41no—
17C22×#1055—21no—
18C13×C22⋊C8—41no—
19C13×#95—41no—
20#88076—22no—
21#88076—41no—
22#88075—42no—
23#88047—42no—
24#7436—131nomaximal, Sylow
25C2×Q8×C13—21no—
26C2×Q8×C13—41no—
27C2×Q8×C13—41no—
28C2×Q8×C13SD1611yescharacteristic
29C2×Q8×C13Q1611yescharacteristic
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—
40C4⋊Dic13—82no—
41#6099—42no—
42#6099—81no—
43C2×#1055—22no—
44C2×#1055—41no—
45C2×#1055—41no—
46C2×#1055—81no—
47#2095—131no—
48#1394—131no—
49#1319D1311yescharacteristic
50C23×C13#9911yescharacteristic
51Q8×C13—41no—
52Q8×C13—41no—
53Q8×C13—81no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—22no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—41no—
60C2×C4×C13—41no—
61C2×C4×C13—41no—
62C2×C4×C13—41no—
63C2×C4×C13—41no—
64C2×C4×C13—81no—
65C2×C4×C13#10311yescharacteristic
66C2×C4×C13#10411yescharacteristic
67C2×Dic13—82no—
68C2×Dic13—81no—
69C8×C13—161no—
70#1055—42no—
71#1055—82no—
72C2×#107—261no—
73C2×#103—261no—
74C2×#101—261no—
75#391C2×D1311yescharacteristic
76#384—131no—
77#336—131no—
78#324—21no—
79C22×C13—21no—
80C22×C13—21no—
81C22×C13#32811yescharacteristic
82C22×C13#35211yescharacteristic
83C22×C13#35311yescharacteristic
84C4×C13—21no—
85C4×C13—21no—
86C4×C13—42no—
87C4×C13—41no—
88C4×C13—41no—
89C4×C13—81no—
90Dic13—161no—
91C22×Q8D5211yescharacteristic
92C2×M16—521no—
93C22×C8—261no—
94C2×C4⋊C4—261no—
95C2×C4⋊C4—521no—
96C2×C4⋊C4C22⋊D1311yescharacteristic
97C2×C42C4×D1311yescharacteristic
98#107—522no—
99#103—522no—
100#101—262no—
101#101—521no—
102C22⋊C8—41no—
103#95—41no—
104C2×C13—21no—
105C2×C13—21no—
106C2×C13#135211yescharacteristic
107C2×C13#140611yescharacteristic
108C2×C13#141111yescharacteristic
109C2×Q8—21no—
110C2×Q8—41no—
111C2×Q8—41no—
112C2×Q8#609511yescharacteristic
113C2×Q8Dic5211yescharacteristic
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—521no—
118C22×C4#610311yescharacteristic
119M16—522no—
120M16—1041no—
121C2×C8—81no—
122C2×C8—262no—
123C2×C8—521no—
124C2×C8—521no—
125C2×C8—1041no—
126C4⋊C4—41no—
127C4⋊C4—521no—
128C4⋊C4—521no—
129C4⋊C4—1042no—
130C42—41no—
131C13#743611yescharacteristic, complemented, Sylow
132C23#8804611yescharacteristic
133Q8—41no—
134Q8—41no—
135Q8—81no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—1042no—
148C2×C4—1041no—
149C2×C4#8805611yescharacteristic
150C2×C4#8806511yescharacteristic
151C8—161no—
152C8—522no—
153C8—1042no—
154C22—21no—
155C22—21no—
156C22#1171805911yescharacteristic
157C22#1171806611yescharacteristic
158C22#1171806811yescharacteristic
159C4—21no—
160C4—21no—
161C4—42no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—2081no—
166C2—21no—
167C2—21no—
168C2#1311286111yescharacteristic
169C2#1311299211yescharacteristic
170C2#1311300411yescharacteristic
subgroupG/H
centerC22#11718066
commutatorC2×C42×C13C2×C4
Frattini#391C2×D13
FittingC13×#1319C2
socleC22×C13#353
prime radicalC23×C13#99
cosocleC13×#391C22
hypercenter#1319D13
hypocenterC13#7436
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
131. C13#7436semidirect

Maximal subgroups

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

subgroupindex
#131163742
#131129632
C13×#13192
#743613