Finite Group Databasebeta

← #15750507

Subgroups — #15750507

Order 3328.

196 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 43 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#13112963C211yesmaximal, characteristic
2#13112770C211yesmaximal, characteristic
3C13×#2026C211yesmaximal, characteristic
4C2×C13×#125C411yescharacteristic
5C2×C13×#103—21no—
6C13×#391C2211yescharacteristic
7C2×#88076—21no—
8C13×#340—21no—
9C13×#336C411yescharacteristic
10#11718120—21no—
11C22×Q8×C13D411yescharacteristic
12C22×C8×C13—21no—
13C13×#125—42no—
14C2×C13×C4⋊C4—21no—
15C2×C13×C4⋊C4—41no—
16C2×C13×C4⋊C4D411yescharacteristic
17C2×C42×C13C2×C411yescharacteristic
18C2×#6099—41no—
19C13×#103—42no—
20C13×#95—41no—
21#88076—22no—
22#88076—41no—
23C22⋊#1055—41no—
24#7429—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×C13—41no—
34C22×C4×C13C22⋊C411yescharacteristic
35C2×C8×C13—41no—
36C2×C8×C13—41no—
37C2×C8×C13—41no—
38C13×C4⋊C4—22no—
39C13×C4⋊C4—41no—
40C13×C4⋊C4—41no—
41C13×C4⋊C4—42no—
42C13×C4⋊C4—42no—
43C42×C13—41no—
44#6099—42no—
45#6099—81no—
46C2×#1055—81no—
47C2×#1055—81no—
48#2026D1311yescharacteristic
49#1394—131no—
50#1319—131no—
51C23×C13#9911yescharacteristic
52Q8×C13—41no—
53Q8×C13—41no—
54Q8×C13—81no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
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—42no—
65C2×C4×C13—41no—
66C2×C4×C13—81no—
67C2×C4×C13—81no—
68C2×C4×C13—81no—
69C2×C4×C13#10311yescharacteristic
70C2×C4×C13#10411yescharacteristic
71C8×C13—81no—
72#1055—82no—
73#1055—161no—
74C2×#125Dic1311yescharacteristic
75C2×#103—21no—
76C2×#101—261no—
77#391C2×D1311yescharacteristic
78#340—21no—
79#336Dic1311yescharacteristic
80#324—261no—
81C22×C13—21no—
82C22×C13—21no—
83C22×C13#32811yescharacteristic
84C22×C13AΣL(1,𝔽16)11yescharacteristic
85C22×C13#35411yescharacteristic
86C4×C13—21no—
87C4×C13—21no—
88C4×C13—41no—
89C4×C13—41no—
90C4×C13—81no—
91C4×C13—82no—
92C4×C13—81no—
93C22×Q8C22⋊D1311yescharacteristic
94C2×M16—521no—
95C22×C8—21no—
96#125—42no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4C22⋊D1311yescharacteristic
100C2×C42C2×Dic1311yescharacteristic
101#103—42no—
102#101—262no—
103#101—521no—
104C22⋊C8—521no—
105#95—41no—
106C2×C13—21no—
107C2×C13—21no—
108C2×C13#135111yescharacteristic
109C2×C13#141311yescharacteristic
110C2×C13#141411yescharacteristic
111C2×Q8—21no—
112C2×Q8—41no—
113C2×Q8—41no—
114C2×Q8#610611yescharacteristic
115C2×Q8#610711yescharacteristic
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—41no—
120C22×C4C22⋊Dic1311yescharacteristic
121M16—522no—
122M16—1041no—
123C2×C8—41no—
124C2×C8—41no—
125C2×C8—41no—
126C2×C8—1041no—
127C2×C8—1041no—
128C4⋊C4—22no—
129C4⋊C4—41no—
130C4⋊C4—41no—
131C4⋊C4—42no—
132C4⋊C4—42no—
133C42—41no—
134C13#742911yescharacteristic, complemented, Sylow
135C23#8807411yescharacteristic
136Q8—41no—
137Q8—41no—
138Q8—81no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—41no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4—81no—
153C2×C4#8807511yescharacteristic
154C2×C4#8807711yescharacteristic
155C8—81no—
156C8—1042no—
157C8—2081no—
158C22—21no—
159C22—21no—
160C22#1171812811yescharacteristic
161C22#1171813011yescharacteristic
162C22#1171813311yescharacteristic
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—81no—
168C4—82no—
169C4—81no—
170C2—21no—
171C2—21no—
172C2#1311285711yescharacteristic
173C2#1311300911yescharacteristic
174C2#1311301111yescharacteristic
subgroupG/H
centerC22#11718133
commutatorC2×C42×C13C2×C4
Frattini#391C2×D13
FittingC13×#2026C2
socleC22×C13#354
prime radicalC23×C13#99
cosocleC13×#391C22
hypercenter#2026D13
hypocenterC13#7429
LCSG ▷ C2×C42×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #2026

Complements

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

NH ≅ G/Ntype
134. C13#7429semidirect

Maximal subgroups

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

subgroupindex
#131129632
#131127702
C13×#20262
#742913