Finite Group Databasebeta

← #16776982

Subgroups — #16776982

Order 3328.

196 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 40 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#13129757C211yesmaximal, characteristic
2#13129708C211yesmaximal, characteristic
3#13116266C211yesmaximal, characteristic
4#11719127—21no—
5C2×#88060C2211yescharacteristic
6C2×#88058C411yescharacteristic
7#11718648—21no—
8C22⋊#6092—21no—
9C13×#340C411yescharacteristic
10#11718121—21no—
11C22×C4×D13D411yescharacteristic
12C2×#6118—41no—
13C22×C8×C13C2×C411yescharacteristic
14C2×C13×C4⋊C4—21no—
15C2×#6103—41no—
16C2×C4⋊Dic13—21no—
17C22×#1055D411yescharacteristic
18C22⋊#1057—41no—
19#88111—22no—
20C2×#6092—41no—
21#88071—41no—
22#88060—41no—
23#88058—41no—
24#7085—131nomaximal, Sylow
25C23×D13SD1611yescharacteristic
26C22×C4×C13—41no—
27C22×C4×C13C22⋊C411yescharacteristic
28C22×Dic13—41no—
29C22×Dic13D811yescharacteristic
30C2×C4×D13—21no—
31C2×C4×D13—21no—
32C2×C4×D13—41no—
33C2×C4×D13—41no—
34C2×#1057—42no—
35#6118—81no—
36#6118—81no—
37C2×C8×C13—21no—
38C2×C8×C13—41no—
39C13×C4⋊C4—41no—
40C13×C4⋊C4—41no—
41#6103—82no—
42C4⋊Dic13—41no—
43C4⋊Dic13—41no—
44C2×#1055—21no—
45C2×#1055—41no—
46#6092—81no—
47#2076—131no—
48#1314—131no—
49#1293—131no—
50C23×C13#10211yescharacteristic
51C22×D13—21no—
52C22×D13—21no—
53C22×D13—21no—
54C22×D13—41no—
55C22×D13—41no—
56C2×C4×C13—21no—
57C2×C4×C13—21no—
58C2×C4×C13—81no—
59C2×C4×C13—81no—
60C2×C4×C13—81no—
61C2×C4×C13#9911yescharacteristic
62C2×C4×C13#10411yescharacteristic
63C2×Dic13—21no—
64C2×Dic13—41no—
65C2×Dic13—81no—
66C2×Dic13—81no—
67C2×Dic13—81no—
68C4×D13—41no—
69C4×D13—41no—
70C4×D13—81no—
71#1057—82no—
72C8×C13—41no—
73#1055—41no—
74C2×#107—131no—
75#407—261no—
76C2×C22⋊C8—131no—
77#380—261no—
78C22⋊C16—261no—
79#340—261no—
80#340#26111yescharacteristic
81C22×C13—21no—
82C22×C13—21no—
83C22×C13#32711yescharacteristic
84C22×C13#35911yescharacteristic
85C22×C13#36211yescharacteristic
86C2×D13—42no—
87C2×D13—41no—
88C2×D13—41no—
89C2×D13—41no—
90C2×D13—81no—
91C4×C13—21no—
92C4×C13—161no—
93C4×C13#35211yescharacteristic
94C4×C13#35411yescharacteristic
95Dic13—41no—
96Dic13—161no—
97C23×C4—131no—
98C2×M16—521no—
99C22×C8—131no—
100C22×C8C2×#26111yescharacteristic
101C2×C4⋊C4—21no—
102C2×C4⋊C4—261no—
103C2×C22⋊C4—521no—
104C2×C16—521no—
105#107—521no—
106C22⋊C8—262no—
107C22⋊C8—521no—
108C22⋊C8—521no—
109#95—521no—
110C2×C13—21no—
111C2×C13—21no—
112C2×C13#134111yescharacteristic
113C2×C13#134411yescharacteristic
114C2×C13#135011yescharacteristic
115D13—81no—
116C24—131no—
117C22×C4—41no—
118C22×C4—131no—
119C22×C4—261no—
120C22×C4—261no—
121C22×C4—521no—
122C22×C4—521no—
123C22×C4—521no—
124C22×C4C22⋊#26111yescharacteristic
125M16—1041no—
126M16—1041no—
127C2×C8—21no—
128C2×C8—41no—
129C2×C8—261no—
130C2×C8—521no—
131C2×C8—522no—
132C4⋊C4—41no—
133C4⋊C4—41no—
134C4⋊C4—521no—
135C4⋊C4—521no—
136C22⋊C4—1042no—
137C16—1041no—
138C13#708511yescharacteristic, complemented, Sylow
139C23—261no—
140C23—261no—
141C23—261no—
142C23—521no—
143C23—521no—
144C23#8811511yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—81no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4—261no—
151C2×C4—521no—
152C2×C4—521no—
153C2×C4—521no—
154C2×C4—1041no—
155C2×C4—1041no—
156C2×C4—1041no—
157C2×C4—1041no—
158C2×C4#8810711yescharacteristic
159C2×C4#8811811yescharacteristic
160C8—41no—
161C8—521no—
162C8—1042no—
163C22—21no—
164C22—21no—
165C22—522no—
166C22—521no—
167C22—521no—
168C22—521no—
169C22—1041no—
170C22#1171824011yescharacteristic
171C22#1171827711yescharacteristic
172C22#1171828211yescharacteristic
173C4—21no—
174C4—161no—
175C4—521no—
176C4—2081no—
177C4#1171822611yescharacteristic
178C4#1171823711yescharacteristic
179C2—21no—
180C2—21no—
181C2—1041no—
182C2#1312981111yescharacteristic
183C2#1312981711yescharacteristic
184C2#1312982911yescharacteristic
subgroupG/H
centerC22#11718240
commutatorC22×C8×C13C2×C4
FrattiniC22×C8C2×#261
FittingC13×#340C4
socleC22×C13#327
prime radicalC23×D13SD16
cosocleC2×#88060C22
hypercenter#340#261
hypocenterC13#7085
LCSG ▷ C22×C8×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
138. C13#7085semidirect

Maximal subgroups

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

subgroupindex
#131297572
#131297082
#131162662
#708513