Finite Group Databasebeta

← #15749596

Subgroups — #15749596

Order 3328.

218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 49 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#13116264C211yesmaximal, characteristic
2#13112704C211yesmaximal, characteristic
3C13×#1314C211yesmaximal, characteristic
4C2×C13×C22⋊C8C2211yescharacteristic
5#11718873—21no—
6#11718873—21no—
7C2×#88058C411yescharacteristic, complemented
8C13×C22⋊C16—21no—
9#11718143—21no—
10#11718143C411yescharacteristic, complemented
11C23×C4×C13D411yescharacteristic
12C22×C8×C13C2×C411yescharacteristic
13C22×C8×C13D411yescharacteristic
14C2×C22⋊Dic13—41no—
15C2×C22⋊Dic13—41no—
16C2×C4⋊Dic13—21no—
17C2×C4⋊Dic13—21no—
18C2×C4⋊Dic13—41no—
19C2×C13×C16—41no—
20C13×C22⋊C8—41no—
21#88071—22no—
22#88071—41no—
23#88058—41no—
24#7077—131nomaximal, Sylow
25C24×C13D811yescharacteristic
26C22×C4×C13—21no—
27C22×C4×C13—21no—
28C22×C4×C13—41no—
29C22×C4×C13—41no—
30C22×C4×C13C22⋊C411yescharacteristic
31C22×C4×C13SD1611yescharacteristic
32C22×Dic13—42no—
33C22×Dic13—41no—
34C22×Dic13—41no—
35C2×C8×C13—21no—
36C2×C8×C13—21no—
37C2×C8×C13—41no—
38C2×C8×C13—41no—
39C22⋊Dic13—81no—
40C22⋊Dic13—82no—
41C22⋊Dic13—81no—
42C4⋊Dic13—41no—
43C4⋊Dic13—41no—
44C4⋊Dic13—41no—
45C4⋊Dic13—41no—
46C4⋊Dic13—81no—
47C4⋊Dic13—81no—
48C13×C16—81no—
49#2076—131no—
50#1314D1311yescharacteristic
51#1289—131no—
52C23×C13—21no—
53C23×C13—21no—
54C23×C13—41no—
55C23×C13—41no—
56C23×C13#10211yescharacteristic
57C23×C13SD3211yescharacteristic
58C23×C13Q3211yescharacteristic
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—41no—
63C2×C4×C13—41no—
64C2×C4×C13—41no—
65C2×C4×C13—81no—
66C2×C4×C13#9911yescharacteristic
67C2×C4×C13#10411yescharacteristic
68C2×Dic13—81no—
69C2×Dic13—81no—
70C2×Dic13—82no—
71C2×Dic13—81no—
72C2×Dic13—81no—
73C2×Dic13—82no—
74C2×Dic13—82no—
75C2×Dic13—81no—
76C2×Dic13—81no—
77C8×C13—41no—
78C8×C13—41no—
79C2×#107—131no—
80C2×C22⋊C8C2×D1311yescharacteristic
81#380—261no—
82#380—261no—
83C22⋊C16—21no—
84#340—131no—
85#340—261no—
86C22×C13—21no—
87C22×C13—21no—
88C22×C13—21no—
89C22×C13—21no—
90C22×C13—41no—
91C22×C13—41no—
92C22×C13—41no—
93C22×C13—41no—
94C22×C13—81no—
95C22×C13#32711yescharacteristic
96C22×C13#35811yescharacteristic
97C22×C13#36011yescharacteristic
98C4×C13—21no—
99C4×C13—41no—
100C4×C13#35211yescharacteristic
101C4×C13#35411yescharacteristic
102Dic13—161no—
103Dic13—162no—
104Dic13—161no—
105C23×C4D5211yescharacteristic
106C22×C8C4×D1311yescharacteristic
107C22×C8C22⋊D1311yescharacteristic
108C2×C4⋊C4—261no—
109C2×C4⋊C4—261no—
110C2×C4⋊C4—521no—
111C2×C22⋊C4—521no—
112C2×C22⋊C4—521no—
113C2×C16—41no—
114#107—521no—
115C22⋊C8—41no—
116#95—262no—
117#95—521no—
118C2×C13—21no—
119C2×C13—21no—
120C2×C13—41no—
121C2×C13—41no—
122C2×C13#133911yescharacteristic
123C2×C13#134411yescharacteristic
124C2×C13#134811yescharacteristic
125C24D10411yescharacteristic
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—41no—
129C22×C4—41no—
130C22×C4—522no—
131C22×C4—521no—
132C22×C4—521no—
133C22×C4#609511yescharacteristic
134C22×C4#610311yescharacteristic
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—41no—
138C2×C8—41no—
139C4⋊C4—521no—
140C4⋊C4—521no—
141C4⋊C4—521no—
142C4⋊C4—521no—
143C4⋊C4—1041no—
144C4⋊C4—1041no—
145C22⋊C4—1041no—
146C22⋊C4—1042no—
147C22⋊C4—1041no—
148C16—81no—
149C13#707711yescharacteristic, complemented, Sylow
150C23—21no—
151C23—21no—
152C23—41no—
153C23—41no—
154C23#8804011yescharacteristic
155C23Dic10411yescharacteristic
156C23#8806111yescharacteristic
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—81no—
164C2×C4—1041no—
165C2×C4—1042no—
166C2×C4—1041no—
167C2×C4—1041no—
168C2×C4—1041no—
169C2×C4—1042no—
170C2×C4—1042no—
171C2×C4—1041no—
172C2×C4—1041no—
173C2×C4#8804611yescharacteristic
174C2×C4#8806511yescharacteristic
175C8—41no—
176C8—41no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22—81no—
186C22#1171806211yescharacteristic
187C22#1171809511yescharacteristic
188C22#1171811011yescharacteristic
189C4—21no—
190C4—41no—
191C4—2081no—
192C4—2082no—
193C4—2081no—
194C4#1171806511yescharacteristic
195C4#1171806811yescharacteristic
196C2—21no—
197C2—21no—
198C2—41no—
199C2—41no—
200C2#1311282211yescharacteristic
201C2#1311283711yescharacteristic
202C2#1311284911yescharacteristic
subgroupG/H
centerC22#11718062
commutatorC22×C8×C13C2×C4
FrattiniC2×C22⋊C8C2×D13
FittingC13×#1314C2
socleC22×C13#327
prime radicalC24×C13D8
cosocleC2×C13×C22⋊C8C22
hypercenter#1314D13
hypocenterC13#7077
LCSG ▷ C22×C8×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
7. C2×#88058C4semidirect
10. #11718143C4semidirect
149. C13#7077semidirect

Maximal subgroups

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

subgroupindex
#131162642
#131127042
C13×#13142
#707713