Finite Group Databasebeta

← #16787065

Subgroups — #16787065

Order 3328.

288 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 66 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#13131206C212yesmaximal, complemented
2#13129784C212yesmaximal, complemented
3#13129771C212yesmaximal
4#13123479C211yesmaximal, characteristic
5#11719227C411yescharacteristic
6C13×#424C411yescharacteristic
7#11718790C411yescharacteristic
8M16×Dic13C2211yescharacteristic
9#11718771C2211yescharacteristic
10C2×C8×Dic13C411yescharacteristic
11#11718660C2211yescharacteristic
12#11718501—22no—
13#11718494—22no—
14#11718284C2214yes—
15#11718262—22no—
16#11718261—22no—
17C2×#6127C2×C411yescharacteristic
18C2×C13×M16C2×C411yescharacteristic
19C22×C8×C13C2×C411yescharacteristic
20C13×#117C2×C411yescharacteristic
21C2×C4×Dic13C2×C411yescharacteristic
22C2×#6099C2311yescharacteristic
23C22×#1055C2×C411yescharacteristic
24#88147—21no—
25#88141—21no—
26#88135—22no—
27#88126—21no—
28C42×D13—21no—
29#88106—24no—
30C13×C4⋊C8—22no—
31#88060—22no—
32#88060—22no—
33#88055D412yes—
34C8×Dic13—21no—
35C8×Dic13—21no—
36C8×Dic13D412yes—
37C4⋊#1055—22no—
38#11524—131nomaximal, Sylow
39C22×C4×C13C22×C411yescharacteristic
40C2×C22⋊D13—21no—
41C22×Dic13—21no—
42#6127—41no—
43#6127—41no—
44C2×D52M1611yescharacteristic
45C2×C4×D13—22no—
46C2×C4×D13—21no—
47C2×Dic26M1611yescharacteristic
48C13×M16—41no—
49C2×C8×C13—21no—
50C2×C8×C13—41no—
51C2×C8×C13C22⋊C412yes—
52C13×C4⋊C4—21no—
53C13×C22⋊C4M1612yes—
54C42×C13—21no—
55#6103—22no—
56#6101—22no—
57C4×Dic13—22no—
58C4×Dic13—21no—
59C4×Dic13C22⋊C411yescharacteristic
60C4×Dic13C22⋊C411yescharacteristic
61#6099—41no—
62C2×#1055—21no—
63C2×#1055—41no—
64C2×#1055C2×D412yes—
65#6092—44no—
66#2922—131no—
67#2165—132no—
68#1328—132no—
69#1321—132no—
70C23×C13C2×M1611yescharacteristic
71C22×D13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—22no—
75C2×C4×C13C2×C22⋊C411yescharacteristic
76C2×C4×C13C2×M1611yescharacteristic
77C22⋊D13—42no—
78C2×Dic13—21no—
79C2×Dic13—21no—
80C2×Dic13—21no—
81C2×Dic13—42no—
82D52—41no—
83C4×D13—44no—
84C4×D13—41no—
85C4×D13—41no—
86Dic26—41no—
87C8×C13—22no—
88C8×C13—41no—
89#1055—22no—
90#1055—41no—
91C4×#41—131no—
92#433—262no—
93#431—262no—
94#424—131no—
95#424#26111yescharacteristic
96#408—131no—
97#408—131no—
98C4×M16—131no—
99C2×C4×C8—131no—
100#364—262no—
101#349—134no—
102#347—262no—
103C22×C13—21no—
104C22×C13—41no—
105C22×C13#40711yescharacteristic
106C2×D13—42no—
107C2×D13—41no—
108C4×C13—21no—
109C4×C13—42no—
110C4×C13#41011yescharacteristic
111C4×C13#41311yescharacteristic
112Dic13—22no—
113Dic13—41no—
114Dic13—41no—
115C2×#41—131no—
116C2×M16—131no—
117C2×M16C2×#26111yescharacteristic
118C22×C8—131no—
119C22×C8C2×#26111yescharacteristic
120C4×Q8—261no—
121C4×D4—261no—
122C4×D4—262no—
123#117—261no—
124#117C2×#26111yescharacteristic
125C2×C42—131no—
126C2×C42—261no—
127M32—264no—
128C4⋊C8—22no—
129C4⋊C8—262no—
130C22⋊C8—262no—
131C22⋊C8—262no—
132#97—132no—
133C4×C8—132no—
134C4×C8—261no—
135C4×C8—261no—
136C2×C13—21no—
137C2×C13—41no—
138C2×C13#146411yescharacteristic
139D13—81no—
140#41—521no—
141#41—521no—
142C2×Q8—131no—
143C2×D4—131no—
144C2×D4—261no—
145C22×C4—262no—
146C22×C4—261no—
147C22×C4—261no—
148C22×C4C22×#26111yescharacteristic
149M16—41no—
150M16—521no—
151C2×C8—21no—
152C2×C8—41no—
153C2×C8—132no—
154C2×C8—261no—
155C2×C8—521no—
156C2×C8C22⋊#26112yes—
157C4⋊C4—21no—
158C4⋊C4—262no—
159C22⋊C4—262no—
160C22⋊C4#611812yes—
161C42—21no—
162C42—131no—
163C42—131no—
164C42—262no—
165C42—261no—
166C16—524no—
167C13#1152411yescharacteristic, complemented, Sylow
168C23—261no—
169C23C2×#611811yescharacteristic
170Q8—521no—
171D4—521no—
172D4—522no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—261no—
177C2×C4—261no—
178C2×C4—261no—
179C2×C4—524no—
180C2×C4—522no—
181C2×C4—521no—
182C2×C4—521no—
183C2×C4D13⋊M1611yescharacteristic
184C2×C4C2×C22⋊#26111yescharacteristic
185C8—22no—
186C8—41no—
187C8—262no—
188C8—521no—
189C22—21no—
190C22—41no—
191C22—522no—
192C22—521no—
193C22#1171912711yescharacteristic
194C4—21no—
195C4—42no—
196C4—262no—
197C4—521no—
198C4—521no—
199C4#1171914811yescharacteristic
200C4#1171915611yescharacteristic
201C2—21no—
202C2—41no—
203C2—1041no—
204C2#1313009011yescharacteristic
subgroupG/H
centerC4#11719156
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#424C4
socleC2×C13#1464
prime radicalC2×#6127C2×C4
cosocleC2×#6099C23
hypercenter#424#261
hypocenterC13#11524
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #13131206C2semidirect
2. #13129784C2semidirect
167. C13#11524semidirect

Maximal subgroups

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

subgroupindex
#131312062
#131297842
#131297712
#131234792
#1152413