Finite Group Databasebeta

← #16786811

Subgroups — #16786811

Order 3328.

462 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 104 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#13130067C212yesmaximal
2#13129781C214yesmaximal
3#13117319C211yesmaximal, characteristic
4C22×C42×C13C411yescharacteristic
5C2×#88180C411yescharacteristic
6C2×#88180C2211yescharacteristic
7#11719119—22no—
8#11718871C412yes—
9#11718871C2212yes—
10C4×#6101—22no—
11#11718589—22no—
12#11718305C2214yes—
13#11718285—22no—
14C23×C4×C13C2×C412yes—
15C23×C4×C13C2×C411yescharacteristic
16C2×C42×C13—21no—
17C2×C42×C13—21no—
18C2×C42×C13—41no—
19C2×C42×C13—41no—
20C2×C22⋊Dic13C2×C412yes—
21C2×C22⋊Dic13C2×C411yescharacteristic
22C2×C22⋊Dic13C2311yescharacteristic
23#88180—22no—
24#88180—41no—
25#88180—41no—
26#88180C814yescomplemented
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13D412yes—
29C2×#6101—22no—
30C2×#6101—22no—
31C2×C4×Dic13—21no—
32C2×C4×Dic13D412yes—
33C22⋊#1057—24no—
34C4⋊#1057—42no—
35C4×#1057—42no—
36#88071—22no—
37#88071—22no—
38#11452—131nomaximal, Sylow
39C24×C13C22×C411yescharacteristic
40C22×C4×C13—21no—
41C22×C4×C13—21no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—44no—
45C22×C4×C13—42no—
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C2×C812yes—
49C22×C4×C13M1612yes—
50C22×Dic13—22no—
51C22×Dic13C22⋊C412yes—
52C22×Dic13C2×D412yes—
53C2×#1057—44no—
54C42×C13—42no—
55C42×C13—41no—
56C42×C13—41no—
57C22⋊Dic13—22no—
58C22⋊Dic13—41no—
59C22⋊Dic13—41no—
60C22⋊Dic13C2×C814yes—
61C4⋊Dic13—24no—
62C4⋊Dic13—42no—
63#6101—44no—
64#6101—44no—
65C4×Dic13—24no—
66C4×Dic13—22no—
67C4×Dic13—22no—
68#2296—131no—
69#1458—132no—
70#1326—134no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13—42no—
74C23×C13C2×C22⋊C411yescharacteristic
75C23×C13C22×C811yescharacteristic
76C23×C13C2×M1611yescharacteristic
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—24no—
84C2×C4×C13—42no—
85C2×C4×C13—44no—
86C2×C4×C13—42no—
87C2×C4×C13—44no—
88C2×C4×C13C22⋊C812yes—
89C2×C4×C13C22⋊C812yes—
90C2×C4×C13#9911yescharacteristic
91C2×C4×C13#9911yescharacteristic
92C2×C4×C13#10112yes—
93C2×Dic13—24no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100#1057—84no—
101C2×#117—131no—
102C2×#117—131no—
103C22×C42#26111yescharacteristic
104#431—262no—
105#389—262no—
106#385—132no—
107#385—132no—
108C4×C4⋊C4—262no—
109#324—262no—
110#323—134no—
111C22×C13—22no—
112C22×C13—21no—
113C22×C13—21no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13C2×C22⋊C811yescharacteristic
119C22×C13C2×#9911yescharacteristic
120C22×C13C2×#10111yescharacteristic
121C4×C13—22no—
122C4×C13—44no—
123C4×C13#32412yes—
124C4×C13#32412yes—
125Dic13—44no—
126Dic13—42no—
127Dic13—42no—
128C23×C4C2×#26112yes—
129C23×C4C2×#26111yescharacteristic
130#117—134no—
131#117—262no—
132#117—521no—
133#117—521no—
134C2×C4⋊C4—132no—
135C2×C4⋊C4—261no—
136C2×C4⋊C4—262no—
137C2×C4⋊C4—262no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—131no—
140C2×C22⋊C4—131no—
141C2×C42—21no—
142C2×C42—21no—
143C2×C42—41no—
144C2×C42—41no—
145C2×C42—132no—
146C2×C42—261no—
147C4⋊C8—522no—
148C22⋊C8—264no—
149C4×C8—522no—
150#95—262no—
151#95—262no—
152C2×C13—21no—
153C2×C13—21no—
154C2×C13—41no—
155C2×C13—41no—
156C2×C13C2×#32411yescharacteristic
157C2×C13#212012yes—
158C24C22×#26111yescharacteristic
159C22×C4—22no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—22no—
163C22×C4—44no—
164C22×C4—42no—
165C22×C4—132no—
166C22×C4—132no—
167C22×C4—262no—
168C22×C4D13⋊C812yes—
169C22×C4#611812yes—
170C22×C4C22⋊#26111yescharacteristic
171C22×C4C22⋊#26111yescharacteristic
172C2×C8—524no—
173C4⋊C4—264no—
174C4⋊C4—522no—
175C4⋊C4—524no—
176C4⋊C4—524no—
177C22⋊C4—134no—
178C22⋊C4—262no—
179C22⋊C4—521no—
180C22⋊C4—521no—
181C42—42no—
182C42—41no—
183C42—41no—
184C42—264no—
185C42—262no—
186C42—262no—
187C13#1145211yescharacteristic, complemented, Sylow
188C23—21no—
189C23—21no—
190C23—42no—
191C23C2×D13⋊C811yescharacteristic
192C23C2×#611811yescharacteristic
193C23C2×C22⋊#26111yescharacteristic
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—42no—
202C2×C4—44no—
203C2×C4—42no—
204C2×C4—44no—
205C2×C4—264no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—522no—
209C2×C4—522no—
210C2×C4—522no—
211C2×C4—522no—
212C2×C4#8811112yes—
213C2×C4#8811112yes—
214C2×C4#8811312yes—
215C2×C4#8811911yescharacteristic
216C2×C4#8811911yescharacteristic
217C8—1044no—
218C22—22no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22C2×#8811111yescharacteristic
226C22C2×#8811311yescharacteristic
227C22C2×#8811911yescharacteristic
228C4—22no—
229C4—44no—
230C4—524no—
231C4—522no—
232C4—522no—
233C4#1171828612yes—
234C4#1171828612yes—
235C2—21no—
236C2—21no—
237C2—41no—
238C2—41no—
239C2C2×#1171828611yescharacteristic
240C2#1313108712yes—
subgroupG/H
centerC2×C4#88119
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC22×C42×C13C4
socleC22×C13C2×#99
prime radicalC24×C13C22×C4
cosocleC2×C22⋊Dic13C23
hypercenterC22×C42#261
hypocenterC13#11452
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
26. #88180C8semidirect
187. C13#11452semidirect

Maximal subgroups

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

subgroupindex
#131300672
#131297812
#131173192
#1145213