Finite Group Databasebeta

← #16776919

Subgroups — #16776919

Order 3328.

476 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 54 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#13129756C212yesmaximal, complemented
2#13114746C211yesmaximal, characteristic
3C24×C4×C13C411yescharacteristic
4C2×C22⋊#1055—22no—
5C2×C22⋊#1055C411yescharacteristic
6C2×C22⋊#1055C2211yescharacteristic
7C22⋊#6092—22no—
8C25×C13C811yescharacteristic
9C23×C4×C13—21no—
10C23×C4×C13—21no—
11C23×C4×C13—44no—
12C23×C4×C13—41no—
13C23×C4×C13—41no—
14C23×C4×C13C811yescharacteristic
15C23×C4×C13C2×C411yescharacteristic
16C22×#1055—21no—
17C22×#1055D412yes—
18C2×#6092—42no—
19C22⋊#1055—41no—
20C22⋊#1055—44no—
21C22⋊#1055—41no—
22#7054—131nomaximal, Sylow
23C24×C13—21no—
24C24×C13—21no—
25C24×C13—42no—
26C24×C13—41no—
27C24×C13—42no—
28C24×C13—41no—
29C24×C13C1612yescomplemented
30C24×C13C2×C811yescharacteristic
31C22×C4×C13—24no—
32C22×C4×C13—21no—
33C22×C4×C13—21no—
34C22×C4×C13—21no—
35C22×C4×C13—42no—
36C22×C4×C13—42no—
37C22×C4×C13—42no—
38C22×C4×C13—42no—
39C22×C4×C13—42no—
40C22×C4×C13—42no—
41C22×C4×C13—44no—
42C22×C4×C13—44no—
43C22×C4×C13—44no—
44C22×C4×C13—41no—
45C22×C4×C13—41no—
46C22×C4×C13—41no—
47C22×C4×C13—44no—
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13M1611yescharacteristic
50C2×#1055—22no—
51C2×#1055—42no—
52C2×#1055—42no—
53C2×#1055—41no—
54#6092—82no—
55#1779—131no—
56#1314—132no—
57C23×C13—22no—
58C23×C13—22no—
59C23×C13—21no—
60C23×C13—22no—
61C23×C13—21no—
62C23×C13—41no—
63C23×C13—41no—
64C23×C13—44no—
65C23×C13—42no—
66C23×C13—41no—
67C23×C13—44no—
68C23×C13—42no—
69C23×C13—41no—
70C23×C13—42no—
71C23×C13—48no—
72C23×C13—42no—
73C23×C13—41no—
74C23×C13—41no—
75C23×C13—42no—
76C23×C13—42no—
77C23×C13C22⋊C811yescharacteristic
78C23×C13C2×C1611yescharacteristic
79C23×C13M3211yescharacteristic
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—44no—
84C2×C4×C13—42no—
85C2×C4×C13—41no—
86C2×C4×C13—48no—
87C2×C4×C13—42no—
88C2×C4×C13—41no—
89C2×C4×C13—44no—
90C2×C4×C13—42no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13#9911yescharacteristic
94C2×C4×C13#10011yescharacteristic
95#1055—42no—
96#1055—81no—
97C24×C4#26111yescharacteristic
98C2×C22⋊C8—131no—
99C2×C22⋊C8—131no—
100C2×C22⋊C8—262no—
101C22⋊C16—262no—
102C22×C13—21no—
103C22×C13—21no—
104C22×C13—24no—
105C22×C13—21no—
106C22×C13—21no—
107C22×C13—41no—
108C22×C13—41no—
109C22×C13—42no—
110C22×C13—42no—
111C22×C13—42no—
112C22×C13—42no—
113C22×C13—44no—
114C22×C13—44no—
115C22×C13—44no—
116C22×C13—44no—
117C22×C13—42no—
118C22×C13—42no—
119C22×C13—41no—
120C22×C13—42no—
121C22×C13—41no—
122C22×C13#32311yescharacteristic
123C22×C13C22⋊C1611yescharacteristic
124C22×C13#34911yescharacteristic
125C4×C13—21no—
126C4×C13—42no—
127C4×C13—41no—
128C4×C13AΣL(1,𝔽16)12yes—
129C25#105711yescharacteristic
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—44no—
133C23×C4—41no—
134C23×C4—41no—
135C23×C4#105711yescharacteristic
136C23×C4C2×#26111yescharacteristic
137C22×C8—132no—
138C22×C8—261no—
139C2×C16—522no—
140C22⋊C8—521no—
141C22⋊C8—524no—
142C22⋊C8—521no—
143C2×C13—21no—
144C2×C13—21no—
145C2×C13—44no—
146C2×C13—41no—
147C2×C13—41no—
148C2×C13#131411yescharacteristic
149C2×C13#131611yescharacteristic
150C2×C13#132011yescharacteristic
151C24—21no—
152C24—21no—
153C24—42no—
154C24—41no—
155C24—42no—
156C24—41no—
157C24#609212yescomplemented
158C24C2×#105711yescharacteristic
159C22×C4—24no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—44no—
170C22×C4—44no—
171C22×C4—44no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—44no—
176C22×C4#612211yescharacteristic
177C22×C4C22⋊#26111yescharacteristic
178C2×C8—262no—
179C2×C8—522no—
180C2×C8—522no—
181C2×C8—521no—
182C16—1042no—
183C13#705411yescharacteristic, complemented, Sylow
184C23—22no—
185C23—22no—
186C23—22no—
187C23—21no—
188C23—21no—
189C23—41no—
190C23—44no—
191C23—42no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—44no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—48no—
201C23—42no—
202C23—41no—
203C23—41no—
204C23C2×#609211yescharacteristic
205C23#8810611yescharacteristic
206C23C22⋊#105711yescharacteristic
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—48no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—44no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4#8811911yescharacteristic
221C2×C4#8812111yescharacteristic
222C8—522no—
223C8—1041no—
224C22—21no—
225C22—21no—
226C22—24no—
227C22—21no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—42no—
235C22—44no—
236C22—44no—
237C22—44no—
238C22—44no—
239C22—42no—
240C22—42no—
241C22—41no—
242C22—42no—
243C22—41no—
244C22C22⋊#609211yescharacteristic
245C22#1171828411yescharacteristic
246C22#1171830511yescharacteristic
247C4—21no—
248C4—42no—
249C4—41no—
250C4#1171830612yes—
251C2—21no—
252C2—21no—
253C2—44no—
254C2—41no—
255C2—41no—
256C2#1312975611yescharacteristic
257C2#1312976011yescharacteristic
258C2#1312976811yescharacteristic
subgroupG/H
centerC2×C4#88119
commutatorC23×C13C2×C16
FrattiniC23×C4C2×#261
FittingC24×C4×C13C4
socleC22×C13#323
prime radicalC25×C13C8
cosocleC2×C22⋊#1055C22
hypercenterC24×C4#261
hypocenterC13#7054
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. #13129756C2semidirect
29. C24×C13C16semidirect
157. C24#6092semidirect
183. C13#7054semidirect

Maximal subgroups

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

subgroupindex
#131297562
#131147462
#705413