Finite Group Databasebeta

← #16786870

Subgroups — #16786870

Order 3328.

386 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 86 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#13131064C212yesmaximal, complemented
2#13129775C212yesmaximal, complemented
3#13129758C212yesmaximal, complemented
4#13123528C211yesmaximal, characteristic
5C2×C13×#131C411yescharacteristic
6#11719533C411yescharacteristic
7C22×C8×D13C2211yescharacteristic
8C2×#88098—22no—
9#11718895C2211yescharacteristic
10#11718788—22no—
11#11718787C411yescharacteristic
12#11718780C2211yescharacteristic
13C8×C22⋊D13—22no—
14#11718762C411yescharacteristic
15C22⋊#6092C2214yes—
16#11718259—22no—
17C2×C13×#41C2×C411yescharacteristic
18C22×C4×D13C2×C411yescharacteristic
19C13×#131—42no—
20C2×C13×M16—21no—
21C2×C13×M16C2×C411yescharacteristic
22C22×C8×C13—21no—
23C22×C8×C13C2×C411yescharacteristic
24#88200C812yes—
25#88192C812yes—
26#88191—21no—
27#88189—21no—
28C4×C22⋊D13—22no—
29#88180C2×C411yescharacteristic
30C2×#6099C2×C411yescharacteristic
31C22×#1055C2311yescharacteristic
32C2×C8×D13—42no—
33C2×C8×D13D412yes—
34C2×C8×D13D412yes—
35C2×#6092—24no—
36#88098—44no—
37C22⋊#1055—22no—
38#88060—22no—
39#88055—21no—
40#88054—22no—
41C8×Dic13—21no—
42#11469—131nomaximal, Sylow
43C23×D13M1611yescharacteristic
44C13×#41—41no—
45C13×#41—41no—
46C2×Q8×C13C2×C811yescharacteristic
47C2×D4×C13—21no—
48C2×D4×C13C2×C811yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13C22×C411yescharacteristic
51C2×C22⋊D13—22no—
52C22×Dic13M1611yescharacteristic
53C2×C4×D13—41no—
54C2×C4×D13—41no—
55C2×C4×D13C22⋊C412yes—
56C2×C4×D13C2×C812yes—
57C13×M16—42no—
58C13×M16—41no—
59C2×C8×C13—22no—
60C2×C8×C13—21no—
61C2×C8×C13—42no—
62C2×C8×C13C22⋊C411yescharacteristic
63C2×C8×C13C22⋊C411yescharacteristic
64C22⋊Dic13—21no—
65C22⋊Dic13—22no—
66#6103—22no—
67C4⋊Dic13C2×C812yes—
68#6101—22no—
69C4×Dic13—21no—
70#6099—41no—
71C2×#1055—21no—
72C2×#1055—41no—
73C2×#1055C2×D412yes—
74C8×D13—24no—
75C8×D13—42no—
76#6092—44no—
77#2929—131no—
78#2112—132no—
79#1323—132no—
80#1315—132no—
81C23×C13—21no—
82C23×C13C2×M1611yescharacteristic
83C22×D13—41no—
84C22×D13—42no—
85C22×D13C22⋊C812yes—
86Q8×C13—41no—
87D4×C13—41no—
88D4×C13—42no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13C2×C22⋊C411yescharacteristic
95C2×C4×C13C22×C811yescharacteristic
96C22⋊D13—44no—
97C2×Dic13—22no—
98C2×Dic13—41no—
99C2×Dic13C22⋊C812yes—
100C4×D13—22no—
101C4×D13—22no—
102C4×D13—42no—
103C8×C13—21no—
104C8×C13—41no—
105C8×C13#9912yes—
106#1055—22no—
107#1055—41no—
108C2×#131#26111yescharacteristic
109C23×C8—131no—
110#525—131no—
111C2×M32—262no—
112#435—262no—
113C8×D4—262no—
114#424—131no—
115#408—131no—
116#407—131no—
117#405—131no—
118C22⋊C16—134no—
119C22⋊C16—262no—
120C22×C13—22no—
121C22×C13—21no—
122C22×C13—42no—
123C22×C13—41no—
124C22×C13C2×C22⋊C811yescharacteristic
125C2×D13—22no—
126C2×D13—22no—
127C2×D13—22no—
128C2×D13—44no—
129C4×C13—21no—
130C4×C13—41no—
131C4×C13C2×#9911yescharacteristic
132C4×C13#41311yescharacteristic
133Dic13—22no—
134Dic13—42no—
135C2×#41C2×#26111yescharacteristic
136C23×C4—131no—
137#131—42no—
138C2×M16—21no—
139C2×M16—131no—
140C2×M16C2×#26111yescharacteristic
141C22×C8—21no—
142C22×C8—131no—
143C22×C8—132no—
144C22×C8—132no—
145C22×C8—522no—
146C22×C8C2×#26111yescharacteristic
147#123—261no—
148C22⋊Q8—132no—
149#121—132no—
150#120—261no—
151C4×D4—262no—
152#117—131no—
153M32—524no—
154C2×C16—264no—
155C4⋊C8—262no—
156C22⋊C8—262no—
157C22⋊C8—262no—
158#97—261no—
159C4×C8—261no—
160C2×C13—41no—
161C2×C13—81no—
162C2×C13#145911yescharacteristic
163C2×C13#211712yes—
164D13—42no—
165C24—131no—
166#41—41no—
167#41—41no—
168C2×Q8D13⋊C811yescharacteristic
169C2×D4—21no—
170C2×D4—262no—
171C2×D4D13⋊C811yescharacteristic
172C22×C4—21no—
173C22×C4—131no—
174C22×C4—132no—
175C22×C4—132no—
176C22×C4—521no—
177C22×C4—521no—
178C22×C4C22×#26111yescharacteristic
179M16—42no—
180M16—41no—
181M16—521no—
182C2×C8—22no—
183C2×C8—21no—
184C2×C8—42no—
185C2×C8—132no—
186C2×C8—264no—
187C2×C8—261no—
188C2×C8—522no—
189C2×C8—521no—
190C2×C8C22⋊#26111yescharacteristic
191C2×C8C22⋊#26111yescharacteristic
192C4⋊C4—132no—
193C4⋊C4—262no—
194C22⋊C4—262no—
195C22⋊C4—262no—
196C22⋊C4—261no—
197C42—261no—
198C16—524no—
199C13#1146911yescharacteristic, complemented, Sylow
200C23—21no—
201C23—132no—
202C23—521no—
203C23—522no—
204C23D13⋊M1611yescharacteristic
205Q8—41no—
206D4—41no—
207D4—42no—
208D4—524no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—132no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—522no—
219C2×C4—521no—
220C2×C4C2×D13⋊C811yescharacteristic
221C2×C4C2×C22⋊#26111yescharacteristic
222C8—21no—
223C8—41no—
224C8—262no—
225C8—521no—
226C8#8811912yes—
227C22—22no—
228C22—21no—
229C22—42no—
230C22—41no—
231C22—262no—
232C22—262no—
233C22—262no—
234C22—524no—
235C22D13⋊(C22⋊C8)11yescharacteristic
236C4—21no—
237C4—41no—
238C4—262no—
239C4—522no—
240C4#1171913211yescharacteristic
241C4C2×#8811911yescharacteristic
242C2—41no—
243C2—81no—
244C2—522no—
245C2#1313007111yescharacteristic
246C2#1313107912yes—
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#131C4
socleC22×C13C2×C22⋊C8
prime radical#11719533C4
cosocleC22×#1055C23
hypercenterC2×#131#261
hypocenterC13#11469
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #13131064C2semidirect
2. #13129775C2semidirect
3. #13129758C2semidirect
199. C13#11469semidirect

Maximal subgroups

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

subgroupindex
#131310642
#131297752
#131297582
#131235282
#1146913