Finite Group Databasebeta

← #15772575

Subgroups — #15772575

Order 3328.

350 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 91 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#13113180C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic
3#13112782C212yesmaximal
4#13112780C212yesmaximal
5C13×#2565C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#398—21no—
9C13×#398—21no—
10C13×#391C411yescharacteristic
11C13×#391C411yescharacteristic
12C13×#387—21no—
13C13×#387—21no—
14C13×#384C2211yescharacteristic
15C13×#382C2211yescharacteristic
16C4×C13×C4⋊C4C411yescharacteristic
17#11718587—21no—
18#11718586—21no—
19#11718120—21no—
20#11718120—21no—
21#11718120C2212yes—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C13×#125—41no—
25C13×#125—41no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4C2311yescharacteristic
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C13×#95—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52C4⋊#1055—41no—
53C4⋊#1055—41no—
54#88043—41no—
55C4×#1055—41no—
56#11571—131nomaximal, Sylow
57C2×Q8×C13—22no—
58C2×Q8×C13—22no—
59C2×Q8×C13—41no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—22no—
89C42×C13—22no—
90C2×#1055—42no—
91C2×#1055—42no—
92#2565D1311yescharacteristic
93#1467—131no—
94#1461—131no—
95#1325—132no—
96#1324—132no—
97C23×C13C2×C22⋊C411yescharacteristic
98Q8×C13—44no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13#9911yescharacteristic
125C2×C4×C13#9911yescharacteristic
126C2×C4×C13#10112yes—
127C2×C4×C13#13112yes—
128#1055—82no—
129#1055—82no—
130C2×#125Dic1311yescharacteristic
131C2×C4×Q8C2×D1311yescharacteristic
132#432—261no—
133#431—261no—
134#398—21no—
135#398—21no—
136#391Dic1311yescharacteristic
137#391Dic1311yescharacteristic
138#387—21no—
139#387—21no—
140#384C2×D1311yescharacteristic
141#382C2×D1311yescharacteristic
142C4×C4⋊C4Dic1311yescharacteristic
143#324—132no—
144#324—132no—
145#324—261no—
146#324—261no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13#40811yescharacteristic
150C22×C13C2×#9911yescharacteristic
151C22×C13C2×#10111yescharacteristic
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—22no—
155C4×C13—22no—
156C4×C13—42no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—81no—
162C4×C13—81no—
163C4×C13—81no—
164C22×Q8C2×Dic1311yescharacteristic
165#125—41no—
166#125—41no—
167C4×Q8—41no—
168C4×Q8—41no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4C2×Dic1311yescharacteristic
175C2×C4⋊C4C2×Dic1311yescharacteristic
176C2×C4⋊C4C22⋊D1311yescharacteristic
177C2×C4⋊C4C22⋊D1311yescharacteristic
178C2×C4⋊C4C22×D1311yescharacteristic
179C2×C42C2×Dic1311yescharacteristic
180C2×C42C2×Dic1311yescharacteristic
181C2×C42C2×Dic1311yescharacteristic
182C2×C42C22⋊D1311yescharacteristic
183C2×C42C22⋊D1311yescharacteristic
184C4⋊C8—521no—
185C4⋊C8—521no—
186C22⋊C8—262no—
187C22⋊C8—262no—
188#97—521no—
189C4×C8—521no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13#147211yescharacteristic
200C2×C13#212611yescharacteristic
201C2×C13#213311yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4C22⋊Dic1311yescharacteristic
210C22×C4C22⋊Dic1311yescharacteristic
211C22×C4C22⋊Dic1311yescharacteristic
212C22×C4C22⋊Dic1311yescharacteristic
213C22×C4C22×Dic1311yescharacteristic
214C22×C4C2×C22⋊D1311yescharacteristic
215C22×C4C2×C22⋊D1311yescharacteristic
216C2×C8—522no—
217C2×C8—522no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—22no—
236C42—22no—
237C13#1157111yescharacteristic, complemented, Sylow
238C23C2×C22⋊Dic1311yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4#8807411yescharacteristic
266C2×C4#8807411yescharacteristic
267C2×C4#8807612yes—
268C2×C4#8820212yes—
269C8—1042no—
270C8—1042no—
271C22—21no—
272C22—21no—
273C22C2×#8807411yescharacteristic
274C22C2×#8807611yescharacteristic
275C22#1171889511yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—42no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—41no—
285C4—81no—
286C4—81no—
287C4—81no—
288C2—21no—
289C2—21no—
290C2#1311320011yescharacteristic
291C2#1311650111yescharacteristic
292C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2565C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2565D13
hypocenterC13#11571
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2565

Complements

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

NH ≅ G/Ntype
237. C13#11571semidirect

Maximal subgroups

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

subgroupindex
#131131802
#131131602
#131127822
#131127802
C13×#25652
#1157113