Finite Group Databasebeta

← #15760598

Subgroups — #15760598

Order 3328.

518 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 107 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#13119828C211yesmaximal, characteristic
2#13113561C212yesmaximal, complemented
3#13113177C211yesmaximal, characteristic
4#13112693C212yesmaximal, complemented
5C13×#2973C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88190C412yes—
8C2×#88123C2211yescharacteristic
9C13×#435—24no—
10C13×#432C2212yes—
11C13×#407—21no—
12C2×C13×C22⋊C8—21no—
13#11718873—21no—
14#11718873—21no—
15#11718635C412yes—
16#11718614—21no—
17#11718614—21no—
18C4×C4⋊Dic13C2211yescharacteristic
19#11718587C2212yes—
20#11718117—21no—
21#11718117—21no—
22#11718073—24no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C412yes—
27C2×C13×M16—22no—
28C22×C8×C13—22no—
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×C22⋊Dic13—22no—
36C2×C22⋊Dic13—22no—
37#88190—44no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4×Dic13C2×C412yes—
42#88123—22no—
43#88123—22no—
44C13×C4⋊C8D414yes—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×#97—22no—
49#88071—22no—
50#88071—22no—
51#88071—21no—
52C22⋊#1055—22no—
53C4⋊#1055—22no—
54#88043—22no—
55#9451—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C24×C13C22⋊C411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—41no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—22no—
73C22×Dic13—22no—
74C2×Dic26—24no—
75C2×Dic26—42no—
76C2×Dic26—42no—
77C13×M16—82no—
78C2×C8×C13—24no—
79C2×C8×C13—82no—
80C13×C4⋊C4—22no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—22no—
83C42×C13C2×D412yes—
84C42×C13#4112yes—
85C22⋊Dic13—44no—
86C22⋊Dic13—44no—
87C4⋊Dic13—42no—
88C4⋊Dic13—41no—
89C4⋊Dic13—42no—
90C4⋊Dic13—41no—
91C4×Dic13—42no—
92C2×#1055—42no—
93#2973D1311yescharacteristic
94#2547—131no—
95#1558—132no—
96#1466—131no—
97#1285—132no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13#10012yes—
108C23×C13C2×C22⋊C411yescharacteristic
109D4×C13—44no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—41no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—81no—
121C2×C4×C13—81no—
122C2×C4×C13C4×D412yes—
123C2×C4×C13#12011yescharacteristic
124C2×C4×C13#12112yes—
125C2×C4×C13#12311yescharacteristic
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132Dic26—84no—
133C8×C13—44no—
134#1055—82no—
135C2×C4⋊Q8—131no—
136C2×#124—132no—
137C2×C4×D4C2×D1311yescharacteristic
138#435—24no—
139#432—132no—
140#432C2×D1312yes—
141#407—21no—
142C2×C22⋊C8—21no—
143#397—261no—
144#397—261no—
145#391—132no—
146#380—261no—
147#380—261no—
148C4×C4⋊C4—131no—
149#333—264no—
150#323—261no—
151#323—261no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—22no—
155C22×C13—42no—
156C22×C13—42no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13#38611yescharacteristic
165C22×C13C2×#10011yescharacteristic
166C22×C13#41311yescharacteristic
167C4×C13—21no—
168C4×C13—22no—
169C4×C13—22no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13#45512yes—
173Dic13—82no—
174Dic13—82no—
175C22×Q8—132no—
176C22×D4C4×D1311yescharacteristic
177C23×C4C22⋊D1311yescharacteristic
178C23×C4C22⋊D1311yescharacteristic
179C2×M16—22no—
180C22×C8—22no—
181C4⋊Q8—262no—
182C4⋊Q8—262no—
183#124—524no—
184C4×D4—22no—
185C4×D4—22no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4C4×D1311yescharacteristic
190C2×C22⋊C4—262no—
191C2×C22⋊C4—262no—
192C2×C22⋊C4D5211yescharacteristic
193C2×C22⋊C4D5211yescharacteristic
194C2×C42—132no—
195C2×C42C22×D1311yescharacteristic
196C4⋊C8—262no—
197C4⋊C8C22⋊D1314yes—
198C22⋊C8—22no—
199C22⋊C8—22no—
200C22⋊C8—22no—
201C22⋊C8—262no—
202#97—22no—
203#97—262no—
204#95—262no—
205#95—262no—
206#95—261no—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—42no—
210C2×C13—81no—
211C2×C13#188511yescharacteristic
212C2×C13#190011yescharacteristic
213C2×C13#190911yescharacteristic
214C24#610311yescharacteristic
215C24#610311yescharacteristic
216C2×Q8—264no—
217C2×Q8—522no—
218C2×Q8—522no—
219C2×D4—22no—
220C2×D4—22no—
221C2×D4—41no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—262no—
229C22×C4—262no—
230C22×C4#610311yescharacteristic
231C22×C4#610311yescharacteristic
232C22×C4C2×C4×D1311yescharacteristic
233C22×C4C2×D5211yescharacteristic
234C22×C4C2×C22⋊D1311yescharacteristic
235M16—82no—
236C2×C8—24no—
237C2×C8—82no—
238C2×C8—522no—
239C4⋊C4—22no—
240C4⋊C4—522no—
241C4⋊C4—521no—
242C4⋊C4—522no—
243C4⋊C4—521no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—524no—
247C22⋊C4—524no—
248C42—522no—
249C42#612712yes—
250C42C2×C22⋊D1312yes—
251C13#945111yescharacteristic, complemented, Sylow
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23#8806312yes—
262C23C2×#610311yescharacteristic
263Q8—1044no—
264D4—44no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—522no—
278C2×C4—522no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4—522no—
282C2×C4—522no—
283C2×C4C4×C22⋊D1312yes—
284C2×C4#8818311yescharacteristic
285C2×C4#8818412yes—
286C2×C4#8820711yescharacteristic
287C8—44no—
288C8—1042no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22—81no—
301C22C2×#8806311yescharacteristic
302C22#1171879311yescharacteristic
303C22#1171887411yescharacteristic
304C4—21no—
305C4—22no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—1042no—
310C4—1042no—
311C4#1171890312yes—
312C2—21no—
313C2—21no—
314C2—42no—
315C2—81no—
316C2#1311522411yescharacteristic
317C2#1311529911yescharacteristic
318C2#1311535811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2973C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2973D13
hypocenterC13#9451
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13113561C2semidirect
4. #13112693C2semidirect
251. C13#9451semidirect

Maximal subgroups

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

subgroupindex
#131198282
#131135612
#131131772
#131126932
C13×#29732
#945113