Finite Group Databasebeta

← #15760374

Subgroups — #15760374

Order 3328.

606 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 103 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#13119994C211yesmaximal, characteristic
2#13113355C212yesmaximal, complemented
3#13113163C211yesmaximal, characteristic
4#13112722C212yesmaximal, complemented
5C13×#2312C211yesmaximal, characteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C2×#88178C2211yescharacteristic
8C13×#388—24no—
9C13×#380—21no—
10C13×#379—21no—
11C4×C13×C22⋊C4C2212yes—
12#11718908—21no—
13#11718872—21no—
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2212yes—
16#11718614C412yescomplemented
17#11718608C412yescomplemented
18#11718606—22no—
19#11718117—22no—
20#11718044—24no—
21C25×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C2×C13×C4⋊C4—22no—
26C2×C13×C22⋊C4—22no—
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4C2×C412yes—
32C2×C13×C22⋊C4D412yes—
33C2×C42×C13—22no—
34C2×C22⋊Dic13—22no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—22no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39#88178—22no—
40#88178—22no—
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C2×#6099—22no—
44C13×#95—22no—
45C13×#95D414yes—
46#88071—22no—
47#88071—22no—
48#88071C2×C412yes—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9411—131nomaximal, Sylow
52C24×C13—21no—
53C24×C13—21no—
54C24×C13—42no—
55C24×C13—42no—
56C24×C13—81no—
57C24×C13C22⋊C412yes—
58C24×C13C2×D411yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—24no—
62C22×C4×C13—42no—
63C22×C4×C13—81no—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D412yes—
68C22×C4×C13#4112yes—
69C22×Dic13—22no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C2×Dic26—22no—
73C2×Dic26—81no—
74C13×C4⋊C4—82no—
75C13×C22⋊C4—24no—
76C13×C22⋊C4—24no—
77C13×C22⋊C4—44no—
78C13×C22⋊C4—82no—
79C13×C22⋊C4—82no—
80C42×C13—82no—
81C22⋊Dic13—42no—
82C22⋊Dic13—44no—
83C22⋊Dic13—41no—
84C22⋊Dic13—41no—
85C22⋊Dic13—82no—
86C4⋊Dic13—22no—
87#6101—42no—
88C4×Dic13—81no—
89#6099—82no—
90C2×#1055—42no—
91#2561—131no—
92#2312D1311yescharacteristic
93#1508—132no—
94#1462—131no—
95#1297—132no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—22no—
101C23×C13—41no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13—81no—
109C23×C13—81no—
110C23×C13—88no—
111C23×C13C2×C22⋊C411yescharacteristic
112C23×C13#12011yescharacteristic
113C23×C13#12311yescharacteristic
114C2×C4×C13—22no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—44no—
122C2×C4×C13—44no—
123C2×C4×C13—44no—
124C2×C4×C13—81no—
125C2×C4×C13C4×D412yes—
126C2×C4×C13#12112yes—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134Dic26—82no—
135#1055—82no—
136C2×C22⋊Q8—131no—
137C22×C22⋊C4C2×D1311yescharacteristic
138#407—132no—
139#397—132no—
140#393—132no—
141#388—24no—
142#388—262no—
143#381—261no—
144#380—21no—
145#379—21no—
146#379—261no—
147C4×C22⋊C4—131no—
148C4×C22⋊C4C2×D1312yes—
149#328—264no—
150#323—262no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—44no—
159C22×C13—44no—
160C22×C13—42no—
161C22×C13—42no—
162C22×C13—42no—
163C22×C13—82no—
164C22×C13—84no—
165C22×C13—84no—
166C22×C13#38611yescharacteristic
167C22×C13#42112yes—
168C22×C13#45512yes—
169C4×C13—22no—
170C4×C13—22no—
171C4×C13—42no—
172C4×C13—84no—
173Dic13—82no—
174Dic13—81no—
175Dic13—81no—
176C25C22⋊D1311yescharacteristic
177C22×Q8—131no—
178C23×C4C22⋊D1311yescharacteristic
179C23×C4C22×D1311yescharacteristic
180C2×M16—262no—
181C22⋊Q8—262no—
182C22⋊Q8—262no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—261no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—262no—
192C2×C22⋊C4—261no—
193C2×C22⋊C4—261no—
194C2×C22⋊C4—262no—
195C2×C22⋊C4C4×D1312yes—
196C2×C22⋊C4D5212yes—
197C2×C42—22no—
198C2×C42—261no—
199C22⋊C8—262no—
200C22⋊C8—262no—
201#95—22no—
202#95—132no—
203#95—262no—
204#95—262no—
205#95C22⋊D1314yes—
206C2×C13—22no—
207C2×C13—22no—
208C2×C13—41no—
209C2×C13—82no—
210C2×C13#188511yescharacteristic
211C2×C13#189711yescharacteristic
212C2×C13#191311yescharacteristic
213C24—21no—
214C24—21no—
215C24—42no—
216C24—42no—
217C24—81no—
218C24#610312yes—
219C24C2×C22⋊D1311yescharacteristic
220C2×Q8—262no—
221C2×Q8—1041no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—24no—
225C22×C4—42no—
226C22×C4—81no—
227C22×C4—262no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4#610312yes—
231C22×C4C2×C4×D1311yescharacteristic
232C22×C4C2×D5211yescharacteristic
233C22×C4#612712yes—
234C22×C4C2×C22⋊D1312yes—
235M16—1042no—
236C2×C8—522no—
237C4⋊C4—82no—
238C4⋊C4—262no—
239C4⋊C4—522no—
240C22⋊C4—24no—
241C22⋊C4—24no—
242C22⋊C4—44no—
243C22⋊C4—82no—
244C22⋊C4—82no—
245C22⋊C4—522no—
246C22⋊C4—524no—
247C22⋊C4—521no—
248C22⋊C4—521no—
249C22⋊C4—1042no—
250C42—82no—
251C42—1041no—
252C13#941111yescharacteristic, complemented, Sylow
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—41no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—81no—
266C23—81no—
267C23—88no—
268C23C2×#610311yescharacteristic
269C23#8818311yescharacteristic
270C23#8820711yescharacteristic
271Q8—1042no—
272C2×C4—22no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—81no—
283C2×C4—522no—
284C2×C4—522no—
285C2×C4—522no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4C4×C22⋊D1312yes—
291C2×C4#8818412yes—
292C8—1042no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—44no—
301C22—44no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—82no—
306C22—84no—
307C22—84no—
308C22#1171866612yes—
309C22#1171887411yescharacteristic
310C22#1171890312yes—
311C4—22no—
312C4—22no—
313C4—42no—
314C4—84no—
315C4—1042no—
316C4—1041no—
317C4—1041no—
318C2—22no—
319C2—22no—
320C2—41no—
321C2—82no—
322C2#1311522411yescharacteristic
323C2#1311528411yescharacteristic
324C2#1311537811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2312C2
socleC22×C13#386
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenter#2312D13
hypocenterC13#9411
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
2. #13113355C2semidirect
4. #13112722C2semidirect
16. #11718614C4semidirect
17. #11718608C4semidirect
252. C13#9411semidirect

Maximal subgroups

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

subgroupindex
#131199942
#131133552
#131131632
#131127222
C13×#23122
#941113