Finite Group Databasebeta

← #15760748

Subgroups — #15760748

Order 3328.

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

normal subgroups only

This group has 614 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#13119110C211yesmaximal, characteristic
2#13114936C212yesmaximal, complemented
3#13113163C211yesmaximal, characteristic
4#13112689C212yesmaximal, complemented
5C13×#2312C211yesmaximal, characteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C2×#88180C2211yescharacteristic
8C13×#388—24no—
9C13×#380—21no—
10C13×#379—21no—
11C4×C13×C22⋊C4C2212yes—
12#11718908—21no—
13#11718872C2211yescharacteristic
14#11718871—21no—
15#11718868C2212yes—
16#11718614C412yescomplemented
17#11718610C412yescomplemented
18#11718605—22no—
19#11718117—22no—
20#11718115—24no—
21C25×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C2×C13×C4⋊C4—22no—
25C2×C13×C22⋊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⋊C4C2×C412yes—
31C2×C13×C22⋊C4D412yes—
32C2×C42×C13D414yes—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—22no—
37#88180—22no—
38#88180—22no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—22no—
42C2×C4×Dic13—21no—
43C2×#6099—22no—
44C13×#95—22no—
45C13×#95—22no—
46#88071—22no—
47#88071—21no—
48#88071C2×C412yes—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9481—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—
72C13×C4⋊C4—82no—
73C13×C22⋊C4—24no—
74C13×C22⋊C4—24no—
75C13×C22⋊C4—44no—
76C13×C22⋊C4—82no—
77C13×C22⋊C4—82no—
78C42×C13—44no—
79C22⋊Dic13—42no—
80C22⋊Dic13—44no—
81C22⋊Dic13—41no—
82C22⋊Dic13—41no—
83C22⋊Dic13—82no—
84C4⋊Dic13—22no—
85C4⋊Dic13—22no—
86#6101—82no—
87C4×Dic13—42no—
88#6099—44no—
89C2×#1055—42no—
90#2482—131no—
91#2312D1311yescharacteristic
92#1826—132no—
93#1462—131no—
94#1284—132no—
95C23×C13—22no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—41no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—81no—
108C23×C13—81no—
109C23×C13—88no—
110C23×C13C2×C22⋊C411yescharacteristic
111C23×C13#12011yescharacteristic
112C23×C13#12311yescharacteristic
113C2×C4×C13—24no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—44no—
121C2×C4×C13—44no—
122C2×C4×C13—44no—
123C2×C4×C13—81no—
124C2×C4×C13C4×D412yes—
125C2×C4×C13#12112yes—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133#1055—82no—
134C2×#117—131no—
135C22×C22⋊C4C2×D1311yescharacteristic
136#407—132no—
137#399—132no—
138#397—132no—
139#388—24no—
140#388—262no—
141#385—261no—
142#381—131no—
143#380—21no—
144#379—21no—
145#379—261no—
146C4×C22⋊C4C2×D1312yes—
147#339—264no—
148#323—262no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—44no—
157C22×C13—44no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—82no—
162C22×C13—84no—
163C22×C13—84no—
164C22×C13#38611yescharacteristic
165C22×C13#42112yes—
166C22×C13#45812yes—
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—42no—
170C4×C13—84no—
171Dic13—82no—
172Dic13—81no—
173Dic13—81no—
174C25C22⋊D1311yescharacteristic
175C23×C4C22⋊D1311yescharacteristic
176C23×C4C22×D1311yescharacteristic
177C2×M16—262no—
178#117—262no—
179#117—262no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—262no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—262no—
190C2×C22⋊C4—261no—
191C2×C22⋊C4—261no—
192C2×C22⋊C4—262no—
193C2×C22⋊C4C4×D1312yes—
194C2×C22⋊C4D5212yes—
195C2×C42—261no—
196C2×C42C22⋊D1314yes—
197C22⋊C8—262no—
198C22⋊C8—262no—
199#95—22no—
200#95—22no—
201#95—132no—
202#95—262no—
203#95—261no—
204C2×C13—22no—
205C2×C13—22no—
206C2×C13—41no—
207C2×C13—82no—
208C2×C13#189011yescharacteristic
209C2×C13#189711yescharacteristic
210C2×C13#191111yescharacteristic
211C24—21no—
212C24—21no—
213C24—42no—
214C24—42no—
215C24—81no—
216C24#610312yes—
217C24C2×C22⋊D1311yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—24no—
221C22×C4—42no—
222C22×C4—81no—
223C22×C4—262no—
224C22×C4—261no—
225C22×C4—261no—
226C22×C4#610312yes—
227C22×C4C2×C4×D1311yescharacteristic
228C22×C4C2×D5211yescharacteristic
229C22×C4#612712yes—
230C22×C4C2×C22⋊D1312yes—
231M16—524no—
232C2×C8—522no—
233C4⋊C4—82no—
234C4⋊C4—262no—
235C4⋊C4—262no—
236C4⋊C4—1042no—
237C22⋊C4—24no—
238C22⋊C4—24no—
239C22⋊C4—44no—
240C22⋊C4—82no—
241C22⋊C4—82no—
242C22⋊C4—522no—
243C22⋊C4—524no—
244C22⋊C4—521no—
245C22⋊C4—521no—
246C22⋊C4—1042no—
247C42—44no—
248C42—522no—
249C13#948111yescharacteristic, complemented, Sylow
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—41no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—81no—
263C23—81no—
264C23—88no—
265C23C2×#610311yescharacteristic
266C23#8818311yescharacteristic
267C23#8820711yescharacteristic
268C2×C4—24no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—81no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4—522no—
282C2×C4—522no—
283C2×C4—522no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4C4×C22⋊D1312yes—
287C2×C4#8818412yes—
288C8—1042no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—44no—
297C22—44no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—82no—
302C22—84no—
303C22—84no—
304C22#1171866612yes—
305C22#1171887411yescharacteristic
306C22#1171890412yes—
307C4—22no—
308C4—22no—
309C4—42no—
310C4—84no—
311C4—1042no—
312C4—1041no—
313C4—1041no—
314C2—22no—
315C2—22no—
316C2—41no—
317C2—82no—
318C2#1311524911yescharacteristic
319C2#1311528411yescharacteristic
320C2#1311536811yescharacteristic
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#9481
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. #13114936C2semidirect
4. #13112689C2semidirect
16. #11718614C4semidirect
17. #11718610C4semidirect
249. C13#9481semidirect

Maximal subgroups

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

subgroupindex
#131191102
#131149362
#131131632
#131126892
C13×#23122
#948113