Finite Group Databasebeta

← #15760889

Subgroups — #15760889

Order 3328.

524 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 111 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#13123865C211yesmaximal, characteristic
2#13114916C212yesmaximal, complemented
3#13113174C211yesmaximal, characteristic
4#13112742C212yesmaximal, complemented
5C13×#2487C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#400—21no—
9C13×#399—21no—
10C13×#389—21no—
11C13×#386C412yes—
12C13×#385C412yes—
13C13×#380—21no—
14C13×#380C2211yescharacteristic
15#11718868C2212yes—
16#11718868C2212yes—
17C2×C22⋊#1055—21no—
18#11718672—24no—
19#11718587—21no—
20#11718122—24no—
21#11718120—21no—
22#11718117—21no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C412yes—
25C23×C4×C13D411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4C2×C412yes—
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×#6099—22no—
42C2×#6099D414yes—
43C22×#1055—22no—
44C13×#95—22no—
45C13×#95—22no—
46C13×#95—21no—
47C22⋊#1055—22no—
48C22⋊#1055—22no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52C4⋊#1055—22no—
53#88043—22no—
54#9509—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C24×C13C22×C411yescharacteristic
57C2×D4×C13—22no—
58C2×D4×C13—22no—
59C2×D4×C13—41no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—24no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13—82no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C2×D412yes—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13#4112yes—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—82no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—82no—
85C42×C13—21no—
86C42×C13—21no—
87#6099—44no—
88#6099—44no—
89C2×#1055—24no—
90C2×#1055—42no—
91C2×#1055—82no—
92#2973—131no—
93#2487D1311yescharacteristic
94#1821—132no—
95#1465—131no—
96#1305—132no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13#10112yes—
106C23×C13C2×C22⋊C411yescharacteristic
107C23×C13C4×D412yes—
108D4×C13—44no—
109C2×C4×C13—24no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—81no—
128C2×C4×C13—84no—
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12112yes—
131C2×C4×C13#12311yescharacteristic
132#1055—44no—
133#1055—82no—
134C2×C4×D4C2×D1311yescharacteristic
135C22×C4⋊C4C2×D1311yescharacteristic
136#435—264no—
137#432—261no—
138#407—132no—
139#407—132no—
140C2×C22⋊C8—261no—
141#400—21no—
142#399—21no—
143#389—21no—
144#386Dic1312yes—
145#385Dic1312yes—
146#380—21no—
147#380C2×D1311yescharacteristic
148#343—264no—
149#324—261no—
150#323—261no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—81no—
163C22×C13#38611yescharacteristic
164C22×C13C2×#10111yescharacteristic
165C22×C13#41311yescharacteristic
166C4×C13—22no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—82no—
172C4×C13—82no—
173C4×C13#45812yes—
174C22×D4C2×Dic1311yescharacteristic
175C23×C4C2×Dic1312yes—
176C23×C4C22⋊D1311yescharacteristic
177C23×C4C22×D1311yescharacteristic
178C2×M16—134no—
179C2×M16—262no—
180C22×C8—262no—
181C4×D4—22no—
182C4×D4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4C22⋊D1311yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4C2×Dic1311yescharacteristic
192C2×C22⋊C4C2×Dic1312yes—
193C2×C22⋊C4C22⋊D1311yescharacteristic
194C2×C42C22⋊D1311yescharacteristic
195C4⋊C8—262no—
196C22⋊C8—262no—
197C22⋊C8—262no—
198C22⋊C8—262no—
199C22⋊C8—262no—
200C22⋊C8—262no—
201#97—262no—
202#95—22no—
203#95—22no—
204#95—21no—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13—42no—
208C2×C13—42no—
209C2×C13#189011yescharacteristic
210C2×C13#190111yescharacteristic
211C2×C13#191411yescharacteristic
212C24C22⋊Dic1311yescharacteristic
213C24C22×Dic1311yescharacteristic
214C2×D4—22no—
215C2×D4—22no—
216C2×D4—41no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—82no—
225C22×C4C22⋊Dic1311yescharacteristic
226C22×C4C22⋊Dic1311yescharacteristic
227C22×C4C22⋊Dic1311yescharacteristic
228C22×C4D4×D1312yes—
229C22×C4#612912yes—
230C22×C4C2×C22⋊D1311yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232M16—524no—
233M16—524no—
234C2×C8—264no—
235C2×C8—522no—
236C2×C8—1042no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—82no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—42no—
246C22⋊C4—82no—
247C42—21no—
248C42—21no—
249C13#950911yescharacteristic, complemented, Sylow
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23#8807612yes—
259C23D4×Dic1312yes—
260C23C2×C22⋊Dic1311yescharacteristic
261D4—44no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—84no—
282C2×C4#8818911yescharacteristic
283C2×C4#8819111yescharacteristic
284C2×C4#8819312yes—
285C8—524no—
286C8—1042no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—42no—
294C22—42no—
295C22—42no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22#1171888111yescharacteristic
300C22C2×#8807611yescharacteristic
301C22#1171889811yescharacteristic
302C4—22no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—82no—
308C4—82no—
309C4#1171871412yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—42no—
314C2#1311525011yescharacteristic
315C2#1311530511yescharacteristic
316C2#1311538411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2487C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC23×C4×C13C23
hypercenter#2487D13
hypocenterC13#9509
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2487

Complements

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

NH ≅ G/Ntype
2. #13114916C2semidirect
4. #13112742C2semidirect
249. C13#9509semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131149162
#131131742
#131127422
C13×#24872
#950913