Finite Group Databasebeta

← #15760634

Subgroups — #15760634

Order 3328.

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

normal subgroups only

This group has 536 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#13123921C211yesmaximal, characteristic, complemented
2#13113550C212yesmaximal
3#13113180C211yesmaximal, characteristic, complemented
4#13112692C212yesmaximal, complemented
5C13×#2548C211yesmaximal, characteristic
6C2×C13×#127C2211yescharacteristic
7C2×C13×#124C412yes—
8C2×C4×Q8×C13C2211yescharacteristic
9C13×#394—21no—
10C13×#394—21no—
11C13×#390—21no—
12C13×#390—21no—
13C13×#390C412yes—
14C4×C13×C4⋊C4C2211yescharacteristic
15#11718685—24no—
16#11718587—21no—
17#11718587C2212yes—
18#11718587C2212yes—
19#11718586—21no—
20#11718136—24no—
21#11718120—21no—
22#11718120—21no—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13—21no—
26C22×D4×C13C2×C412yes—
27C13×#127—22no—
28C13×#127—22no—
29C13×#124—44no—
30C4×Q8×C13—22no—
31C4×Q8×C13—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C42×C13C2×C412yes—
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13C2311yescharacteristic
44C13×#95—21no—
45C22⋊#1055—22no—
46C22⋊#1055—22no—
47C4⋊#1055—22no—
48C4⋊#1055—22no—
49C4⋊#1055—22no—
50C4⋊#1055D414yes—
51#88043—22no—
52#88043—22no—
53#88043—22no—
54C4×#1055—22no—
55#9458—131nomaximal, Sylow
56C24×C13—22no—
57C2×Q8×C13—22no—
58C2×Q8×C13—22no—
59C2×Q8×C13—41no—
60C2×D4×C13—24no—
61C2×D4×C13—42no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C2×D4×C13—42no—
65C2×D4×C13—41no—
66C2×D4×C13—42no—
67C2×D4×C13—41no—
68C2×D4×C13—82no—
69C22×C4×C13—22no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—42no—
81C13×C22⋊C4—44no—
82C13×C22⋊C4—44no—
83C13×C22⋊C4—82no—
84C13×C22⋊C4—82no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—42no—
90C42×C13C2×D412yes—
91C42×C13#4112yes—
92C2×#1055—24no—
93C2×#1055—42no—
94#2983—131no—
95#2548D1311yescharacteristic
96#1555—132no—
97#1467—131no—
98#1285—132no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13C2×C22⋊C411yescharacteristic
107Q8×C13—44no—
108D4×C13—82no—
109D4×C13—84no—
110D4×C13—84no—
111D4×C13—82no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13#10012yes—
129C2×C4×C13C4×D412yes—
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12112yes—
132C2×C4×C13#12311yescharacteristic
133#1055—44no—
134#1055—82no—
135C2×#127C2×D1311yescharacteristic
136C2×#124Dic1312yes—
137C2×C4×Q8C2×D1311yescharacteristic
138#446—264no—
139#432—132no—
140#432—132no—
141#432—261no—
142#431—261no—
143#394—21no—
144#394—21no—
145#390—21no—
146#390—21no—
147#390Dic1312yes—
148C4×C4⋊C4C2×D1311yescharacteristic
149#331—264no—
150#324—261no—
151#324—261no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—82no—
155C22×C13—82no—
156C22×C13—82no—
157C22×C13—82no—
158C22×C13—82no—
159C22×C13—82no—
160C22×C13—82no—
161C22×C13#38611yescharacteristic
162C22×C13C2×#10011yescharacteristic
163C22×C13#41311yescharacteristic
164C4×C13—21no—
165C4×C13—22no—
166C4×C13—22no—
167C4×C13—22no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—82no—
172C4×C13#45412yes—
173C22×Q8C2×Dic1311yescharacteristic
174C22×D4—21no—
175C22×D4—21no—
176C22×D4C2×Dic1312yes—
177#127—22no—
178#127—22no—
179#124—44no—
180C4×Q8—22no—
181C4×Q8—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×Dic1311yescharacteristic
184C2×C4⋊C4C22⋊D1311yescharacteristic
185C2×C4⋊C4C22⋊D1311yescharacteristic
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C42C2×Dic1312yes—
191C2×C42C22⋊D1311yescharacteristic
192C2×C42C22⋊D1311yescharacteristic
193C2×C42C22×D1311yescharacteristic
194C4⋊C8—134no—
195C4⋊C8—262no—
196C4⋊C8—262no—
197C4⋊C8—262no—
198C22⋊C8—262no—
199C22⋊C8—262no—
200#97—262no—
201#97—262no—
202#97—262no—
203C4×C8—262no—
204#95—21no—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13—162no—
208C2×C13#188811yescharacteristic
209C2×C13#190011yescharacteristic
210C2×C13#191011yescharacteristic
211C24—22no—
212C2×Q8—22no—
213C2×Q8—22no—
214C2×Q8—41no—
215C2×D4—24no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—42no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—42no—
223C2×D4—82no—
224C22×C4—22no—
225C22×C4C22⋊Dic1311yescharacteristic
226C22×C4C22⋊Dic1311yescharacteristic
227C22×C4C22⋊Dic1311yescharacteristic
228C22×C4C22⋊Dic1311yescharacteristic
229C22×C4C22×Dic1311yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232C2×C8—264no—
233C2×C8—522no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—42no—
238C22⋊C4—44no—
239C22⋊C4—44no—
240C22⋊C4—82no—
241C22⋊C4—82no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—42no—
247C42D4×D1312yes—
248C42#612912yes—
249C13#945811yescharacteristic, complemented, Sylow
250C23—42no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23C2×C22⋊Dic1311yescharacteristic
258Q8—44no—
259D4—84no—
260D4—82no—
261D4—84no—
262D4—82no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4#8807312yes—
280C2×C4D4×Dic1312yes—
281C2×C4#8818911yescharacteristic
282C2×C4#8819111yescharacteristic
283C2×C4#8819312yes—
284C8—524no—
285C8—1042no—
286C22—21no—
287C22—21no—
288C22—82no—
289C22—82no—
290C22—82no—
291C22—82no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22C2×#8807311yescharacteristic
296C22#1171888111yescharacteristic
297C22#1171889811yescharacteristic
298C4—21no—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—82no—
306C4#1171872312yes—
307C2—21no—
308C2—21no—
309C2—162no—
310C2#1311524011yescharacteristic
311C2#1311530011yescharacteristic
312C2#1311536411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2548C2
socleC22×C13#386
prime radicalC2×C13×#127C22
cosocleC2×C42×C13C23
hypercenter#2548D13
hypocenterC13#9458
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2548

Complements

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

NH ≅ G/Ntype
1. #13123921C2semidirect
3. #13113180C2semidirect
4. #13112692C2semidirect
249. C13#9458semidirect

Maximal subgroups

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

subgroupindex
#131239212
#131135502
#131131802
#131126922
C13×#25482
#945813