Finite Group Databasebeta

← #15772490

Subgroups — #15772490

Order 3328.

366 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 87 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#13113170C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic
3#13112782C212yesmaximal, complemented
4#13112770C212yesmaximal, complemented
5C13×#2499C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C13×#397—21no—
9C13×#397—21no—
10C13×#391C411yescharacteristic
11C13×#391C2211yescharacteristic
12C13×#387—21no—
13C13×#387—21no—
14C13×#384C2211yescharacteristic
15C13×#382C411yescharacteristic
16C4×C13×C22⋊C4C411yescharacteristic
17#11718587—21no—
18#11718586—21no—
19#11718120C2212yes—
20#11718120C2212yes—
21#11718117—21no—
22#11718117—21no—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C13×C22⋊Q8—41no—
26C13×C22⋊Q8—41no—
27C13×#117—41no—
28C13×#117—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C13×#95—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52C4⋊#1055—41no—
53C4⋊#1055—41no—
54#88043—41no—
55C4×#1055—41no—
56#11552—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C2×Q8×C13—22no—
59C2×Q8×C13—41no—
60C2×Q8×C13—41no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—41no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—22no—
91C42×C13—41no—
92C2×#1055—42no—
93C2×#1055—42no—
94#2499D1311yescharacteristic
95#1464—131no—
96#1458—131no—
97#1325—132no—
98#1319—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13C2×C22⋊C411yescharacteristic
105Q8×C13—82no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13#9911yescharacteristic
133C2×C4×C13#9911yescharacteristic
134C2×C4×C13#13112yes—
135#1055—82no—
136#1055—82no—
137C2×C22⋊Q8Dic1311yescharacteristic
138C2×#117C2×D1311yescharacteristic
139#432—261no—
140#431—261no—
141#397—21no—
142#397—21no—
143#391Dic1311yescharacteristic
144#391C2×D1311yescharacteristic
145#387—21no—
146#387—21no—
147#384C2×D1311yescharacteristic
148#382Dic1311yescharacteristic
149C4×C22⋊C4Dic1311yescharacteristic
150#324—132no—
151#324—132no—
152#323—261no—
153#323—261no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—81no—
160C22×C13—81no—
161C22×C13#40811yescharacteristic
162C22×C13C2×#9911yescharacteristic
163C22×C13#41311yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—42no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—81no—
173C4×C13—81no—
174C4×C13—81no—
175C22×Q8C2×Dic1311yescharacteristic
176C23×C4C2×Dic1311yescharacteristic
177C22⋊Q8—41no—
178C22⋊Q8—41no—
179#117—41no—
180#117—41no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4C2×Dic1311yescharacteristic
185C2×C4⋊C4C2×Dic1311yescharacteristic
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4C22⋊D1311yescharacteristic
190C2×C22⋊C4C22⋊D1311yescharacteristic
191C2×C42C2×Dic1311yescharacteristic
192C2×C42C2×Dic1311yescharacteristic
193C2×C42C22⋊D1311yescharacteristic
194C2×C42C22⋊D1311yescharacteristic
195C4⋊C8—521no—
196C4⋊C8—521no—
197C22⋊C8—262no—
198C22⋊C8—262no—
199#97—521no—
200C4×C8—521no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—81no—
211C2×C13#146811yescharacteristic
212C2×C13#212611yescharacteristic
213C2×C13#213511yescharacteristic
214C24C22⋊Dic1311yescharacteristic
215C2×Q8—22no—
216C2×Q8—41no—
217C2×Q8—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4C22⋊Dic1311yescharacteristic
227C22×C4C22⋊Dic1311yescharacteristic
228C22×C4C22⋊Dic1311yescharacteristic
229C22×C4C22×Dic1311yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232C2×C8—522no—
233C2×C8—522no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—22no—
250C42—41no—
251C13#1155211yescharacteristic, complemented, Sylow
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23C2×C22⋊Dic1311yescharacteristic
258Q8—82no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4#8807411yescharacteristic
286C2×C4#8807411yescharacteristic
287C2×C4#8820212yes—
288C8—1042no—
289C8—1042no—
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22C2×#8807411yescharacteristic
298C22#1171889511yescharacteristic
299C22#1171889811yescharacteristic
300C4—21no—
301C4—21no—
302C4—22no—
303C4—42no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—81no—
309C4—81no—
310C4—81no—
311C2—21no—
312C2—21no—
313C2—81no—
314C2#1311318411yescharacteristic
315C2#1311650111yescharacteristic
316C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2499C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2499D13
hypocenterC13#11552
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2499

Complements

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

NH ≅ G/Ntype
3. #13112782C2semidirect
4. #13112770C2semidirect
251. C13#11552semidirect

Maximal subgroups

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

subgroupindex
#131131702
#131131502
#131127822
#131127702
C13×#24992
#1155213