Finite Group Databasebeta

← #15772500

Subgroups — #15772500

Order 3328.

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

normal subgroups only

This group has 408 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, complemented
2#13113150C211yesmaximal, characteristic, complemented
3#13112782C212yesmaximal, complemented
4#13112768C212yesmaximal, complemented
5C13×#2500C211yesmaximal, characteristic
6C2×C13×#121C411yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C13×#394—21no—
9C13×#394—21no—
10C13×#390C411yescharacteristic
11C13×#390C2211yescharacteristic
12C13×#388—21no—
13C13×#388—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×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C13×#121—41no—
27C13×#121—41no—
28C13×#117—41no—
29C13×#117—41no—
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⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C42×C13C2×C411yescharacteristic
44C2×C42×C13C2×C411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×C42×C13D411yescharacteristic
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#11554—131nomaximal, Sylow
57C24×C13—21no—
58C24×C13C22⋊C411yescharacteristic
59C2×D4×C13—22no—
60C2×D4×C13—41no—
61C2×D4×C13—41no—
62C2×D4×C13—42no—
63C2×D4×C13—81no—
64C2×D4×C13—81no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—22no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—41no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—81no—
82C13×C4⋊C4—81no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—81no—
91C13×C22⋊C4—81no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—22no—
97C42×C13—41no—
98C2×#1055—42no—
99C2×#1055—42no—
100#2500D1311yescharacteristic
101#1464—131no—
102#1458—131no—
103#1325—132no—
104#1318—132no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13C2×C22⋊C411yescharacteristic
118D4×C13—82no—
119D4×C13—84no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—22no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13#9911yescharacteristic
144C2×C4×C13#9911yescharacteristic
145C2×C4×C13#13112yes—
146#1055—82no—
147#1055—82no—
148C2×#121Dic1311yescharacteristic
149C2×#117C2×D1311yescharacteristic
150#432—261no—
151#431—261no—
152#394—21no—
153#394—21no—
154#390Dic1311yescharacteristic
155#390C2×D1311yescharacteristic
156#388—21no—
157#388—21no—
158#384C2×D1311yescharacteristic
159#382Dic1311yescharacteristic
160C4×C22⋊C4Dic1311yescharacteristic
161#324—132no—
162#324—132no—
163#323—261no—
164#323—261no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—81no—
171C22×C13—81no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13#40811yescharacteristic
180C22×C13C2×#9911yescharacteristic
181C22×C13#41311yescharacteristic
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—22no—
185C4×C13—42no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—81no—
191C4×C13—81no—
192C22×D4—21no—
193C22×D4C2×Dic1311yescharacteristic
194C23×C4C2×Dic1311yescharacteristic
195#121—41no—
196#121—41no—
197#117—41no—
198#117—41no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×Dic1311yescharacteristic
202C2×C4⋊C4C2×Dic1311yescharacteristic
203C2×C4⋊C4C22×D1311yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4C22⋊D1311yescharacteristic
211C2×C22⋊C4C22⋊D1311yescharacteristic
212C2×C42C2×Dic1311yescharacteristic
213C2×C42C2×Dic1311yescharacteristic
214C2×C42C22⋊D1311yescharacteristic
215C2×C42C22⋊D1311yescharacteristic
216C4⋊C8—521no—
217C4⋊C8—521no—
218C22⋊C8—262no—
219C22⋊C8—262no—
220#97—521no—
221C4×C8—521no—
222#95—21no—
223#95—21no—
224#95—21no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13—81no—
228C2×C13—161no—
229C2×C13#146811yescharacteristic
230C2×C13#212811yescharacteristic
231C2×C13#213211yescharacteristic
232C24—21no—
233C24C22⋊Dic1311yescharacteristic
234C2×D4—22no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—42no—
238C2×D4—81no—
239C2×D4—81no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4C22⋊Dic1311yescharacteristic
248C22×C4C22⋊Dic1311yescharacteristic
249C22×C4C22⋊Dic1311yescharacteristic
250C22×C4C22×Dic1311yescharacteristic
251C22×C4C2×C22⋊D1311yescharacteristic
252C22×C4C2×C22⋊D1311yescharacteristic
253C2×C8—522no—
254C2×C8—522no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—81no—
268C22⋊C4—81no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—22no—
274C42—41no—
275C13#1155411yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23C2×C22⋊Dic1311yescharacteristic
289D4—82no—
290D4—84no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4#8807411yescharacteristic
315C2×C4#8807411yescharacteristic
316C2×C4#8820212yes—
317C8—1042no—
318C8—1042no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22C2×#8807411yescharacteristic
334C22#1171889511yescharacteristic
335C22#1171889811yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—42no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—81no—
345C4—81no—
346C2—21no—
347C2—21no—
348C2—81no—
349C2—161no—
350C2#1311318411yescharacteristic
351C2#1311650811yescharacteristic
352C2#1311652111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2500C2
socleC22×C13C2×#99
prime radicalC2×C13×#121C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2500D13
hypocenterC13#11554
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2500

Complements

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

NH ≅ G/Ntype
1. #13113170C2semidirect
2. #13113150C2semidirect
3. #13112782C2semidirect
4. #13112768C2semidirect
275. C13#11554semidirect

Maximal subgroups

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

subgroupindex
#131131702
#131131502
#131127822
#131127682
C13×#25002
#1155413