Finite Group Databasebeta

← #15772440

Subgroups — #15772440

Order 3328.

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

normal subgroups only

This group has 460 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#13112784C212yesmaximal, complemented
4#13112764C212yesmaximal
5C13×#2482C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C22×C13×C22⋊C4C411yescharacteristic
8C13×#399—21no—
9C13×#397—21no—
10C13×#388—21no—
11C13×#388—21no—
12C13×#385C411yescharacteristic
13C13×#385C2211yescharacteristic
14C13×#381C411yescharacteristic
15C13×#379C411yescharacteristic
16C13×#379C2211yescharacteristic
17#11718587—21no—
18#11718586—21no—
19#11718120—21no—
20#11718120—21no—
21#11718117C2212yes—
22#11718117C2212yes—
23C25×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C13×#117—41no—
27C13×#117—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—41no—
39C2×C13×C22⋊C4—41no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4C2311yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13D411yescharacteristic
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#11542—131nomaximal, Sylow
57C24×C13—21no—
58C24×C13—22no—
59C24×C13—41no—
60C24×C13—42no—
61C24×C13—41no—
62C24×C13—81no—
63C24×C13C22×C411yescharacteristic
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—81no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—81no—
82C13×C4⋊C4—81no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—81no—
93C13×C22⋊C4—81no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—21no—
98C2×#1055—42no—
99C2×#1055—42no—
100#2482D1311yescharacteristic
101#1464—131no—
102#1458—131no—
103#1326—132no—
104#1316—132no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—22no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—42no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—42no—
118C23×C13—82no—
119C23×C13—84no—
120C23×C13—84no—
121C23×C13—82no—
122C23×C13C2×C22⋊C411yescharacteristic
123C23×C13#13112yes—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
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—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—82no—
149C2×C4×C13#9911yescharacteristic
150C2×C4×C13#9911yescharacteristic
151#1055—82no—
152#1055—82no—
153C2×#117C2×D1311yescharacteristic
154C22×C22⋊C4Dic1311yescharacteristic
155#432—261no—
156#431—261no—
157#399—21no—
158#397—21no—
159#388—21no—
160#388—21no—
161#385Dic1311yescharacteristic
162#385C2×D1311yescharacteristic
163#381Dic1311yescharacteristic
164#379Dic1311yescharacteristic
165#379C2×D1311yescharacteristic
166#324—261no—
167#324—261no—
168#323—132no—
169#323—132no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—22no—
173C22×C13—42no—
174C22×C13—42no—
175C22×C13—42no—
176C22×C13—42no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—42no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13—84no—
183C22×C13—84no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#40811yescharacteristic
187C22×C13C2×#9911yescharacteristic
188C22×C13#41311yescharacteristic
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13—81no—
199C25C2×Dic1311yescharacteristic
200C23×C4C2×Dic1311yescharacteristic
201C23×C4C2×Dic1311yescharacteristic
202#117—41no—
203#117—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C22⋊D1311yescharacteristic
207C2×C4⋊C4C22⋊D1311yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—41no—
215C2×C22⋊C4—41no—
216C2×C22⋊C4C2×Dic1311yescharacteristic
217C2×C22⋊C4C2×Dic1311yescharacteristic
218C2×C22⋊C4C2×Dic1311yescharacteristic
219C2×C22⋊C4C22×D1311yescharacteristic
220C2×C42C22⋊D1311yescharacteristic
221C2×C42C22⋊D1311yescharacteristic
222C4⋊C8—521no—
223C4⋊C8—521no—
224C22⋊C8—262no—
225C22⋊C8—262no—
226#97—521no—
227C4×C8—521no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232C2×C13—21no—
233C2×C13—21no—
234C2×C13—42no—
235C2×C13—82no—
236C2×C13#146811yescharacteristic
237C2×C13#212011yescharacteristic
238C2×C13#212211yescharacteristic
239C24—21no—
240C24—22no—
241C24—41no—
242C24—42no—
243C24—41no—
244C24—81no—
245C24C22×Dic1311yescharacteristic
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—81no—
255C22×C4C22⋊Dic1311yescharacteristic
256C22×C4C22⋊Dic1311yescharacteristic
257C22×C4C22⋊Dic1311yescharacteristic
258C22×C4C22⋊Dic1311yescharacteristic
259C22×C4C2×C22⋊D1311yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261C2×C8—522no—
262C2×C8—522no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C22⋊C4—22no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—81no—
277C22⋊C4—81no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—21no—
282C13#1154211yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—22no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—42no—
292C23—42no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—82no—
297C23—84no—
298C23—84no—
299C23—82no—
300C23#8820212yes—
301C23C2×C22⋊Dic1311yescharacteristic
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—82no—
327C2×C4#8807411yescharacteristic
328C2×C4#8807411yescharacteristic
329C8—1042no—
330C8—1042no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—42no—
341C22—81no—
342C22—81no—
343C22—84no—
344C22—84no—
345C22—81no—
346C22—81no—
347C22C2×#8807411yescharacteristic
348C22#1171889511yescharacteristic
349C22#1171889811yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—82no—
364C2#1311318411yescharacteristic
365C2#1311647711yescharacteristic
366C2#1311648611yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2482C2
socleC22×C13C2×#99
prime radicalC25×C13C2×C4
cosocleC2×C13×C22⋊C4C23
hypercenter#2482D13
hypocenterC13#11542
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2482

Complements

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

NH ≅ G/Ntype
1. #13113170C2semidirect
2. #13113150C2semidirect
3. #13112784C2semidirect
282. C13#11542semidirect

Maximal subgroups

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

subgroupindex
#131131702
#131131502
#131127842
#131127642
C13×#24822
#1154213