Finite Group Databasebeta

← #15760589

Subgroups — #15760589

Order 3328.

490 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 107 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#13113463C212yesmaximal, complemented
3#13113177C211yesmaximal, characteristic
4#13112692C212yesmaximal, complemented
5C13×#2566C211yesmaximal, characteristic
6C2×C13×#125C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#396—21no—
9C13×#396—21no—
10C13×#390C411yescharacteristic
11C13×#390C411yescharacteristic
12C13×#385—21no—
13C13×#385—21no—
14C13×#384C411yescharacteristic
15C13×#382C411yescharacteristic
16C4×C13×C4⋊C4C2211yescharacteristic
17#11718868—21no—
18C2×C22⋊#1055—21no—
19#11718672—24no—
20#11718587C2212yes—
21#11718587C2212yes—
22#11718135—24no—
23#11718117—21no—
24#11718117—21no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×#125—22no—
29C13×#125—22no—
30C4×D4×C13—22no—
31C4×D4×C13—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C42×C13C2×C411yescharacteristic
47C2×C42×C13C2×C411yescharacteristic
48C2×C42×C13C2311yescharacteristic
49C2×#6099—22no—
50C22×#1055—22no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C22⋊#1055—22no—
55C22⋊#1055—22no—
56C22⋊#1055—22no—
57C22⋊#1055—22no—
58C4⋊#1055—22no—
59C4⋊#1055—22no—
60#88043—22no—
61#88043D414yes—
62#9449—131nomaximal, Sylow
63C24×C13C22⋊C411yescharacteristic
64C24×C13C22⋊C411yescharacteristic
65C2×D4×C13—22no—
66C2×D4×C13—22no—
67C2×D4×C13—41no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—81no—
77C22×C4×C13—81no—
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C13×C4⋊C4—22no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—81no—
91C13×C4⋊C4—81no—
92C13×C22⋊C4—22no—
93C13×C22⋊C4—22no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—81no—
97C13×C22⋊C4—81no—
98C42×C13—41no—
99C42×C13—41no—
100C42×C13C2×D412yes—
101C42×C13#4112yes—
102#6099—82no—
103C2×#1055—24no—
104C2×#1055—42no—
105C2×#1055—82no—
106#2973—131no—
107#2566D1311yescharacteristic
108#1534—132no—
109#1466—131no—
110#1285—132no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13#10112yes—
121C23×C13C2×C22⋊C411yescharacteristic
122D4×C13—44no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—22no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
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—41no—
144C2×C4×C13—41no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13C4×D412yes—
148C2×C4×C13#12011yescharacteristic
149C2×C4×C13#12112yes—
150C2×C4×C13#12311yescharacteristic
151#1055—44no—
152#1055—82no—
153C2×#125C2×D1311yescharacteristic
154C2×C4×D4C2×D1311yescharacteristic
155#435—264no—
156#432—132no—
157#432—132no—
158#407—261no—
159C2×C22⋊C8—261no—
160#396—21no—
161#396—21no—
162#390Dic1311yescharacteristic
163#390Dic1311yescharacteristic
164#385—21no—
165#385—21no—
166#384Dic1311yescharacteristic
167#382Dic1311yescharacteristic
168C4×C4⋊C4C2×D1311yescharacteristic
169#330—264no—
170#323—261no—
171#323—261no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—22no—
175C22×C13—42no—
176C22×C13—42no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13#38611yescharacteristic
185C22×C13C2×#10111yescharacteristic
186C22×C13#41311yescharacteristic
187C4×C13—22no—
188C4×C13—22no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—42no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—81no—
197C22×D4C2×Dic1311yescharacteristic
198C23×C4C22⋊D1311yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200C2×M16—262no—
201C22×C8—262no—
202#125—22no—
203#125—22no—
204C4×D4—22no—
205C4×D4—22no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4C2×Dic1311yescharacteristic
212C2×C4⋊C4C2×Dic1311yescharacteristic
213C2×C4⋊C4C2×Dic1311yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4C22⋊D1311yescharacteristic
219C2×C22⋊C4C22⋊D1311yescharacteristic
220C2×C42C2×Dic1311yescharacteristic
221C2×C42C2×Dic1311yescharacteristic
222C2×C42C22×D1311yescharacteristic
223C4⋊C8—262no—
224C4⋊C8—262no—
225C22⋊C8—262no—
226C22⋊C8—262no—
227C22⋊C8—262no—
228C22⋊C8—262no—
229#97—134no—
230#97—262no—
231#95—21no—
232#95—21no—
233#95—21no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—42no—
237C2×C13—81no—
238C2×C13#188411yescharacteristic
239C2×C13#190111yescharacteristic
240C2×C13#191111yescharacteristic
241C24C22⋊Dic1311yescharacteristic
242C24C22⋊Dic1311yescharacteristic
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—41no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4C22⋊Dic1311yescharacteristic
257C22×C4C22⋊Dic1311yescharacteristic
258C22×C4C22×Dic1311yescharacteristic
259C22×C4C2×C22⋊D1311yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261M16—1042no—
262C2×C8—264no—
263C2×C8—522no—
264C2×C8—1042no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—81no—
279C22⋊C4—81no—
280C42—41no—
281C42—41no—
282C42D4×D1312yes—
283C42#612912yes—
284C13#944911yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#8807612yes—
295C23C2×C22⋊Dic1311yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
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—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4D4×Dic1312yes—
322C2×C4#8818911yescharacteristic
323C2×C4#8819111yescharacteristic
324C2×C4#8819312yes—
325C8—524no—
326C8—1042no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#1171888111yescharacteristic
340C22C2×#8807611yescharacteristic
341C22#1171889811yescharacteristic
342C4—22no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—81no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2#1311522011yescharacteristic
357C2#1311530511yescharacteristic
358C2#1311536911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2566C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2566D13
hypocenterC13#9449
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2566

Complements

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

NH ≅ G/Ntype
2. #13113463C2semidirect
4. #13112692C2semidirect
284. C13#9449semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131134632
#131131772
#131126922
C13×#25662
#944913