Finite Group Databasebeta

← #15757620

Subgroups — #15757620

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123865C211yesmaximal, characteristic
2#13114904C212yesmaximal, complemented
3#13113154C211yesmaximal, characteristic
4#13112684C212yesmaximal, complemented
5C4×C13×#123C211yesmaximal, characteristic
6C2×C13×#123C411yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C13×#388—21no—
10C13×#387—21no—
11C13×#386C411yescharacteristic
12C13×#385C411yescharacteristic
13C13×#381C411yescharacteristic
14C4×C13×C4⋊C4—21no—
15C4×C13×C22⋊C4—21no—
16C4×C13×C22⋊C4C2211yescharacteristic
17#11718868—21no—
18C2×C22⋊#1055C2212yes—
19C2×C22⋊#1055C2212yes—
20#11718672—24no—
21#11718587—21no—
22#11718120—21no—
23#11718117—21no—
24#11718116—24no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C13×#123—22no—
31C13×#123—22no—
32C4×D4×C13—22no—
33C4×D4×C13—22no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C42×C13—21no—
44C2×C42×C13—21no—
45C2×C42×C13—21no—
46C2×C42×C13—22no—
47C2×C42×C13—22no—
48C2×C42×C13D411yescharacteristic
49C2×#6099—22no—
50C22×#1055—22no—
51C22×#1055D414yes—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C22⋊#1055—22no—
58C22⋊#1055—22no—
59C22⋊#1055—22no—
60C22⋊#1055—22no—
61C22⋊#1055—22no—
62C4⋊#1055—22no—
63#88043—22no—
64#8968—131nomaximal, Sylow
65C24×C13C22⋊C411yescharacteristic
66C24×C13C22×C411yescharacteristic
67C2×D4×C13—22no—
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13—22no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—22no—
75C22×C4×C13—22no—
76C22×C4×C13—21no—
77C22×C4×C13—22no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—42no—
82C22×C4×C13—42no—
83C22×C4×C13—42no—
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C22⋊C411yescharacteristic
87C22×C4×C13M1612yescomplemented
88C22×C4×C13C2×D412yes—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13#4112yes—
92C13×C4⋊C4—24no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—42no—
95C13×C22⋊C4—24no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—21no—
98C13×C22⋊C4—22no—
99C13×C22⋊C4—22no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4M1612yescomplemented
102C42×C13—21no—
103C42×C13—21no—
104C42×C13—42no—
105C42×C13—41no—
106C42×C13—42no—
107C42×C13—41no—
108#6099—82no—
109C2×#1055—24no—
110C2×#1055—44no—
111C2×#1055—44no—
112C2×#1055—42no—
113#2973—131no—
114C4×#123D1311yescharacteristic
115#1817—132no—
116#1459—131no—
117#1282—132no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13C2×C22⋊C411yescharacteristic
126C23×C13C4×D412yes—
127C23×C13C2×M1611yescharacteristic
128C23×C13C2×M1611yescharacteristic
129C23×C13#13112yes—
130D4×C13—42no—
131D4×C13—42no—
132C2×C4×C13—24no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—24no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—24no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—81no—
161C2×C4×C13#12011yescharacteristic
162C2×C4×C13#12112yes—
163C2×C4×C13#12311yescharacteristic
164#1055—44no—
165#1055—82no—
166C2×#123Dic1311yescharacteristic
167C2×C4×D4C2×D1311yescharacteristic
168C22×C42C2×D1311yescharacteristic
169#435—264no—
170#432—261no—
171#407—261no—
172C2×C22⋊C8—132no—
173C2×C22⋊C8—132no—
174#388—21no—
175#387—21no—
176#386Dic1311yescharacteristic
177#385Dic1311yescharacteristic
178#381Dic1311yescharacteristic
179C4×C4⋊C4—21no—
180C4×C22⋊C4—21no—
181C4×C22⋊C4C2×D1311yescharacteristic
182#336—264no—
183#324—261no—
184#323—261no—
185C22×C13—21no—
186C22×C13—22no—
187C22×C13—21no—
188C22×C13—22no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—42no—
192C22×C13—42no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—81no—
197C22×C13#38611yescharacteristic
198C22×C13#40711yescharacteristic
199C22×C13#40811yescharacteristic
200C22×C13#43512yes—
201C22×C13#43612yes—
202C4×C13—22no—
203C4×C13—21no—
204C4×C13—42no—
205C4×C13—42no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—42no—
209C4×C13—41no—
210C4×C13—81no—
211C4×C13#45812yes—
212C22×D4C2×Dic1311yescharacteristic
213C23×C4C2×Dic1311yescharacteristic
214C23×C4C2×Dic1311yescharacteristic
215C23×C4C22⋊D1311yescharacteristic
216C23×C4C22×D1311yescharacteristic
217C2×M16—262no—
218C22×C8—134no—
219C22×C8—262no—
220#123—22no—
221#123—22no—
222C4×D4—22no—
223C4×D4—22no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C22⋊D1311yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4C2×Dic1311yescharacteristic
230C2×C22⋊C4C2×Dic1311yescharacteristic
231C2×C22⋊C4C2×Dic1311yescharacteristic
232C2×C22⋊C4C22⋊D1311yescharacteristic
233C2×C42—22no—
234C2×C42—22no—
235C2×C42—21no—
236C2×C42—21no—
237C2×C42—21no—
238C2×C42C22⋊D1311yescharacteristic
239C4⋊C8—262no—
240C22⋊C8—262no—
241C22⋊C8—262no—
242C22⋊C8—262no—
243C22⋊C8—262no—
244C22⋊C8—262no—
245#97—262no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251C2×C13—21no—
252C2×C13—21no—
253C2×C13—22no—
254C2×C13—22no—
255C2×C13—81no—
256C2×C13#187011yescharacteristic
257C2×C13#189011yescharacteristic
258C2×C13#189111yescharacteristic
259C24C22⋊Dic1311yescharacteristic
260C24C22×Dic1311yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—22no—
264C2×D4—22no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4#609912yescomplemented
279C22×C4C22⋊Dic1311yescharacteristic
280C22×C4C22⋊Dic1311yescharacteristic
281C22×C4C22⋊Dic1311yescharacteristic
282C22×C4D4×D1312yes—
283C22×C4#612912yes—
284C22×C4C2×C22⋊D1311yescharacteristic
285C22×C4C2×C22⋊D1311yescharacteristic
286M16—1042no—
287C2×C8—264no—
288C2×C8—524no—
289C2×C8—524no—
290C2×C8—522no—
291C4⋊C4—24no—
292C4⋊C4—22no—
293C4⋊C4—42no—
294C22⋊C4—24no—
295C22⋊C4—21no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—42no—
300C22⋊C4#609912yescomplemented
301C42—21no—
302C42—21no—
303C42—42no—
304C42—41no—
305C42—41no—
306C42—42no—
307C13#896811yescharacteristic, complemented, Sylow
308C23—21no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23C2×#609911yescharacteristic
316C23C2×#609911yescharacteristic
317C23D4×Dic1312yes—
318C23#8820212yes—
319C23C2×C22⋊Dic1311yescharacteristic
320D4—42no—
321D4—42no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4#8818911yescharacteristic
352C2×C4#8819111yescharacteristic
353C2×C4#8819312yes—
354C8—524no—
355C8—1042no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—42no—
363C22—42no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—81no—
368C22#1171867212yes—
369C22#1171867312yes—
370C22#1171886811yescharacteristic
371C22#1171888111yescharacteristic
372C22#1171889511yescharacteristic
373C4—22no—
374C4—21no—
375C4—42no—
376C4—41no—
377C4—42no—
378C4—41no—
379C4—42no—
380C4—41no—
381C4—81no—
382C4#1171871412yes—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—22no—
387C2—81no—
388C2#1311513411yescharacteristic
389C2#1311525011yescharacteristic
390C2#1311525511yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC4×C13×#123C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC23×C4×C13C23
hypercenterC4×#123D13
hypocenterC13#8968
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
2. #13114904C2semidirect
4. #13112684C2semidirect
87. C22×C4×C13M16semidirect
101. C13×C22⋊C4M16semidirect
278. C22×C4#6099semidirect
300. C22⋊C4#6099semidirect
307. C13#8968semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131149042
#131131542
#131126842
C4×C13×#1232
#896813