Finite Group Databasebeta

← #16016025

Subgroups — #16016025

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#405C211yesmaximal, characteristic
2#13116642C212yesmaximal, complemented
3#13116642C212yesmaximal, complemented
4#13116638C212yesmaximal, complemented
5#13116634C212yesmaximal, complemented
6#13116595C211yesmaximal, characteristic, complemented
7#13116446C211yesmaximal, characteristic
8C2×#11718099C211yesmaximal, characteristic
9#13116435C211yesmaximal, characteristic, complemented
10#13116432C211yesmaximal, characteristic, complemented
11C13×#2151C211yesmaximal, characteristic, complemented
12C2×M16×D13C411yescharacteristic
13C22×C8×D13C2211yescharacteristic
14D13×#117C411yescharacteristic
15C2×C13×M32C2211yescharacteristic
16C22×C13×C16C2211yescharacteristic
17C13×#405C2211yescharacteristic
18#11718783C411yescharacteristic
19#11718762C2211yescharacteristic
20C2×#88052C2211yescharacteristic
21C22×#6090C2211yescharacteristic
22#11718658C411yescharacteristic
23#11718369C412yes—
24D13×#97C412yes—
25#11718350C2212yes—
26C4×C8×D13C2212yes—
27C13×C4⋊C16C2212yescomplemented
28C13×C4⋊C16C2212yescomplemented
29#11718099C2211yescharacteristic
30#11718099C2211yescharacteristic
31#11718099C2211yescharacteristic
32#11718099C2211yescharacteristic
33#11718099C2212yes—
34#11718099C2212yes—
35#11718094C2212yescomplemented
36#11718094C2212yescomplemented
37C16×Dic13C2212yescomplemented
38C16×Dic13C2212yescomplemented
39C4⋊#6090C2212yescomplemented
40C4⋊#6090C2212yescomplemented
41C22×C4×D13C2×C411yescharacteristic
42C2×C13×M16C2×C411yescharacteristic
43C22×C8×C13C2311yescharacteristic
44C13×#117C2×C411yescharacteristic
45#88180C2×C411yescharacteristic
46C2×#6099C2×C411yescharacteristic
47C22×#1055C2×C411yescharacteristic
48M16×D13—24no—
49C2×#6094C2×C412yes—
50C2×C8×D13—22no—
51C2×C8×D13—22no—
52C2×C8×D13C2×C411yescharacteristic
53C2×C8×D13C2×C411yescharacteristic
54C2×C8×D13C2×C412yes—
55C2×C8×D13C2311yescharacteristic
56C2×C8×D13C2311yescharacteristic
57#88146C811yescharacteristic
58#88146C811yescharacteristic
59C4⋊C4×D13C811yescharacteristic
60C4⋊C4×D13C811yescharacteristic
61C22⋊C4×D13C812yes—
62#88131C812yes—
63#88126C2×C412yes—
64C42×D13C2×C412yes—
65C13×M32—22no—
66C2×C13×C16—22no—
67C2×C13×C16C2311yescharacteristic
68C2×C13×C16C2311yescharacteristic
69C2×C13×C16C2312yes—
70C13×#97C2×C412yes—
71C4×C8×C13C2312yes—
72#88055C2×C412yes—
73#88055C2×C412yes—
74C8×Dic13C2×C412yes—
75C8×Dic13C2312yes—
76#88052—22no—
77C2×#6090—22no—
78C2×#6090C2311yescharacteristic
79C2×#6090C2311yescharacteristic
80C2×#6090C2312yes—
81#88043C2×C412yes—
82C4×#1055C2×C412yes—
83#33422—131nomaximal, Sylow
84C23×D13C2×C811yescharacteristic
85C22×C4×C13C22×C411yescharacteristic
86C22×Dic13C2×C811yescharacteristic
87C2×C4×D13—22no—
88C2×C4×D13—22no—
89C2×C4×D13C2×C812yes—
90C2×C4×D13C2×C811yescharacteristic
91C2×C4×D13C2×C811yescharacteristic
92C2×C4×D13C2×C812yes—
93C2×C4×D13C22×C411yescharacteristic
94C2×C4×D13C22×C411yescharacteristic
95C13×M16—22no—
96C2×C8×C13C22×C412yes—
97C2×C8×C13C22×C411yescharacteristic
98C2×C8×C13#4112yes—
99C2×C8×C13#4112yes—
100C2×C8×C13C2411yescharacteristic
101C13×C4⋊C4C2×C811yescharacteristic
102C13×C4⋊C4C2×C811yescharacteristic
103C13×C22⋊C4C2×C812yes—
104C42×C13C22×C412yes—
105C22⋊Dic13C2×C812yes—
106#6103C2×C812yes—
107#6103C2×C812yes—
108C4⋊Dic13C2×C811yescharacteristic
109C4⋊Dic13C2×C811yescharacteristic
110#6101C2×C812yes—
111#6101C2×C812yes—
112C4×Dic13C2×C812yes—
113C4×Dic13C2×C812yes—
114C4×Dic13C22×C412yes—
115#6099M1614yes—
116C2×#1055—22no—
117C2×#1055C22×C411yescharacteristic
118C2×#1055C22×C411yescharacteristic
119C2×#1055C22×C412yes—
120#6094—24no—
121C8×D13—22no—
122C8×D13—22no—
123C8×D13—21no—
124C8×D13—21no—
125C8×D13—21no—
126C8×D13—21no—
127C8×D13—24no—
128C13×C16—21no—
129C13×C16—21no—
130C13×C16—22no—
131#6090—21no—
132#6090—21no—
133#6090—22no—
134C2×#405—131no—
135#2164—132no—
136#2164—132no—
137#2163—132no—
138#2162—132no—
139#2151—131no—
140#2151D1311yescharacteristic, complemented
141#2112—131no—
142C2×C22⋊C16—131no—
143#2108—131no—
144#2108—131no—
145C23×C13C22×C811yescharacteristic
146C22×D13—22no—
147C22×D13—22no—
148C22×D13—41no—
149C22×D13C22×C811yescharacteristic
150C22×D13C22×C811yescharacteristic
151C2×C4×C13#11712yes—
152C2×C4×C13C22×C812yes—
153C2×C4×C13C22×C812yes—
154C2×C4×C13C22×C811yescharacteristic
155C2×C4×C13C2×M1612yes—
156C2×C4×C13C23×C411yescharacteristic
157C2×Dic13—22no—
158C2×Dic13C22×C811yescharacteristic
159C2×Dic13C22×C812yes—
160C2×Dic13C22×C812yes—
161C2×Dic13C22×C811yescharacteristic
162C4×D13—24no—
163C4×D13—21no—
164C4×D13—21no—
165C4×D13—21no—
166C4×D13—21no—
167C4×D13—22no—
168C4×D13—22no—
169C4×D13—42no—
170C8×C13—22no—
171C8×C13#11712yes—
172C8×C13C2×#4111yescharacteristic
173C8×C13C2×#4111yescharacteristic
174#1055—21no—
175#1055—21no—
176#1055C2×M1614yes—
177C22×M16—131no—
178C23×C8—131no—
179C2×#117—131no—
180C2×M32—131no—
181C2×M32C2×D1311yescharacteristic
182C22×C16—131no—
183C22×C16C2×D1311yescharacteristic
184#405—131no—
185#405—131no—
186#405—131no—
187#405—132no—
188#405—132no—
189#405C2×D1311yescharacteristic
190C2×#97—132no—
191C2×C4×C8—132no—
192C4⋊C16—132no—
193C4⋊C16—132no—
194C4⋊C16C2×D1312yescomplemented
195C4⋊C16C2×D1312yescomplemented
196C22⋊C16—131no—
197C22⋊C16—131no—
198C22⋊C16—131no—
199C22⋊C16—131no—
200C22⋊C16—132no—
201C22⋊C16—132no—
202#346—132no—
203#346—132no—
204C4×C16—132no—
205C4×C16—132no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13#43112yes—
209C22×C13C23×C811yescharacteristic
210C2×D13—21no—
211C2×D13—21no—
212C2×D13—21no—
213C2×D13—21no—
214C2×D13—21no—
215C2×D13—44no—
216C2×D13#50412yes—
217C4×C13—22no—
218C4×C13—22no—
219C4×C13#43112yes—
220C4×C13C2×#11711yescharacteristic
221C4×C13C22×M1611yescharacteristic
222Dic13—22no—
223Dic13—22no—
224Dic13—21no—
225Dic13—21no—
226C23×C4—131no—
227C2×M16—131no—
228C2×M16—132no—
229C2×M16—264no—
230C2×M16C4×D1311yescharacteristic
231C22×C8—131no—
232C22×C8—131no—
233C22×C8—131no—
234C22×C8—132no—
235C22×C8—131no—
236C22×C8—131no—
237C22×C8—262no—
238C22×C8—262no—
239C22×C8C22×D1311yescharacteristic
240#117—131no—
241#117—131no—
242#117—131no—
243#117—132no—
244#117—132no—
245#117C4×D1311yescharacteristic
246C2×C4⋊C4—131no—
247C2×C4⋊C4—131no—
248C2×C22⋊C4—132no—
249C2×C42—132no—
250M32—22no—
251M32—262no—
252C2×C16—22no—
253C2×C16—131no—
254C2×C16—132no—
255C2×C16—131no—
256C2×C16—262no—
257C2×C16C22×D1311yescharacteristic
258C2×C16C22×D1312yes—
259C2×C16C22×D1311yescharacteristic
260#97—132no—
261#97—132no—
262#97—132no—
263#97C4×D1312yes—
264C4×C8—132no—
265C4×C8—132no—
266C4×C8—132no—
267C4×C8C22×D1312yes—
268C2×C13—22no—
269C2×C13C2×#43111yescharacteristic
270C2×C13C2×#50411yescharacteristic
271C2×C13#340711yescharacteristic
272D13—22no—
273D13—41no—
274C24—131no—
275C22×C4—131no—
276C22×C4—132no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—132no—
282C22×C4—262no—
283C22×C4—262no—
284C22×C4C2×C4×D1311yescharacteristic
285M16—22no—
286M16—134no—
287M16—264no—
288C2×C8—132no—
289C2×C8—131no—
290C2×C8—131no—
291C2×C8—264no—
292C2×C8—262no—
293C2×C8—262no—
294C2×C8—262no—
295C2×C8—261no—
296C2×C8—261no—
297C2×C8—261no—
298C2×C8—261no—
299C2×C8C2×C4×D1312yes—
300C2×C8C2×C4×D1311yescharacteristic
301C2×C8#612912yes—
302C2×C8#613112yes—
303C2×C8C23×D1311yescharacteristic
304C4⋊C4—132no—
305C4⋊C4—132no—
306C4⋊C4—131no—
307C4⋊C4—131no—
308C4⋊C4C8×D1311yescharacteristic
309C4⋊C4C8×D1311yescharacteristic
310C22⋊C4—132no—
311C22⋊C4—132no—
312C22⋊C4—132no—
313C22⋊C4C8×D1312yes—
314C42—132no—
315C42—132no—
316C42—132no—
317C42C2×C4×D1312yes—
318C16—21no—
319C16—21no—
320C16—22no—
321C16—261no—
322C16—261no—
323C16—262no—
324C13#3342211yescharacteristic, complemented, Sylow
325C23—131no—
326C23—131no—
327C23—262no—
328C23—262no—
329C23—521no—
330C23C2×C8×D1311yescharacteristic
331C2×C4—131no—
332C2×C4—132no—
333C2×C4—132no—
334C2×C4—131no—
335C2×C4—264no—
336C2×C4—262no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—262no—
342C2×C4—262no—
343C2×C4—522no—
344C2×C4#8814612yes—
345C2×C4C2×C8×D1312yes—
346C2×C4C2×C8×D1312yes—
347C2×C4C2×C8×D1311yescharacteristic
348C2×C4M16×D1312yes—
349C2×C4C22×C4×D1311yescharacteristic
350C8—22no—
351C8—134no—
352C8—261no—
353C8—261no—
354C8#8814612yes—
355C8C2×#612911yescharacteristic
356C8C2×#613111yescharacteristic
357C22—21no—
358C22—21no—
359C22—132no—
360C22—261no—
361C22—261no—
362C22—261no—
363C22—261no—
364C22—261no—
365C22—524no—
366C22#1171849412yes—
367C22C22×C8×D1311yescharacteristic
368C4—22no—
369C4—22no—
370C4—262no—
371C4—261no—
372C4—261no—
373C4—262no—
374C4#1171849412yes—
375C4C2×#8814611yescharacteristic
376C4C2×M16×D1311yescharacteristic
377C2—22no—
378C2—262no—
379C2—521no—
380C2C2×#1171849411yescharacteristic
381C2D13×#50411yescharacteristic
382C2#1312793711yescharacteristic
subgroupG/H
center, FrattiniC2×C8C23×D13
commutator, socleC22×C13C23×C8
FittingC13×#2151C2
prime radicalC23×D13C2×C8
cosocleC2×C8×C13C24
hypercenter#2151D13
hypocenterC13#33422
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ #2151

Complements

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

NH ≅ G/Ntype
2. #13116642C2semidirect
3. #13116642C2semidirect
4. #13116638C2semidirect
5. #13116634C2semidirect
6. #13116595C2semidirect
9. #13116435C2semidirect
10. #13116432C2semidirect
11. C13×#2151C2semidirect
27. C13×C4⋊C16C22semidirect
28. C13×C4⋊C16C22semidirect
35. #11718094C22semidirect
36. #11718094C22semidirect
37. C16×Dic13C22semidirect
38. C16×Dic13C22semidirect
39. C4⋊#6090C22semidirect
40. C4⋊#6090C22semidirect
140. #2151D13semidirect
194. C4⋊C16C2×D13semidirect
195. C4⋊C16C2×D13semidirect
324. C13#33422semidirect

Maximal subgroups

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

subgroupindex
D13×#4052
#131166422
#131166382
#131166342
#131165952
#131164462
C2×#117180992
#131164352
#131164322
C13×#21512
#3342213