Finite Group Databasebeta

← #13127544

Subgroups — #13127544

Order 1664.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719258C211yesmaximal, characteristic, complemented
2#11719244C211yesmaximal, characteristic, complemented
3C13×#442C211yesmaximal, characteristic, complemented
4#11718811C211yesmaximal, characteristic, complemented
5#11718811C211yesmaximal, characteristic, complemented
6#11718676C211yesmaximal, characteristic, complemented
7#11718670C211yesmaximal, characteristic, complemented
8#11718532C211yesmaximal, characteristic, complemented
9#11718531C211yesmaximal, characteristic, complemented
10#11718446C211yesmaximal, characteristic, complemented
11#11718425C211yesmaximal, characteristic, complemented
12#11718421C211yesmaximal, characteristic, complemented
13#11718417C211yesmaximal, characteristic, complemented
14#11718374C211yesmaximal, characteristic, complemented
15#11718362C211yesmaximal, characteristic, complemented
16C2×#6127—21no—
17C2×C13×D8C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20#88194C2211yescharacteristic
21#88194C2211yescharacteristic
22D4×Dic13C2211yescharacteristic
23D4×Dic13C2211yescharacteristic
24C2×#6104C2211yescharacteristic
25C2×#6104C2211yescharacteristic
26#88184—21no—
27#88178—21no—
28C2×#6101—21no—
29#88147C2211yescharacteristic
30#88147C2211yescharacteristic
31#88144C2211yescharacteristic
32#88142C2211yescharacteristic
33#88138—21no—
34#88138—21no—
35#88132—21no—
36#88132—21no—
37#88128C2211yescharacteristic
38#88124C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×#102C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#97C2211yescharacteristic
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88055C2211yescharacteristic
51#88054C2211yescharacteristic
52#88054C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×D4×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69#6127—44no—
70C2×D52—21no—
71C2×D52—21no—
72C2×D52C2311yescharacteristic
73C2×D52C2311yescharacteristic
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×Dic26—21no—
77C2×Dic26D411yescharacteristic
78C13×D8—22no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C42×C13C2311yescharacteristic
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88#6104—22no—
89#6104—22no—
90#6103—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13D411yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101D411yescharacteristic
101#6101D411yescharacteristic
102C4×Dic13C2311yescharacteristic
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#3366—131nomaximal, Sylow
107C23×C13—21no—
108C23×C13—21no—
109C22×D13—21no—
110C22×D13—21no—
111D4×C13—21no—
112D4×C13—21no—
113D4×C13—21no—
114D4×C13#4112yescomplemented
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—42no—
118C2×C4×C13—81no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C22⋊D13—42no—
123C22⋊D13—42no—
124C22⋊D13—81no—
125C22⋊D13—81no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—42no—
129C2×Dic13—81no—
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134D52—21no—
135D52—21no—
136D52—21no—
137D52—21no—
138D52—42no—
139D52—81no—
140C4×D13—42no—
141C4×D13—42no—
142Dic26—22no—
143Dic26—81no—
144C8×C13—21no—
145C8×C13—21no—
146#1055—21no—
147#1055—21no—
148#554—131no—
149#550—131no—
150#490—131no—
151#490—131no—
152#486—131no—
153#478—131no—
154#478—131no—
155#476—131no—
156#459—131no—
157#459—131no—
158#459—131no—
159#446—131no—
160#442—131no—
161#442D1311yescharacteristic, complemented
162C4×D8—131no—
163C22×C13—22no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13C22×D411yescharacteristic
170C2×D13—41no—
171C2×D13—41no—
172C2×D13—41no—
173C2×D13—41no—
174C2×D13—41no—
175C2×D13—41no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13C2×#4111yescharacteristic
181C4×C132−1+411yescharacteristic
182Dic13—21no—
183Dic13—21no—
184Dic13—21no—
185Dic13—41no—
186Dic13—41no—
187Dic13AGL(1,ℤ/8)12yes—
188C2×#41—261no—
189C2×D8—131no—
190C2×D8—131no—
191C2×D8C2×D1311yescharacteristic
192C4⋊Q8—131no—
193#127—131no—
194#127—131no—
195#127—131no—
196#125—131no—
197#125—131no—
198C22⋊Q8—261no—
199C22⋊Q8—261no—
200C22⋊Q8—261no—
201#121—261no—
202#121—261no—
203#121—261no—
204C4×Q8—131no—
205C4×D4—131no—
206C4×D4—131no—
207C4×D4—131no—
208C4×D4—131no—
209C4×D4C2×D1311yescharacteristic
210C4×D4C2×D1311yescharacteristic
211C2×C4⋊C4—261no—
212#107—131no—
213#106—131no—
214#106C2×D1311yescharacteristic
215C4⋊C8—131no—
216C4⋊C8—131no—
217C4⋊C8—131no—
218#102—131no—
219#102—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223#102—131no—
224#102—131no—
225#102—131no—
226#102C2×D1311yescharacteristic
227#102C2×D1311yescharacteristic
228#97—131no—
229#97C2×D1311yescharacteristic
230C4×C8—131no—
231C2×C13—42no—
232C2×C13—81no—
233C2×C13#54811yescharacteristic
234C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
235C2×C13#57611yescharacteristic
236D13—81no—
237D13—81no—
238#41—524no—
239C2×Q8—131no—
240C2×Q8—261no—
241C2×D4—131no—
242C2×D4—131no—
243C2×D4—261no—
244C2×D4—261no—
245C2×D4—261no—
246C2×D4—261no—
247C2×D4—261no—
248C2×D4—261no—
249C2×D4C22×D1311yescharacteristic
250C2×D4C22×D1311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257D8—22no—
258D8—262no—
259D8—262no—
260C2×C8—131no—
261C2×C8—131no—
262C2×C8C22×D1311yescharacteristic
263C2×C8C22×D1311yescharacteristic
264C4⋊C4—131no—
265C4⋊C4—131no—
266C4⋊C4—131no—
267C4⋊C4—131no—
268C4⋊C4—131no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4C22×D1311yescharacteristic
275C4⋊C4C22×D1311yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C42—131no—
283C42—131no—
284C42C22×D1311yescharacteristic
285C13#336611yescharacteristic, complemented, Sylow
286C23—21no—
287C23—21no—
288C23—261no—
289C23—261no—
290Q8—262no—
291Q8—1041no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—261no—
296D4—261no—
297D4—261no—
298D4—261no—
299D4—522no—
300D4—522no—
301D4—522no—
302D4—1041no—
303D4—1041no—
304D4—1041no—
305D4#612712yescomplemented
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—131no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—131no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—522no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4—1041no—
320C2×C4D4×D1311yescharacteristic
321C2×C4D4×D1311yescharacteristic
322C2×C4C23×D1311yescharacteristic
323C8—21no—
324C8—21no—
325C8—261no—
326C8—261no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—521no—
334C22—521no—
335C22—521no—
336C22—521no—
337C22—521no—
338C22—521no—
339C22C2×D4×D1311yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—132no—
345C4—261no—
346C4—261no—
347C4—261no—
348C4—521no—
349C4—521no—
350C4C2×#612711yescharacteristic
351C4#8825711yescharacteristic
352C2—42no—
353C2—81no—
354C2—1041no—
355C2—1041no—
356C2#1171925711yescharacteristic
357C2D13×AGL(1,ℤ/8)11yescharacteristic
358C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#442C2
socleC22×C13C22×D4
hypercenter#442D13
hypocenterC13#3366
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #11719258C2semidirect
2. #11719244C2semidirect
3. C13×#442C2semidirect
4. #11718811C2semidirect
5. #11718811C2semidirect
6. #11718676C2semidirect
7. #11718670C2semidirect
8. #11718532C2semidirect
9. #11718531C2semidirect
10. #11718446C2semidirect
11. #11718425C2semidirect
12. #11718421C2semidirect
13. #11718417C2semidirect
14. #11718374C2semidirect
15. #11718362C2semidirect
114. D4×C13#41semidirect
161. #442D13semidirect
285. C13#3366semidirect
305. D4#6127semidirect

Maximal subgroups

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

subgroupindex
#117192582
#117192442
C13×#4422
#117188112
#117186762
#117186702
#117185322
#117185312
#117184462
#117184252
#117184212
#117184172
#117183742
#117183622
#336613