Finite Group Databasebeta

← #15781982

Subgroups — #15781982

Order 3328.

450 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718535C211yesmaximal, characteristic, complemented
2C2×#11718101C211yesmaximal, characteristic
3C2×#11718083C211yesmaximal, characteristic
4#13115700C211yesmaximal, characteristic
5#13112927C211yesmaximal, characteristic, complemented
6#13112913C211yesmaximal, characteristic, complemented
7C13×#1380C211yesmaximal, characteristic, complemented
8C22×D104C2211yescharacteristic
9C2×#88142—21no—
10C22×C13×C16C2211yescharacteristic
11C2×C13×#107C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13C2×#88058C2211yescharacteristic
14C2×C8×Dic13C2211yescharacteristic
15C22×#6090C2211yescharacteristic
16#11718649—21no—
17C2×#88049—21no—
18C2×#88047—21no—
19#11718535—22no—
20#11718535—22no—
21#11718101—22no—
22#11718083—22no—
23C22×D52—21no—
24C22×Dic26—41no—
25C22×C8×C13C2311yescharacteristic
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×#6103—41no—
29C2×#6103—41no—
30C2×C4⋊Dic13—21no—
31C2×#6101—41no—
32C2×C4×Dic13D411yescharacteristic
33C22×#1055D411yescharacteristic
34C2×D104—21no—
35C2×D104—21no—
36C2×D104—21no—
37C2×D104—21no—
38C2×D104—21no—
39C2×D104Q812yescomplemented
40#88142—24no—
41#88142—42no—
42C2×C13×C16—21no—
43C2×C13×C16—21no—
44C2×C13×C16—21no—
45C13×#107—21no—
46C13×#107—21no—
47C13×#107—21no—
48C13×#107D412yes—
49#88058—21no—
50#88058D412yes—
51C8×Dic13—21no—
52C8×Dic13—21no—
53C2×#6090—21no—
54C2×#6090—21no—
55C2×#6090—21no—
56#88049—42no—
57#88047—24no—
58#13363—131nomaximal, Sylow
59C23×D13—41no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—41no—
64C22×Dic13D811yescharacteristic
65C22×Dic13D811yescharacteristic
66C2×D52—22no—
67C2×D52—41no—
68C2×D52—41no—
69C2×D52—41no—
70C2×D52—41no—
71C2×D52—41no—
72C2×Dic26—44no—
73C2×Dic26—82no—
74C2×Dic26—82no—
75C2×C8×C13C2×D411yescharacteristic
76C2×C8×C13C2×D411yescharacteristic
77C2×C8×C13C2×Q811yescharacteristic
78C2×C8×C13#4111yescharacteristic
79C2×C8×C13#4111yescharacteristic
80C2×C8×C13#4111yescharacteristic
81C13×C4⋊C4—22no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85#6103—82no—
86#6103—82no—
87C4⋊Dic13—22no—
88C4⋊Dic13—41no—
89#6101—44no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92C2×#1055—21no—
93C2×#1055—21no—
94C2×#1055SD1612yes—
95D104—22no—
96D104—22no—
97D104—41no—
98D104—41no—
99C13×C16—41no—
100#6090—41no—
101C2×#500—131no—
102C2×#357—131no—
103C2×#357—131no—
104#1970—131no—
105#1380—131no—
106#1380D1311yescharacteristic, complemented
107#1374—131no—
108C23×C13C2×D811yescharacteristic
109C22×D13—42no—
110C22×D13—81no—
111C22×D13—81no—
112C22×D13—81no—
113C22×D13—81no—
114C22×D13—81no—
115C22×D13—81no—
116C2×C4×C13—42no—
117C2×C4×C13—81no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13—81no—
121C2×C4×C13—81no—
122C2×C4×C13#12011yescharacteristic
123C2×C4×C13C22⋊Q811yescharacteristic
124C2×C4×C13#12411yescharacteristic
125C2×C4×C13C2×SD1611yescharacteristic
126C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C13#13711yescharacteristic
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—42no—
133C2×Dic13—81no—
134C2×Dic13—81no—
135C2×Dic13D1612yes—
136C2×Dic13SD3212yes—
137D52—42no—
138D52—42no—
139D52—81no—
140D52—81no—
141Dic26—88no—
142C8×C13C22⋊Q811yescharacteristic
143C8×C13C22⋊Q811yescharacteristic
144C8×C13#12411yescharacteristic
145C8×C13#12411yescharacteristic
146#1055—22no—
147C22×D8—131no—
148C2×C4⋊Q8—261no—
149C22×C16—131no—
150C22×C16C2×D1311yescharacteristic
151#500—262no—
152#500—262no—
153C2×#107—131no—
154C2×#107—261no—
155C2×#107C2×D1311yescharacteristic
156C2×#107C2×D1311yescharacteristic
157C2×#102—261no—
158C2×C4×C8—131no—
159#390—261no—
160#357—262no—
161#357—262no—
162C22×C13#44711yescharacteristic
163C22×C13#47411yescharacteristic
164C22×C13#48611yescharacteristic
165C22×C13C2×D1611yescharacteristic
166C22×C13C2×SD3211yescharacteristic
167C22×C13#50911yescharacteristic
168C22×C13#51011yescharacteristic
169C2×D13—82no—
170C2×D13—82no—
171C2×D13—82no—
172C2×D13—161no—
173C2×D13—161no—
174C2×D13—161no—
175C2×D13—161no—
176C4×C13—82no—
177C4×C13—161no—
178C4×C13#39311yescharacteristic
179C4×C13#44811yescharacteristic
180C4×C13#47611yescharacteristic
181C4×C13#48911yescharacteristic
182Dic13—22no—
183Dic13—22no—
184Dic13—82no—
185C22×Q8—521no—
186C22×D4—261no—
187C2×D8—132no—
188C2×D8—261no—
189C2×D8—261no—
190C2×D8—261no—
191C2×D8—261no—
192C2×D8—261no—
193C22×C8—131no—
194C22×C8C22×D1311yescharacteristic
195C4⋊Q8—264no—
196C4⋊Q8—522no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—521no—
201C2×C22⋊C4—521no—
202C2×C22⋊C4—521no—
203C2×C42—131no—
204C2×C16—21no—
205C2×C16—21no—
206C2×C16—21no—
207C2×C16—261no—
208C2×C16—261no—
209C2×C16—261no—
210#107—21no—
211#107—21no—
212#107—21no—
213#107—132no—
214#107—264no—
215#107—261no—
216#107D5212yes—
217#102—522no—
218C4×C8—261no—
219C4×C8—261no—
220C2×C13#202311yescharacteristic
221C2×C13#218411yescharacteristic
222C2×C13#218511yescharacteristic
223C2×C13#222411yescharacteristic
224C2×C13#222611yescharacteristic
225C2×C13#224011yescharacteristic
226C2×C13#224311yescharacteristic
227D13—162no—
228C24—521no—
229C2×Q8—524no—
230C2×Q8—1042no—
231C2×Q8—1042no—
232C2×D4—262no—
233C2×D4—521no—
234C2×D4—521no—
235C2×D4—521no—
236C2×D4—521no—
237C2×D4—521no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—521no—
243C22×C4D4×D1311yescharacteristic
244D8—262no—
245D8—262no—
246D8—521no—
247D8—521no—
248C2×C8—132no—
249C2×C8—261no—
250C2×C8—261no—
251C2×C8C2×D5211yescharacteristic
252C2×C8#612711yescharacteristic
253C2×C8#612711yescharacteristic
254C2×C8D4×D1311yescharacteristic
255C2×C8#612911yescharacteristic
256C2×C8Q8×D1311yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—262no—
262C4⋊C4—524no—
263C4⋊C4—521no—
264C22⋊C4—1042no—
265C22⋊C4—1042no—
266C42—261no—
267C42—261no—
268C16—41no—
269C16—521no—
270C13#1336311yescharacteristic, complemented, Sylow
271C23—522no—
272C23—1041no—
273C23—1041no—
274C23—1041no—
275C23—1041no—
276C23—1041no—
277C23—1041no—
278C23D8×D1311yescharacteristic
279Q8—1048no—
280D4—522no—
281D4—522no—
282D4—1041no—
283D4—1041no—
284C2×C4—42no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—132no—
291C2×C4—132no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—522no—
297C2×C4—1041no—
298C2×C4—1041no—
299C2×C4#8813611yescharacteristic
300C2×C4#8813911yescharacteristic
301C2×C4#8815011yescharacteristic
302C2×C4SD16×D1311yescharacteristic
303C2×C4#8816811yescharacteristic
304C2×C4#8817211yescharacteristic
305C8—262no—
306C8#8812911yescharacteristic
307C8#8813911yescharacteristic
308C8#8815011yescharacteristic
309C8#8815111yescharacteristic
310C22—1042no—
311C22—1042no—
312C22—1042no—
313C22—2081no—
314C22—2081no—
315C22—2081no—
316C22—2081no—
317C22#1171842111yescharacteristic
318C22#1171843411yescharacteristic
319C22#1171855111yescharacteristic
320C22D13×D1611yescharacteristic
321C22D13×SD3211yescharacteristic
322C22#1171857511yescharacteristic
323C22#1171857911yescharacteristic
324C4—82no—
325C4—161no—
326C4—262no—
327C4—262no—
328C4—1042no—
329C4#1171833411yescharacteristic
330C4#1171845611yescharacteristic
331C4#1171846711yescharacteristic
332C4#1171853111yescharacteristic
333C2—2082no—
334C2#1311597111yescharacteristic
335C2#1311674911yescharacteristic
336C2#1311675411yescharacteristic
337C2#1311697211yescharacteristic
338C2#1311698211yescharacteristic
339C2#1311705811yescharacteristic
340C2#1311707411yescharacteristic
subgroupG/H
centerC23D8×D13
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#1380C2
socleC23×C13C2×D8
prime radicalC22×D104C22
hypercenter#1380D13
hypocenterC13#13363
LCSG ▷ C22×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
1. C2×#11718535C2semidirect
5. #13112927C2semidirect
6. #13112913C2semidirect
7. C13×#1380C2semidirect
39. C2×D104Q8semidirect
106. #1380D13semidirect
270. C13#13363semidirect

Maximal subgroups

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

subgroupindex
C2×#117185352
C2×#117181012
C2×#117180832
#131157002
#131129272
#131129132
C13×#13802
#1336313