Finite Group Databasebeta

← #15781992

Subgroups — #15781992

Order 3328.

418 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718539C211yesmaximal, 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×#88144—21no—
10C22×C13×C16C2211yescharacteristic
11C2×C13×#107C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13C2×#88058C2211yescharacteristic
14C2×C8×Dic13C2211yescharacteristic
15C22×#6090C2211yescharacteristic
16#11718649—21no—
17C2×#88049—21no—
18C2×#88048—21no—
19#11718539—22no—
20#11718539—22no—
21#11718101—22no—
22#11718083—22no—
23C22×D52—21no—
24C22×C8×C13C2311yescharacteristic
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×#6103—41no—
28C2×#6103—41no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—41no—
31C2×#6101—41no—
32C2×C4×Dic13D411yescharacteristic
33C22×#1055D411yescharacteristic
34C2×D104—21no—
35C2×D104—21no—
36C2×D104—21no—
37C2×D104—21no—
38C2×D104—21no—
39C2×D104Q812yes—
40#88144—24no—
41#88144—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#88048—24no—
58#13365—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×C8×C13C2×D411yescharacteristic
73C2×C8×C13C2×D411yescharacteristic
74C2×C8×C13C2×Q811yescharacteristic
75C2×C8×C13#4111yescharacteristic
76C2×C8×C13#4111yescharacteristic
77C2×C8×C13#4111yescharacteristic
78C13×C4⋊C4—22no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82#6103—82no—
83#6103—82no—
84C4⋊Dic13—22no—
85C4⋊Dic13—44no—
86C4⋊Dic13—41no—
87#6101—44no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C2×#1055—21no—
91C2×#1055—21no—
92C2×#1055SD1612yes—
93D104—22no—
94D104—22no—
95D104—41no—
96D104—41no—
97C13×C16—41no—
98#6090—41no—
99C2×#499—131no—
100C2×#357—131no—
101C2×#357—131no—
102#1970—131no—
103#1380—131no—
104#1380D1311yescharacteristic, complemented
105#1374—131no—
106C23×C13C2×D811yescharacteristic
107C22×D13—42no—
108C22×D13—81no—
109C22×D13—81no—
110C22×D13—81no—
111C22×D13—81no—
112C22×D13—81no—
113C22×D13—81no—
114C2×C4×C13—42no—
115C2×C4×C13—81no—
116C2×C4×C13—81no—
117C2×C4×C13—81no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13C22⋊Q811yescharacteristic
122C2×C4×C13#12411yescharacteristic
123C2×C4×C13C2×SD1611yescharacteristic
124C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C13#13711yescharacteristic
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—42no—
133C2×Dic13—81no—
134C2×Dic13—81no—
135D52—42no—
136D52—42no—
137D52—81no—
138D52—81no—
139C8×C13C22⋊Q811yescharacteristic
140C8×C13C22⋊Q811yescharacteristic
141C8×C13#12411yescharacteristic
142C8×C13#12411yescharacteristic
143#1055—22no—
144C22×D8—131no—
145C2×#125—261no—
146C22×C16—131no—
147C22×C16C2×D1311yescharacteristic
148#499—262no—
149#499—262no—
150C2×#107—131no—
151C2×#107C2×D1311yescharacteristic
152C2×#107C2×D1311yescharacteristic
153C2×#106—261no—
154C2×#102—261no—
155C2×C4×C8—131no—
156#390—261no—
157#357—262no—
158#357—262no—
159C22×C13#44711yescharacteristic
160C22×C13#47411yescharacteristic
161C22×C13#48611yescharacteristic
162C22×C13#50811yescharacteristic
163C22×C13#50811yescharacteristic
164C22×C13#50911yescharacteristic
165C22×C13#50911yescharacteristic
166C2×D13—82no—
167C2×D13—82no—
168C2×D13—82no—
169C2×D13—161no—
170C2×D13—161no—
171C2×D13—161no—
172C2×D13—161no—
173C4×C13—82no—
174C4×C13—161no—
175C4×C13#39311yescharacteristic
176C4×C13#44811yescharacteristic
177C4×C13#47611yescharacteristic
178C4×C13#48911yescharacteristic
179Dic13—41no—
180Dic13—41no—
181Dic13—82no—
182C22×D4—261no—
183C2×D8—132no—
184C2×D8—261no—
185C2×D8—261no—
186C2×D8—261no—
187C2×D8—261no—
188C2×D8—261no—
189C22×C8—131no—
190C22×C8C22×D1311yescharacteristic
191#125—264no—
192#125—522no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—521no—
197C2×C4⋊C4—521no—
198C2×C22⋊C4—521no—
199C2×C22⋊C4—521no—
200C2×C42—131no—
201C2×C16—21no—
202C2×C16—21no—
203C2×C16—21no—
204C2×C16—261no—
205C2×C16—261no—
206C2×C16—261no—
207#107—21no—
208#107—21no—
209#107—21no—
210#107—132no—
211#107—261no—
212#107D5212yes—
213#106—264no—
214#102—522no—
215C4×C8—261no—
216C4×C8—261no—
217C2×C13#202311yescharacteristic
218C2×C13#218611yescharacteristic
219C2×C13#218611yescharacteristic
220C2×C13#222811yescharacteristic
221C2×C13#222811yescharacteristic
222C2×C13#224211yescharacteristic
223C2×C13#224411yescharacteristic
224D13—162no—
225C24—521no—
226C2×D4—262no—
227C2×D4—521no—
228C2×D4—521no—
229C2×D4—521no—
230C2×D4—521no—
231C2×D4—521no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—521no—
237C22×C4D4×D1311yescharacteristic
238D8—262no—
239D8—262no—
240D8—521no—
241D8—521no—
242C2×C8—132no—
243C2×C8—261no—
244C2×C8—261no—
245C2×C8C2×D5211yescharacteristic
246C2×C8#612711yescharacteristic
247C2×C8#612711yescharacteristic
248C2×C8D4×D1311yescharacteristic
249C2×C8#612911yescharacteristic
250C2×C8Q8×D1311yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—262no—
256C4⋊C4—524no—
257C4⋊C4—524no—
258C4⋊C4—521no—
259C22⋊C4—1042no—
260C22⋊C4—1042no—
261C42—261no—
262C42—261no—
263C16—41no—
264C16—521no—
265C13#1336511yescharacteristic, complemented, Sylow
266C23—522no—
267C23—1041no—
268C23—1041no—
269C23—1041no—
270C23—1041no—
271C23—1041no—
272C23—1041no—
273C23D8×D1311yescharacteristic
274D4—522no—
275D4—522no—
276D4—1041no—
277D4—1041no—
278C2×C4—42no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—522no—
291C2×C4—1041no—
292C2×C4—1041no—
293C2×C4#8813611yescharacteristic
294C2×C4#8813911yescharacteristic
295C2×C4#8815011yescharacteristic
296C2×C4SD16×D1311yescharacteristic
297C2×C4#8816811yescharacteristic
298C2×C4#8817211yescharacteristic
299C8—262no—
300C8#8812911yescharacteristic
301C8#8813911yescharacteristic
302C8#8815011yescharacteristic
303C8#8815111yescharacteristic
304C22—1042no—
305C22—1042no—
306C22—1042no—
307C22—2081no—
308C22—2081no—
309C22—2081no—
310C22—2081no—
311C22#1171842111yescharacteristic
312C22#1171843411yescharacteristic
313C22#1171855111yescharacteristic
314C22#1171857211yescharacteristic
315C22#1171857511yescharacteristic
316C22#1171857711yescharacteristic
317C22#1171858011yescharacteristic
318C4—82no—
319C4—161no—
320C4—521no—
321C4—521no—
322C4—1042no—
323C4#1171833411yescharacteristic
324C4#1171845611yescharacteristic
325C4#1171846711yescharacteristic
326C4#1171853111yescharacteristic
327C2—2082no—
328C2#1311597111yescharacteristic
329C2#1311676011yescharacteristic
330C2#1311676211yescharacteristic
331C2#1311699211yescharacteristic
332C2#1311699611yescharacteristic
333C2#1311706911yescharacteristic
334C2#1311707611yescharacteristic
subgroupG/H
centerC23D8×D13
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#1380C2
socleC23×C13C2×D8
prime radicalC22×D104C22
hypercenter#1380D13
hypocenterC13#13365
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×#11718539C2semidirect
5. #13112927C2semidirect
6. #13112913C2semidirect
7. C13×#1380C2semidirect
104. #1380D13semidirect
265. C13#13365semidirect

Maximal subgroups

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

subgroupindex
C2×#117185392
C2×#117181012
C2×#117180832
#131157002
#131129272
#131129132
C13×#13802
#1336513