Finite Group Databasebeta

← #15780716

Subgroups — #15780716

Order 3328.

390 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718081C211yesmaximal, characteristic, complemented
2C2×#11718083C211yesmaximal, characteristic
3C2×#11718083C211yesmaximal, characteristic
4#13115702C211yesmaximal, characteristic
5#13112927C211yesmaximal, characteristic, complemented
6#13112914C211yesmaximal, characteristic, complemented
7C4×C13×#107C211yesmaximal, characteristic, complemented
8C22×D104C2211yescharacteristic
9C2×C13×#107C2211yescharacteristic
10C2×C13×#107C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C4×C13×C4⋊C4—21no—
13C2×#88061—21no—
14C2×#88058C2211yescharacteristic
15C22×#6090C2211yescharacteristic
16C22×#6090C2211yescharacteristic
17#11718600—21no—
18C13×#340—21no—
19#11718083—22no—
20#11718083C414yescomplemented
21#11718081—22no—
22C22×D52—21no—
23C22×C8×C13D411yescharacteristic
24C22×C8×C13C2311yescharacteristic
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C42×C13—41no—
28C2×C42×C13D411yescharacteristic
29C2×#6103—41no—
30C2×#6103—41no—
31C2×C4⋊Dic13—21no—
32C2×D104—21no—
33C2×D104—21no—
34C2×D104—21no—
35C2×D104—21no—
36C2×D104—21no—
37C2×D104C2×C412yes—
38C13×#107—21no—
39C13×#107—21no—
40C13×#107C2×C412yes—
41C13×#107D412yes—
42C4×C8×C13—21no—
43C4×C8×C13—21no—
44C13×#95—41no—
45#88061—42no—
46#88058—21no—
47#88058—21no—
48C2×#6090—21no—
49C2×#6090—21no—
50C2×#6090—21no—
51C2×#6090—21no—
52C2×#6090—21no—
53C2×#6090C2×C412yes—
54#13130—131nomaximal, Sylow
55C23×D13—41no—
56C22×C4×C13—41no—
57C22×C4×C13—41no—
58C22×C4×C13D811yescharacteristic
59C22×C4×C13D811yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×Dic13—41no—
62C2×D52—22no—
63C2×D52—41no—
64C2×D52—41no—
65C2×D52—41no—
66C2×D52—41no—
67C2×D52—41no—
68C2×C8×C13—21no—
69C2×C8×C13—21no—
70C2×C8×C13—21no—
71C2×C8×C13C22×C411yescharacteristic
72C2×C8×C13C2×D411yescharacteristic
73C2×C8×C13#4111yescharacteristic
74C2×C8×C13#4111yescharacteristic
75C2×C8×C13#4111yescharacteristic
76C2×C8×C13#4111yescharacteristic
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—82no—
84#6103—82no—
85#6103—82no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88D104—22no—
89D104—22no—
90D104—41no—
91D104—41no—
92#6090—22no—
93#6090—41no—
94C2×#366—131no—
95C2×#357—131no—
96C2×#357—131no—
97#1970—131no—
98C4×#107D1311yescharacteristic, complemented
99#1380—131no—
100#1374—131no—
101C23×C13C2×D811yescharacteristic
102C22×D13—42no—
103C22×D13—81no—
104C22×D13—81no—
105C22×D13—81no—
106C22×D13—81no—
107C22×D13—81no—
108C22×D13—81no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—81no—
117C2×C4×C13—81no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13D1612yes—
121C2×C4×C13C4×D411yescharacteristic
122C2×C4×C13#12111yescharacteristic
123C2×C4×C13#12311yescharacteristic
124C2×C4×C13#13511yescharacteristic
125C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C13#13711yescharacteristic
127C2×Dic13—81no—
128C2×Dic13—81no—
129C2×Dic13—81no—
130D52—42no—
131D52—42no—
132D52—81no—
133D52—81no—
134C8×C13—41no—
135C8×C13#11711yescharacteristic
136C8×C13C4×D411yescharacteristic
137C8×C13#12411yescharacteristic
138C8×C13#12611yescharacteristic
139C22×D8—131no—
140C22×C16—131no—
141C22×C16—131no—
142C2×#107—131no—
143C2×#107C2×D1311yescharacteristic
144C2×#107C2×D1311yescharacteristic
145C2×#102—261no—
146C2×C4×C8C2×D1311yescharacteristic
147#390—261no—
148C4×C4⋊C4—21no—
149#366—262no—
150#357—134no—
151#357—262no—
152#340—21no—
153C22×C13C4×D811yescharacteristic
154C22×C13#45911yescharacteristic
155C22×C13#48011yescharacteristic
156C22×C13C2×D1611yescharacteristic
157C22×C13#50811yescharacteristic
158C22×C13#50911yescharacteristic
159C22×C13#51011yescharacteristic
160C2×D13—82no—
161C2×D13—82no—
162C2×D13—82no—
163C2×D13—161no—
164C2×D13—161no—
165C2×D13—161no—
166C2×D13—161no—
167C4×C13—22no—
168C4×C13—41no—
169C4×C13—82no—
170C4×C13—82no—
171C4×C13#38811yescharacteristic
172C4×C13#44011yescharacteristic
173C4×C13#46411yescharacteristic
174C4×C13#48211yescharacteristic
175Dic13—161no—
176C22×D4—261no—
177C2×D8—132no—
178C2×D8—261no—
179C2×D8—261no—
180C2×D8—261no—
181C2×D8—261no—
182C2×D8—261no—
183C22×C8C22⋊D1311yescharacteristic
184C22×C8C22×D1311yescharacteristic
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—261no—
188C2×C22⋊C4—521no—
189C2×C22⋊C4—521no—
190C2×C42—41no—
191C2×C42C22⋊D1311yescharacteristic
192C2×C16—132no—
193C2×C16—261no—
194C2×C16—261no—
195C2×C16—261no—
196C2×C16—261no—
197C2×C16—261no—
198#107—21no—
199#107—21no—
200#107—261no—
201#107—261no—
202#107C4×D1312yes—
203#107D5212yes—
204#102—522no—
205C4×C8—21no—
206C4×C8—21no—
207#95—41no—
208C2×C13#192511yescharacteristic
209C2×C13C4×D1611yescharacteristic
210C2×C13#217511yescharacteristic
211C2×C13#220611yescharacteristic
212C2×C13#221111yescharacteristic
213C2×C13#223211yescharacteristic
214C2×C13#223411yescharacteristic
215D13—162no—
216C24—521no—
217C2×D4—262no—
218C2×D4—521no—
219C2×D4—521no—
220C2×D4—521no—
221C2×D4—521no—
222C2×D4—521no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—521no—
226C22×C4#610411yescharacteristic
227C22×C4#610411yescharacteristic
228C22×C4C2×C22⋊D1311yescharacteristic
229D8—262no—
230D8—262no—
231D8—521no—
232D8—521no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8C2×C4×D1311yescharacteristic
237C2×C8C2×D5211yescharacteristic
238C2×C8#612711yescharacteristic
239C2×C8#612711yescharacteristic
240C2×C8#612711yescharacteristic
241C2×C8#612711yescharacteristic
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—521no—
247C4⋊C4—521no—
248C22⋊C4—1042no—
249C22⋊C4—1042no—
250C42—21no—
251C42—21no—
252C42—82no—
253C16—262no—
254C16—521no—
255C13#1313011yescharacteristic, complemented, Sylow
256C23—522no—
257C23—1041no—
258C23—1041no—
259C23—1041no—
260C23—1041no—
261C23—1041no—
262C23—1041no—
263C23C2×#610411yescharacteristic
264D4—522no—
265D4—522no—
266D4—1041no—
267D4—1041no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—1041no—
280C2×C4—1041no—
281C2×C4—1041no—
282C2×C4#8806612yes—
283C2×C4C4×C22⋊D1311yescharacteristic
284C2×C4#8818311yescharacteristic
285C2×C4#8818411yescharacteristic
286C2×C4#8819611yescharacteristic
287C2×C4#8820311yescharacteristic
288C2×C4#8820411yescharacteristic
289C8—41no—
290C8#8812611yescharacteristic
291C8C4×D5211yescharacteristic
292C8#8812911yescharacteristic
293C8#8813011yescharacteristic
294C22—1042no—
295C22—1042no—
296C22—1042no—
297C22—2081no—
298C22—2081no—
299C22—2081no—
300C22—2081no—
301C22#1171862811yescharacteristic
302C22C4×#610411yescharacteristic
303C22#1171867611yescharacteristic
304C22C2×#8806611yescharacteristic
305C22#1171884011yescharacteristic
306C22#1171885411yescharacteristic
307C22#1171885511yescharacteristic
308C4—22no—
309C4—41no—
310C4—82no—
311C4—82no—
312C4—2081no—
313C4#1171860111yescharacteristic
314C4#1171866411yescharacteristic
315C4#1171868711yescharacteristic
316C4#1171868911yescharacteristic
317C2—2082no—
318C2#1311545611yescharacteristic
319C2C4×#8806611yescharacteristic
320C2#1311669811yescharacteristic
321C2#1311687111yescharacteristic
322C2#1311689811yescharacteristic
323C2#1311701611yescharacteristic
324C2#1311702711yescharacteristic
subgroupG/H
centerC23C2×#6104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC4×C13×#107C2
socleC23×C13C2×D8
prime radicalC22×D104C22
cosocleC22×C8×C13C23
hypercenterC4×#107D13
hypocenterC13#13130
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
1. C2×#11718081C2semidirect
5. #13112927C2semidirect
6. #13112914C2semidirect
7. C4×C13×#107C2semidirect
20. #11718083C4semidirect
98. C4×#107D13semidirect
255. C13#13130semidirect

Maximal subgroups

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

subgroupindex
C2×#117180812
C2×#117180832
#131157022
#131129272
#131129142
C4×C13×#1072
#1313013