Finite Group Databasebeta

← #15780312

Subgroups — #15780312

Order 3328.

510 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88052C211yesmaximal, characteristic, complemented
2C2×#11718158C212yesmaximal, complemented
3#13114861C211yesmaximal, characteristic, complemented
4#13112941C212yesmaximal, complemented
5C13×#3050C211yesmaximal, characteristic
6C2×C13×#135C2211yescharacteristic
7C23×C8×C13C2211yescharacteristic
8C13×#525—21no—
9C13×#467C411yescharacteristic, complemented
10C13×#467C411yescharacteristic, complemented
11C13×#466C411yescharacteristic, complemented
12C13×#466C411yescharacteristic, complemented
13C13×#465—21no—
14C13×#465—21no—
15C13×#427C2211yescharacteristic
16C13×#416—21no—
17#11718873—21no—
18C2×#88057C2212yes—
19C2×#88052—24no—
20C2×#88052—21no—
21C2×#88052C2212yes—
22C22×#6090—21no—
23#11718158—24no—
24#11718143—21no—
25C2×C13×#41—21no—
26C23×C4×C13D411yescharacteristic
27C13×#135—22no—
28C13×#135—22no—
29C2×C13×Q16C2×C411yescharacteristic
30C2×C13×SD16—21no—
31C2×C13×D8C2×C411yescharacteristic
32C22×C8×C13—22no—
33C22×C8×C13—22no—
34C22×C8×C13C2×C411yescharacteristic
35C22×C8×C13C2×C411yescharacteristic
36C22×C8×C13D411yescharacteristic
37C22×C8×C13D411yescharacteristic
38C22×C8×C13D411yescharacteristic
39C22×C8×C13C2311yescharacteristic
40C13×#123—41no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×#121—21no—
44C13×#121—21no—
45C13×#120—41no—
46C4×D4×C13—41no—
47C4×D4×C13—41no—
48C13×#117—21no—
49C2×C22⋊Dic13—41no—
50C2×C4⋊Dic13—22no—
51C13×#107C2×C411yescharacteristic
52C13×#107C2×C411yescharacteristic
53C13×#106—21no—
54C13×#103—21no—
55C13×#103—21no—
56C13×#102—21no—
57C13×#102—21no—
58#88071—41no—
59#88057—22no—
60#88057—22no—
61#88052—24no—
62#88052—22no—
63#88052D414yescomplemented
64C2×#6090—24no—
65C2×#6090—22no—
66#13065—131nomaximal, Sylow
67C24×C13D811yescharacteristic
68C13×#41—42no—
69C13×#41—42no—
70C2×Q8×C13—21no—
71C2×D4×C13—21no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C22×C4×C13—22no—
76C22×C4×C13—22no—
77C22×C4×C13—41no—
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13D811yescharacteristic
81C22×C4×C13SD1611yescharacteristic
82C22×C4×C13SD1611yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×Dic13—42no—
85C13×Q16—22no—
86C13×SD16—41no—
87C13×SD16—41no—
88C13×D8—22no—
89C2×C8×C13—22no—
90C2×C8×C13—22no—
91C2×C8×C13—22no—
92C2×C8×C13—21no—
93C2×C8×C13—21no—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13C22⋊C411yescharacteristic
97C2×C8×C13C22⋊C411yescharacteristic
98C2×C8×C13C22×C411yescharacteristic
99C2×C8×C13C2×D412yes—
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13#4112yes—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C42×C13—41no—
112C22⋊Dic13—82no—
113C4⋊Dic13—42no—
114C4⋊Dic13—42no—
115#6090—24no—
116C22×M32—131no—
117#3050D1311yescharacteristic
118C2×#360—132no—
119#1807—131no—
120#1386—132no—
121C23×C13—22no—
122C23×C13—22no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13#10211yescharacteristic
126C23×C13#10211yescharacteristic
127C23×C13C2×D811yescharacteristic
128Q8×C13—41no—
129Q8×C13—41no—
130D4×C13—41no—
131D4×C13—41no—
132D4×C13—82no—
133D4×C13—82no—
134D4×C13—82no—
135C2×C4×C13—22no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—82no—
146C2×C4×C13#10211yescharacteristic
147C2×C4×C13#10211yescharacteristic
148C2×C4×C13C2×C22⋊C411yescharacteristic
149C2×C4×C13#12112yes—
150C2×C4×C13C2×SD1611yescharacteristic
151C2×C4×C13#13512yes—
152C2×Dic13—82no—
153C2×Dic13—82no—
154C2×Dic13—82no—
155C8×C13—21no—
156C8×C13—21no—
157C8×C13C4×D412yes—
158C8×C13#12011yescharacteristic
159C8×C13#12311yescharacteristic
160C2×#135C2×D1311yescharacteristic
161C23×C8C2×D1311yescharacteristic
162#525—21no—
163C2×M32—132no—
164C2×M32—264no—
165C2×M32—261no—
166C22×C16—261no—
167#467Dic1311yescharacteristic, complemented
168#467Dic1311yescharacteristic, complemented
169#466Dic1311yescharacteristic, complemented
170#466Dic1311yescharacteristic, complemented
171#465—21no—
172#465—21no—
173#427C2×D1311yescharacteristic
174C2×#106—132no—
175#416—21no—
176#380—261no—
177#360—264no—
178#340—261no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—44no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13#36012yescomplemented
191C22×C13C2×#10211yescharacteristic
192C22×C13#46612yes—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13#38611yescharacteristic
199C4×C13#41611yescharacteristic
200C4×C13#46512yes—
201Dic13—162no—
202C2×#41—21no—
203C23×C4C22⋊D1311yescharacteristic
204#135—22no—
205#135—22no—
206C2×Q16C2×Dic1311yescharacteristic
207C2×SD16—21no—
208C2×D8C2×Dic1311yescharacteristic
209C22×C8—22no—
210C22×C8—22no—
211C22×C8C2×Dic1311yescharacteristic
212C22×C8C2×Dic1311yescharacteristic
213C22×C8C22⋊D1311yescharacteristic
214C22×C8C22⋊D1311yescharacteristic
215C22×C8C22⋊D1311yescharacteristic
216C22×C8C22×D1311yescharacteristic
217#123—41no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220#121—21no—
221#121—21no—
222#120—41no—
223C4×D4—41no—
224C4×D4—41no—
225#117—21no—
226C2×C4⋊C4—262no—
227C2×C22⋊C4—521no—
228M32—134no—
229M32—264no—
230M32—262no—
231C2×C16—264no—
232C2×C16—262no—
233#107C2×Dic1311yescharacteristic
234#107C2×Dic1311yescharacteristic
235#106—21no—
236#106—262no—
237#106—262no—
238#103—21no—
239#103—21no—
240#102—21no—
241#102—21no—
242#95—521no—
243C2×C13—22no—
244C2×C13—22no—
245C2×C13—41no—
246C2×C13—161no—
247C2×C13#189311yescharacteristic
248C2×C13C2×#36011yescharacteristic
249C2×C13#214511yescharacteristic
250C24#610411yescharacteristic
251#41—42no—
252#41—42no—
253C2×Q8—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—522no—
262C22×C4#610411yescharacteristic
263C22×C4#610511yescharacteristic
264C22×C4#610511yescharacteristic
265C22×C4C22⋊Dic1311yescharacteristic
266C22×C4C22⋊Dic1311yescharacteristic
267C22×C4C2×C22⋊D1311yescharacteristic
268Q16—22no—
269SD16—41no—
270SD16—41no—
271D8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8C22⋊Dic1311yescharacteristic
280C2×C8C22⋊Dic1311yescharacteristic
281C2×C8D4×D1312yes—
282C2×C8#612912yes—
283C2×C8C22×Dic1311yescharacteristic
284C2×C8C2×C22⋊D1311yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—522no—
290C4⋊C4—522no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—1042no—
297C42—41no—
298C16—264no—
299C13#1306511yescharacteristic, complemented, Sylow
300C23—22no—
301C23—22no—
302C23—41no—
303C23—41no—
304C23#8807211yescharacteristic
305C23#8807211yescharacteristic
306C23C2×#610411yescharacteristic
307Q8—41no—
308Q8—41no—
309D4—41no—
310D4—41no—
311D4—82no—
312D4—82no—
313D4—82no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—82no—
325C2×C4—1042no—
326C2×C4—1042no—
327C2×C4—1042no—
328C2×C4#8807211yescharacteristic
329C2×C4#8807211yescharacteristic
330C2×C4C2×#610511yescharacteristic
331C2×C4#8819312yes—
332C2×C4#8820412yes—
333C2×C4C2×C22⋊Dic1311yescharacteristic
334C8—21no—
335C8—21no—
336C8D4×Dic1312yes—
337C8#8818911yescharacteristic
338C8#8819111yescharacteristic
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22#1171815812yescomplemented
351C22#1171869912yes—
352C22C2×#8807211yescharacteristic
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—2082no—
359C4#1171870212yes—
360C4#1171888111yescharacteristic
361C4#1171889411yescharacteristic
362C2—22no—
363C2—22no—
364C2—41no—
365C2—161no—
366C2#1311526511yescharacteristic
367C2C2×#1171815811yescharacteristic
368C2#1311657211yescharacteristic
subgroupG/H
centerC22C2×#88072
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
Fitting, prime radicalC13×#3050C2
socleC22×C13C2×#102
cosocleC22×C8×C13C23
hypercenter#3050D13
hypocenterC13#13065
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C22×#88052C2semidirect
2. C2×#11718158C2semidirect
3. #13114861C2semidirect
4. #13112941C2semidirect
9. C13×#467C4semidirect
10. C13×#467C4semidirect
11. C13×#466C4semidirect
12. C13×#466C4semidirect
63. #88052D4semidirect
167. #467Dic13semidirect
168. #467Dic13semidirect
169. #466Dic13semidirect
170. #466Dic13semidirect
190. C22×C13#360semidirect
299. C13#13065semidirect
350. C22#11718158semidirect

Maximal subgroups

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

subgroupindex
C22×#880522
C2×#117181582
#131148612
#131129412
C13×#30502
#1306513