Finite Group Databasebeta

← #15780311

Subgroups — #15780311

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
1#13124417C211yesmaximal, characteristic
2C2×#11718110C212yesmaximal, complemented
3#13114861C211yesmaximal, characteristic, complemented
4#13112942C212yesmaximal, complemented
5C22×C13×M32C211yesmaximal, characteristic, complemented
6C23×C8×C13C2211yescharacteristic
7#11719496—21no—
8C2×#88158C2211yescharacteristic
9C2×C13×M32—21no—
10C2×C13×M32—24no—
11C2×C13×M32C2212yes—
12C22×C13×C16—21no—
13#11718873—21no—
14#11718777C411yescharacteristic, complemented
15#11718777C411yescharacteristic, complemented
16#11718776C411yescharacteristic, complemented
17#11718776C411yescharacteristic, complemented
18#11718775—21no—
19#11718775—21no—
20#11718774—21no—
21#11718767C2211yescharacteristic
22C2×#88057C2212yes—
23#11718143—21no—
24#11718110—24no—
25C23×C4×C13D411yescharacteristic
26C2×#6127—21no—
27C22×C8×C13—22no—
28C22×C8×C13—22no—
29C22×C8×C13C2×C411yescharacteristic
30C22×C8×C13C2×C411yescharacteristic
31C22×C8×C13D411yescharacteristic
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C22×C8×C13C2311yescharacteristic
35#88207—41no—
36C2×C22⋊Dic13—41no—
37#88184—21no—
38#88184—21no—
39#88183—41no—
40C4×C22⋊D13—41no—
41C4×C22⋊D13—41no—
42#88180—21no—
43C2×C4⋊Dic13—22no—
44#88178—21no—
45#88178—21no—
46C2×Dic52C2×C411yescharacteristic
47#88158—22no—
48#88158—22no—
49C2×D104C2×C411yescharacteristic
50C2×#6095—21no—
51C13×M32—24no—
52C13×M32—22no—
53C13×M32D414yescomplemented
54C2×C13×C16—24no—
55C2×C13×C16—22no—
56#88071—41no—
57#88061—21no—
58#88061—21no—
59#88058C2×C411yescharacteristic
60#88058C2×C411yescharacteristic
61#88057—21no—
62#88057—22no—
63#88057—22no—
64#88056—21no—
65#88056—21no—
66#13065—131nomaximal, Sylow
67C24×C13D811yescharacteristic
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13D811yescharacteristic
73C22×C4×C13SD1611yescharacteristic
74C22×C4×C13SD1611yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C2×C22⋊D13—41no—
77C2×C22⋊D13—41no—
78C2×C22⋊D13—41no—
79C22×Dic13—42no—
80#6127—42no—
81#6127—42no—
82C2×D52—21no—
83C2×C4×D13—41no—
84C2×Dic26—21no—
85C2×C8×C13—22no—
86C2×C8×C13—22no—
87C2×C8×C13—22no—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13C22⋊C411yescharacteristic
93C2×C8×C13C22⋊C411yescharacteristic
94C2×C8×C13C22×C411yescharacteristic
95C2×C8×C13C2×D412yes—
96C2×C8×C13C2×D411yescharacteristic
97C2×C8×C13#4112yes—
98C22⋊Dic13—41no—
99C22⋊Dic13—41no—
100C22⋊Dic13—41no—
101C22⋊Dic13—82no—
102#6103—41no—
103#6103—41no—
104C4⋊Dic13—21no—
105C4⋊Dic13—21no—
106C4⋊Dic13—42no—
107C4⋊Dic13—42no—
108#6101—41no—
109#6101—41no—
110C4×Dic13—41no—
111Dic52—22no—
112D104—22no—
113#6095—41no—
114#6095—41no—
115C13×C16—24no—
116C22×M32D1311yescharacteristic, complemented
117#3050—131no—
118C2×#360—132no—
119#1807—131no—
120#1386—132no—
121C23×C13—22no—
122C23×C13—22no—
123C23×C13—41no—
124C23×C13#10211yescharacteristic
125C23×C13#10211yescharacteristic
126C23×C13C2×D811yescharacteristic
127C22×D13—41no—
128C2×C4×C13—22no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13#10211yescharacteristic
136C2×C4×C13#10211yescharacteristic
137C2×C4×C13C2×C22⋊C411yescharacteristic
138C2×C4×C13#12112yes—
139C2×C4×C13C2×SD1611yescharacteristic
140C2×C4×C13#13512yes—
141C22⋊D13—82no—
142C22⋊D13—82no—
143C22⋊D13—82no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—82no—
148C2×Dic13—82no—
149C2×Dic13—82no—
150D52—41no—
151D52—41no—
152C4×D13—82no—
153Dic26—41no—
154Dic26—41no—
155C8×C13—21no—
156C8×C13—21no—
157C8×C13C4×D412yes—
158C8×C13#12011yescharacteristic
159C8×C13#12311yescharacteristic
160C2×#135—131no—
161C23×C8C2×D1311yescharacteristic
162#525—261no—
163C2×M32—21no—
164C2×M32—24no—
165C2×M32C2×D1312yes—
166C22×C16—21no—
167#467—131no—
168#467—131no—
169#466—131no—
170#466—131no—
171#465—261no—
172#465—261no—
173#427—131no—
174C2×#106—132no—
175#416—261no—
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#36012yescomplemented
188C22×C13C2×#10211yescharacteristic
189C22×C13#46612yes—
190C2×D13—81no—
191C2×D13—81no—
192C2×D13—81no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13#38611yescharacteristic
196C4×C13#41611yescharacteristic
197C4×C13#46512yes—
198Dic13—81no—
199Dic13—81no—
200Dic13—81no—
201Dic13—162no—
202C2×#41—261no—
203C23×C4D5211yescharacteristic
204#135—262no—
205#135—262no—
206C2×Q16—131no—
207C2×SD16—261no—
208C2×D8—131no—
209C22×C8—22no—
210C22×C8—22no—
211C22×C8C4×D1311yescharacteristic
212C22×C8C4×D1311yescharacteristic
213C22×C8D5211yescharacteristic
214C22×C8C22⋊D1311yescharacteristic
215C22×C8C22⋊D1311yescharacteristic
216C22×C8C22×D1311yescharacteristic
217#123—521no—
218C22⋊Q8—261no—
219C22⋊Q8—261no—
220#121—261no—
221#121—261no—
222#120—521no—
223C4×D4—521no—
224C4×D4—521no—
225#117—261no—
226C2×C4⋊C4—262no—
227C2×C22⋊C4—521no—
228M32—24no—
229M32—22no—
230M32C22⋊D1314yescomplemented
231C2×C16—24no—
232C2×C16—22no—
233#107—131no—
234#107—131no—
235#106—261no—
236#106—262no—
237#106—262no—
238#103—261no—
239#103—261no—
240#102—261no—
241#102—261no—
242#95—521no—
243C2×C13—22no—
244C2×C13—22no—
245C2×C13—41no—
246C2×C13#189311yescharacteristic
247C2×C13C2×#36011yescharacteristic
248C2×C13#214511yescharacteristic
249D13—161no—
250C24D10411yescharacteristic
251#41—522no—
252#41—522no—
253C2×Q8—261no—
254C2×D4—261no—
255C2×D4—521no—
256C2×D4—521no—
257C2×D4—521no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—521no—
261C22×C4—522no—
262C22×C4#609511yescharacteristic
263C22×C4#609511yescharacteristic
264C22×C4D10411yescharacteristic
265C22×C4#610311yescharacteristic
266C22×C4#610311yescharacteristic
267C22×C4C2×D5211yescharacteristic
268Q16—262no—
269SD16—521no—
270SD16—521no—
271D8—262no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8#610311yescharacteristic
280C2×C8#610311yescharacteristic
281C2×C8C2×C4×D1311yescharacteristic
282C2×C8#612712yes—
283C2×C8C2×C22⋊D1312yes—
284C2×C8C2×C22⋊D1311yescharacteristic
285C4⋊C4—261no—
286C4⋊C4—261no—
287C4⋊C4—521no—
288C4⋊C4—521no—
289C4⋊C4—522no—
290C4⋊C4—522no—
291C22⋊C4—521no—
292C22⋊C4—521no—
293C22⋊C4—521no—
294C22⋊C4—521no—
295C22⋊C4—521no—
296C22⋊C4—1042no—
297C42—521no—
298C16—24no—
299C13#1306511yescharacteristic, complemented, Sylow
300C23—22no—
301C23—22no—
302C23—41no—
303C23—521no—
304C23#8806111yescharacteristic
305C23#8806111yescharacteristic
306C23C2×D10411yescharacteristic
307Q8—521no—
308Q8—521no—
309D4—521no—
310D4—521no—
311D4—1042no—
312D4—1042no—
313D4—1042no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—1042no—
325C2×C4—1042no—
326C2×C4—1042no—
327C2×C4—1042no—
328C2×C4#8806111yescharacteristic
329C2×C4#8806111yescharacteristic
330C2×C4C2×#609511yescharacteristic
331C2×C4#8815812yes—
332C2×C4C2×#610311yescharacteristic
333C2×C4#8818412yes—
334C8—21no—
335C8—21no—
336C8C4×C22⋊D1312yes—
337C8#8818311yescharacteristic
338C8#8820711yescharacteristic
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22—1041no—
348C22—1041no—
349C22—1041no—
350C22#1171811012yescomplemented
351C22C2×#8806111yescharacteristic
352C22#1171877612yes—
353C4—21no—
354C4—21no—
355C4—1041no—
356C4—1041no—
357C4—1041no—
358C4—2082no—
359C4#1171877411yescharacteristic
360C4#1171877512yes—
361C4#1171887411yescharacteristic
362C2—22no—
363C2—22no—
364C2—41no—
365C2—2081no—
366C2#1311526411yescharacteristic
367C2C2×#1171811011yescharacteristic
368C2#1311657311yescharacteristic
subgroupG/H
centerC22C2×#88061
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC22×C13×M32C2
socleC22×C13C2×#102
prime radical#13124417C2
cosocleC22×C8×C13C23
hypercenterC22×M32D13
hypocenterC13#13065
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

Complements

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

NH ≅ G/Ntype
2. C2×#11718110C2semidirect
3. #13114861C2semidirect
4. #13112942C2semidirect
5. C22×C13×M32C2semidirect
14. #11718777C4semidirect
15. #11718777C4semidirect
16. #11718776C4semidirect
17. #11718776C4semidirect
53. C13×M32D4semidirect
116. C22×M32D13semidirect
187. C22×C13#360semidirect
230. M32C22⋊D13semidirect
299. C13#13065semidirect
350. C22#11718110semidirect

Maximal subgroups

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

subgroupindex
#131244172
C2×#117181102
#131148612
#131129422
C22×C13×M322
#1306513