Finite Group Databasebeta

← #16796864

Subgroups — #16796864

Order 3328.

908 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131399C212yesmaximal
2#13130558C214yesmaximal, complemented
3#13130557C214yesmaximal, complemented
4D13⋊#338C211yesmaximal, characteristic
5#13130508C211yesmaximal, characteristic
6C2×#11718235C212yesmaximal
7#13123253C211yesmaximal, characteristic
8C2×#88237C2212yes—
9C2×D13⋊M16C2212yes—
10C2×M16×D13C2211yescharacteristic
11C2×M16×D13C2211yescharacteristic
12C2×#88126C2211yescharacteristic
13#11719099C418yescomplemented
14M16×#261C418yescomplemented
15#11719089C2218yes—
16C4×C13×M16C411yescharacteristic, complemented
17M16×Dic13C411yescharacteristic, complemented
18M16×Dic13C411yescharacteristic, complemented
19C4×#6099C411yescharacteristic, complemented
20#11718369C412yescomplemented
21#11718369C2212yes—
22#11718350C412yescomplemented
23#11718350C2212yes—
24#11718269C2214yes—
25#11718267C2214yes—
26#11718235C2214yes—
27#11718235C2214yes—
28C22×C4×D13C2311yescharacteristic
29C2×C22⋊#261—22no—
30C2×#6122—22no—
31#88237—22no—
32#88237—22no—
33#88237C2×C414yes—
34#88237C2314yes—
35C2×C4⋊#261—22no—
36C2×C4×#261C2×C414yes—
37D13⋊M16—22no—
38D13⋊M16—22no—
39D13⋊M16C2×C414yes—
40D13⋊M16C2314yes—
41C2×#6118—22no—
42C2×D13⋊C8C2×C414yes—
43C2×C13×M16C2×C411yescharacteristic
44C2×C13×M16C2×C411yescharacteristic
45C2×C42×C13C2×C411yescharacteristic
46C2×#6103—21no—
47C2×#6101—21no—
48C2×C4×Dic13C2×C411yescharacteristic
49C2×#6099C2×C411yescharacteristic
50C2×#6099C2×C411yescharacteristic
51M16×D13—22no—
52M16×D13—22no—
53M16×D13C2×C414yes—
54M16×D13C2×C414yes—
55C2×#6094C2×C412yes—
56C2×#6094C2312yes—
57C2×C8×D13C2×C412yes—
58C2×C8×D13C2312yes—
59#88126—21no—
60#88126—21no—
61#88126C2×C411yescharacteristic
62#88126C2×C411yescharacteristic
63#88126C2311yescharacteristic
64#88126C2311yescharacteristic
65#88100C2×C4116yescomplemented
66C8×#261C2×C4116yescomplemented
67C13×#97C2×C412yescomplemented
68C4×C8×C13C2×C412yescomplemented
69#88055C2×C412yescomplemented
70#88055C2×C412yescomplemented
71C8×Dic13C2×C412yescomplemented
72C8×Dic13C2×C412yescomplemented
73#88043C2×C412yescomplemented
74C4×#1055C2×C412yescomplemented
75#20370—131nomaximal, Sylow
76C23×D13#4111yescharacteristic
77C22×#261—24no—
78C22×C4×C13—21no—
79C22×C4×C13C22×C411yescharacteristic
80C22×Dic13—21no—
81C22×Dic13#4111yescharacteristic
82C2×C4×D13C22×C411yescharacteristic
83C2×C4×D13C22×C412yes—
84C2×C4×D13C22×C412yes—
85C2×C4×D13#4111yescharacteristic
86C2×C4×D13#4111yescharacteristic
87C2×C4×D13#4112yes—
88C2×C4×D13#4112yes—
89C2×C4×D13C2411yescharacteristic
90C22⋊#261—24no—
91C22⋊#261—24no—
92#6122—24no—
93#6122—24no—
94C2×#1057—24no—
95C4⋊#261—24no—
96C4⋊#261—24no—
97C4×#261—24no—
98C4×#261C22×C418yes—
99#6118—24no—
100#6118—24no—
101D13⋊C8—24no—
102D13⋊C8C22×C418yes—
103C13×M16—22no—
104C13×M16C4214yes—
105C2×C8×C13C22×C412yes—
106C2×C8×C13C22×C412yes—
107C42×C13—21no—
108C42×C13C22×C411yescharacteristic
109C42×C13C22×C411yescharacteristic
110#6103—21no—
111#6103—21no—
112#6103—21no—
113#6103—21no—
114#6101—21no—
115#6101—21no—
116#6101—21no—
117#6101—21no—
118C4×Dic13—21no—
119C4×Dic13C22×C411yescharacteristic
120C4×Dic13C22×C411yescharacteristic
121#6099—22no—
122#6099C4214yes—
123C2×#1055C22×C412yes—
124C2×#1055C22×C412yes—
125#6094—24no—
126#6094C4214yes—
127#6094C4214yes—
128C8×D13—22no—
129C8×D13—22no—
130C8×D13C22×C418yes—
131#2873—132no—
132#2873—131no—
133#1747—134no—
134#1747—134no—
135C2×#338—131no—
136C2×H(3,ℤ/4)—132no—
137C2×H(3,ℤ/4)—131no—
138C23×C13#11711yescharacteristic
139C22×D13—81no—
140C22×D13#11712yes—
141C22×D13#11712yes—
142C22×D13#11711yescharacteristic
143C22×D13C2×#4111yescharacteristic
144C2×#261—28no—
145C2×#261—84no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—81no—
149C2×C4×C13C2×C4212yes—
150C2×C4×C13#11712yes—
151C2×C4×C13#11711yescharacteristic
152C2×C4×C13C23×C411yescharacteristic
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—81no—
156C2×Dic13#11712yes—
157C2×Dic13#11712yes—
158C2×Dic13#11711yescharacteristic
159C2×Dic13C2×#4111yescharacteristic
160C4×D13C2×C4211yescharacteristic
161C4×D13C2×C4211yescharacteristic
162C4×D13#11712yes—
163C4×D13#11712yes—
164C4×D13#11711yescharacteristic
165C4×D13#11711yescharacteristic
166C4×D13#11712yes—
167C4×D13#11712yes—
168C4×D13C23×C412yes—
169C4×D13C2×#4112yes—
170#1057—28no—
171C8×C13—22no—
172C8×C13C2×C4214yes—
173#1055—22no—
174#1055C2×C4214yes—
175C22×M16—131no—
176C22×M16—132no—
177C22×M16—131no—
178C2×#117—132no—
179C2×#117—131no—
180#405—138no—
181#405—138no—
182#405—132no—
183#405—132no—
184#405—132no—
185#405—132no—
186C4×M16—138no—
187C4×M16—131no—
188C4×M16—131no—
189C4×M16—131no—
190C4×M16#26111yescharacteristic, complemented
191#338—134no—
192H(3,ℤ/4)—134no—
193H(3,ℤ/4)—134no—
194H(3,ℤ/4)—134no—
195C22×C13—41no—
196C22×C13#37612yes—
197C22×C13C2×#11711yescharacteristic
198C2×D13—42no—
199C2×D13—42no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13#37611yescharacteristic
203C2×D13#37611yescharacteristic
204C2×D13C2×#11712yes—
205#261—48no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13#37612yes—
209C4×C13C22×C4211yescharacteristic
210C4×C13C2×#11711yescharacteristic
211Dic13—41no—
212Dic13—41no—
213Dic13#37611yescharacteristic
214Dic13#37611yescharacteristic
215Dic13C2×#11712yes—
216C23×C4—131no—
217C2×M16—131no—
218C2×M16—134no—
219C2×M16—134no—
220C2×M16—134no—
221C2×M16—134no—
222C2×M16—131no—
223C2×M16—132no—
224C2×M16—132no—
225C2×M16—262no—
226C2×M16—262no—
227C2×M16—262no—
228C2×M16—262no—
229C2×M16—262no—
230C2×M16—262no—
231C2×M16C2×#26111yescharacteristic
232C2×M16C2×#26111yescharacteristic
233C22×C8—132no—
234C22×C8—134no—
235C22×C8—132no—
236#117—134no—
237#117—134no—
238#117—131no—
239#117—131no—
240#117—131no—
241#117—131no—
242#117—261no—
243#117—261no—
244#117—262no—
245#117—262no—
246C2×C4⋊C4—261no—
247C2×C4⋊C4—262no—
248C2×C22⋊C4—261no—
249C2×C22⋊C4—262no—
250C2×C42—134no—
251C2×C42—131no—
252C2×C42C2×#26111yescharacteristic
253#97—1316no—
254#97—132no—
255#97—132no—
256#97—132no—
257#97C2×#26112yescomplemented
258C4×C8—1316no—
259C4×C8—132no—
260C4×C8—132no—
261C4×C8—132no—
262C4×C8C2×#26112yescomplemented
263C2×C13—21no—
264C2×C13—22no—
265C2×C13C2×#37611yescharacteristic
266D13—22no—
267D13—21no—
268D13—21no—
269C24—131no—
270C22×C4—21no—
271C22×C4—131no—
272C22×C4—132no—
273C22×C4—132no—
274C22×C4—132no—
275C22×C4—131no—
276C22×C4—132no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—264no—
281C22×C4—261no—
282C22×C4C22×#26111yescharacteristic
283M16—22no—
284M16—134no—
285M16—134no—
286M16—134no—
287M16—264no—
288M16—264no—
289M16—264no—
290M16—264no—
291M16—264no—
292M16—262no—
293M16C4×#26114yes—
294C2×C8—132no—
295C2×C8—138no—
296C2×C8—138no—
297C2×C8—132no—
298C2×C8—262no—
299C2×C8—262no—
300C2×C8—264no—
301C2×C8—264no—
302C2×C8C22×#26112yes—
303C2×C8C22×#26112yes—
304C4⋊C4—261no—
305C4⋊C4—261no—
306C4⋊C4—261no—
307C4⋊C4—261no—
308C4⋊C4—264no—
309C4⋊C4—264no—
310C22⋊C4—261no—
311C22⋊C4—261no—
312C22⋊C4—261no—
313C22⋊C4—261no—
314C22⋊C4—264no—
315C22⋊C4—264no—
316C42—21no—
317C42—138no—
318C42—131no—
319C42—131no—
320C42—264no—
321C42—261no—
322C42C22×#26111yescharacteristic
323C42C22×#26111yescharacteristic
324C13#2037011yescharacteristic, complemented, Sylow
325C23—132no—
326C23—132no—
327C23—131no—
328C23—131no—
329C23—1041no—
330C23#8823711yescharacteristic
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—81no—
334C2×C4—132no—
335C2×C4—132no—
336C2×C4—131no—
337C2×C4—131no—
338C2×C4—132no—
339C2×C4—132no—
340C2×C4—132no—
341C2×C4—132no—
342C2×C4—132no—
343C2×C4—131no—
344C2×C4—131no—
345C2×C4—132no—
346C2×C4—131no—
347C2×C4—131no—
348C2×C4—268no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—1041no—
352C2×C4—1044no—
353C2×C4C2×C4×#26112yes—
354C2×C4#8823711yescharacteristic
355C2×C4#8823712yes—
356C2×C4C23×#26111yescharacteristic
357C8—22no—
358C8—134no—
359C8—268no—
360C8—262no—
361C8C2×C4×#26114yes—
362C22—41no—
363C22—132no—
364C22—131no—
365C22—131no—
366C22—522no—
367C22—521no—
368C22—521no—
369C22—522no—
370C22#1171905712yes—
371C22C2×#8823711yescharacteristic
372C4—41no—
373C4—41no—
374C4—132no—
375C4—131no—
376C4—131no—
377C4—521no—
378C4—521no—
379C4—528no—
380C4#1171905712yes—
381C4C22×C4×#26111yescharacteristic
382C4C2×#8823711yescharacteristic
383C2—21no—
384C2—22no—
385C2—262no—
386C2—261no—
387C2—261no—
388C2C2×#1171905711yescharacteristic
subgroupG/H
centerC4C22×C4×#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC4×C13×M16C4
socleC2×C13C2×#376
prime radicalC23×D13#41
cosocleC2×C4×D13C24
hypercenterC4×M16#261
hypocenterC13#20370
LCSG ▷ C4×C13 ▷ C13
UCSC1 ◁ C4 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #13130558C2semidirect
3. #13130557C2semidirect
13. #11719099C4semidirect
14. M16×#261C4semidirect
16. C4×C13×M16C4semidirect
17. M16×Dic13C4semidirect
18. M16×Dic13C4semidirect
19. C4×#6099C4semidirect
20. #11718369C4semidirect
22. #11718350C4semidirect
65. #88100C2×C4semidirect
66. C8×#261C2×C4semidirect
67. C13×#97C2×C4semidirect
68. C4×C8×C13C2×C4semidirect
69. #88055C2×C4semidirect
70. #88055C2×C4semidirect
71. C8×Dic13C2×C4semidirect
72. C8×Dic13C2×C4semidirect
73. #88043C2×C4semidirect
74. C4×#1055C2×C4semidirect
190. C4×M16#261semidirect
257. #97C2×#261semidirect
262. C4×C8C2×#261semidirect
324. C13#20370semidirect

Maximal subgroups

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

subgroupindex
#131313992
#131305582
#131305572
D13⋊#3382
#131305082
C2×#117182352
#131232532
#2037013