Finite Group Databasebeta

← #15753955

Subgroups — #15753955

Order 3328.

444 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123805C211yesmaximal, characteristic
2#13114523C211yesmaximal, characteristic, complemented
3#13113425C211yesmaximal, characteristic
4#13113320C211yesmaximal, characteristic
5M16×#1055C211yesmaximal, characteristic, complemented
6#13112734C211yesmaximal, characteristic, complemented
7C13×#1300C211yesmaximal, characteristic, complemented
8#11719184C2211yescharacteristic
9C13×#432C2211yescharacteristic
10C4×C13×M16C2211yescharacteristic
11C13×#376C2211yescharacteristic
12#11718586C2211yescharacteristic
13C2×#88043—21no—
14C2×#88043C2211yescharacteristic
15C2×C4×#1055—21no—
16C2×C4×#1055C2211yescharacteristic
17#11718499C411yescharacteristic, complemented
18#11718495C411yescharacteristic, complemented
19#11718492C411yescharacteristic, complemented
20#11718491C411yescharacteristic, complemented
21#11718391—21no—
22#11718386—21no—
23#11718370—21no—
24#11718369—21no—
25#11718057C412yescomplemented
26#11718056C412yescomplemented
27#11718047—21no—
28C8×#1055—21no—
29#11718044C412yes—
30#11718043C412yes—
31C2×C13×M16—21no—
32C2×C42×C13—21no—
33C2×C42×C13C2311yescharacteristic
34#88184C2×C411yescharacteristic
35#88183—21no—
36C4×C22⋊D13—21no—
37#88178C2×C411yescharacteristic
38C22×#1055—21no—
39C22×#1055D411yescharacteristic
40C22×#1055D411yescharacteristic
41C2×#6094—21no—
42C2×C8×D13—21no—
43#88130—21no—
44#88129C2×C411yescharacteristic
45C4×D52C2×C411yescharacteristic
46#88126—21no—
47#88124C2×C411yescharacteristic
48C4×Dic26C2×C411yescharacteristic
49C13×C4⋊C8C2×C411yescharacteristic
50C13×C4⋊C8C2×C411yescharacteristic
51C13×C22⋊C8—21no—
52C13×#97—21no—
53C13×#97C2×C412yes—
54C4×C8×C13—21no—
55C13×#95—21no—
56C13×#95C2×C412yes—
57C22⋊#1055C2×C412yes—
58#88060—21no—
59#88060—21no—
60#88055—21no—
61#88054—21no—
62#88054—21no—
63C8×Dic13—21no—
64C4⋊#1055—21no—
65#88043—24no—
66#88043—21no—
67#88043C2×C412yes—
68C4×#1055—24no—
69C4×#1055—21no—
70C4×#1055C2×C411yescharacteristic
71C4×#1055C2×C411yescharacteristic
72C4×#1055D411yescharacteristic
73C4×#1055D411yescharacteristic
74#8247—131nomaximal, Sylow
75C22×C4×C13—22no—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C2×C22⋊D13—21no—
80C2×D52C4211yescharacteristic
81C2×C4×D13—21no—
82C2×Dic26C4211yescharacteristic
83C13×M16—24no—
84C2×C8×C13—22no—
85C2×C8×C13—21no—
86C2×C8×C13—21no—
87C42×C13—22no—
88C42×C13—22no—
89C42×C13C22×C411yescharacteristic
90C42×C13C22×C411yescharacteristic
91C42×C13C2×D411yescharacteristic
92C42×C13#4111yescharacteristic
93C22⋊Dic13—21no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98C4⋊Dic13C4211yescharacteristic
99C4⋊Dic13C4211yescharacteristic
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104C4×Dic13—21no—
105C2×#1055—22no—
106C2×#1055—22no—
107C2×#1055—22no—
108C2×#1055—22no—
109C2×#1055—22no—
110C2×#1055—22no—
111C2×#1055C22⋊C411yescharacteristic
112C2×#1055C22⋊C411yescharacteristic
113C2×#1055C22⋊C411yescharacteristic
114C2×#1055C22⋊C411yescharacteristic
115#6094—42no—
116C8×D13—42no—
117#2966—131no—
118#1726—131no—
119#1524—131no—
120#1500—131no—
121C8×M16—131no—
122#1302—131no—
123#1300D1311yescharacteristic, complemented
124C23×C13C4×D411yescharacteristic
125C22×D13—21no—
126C2×C4×C13—22no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—24no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13C2×C4211yescharacteristic
134C2×C4×C13C2×C22⋊C411yescharacteristic
135C2×C4×C13#11711yescharacteristic
136C2×C4×C13C4×D411yescharacteristic
137C2×C4×C13C4×D411yescharacteristic
138C2×C4×C13C4×D411yescharacteristic
139C22⋊D13—42no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143D52—41no—
144C4×D13—41no—
145C4×D13—41no—
146Dic26—41no—
147C8×C13—24no—
148C8×C13—41no—
149C8×C13—41no—
150#1055—24no—
151#1055—21no—
152#1055—21no—
153#1055—42no—
154#1055#10412yes—
155#1055#10412yes—
156#529—131no—
157#446—131no—
158C8×Q8—131no—
159#436—131no—
160#435—261no—
161C8×D4—131no—
162C8×D4—261no—
163#433—261no—
164#432C2×D1311yescharacteristic
165#431—131no—
166#405—261no—
167C4×M16C2×D1311yescharacteristic
168C2×#97—131no—
169C2×#97—261no—
170C2×C4×C8—131no—
171C2×C4×C8—261no—
172#376C2×D1311yescharacteristic
173#330—132no—
174#329—132no—
175#328—132no—
176#327—132no—
177#322—261no—
178C82—261no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13C4×C22⋊C411yescharacteristic
182C22×C13#44312yes—
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—41no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—44no—
192C4×C13C2×#10411yescharacteristic
193C4×C13C2×#10411yescharacteristic
194Dic13—41no—
195Dic13—41no—
196Dic13—41no—
197C2×M16—21no—
198C2×M16—261no—
199C22×C8—131no—
200C22×C8—131no—
201C22×C8—261no—
202C22×C8—261no—
203#126—261no—
204#125—131no—
205#124—131no—
206#123—261no—
207C22⋊Q8—131no—
208#121—131no—
209C4×Q8—131no—
210C4×D4—131no—
211C4×D4—261no—
212#117—261no—
213C2×C42—21no—
214C2×C42C22×D1311yescharacteristic
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4⋊C8—261no—
218C4⋊C8C4×D1311yescharacteristic
219C4⋊C8C4×D1311yescharacteristic
220C22⋊C8—21no—
221C22⋊C8—132no—
222C22⋊C8—261no—
223C22⋊C8—261no—
224#97—21no—
225#97—132no—
226#97—264no—
227#97—261no—
228#97—261no—
229#97C4×D1312yes—
230C4×C8—21no—
231C4×C8—131no—
232C4×C8—131no—
233C4×C8—131no—
234C4×C8—131no—
235C4×C8—264no—
236C4×C8—261no—
237C4×C8—261no—
238#95—21no—
239#95C4×D1312yes—
240C2×C13—22no—
241C2×C13#175711yescharacteristic
242C2×C13C4×#10411yescharacteristic
243C2×C13#176411yescharacteristic
244D13—81no—
245C2×Q8—131no—
246C2×D4—131no—
247C2×D4—261no—
248C22×C4—22no—
249C22×C4—261no—
250C22×C4C2×C4×D1311yescharacteristic
251C22×C4D4×D1311yescharacteristic
252C22×C4#612911yescharacteristic
253M16—24no—
254M16—522no—
255C2×C8—22no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—131no—
261C2×C8—131no—
262C2×C8—262no—
263C2×C8—262no—
264C2×C8—262no—
265C2×C8—262no—
266C2×C8—262no—
267C2×C8—262no—
268C2×C8—522no—
269C4⋊C4—131no—
270C4⋊C4—131no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C42—22no—
281C42—22no—
282C42—261no—
283C42C2×C4×D1311yescharacteristic
284C42C2×C4×D1311yescharacteristic
285C42D4×D1311yescharacteristic
286C42#613111yescharacteristic
287C13#824711yescharacteristic, complemented, Sylow
288C23—261no—
289C23#8813511yescharacteristic
290Q8—521no—
291D4—521no—
292D4—522no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—24no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4C42×D1311yescharacteristic
306C2×C4C22⋊C4×D1311yescharacteristic
307C2×C4#8813511yescharacteristic
308C2×C4#8814611yescharacteristic
309C2×C4#8814711yescharacteristic
310C2×C4#8814711yescharacteristic
311C8—24no—
312C8—41no—
313C8—41no—
314C8—132no—
315C8—132no—
316C8—264no—
317C8—261no—
318C8—261no—
319C8—522no—
320C22—21no—
321C22—21no—
322C22—521no—
323C22—521no—
324C22—521no—
325C22#1171832711yescharacteristic
326C22#1171848512yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—44no—
333C4—521no—
334C4—521no—
335C4—521no—
336C4D13×#10411yescharacteristic
337C4D13×#10411yescharacteristic
338C2—22no—
339C2—1041no—
340C2#1311463511yescharacteristic
341C2#1311464011yescharacteristic
342C2#1311467011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC13×#1300C2
socleC22×C13C4×C22⋊C4
prime radical#88184C2×C4
cosocleC2×C42×C13C23
hypercenter#1300D13
hypocenterC13#8247
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
2. #13114523C2semidirect
5. M16×#1055C2semidirect
6. #13112734C2semidirect
7. C13×#1300C2semidirect
17. #11718499C4semidirect
18. #11718495C4semidirect
19. #11718492C4semidirect
20. #11718491C4semidirect
25. #11718057C4semidirect
26. #11718056C4semidirect
123. #1300D13semidirect
287. C13#8247semidirect

Maximal subgroups

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

subgroupindex
#131238052
#131145232
#131134252
#131133202
M16×#10552
#131127342
C13×#13002
#824713