Finite Group Databasebeta

← #15767652

Subgroups — #15767652

Order 3328.

366 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115771C211yesmaximal, characteristic
2#13114992C211yesmaximal, characteristic
3#13114842C211yesmaximal, characteristic
4#13114838C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic
7C13×#1296C211yesmaximal, characteristic
8C2×C4×Dic26C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C2×#88056—21no—
13C2×#88050—21no—
14C2×#88048—21no—
15C2×#88048—21no—
16#11718596C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19#11718143—21no—
20#11718142—21no—
21#11718142—21no—
22#11718121—21no—
23C22×Dic26D411yescharacteristic
24C22×C8×C13—21no—
25C22×C8×C13—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C42×C13C2311yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13D411yescharacteristic
34C2×#6101—21no—
35C2×C4×Dic13—21no—
36C22×#1055—21no—
37C22×#1055D411yescharacteristic
38C22×#1055D411yescharacteristic
39C4×Dic26—21no—
40C4×Dic26—21no—
41C4×Dic26—21no—
42C4×Dic26—21no—
43C13×C4⋊C8—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47#88056—42no—
48#88050—42no—
49#88048—42no—
50#88048—42no—
51C4⋊#1055—21no—
52C4⋊#1055—21no—
53C4×#1055—21no—
54C4×#1055—21no—
55#10620—131nomaximal, Sylow
56C22×C4×C13—41no—
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13#4111yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13—41no—
63C2×Dic26—21no—
64C2×Dic26—21no—
65C2×Dic26—21no—
66C2×Dic26—21no—
67C2×Dic26—21no—
68C2×Dic26SD1612yes—
69C2×C8×C13—41no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—81no—
80C42×C13#4111yescharacteristic
81C42×C13#4111yescharacteristic
82C42×C13#4111yescharacteristic
83C42×C13#4111yescharacteristic
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90C4⋊Dic13—81no—
91#6101—41no—
92#6101—41no—
93C4×Dic13—41no—
94C4×Dic13—41no—
95C2×#1055—21no—
96C2×#1055—21no—
97C2×#1055—21no—
98C2×#1055—21no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055SD1612yes—
103C2×#1055Q1612yes—
104#1984—131no—
105#1844—131no—
106#1803—131no—
107#1803—131no—
108#1296—131no—
109#1296D1311yescharacteristic
110#1277—131no—
111C23×C13#12111yescharacteristic
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—81no—
115C2×C4×C13—81no—
116C2×C4×C13—81no—
117C2×C4×C13#12311yescharacteristic
118C2×C4×C13#12311yescharacteristic
119C2×C4×C13#12311yescharacteristic
120C2×C4×C13#12411yescharacteristic
121C2×C4×C13#12611yescharacteristic
122C2×C4×C13#12611yescharacteristic
123C2×C4×C13C2×SD1611yescharacteristic
124C2×C4×C13C2×SD1611yescharacteristic
125C2×C4×C13C2×Q1611yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C13#13711yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×Dic13—22no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—81no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140Dic26—22no—
141Dic26—22no—
142Dic26—41no—
143Dic26—41no—
144C8×C13—81no—
145C8×C13—81no—
146#1055—22no—
147#1055—22no—
148#1055—81no—
149C2×C4×Q8—131no—
150C2×#106—261no—
151C2×#106—261no—
152C2×C4⋊C8—131no—
153C2×C4⋊C8C2×D1311yescharacteristic
154C2×C4⋊C8C2×D1311yescharacteristic
155C2×#103—261no—
156C2×#103—261no—
157C2×C4×C8—131no—
158#384—131no—
159#384C2×D1311yescharacteristic
160#340—261no—
161#340—261no—
162#336—261no—
163#336—261no—
164C22×C13#39711yescharacteristic
165C22×C13#46011yescharacteristic
166C22×C13#46211yescharacteristic
167C22×C13#46511yescharacteristic
168C22×C13#46811yescharacteristic
169C22×C13#47111yescharacteristic
170C22×C13#47111yescharacteristic
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—161no—
174C4×C13#48111yescharacteristic
175C4×C13#48211yescharacteristic
176C4×C13#48311yescharacteristic
177C4×C13#48311yescharacteristic
178C4×C13#48411yescharacteristic
179C4×C13#48511yescharacteristic
180C4×C13#48711yescharacteristic
181C4×C13#48911yescharacteristic
182Dic13—42no—
183Dic13—81no—
184Dic13—161no—
185C22×Q8—131no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—131no—
189C22×C8—131no—
190C22×C8—261no—
191C4×Q8—261no—
192C4×Q8—261no—
193C4×Q8—261no—
194C4×Q8—261no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C42—261no—
204C2×C42C22×D1311yescharacteristic
205#106—522no—
206#106—522no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—261no—
212C4⋊C8—261no—
213#103—522no—
214#103—522no—
215C4×C8—261no—
216C4×C8—261no—
217C2×C13#166611yescharacteristic
218C2×C13#167211yescharacteristic
219C2×C13#168611yescharacteristic
220C2×C13#169211yescharacteristic
221C2×C13#207211yescharacteristic
222C2×C13#207711yescharacteristic
223C2×C13#207911yescharacteristic
224C2×Q8—132no—
225C2×Q8—261no—
226C2×Q8—261no—
227C2×Q8—261no—
228C2×Q8—261no—
229C2×Q8—261no—
230C22×C4—41no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—521no—
234C22×C4#612711yescharacteristic
235C22×C4D4×D1311yescharacteristic
236C22×C4D4×D1311yescharacteristic
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—132no—
244C2×C8—132no—
245C2×C8—261no—
246C2×C8—261no—
247C2×C8—261no—
248C2×C8—261no—
249C2×C8—521no—
250C2×C8—521no—
251C2×C8—521no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—81no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—1041no—
266C42—521no—
267C42—521no—
268C42#612711yescharacteristic
269C42#612711yescharacteristic
270C42#612911yescharacteristic
271C42#613111yescharacteristic
272C13#1062011yescharacteristic, complemented, Sylow
273C23#8813811yescharacteristic
274Q8—262no—
275Q8—262no—
276Q8—521no—
277Q8—521no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—262no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—1041no—
290C2×C4—1041no—
291C2×C4—1041no—
292C2×C4#8813011yescharacteristic
293C2×C4#8813711yescharacteristic
294C2×C4#8813911yescharacteristic
295C2×C4#8814811yescharacteristic
296C2×C4#8814811yescharacteristic
297C2×C4#8815211yescharacteristic
298C2×C4#8816511yescharacteristic
299C2×C4#8816511yescharacteristic
300C2×C4SD16×D1311yescharacteristic
301C2×C4SD16×D1311yescharacteristic
302C2×C4#8816911yescharacteristic
303C2×C4#8816911yescharacteristic
304C2×C4Q16×D1311yescharacteristic
305C2×C4#8817311yescharacteristic
306C8—81no—
307C8—81no—
308C8—262no—
309C8—262no—
310C8—1041no—
311C22#1171833611yescharacteristic
312C22#1171840911yescharacteristic
313C22#1171841511yescharacteristic
314C22#1171842311yescharacteristic
315C22#1171844111yescharacteristic
316C22#1171845411yescharacteristic
317C22#1171846811yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—522no—
322C4—1041no—
323C4—2081no—
324C4#1171842611yescharacteristic
325C4#1171843811yescharacteristic
326C4#1171845311yescharacteristic
327C4#1171847511yescharacteristic
328C4#1171852311yescharacteristic
329C4#1171852311yescharacteristic
330C4#1171854511yescharacteristic
331C4#1171854611yescharacteristic
332C2#1311418711yescharacteristic
333C2#1311422111yescharacteristic
334C2#1311430711yescharacteristic
335C2#1311434111yescharacteristic
336C2#1311624811yescharacteristic
337C2#1311627511yescharacteristic
338C2#1311628511yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socle, prime radicalC23×C13#121
hypercenter#1296D13
hypocenterC13#10620
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
272. C13#10620semidirect

Maximal subgroups

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

subgroupindex
#131157712
#131149922
#131148422
#131148382
#131127202
#131126702
C13×#12962
#1062013