Finite Group Databasebeta

← #15767683

Subgroups — #15767683

Order 3328.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115773C211yesmaximal, characteristic
2#13114963C211yesmaximal, characteristic
3#13114841C211yesmaximal, characteristic
4#13112720C211yesmaximal, characteristic
5#13112719C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic
7C13×#1803C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×#103—21no—
11C13×#384C2211yescharacteristic
12C2×#88075—21no—
13#11718596C2211yescharacteristic
14C2×C4⋊#1055C2211yescharacteristic
15C2×C4⋊#1055C2211yescharacteristic
16C2×C4×#1055C2211yescharacteristic
17C13×#340—21no—
18#11718121—21no—
19#11718121—21no—
20#11718121—21no—
21#11718116—21no—
22#11718116—21no—
23C22×Q8×C13D411yescharacteristic
24C22×C8×C13—21no—
25C4×Q8×C13—21no—
26C4×Q8×C13—21no—
27C4×Q8×C13—21no—
28C4×Q8×C13—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C42×C13—21no—
35C2×C42×C13C2311yescharacteristic
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C22×#1055—21no—
40C22×#1055—21no—
41C22×#1055D411yescharacteristic
42C22×#1055D411yescharacteristic
43C13×C4⋊C8—21no—
44C13×C4⋊C8—21no—
45C13×#103—42no—
46#88075—42no—
47C4⋊#1055—21no—
48C4⋊#1055—21no—
49C4⋊#1055—21no—
50C4⋊#1055—21no—
51C4×#1055—21no—
52C4×#1055—21no—
53#10626—131nomaximal, Sylow
54C2×Q8×C13—21no—
55C2×Q8×C13—21no—
56C2×Q8×C13—21no—
57C2×Q8×C13—21no—
58C2×Q8×C13—21no—
59C2×Q8×C13SD1612yes—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—41no—
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13#4111yescharacteristic
66C22×Dic13—41no—
67C2×C8×C13—41no—
68C2×C8×C13—41no—
69C2×C8×C13—41no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—81no—
79C42×C13—41no—
80C42×C13—41no—
81C42×C13#4111yescharacteristic
82C42×C13#4111yescharacteristic
83C42×C13#4111yescharacteristic
84C42×C13#4111yescharacteristic
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89C4⋊Dic13—81no—
90C2×#1055—21no—
91C2×#1055—21no—
92C2×#1055—21no—
93C2×#1055—21no—
94C2×#1055—21no—
95C2×#1055—21no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102#1984—131no—
103#1834—131no—
104#1803—131no—
105#1803D1311yescharacteristic
106#1296—131no—
107#1296—131no—
108#1277—131no—
109C23×C13#12111yescharacteristic
110Q8×C13—22no—
111Q8×C13—22no—
112Q8×C13—41no—
113Q8×C13—41no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—81no—
123C2×C4×C13—81no—
124C2×C4×C13—81no—
125C2×C4×C13#12311yescharacteristic
126C2×C4×C13#12311yescharacteristic
127C2×C4×C13#12311yescharacteristic
128C2×C4×C13#12411yescharacteristic
129C2×C4×C13#12611yescharacteristic
130C2×C4×C13#12611yescharacteristic
131C2×C4×C13C2×SD1611yescharacteristic
132C2×C4×C13#13511yescharacteristic
133C2×C4×C13#13511yescharacteristic
134C2×C4×C13#13511yescharacteristic
135C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C2×C4×C13#13711yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C2×Dic13—81no—
140C2×Dic13—81no—
141C2×Dic13—81no—
142C8×C13—81no—
143#1055—41no—
144#1055—41no—
145#1055—81no—
146#1055—81no—
147C2×C4×Q8C2×D1311yescharacteristic
148C2×C4⋊C8—131no—
149C2×C4⋊C8—131no—
150C2×C4⋊C8C2×D1311yescharacteristic
151C2×#103—21no—
152C2×#103—261no—
153C2×C4×C8—131no—
154#384—131no—
155#384C2×D1311yescharacteristic
156#340—21no—
157#340—261no—
158#340—261no—
159#340—261no—
160#336—261no—
161#336—261no—
162C22×C13#39711yescharacteristic
163C22×C13#46411yescharacteristic
164C22×C13#46411yescharacteristic
165C22×C13#46511yescharacteristic
166C22×C13#46811yescharacteristic
167C22×C13#47211yescharacteristic
168C22×C13#47311yescharacteristic
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—42no—
172C4×C13—81no—
173C4×C13—161no—
174C4×C13#48111yescharacteristic
175C4×C13#48211yescharacteristic
176C4×C13#48311yescharacteristic
177C4×C13#48511yescharacteristic
178C4×C13#48511yescharacteristic
179C4×C13#48511yescharacteristic
180C4×C13#48811yescharacteristic
181C4×C13#49111yescharacteristic
182Dic13—161no—
183C22×Q8C22⋊D1311yescharacteristic
184C22×C8—21no—
185C22×C8—131no—
186C22×C8—131no—
187C22×C8—261no—
188C22×C8—261no—
189C4×Q8—21no—
190C4×Q8—21no—
191C4×Q8—21no—
192C4×Q8—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4C22⋊D1311yescharacteristic
201C2×C42—21no—
202C2×C42C22×D1311yescharacteristic
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—261no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208C4⋊C8—261no—
209#103—42no—
210#103—522no—
211C4×C8—261no—
212C4×C8—261no—
213C2×C13#167811yescharacteristic
214C2×C13#168011yescharacteristic
215C2×C13#169811yescharacteristic
216C2×C13#170011yescharacteristic
217C2×C13#207411yescharacteristic
218C2×C13#207711yescharacteristic
219C2×C13#207811yescharacteristic
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8#610512yes—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—521no—
230C22×C4D4×D1311yescharacteristic
231C22×C4#612911yescharacteristic
232C22×C4C2×C22⋊D1311yescharacteristic
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—261no—
237C2×C8—261no—
238C2×C8—261no—
239C2×C8—261no—
240C2×C8—261no—
241C2×C8—261no—
242C2×C8—521no—
243C2×C8—521no—
244C2×C8—521no—
245C2×C8—521no—
246C2×C8—521no—
247C2×C8—521no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—81no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—1041no—
262C42—41no—
263C42—41no—
264C42#612711yescharacteristic
265C42#612711yescharacteristic
266C42#612911yescharacteristic
267C42#612911yescharacteristic
268C13#1062611yescharacteristic, complemented, Sylow
269C23#8819311yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—1041no—
286C2×C4—1041no—
287C2×C4—1041no—
288C2×C4#8813311yescharacteristic
289C2×C4#8813311yescharacteristic
290C2×C4#8813711yescharacteristic
291C2×C4#8813911yescharacteristic
292C2×C4#8816911yescharacteristic
293C2×C4#8817011yescharacteristic
294C2×C4#8817211yescharacteristic
295C2×C4#8817311yescharacteristic
296C2×C4#8818311yescharacteristic
297C2×C4C2×#610511yescharacteristic
298C2×C4#8818911yescharacteristic
299C2×C4#8819611yescharacteristic
300C2×C4#8820311yescharacteristic
301C2×C4#8820411yescharacteristic
302C8—81no—
303C8—521no—
304C8—521no—
305C8—1041no—
306C8—1041no—
307C22#1171861311yescharacteristic
308C22#1171870211yescharacteristic
309C22#1171871011yescharacteristic
310C22#1171882711yescharacteristic
311C22#1171884611yescharacteristic
312C22#1171886011yescharacteristic
313C22#1171886511yescharacteristic
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—161no—
319C4—2081no—
320C4#1171845811yescharacteristic
321C4#1171846111yescharacteristic
322C4#1171847511yescharacteristic
323C4#1171847611yescharacteristic
324C4#1171863211yescharacteristic
325C4#1171866411yescharacteristic
326C4#1171869511yescharacteristic
327C4#1171870611yescharacteristic
328C2#1311425011yescharacteristic
329C2#1311426811yescharacteristic
330C2#1311437811yescharacteristic
331C2#1311438811yescharacteristic
332C2#1311625711yescharacteristic
333C2#1311627211yescharacteristic
334C2#1311627911yescharacteristic
subgroupG/H
centerC23#88193
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1803C2
socle, prime radicalC23×C13#121
hypercenter#1803D13
hypocenterC13#10626
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
268. C13#10626semidirect

Maximal subgroups

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

subgroupindex
#131157732
#131149632
#131148412
#131127202
#131127192
#131126702
C13×#18032
#1062613