Finite Group Databasebeta

← #15761318

Subgroups — #15761318

Order 3328.

386 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#13115798C211yesmaximal, characteristic
2#13115760C211yesmaximal, characteristic
3#13115600C211yesmaximal, characteristic
4#13114706C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic
7C2×C13×#332C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×#88075—21no—
12C2×#88075—21no—
13C2×#88057—21no—
14C2×#88055—21no—
15#11718596C2211yescharacteristic
16C4×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19C13×#332C414yescomplemented
20#11718143—21no—
21#11718142—21no—
22#11718121—21no—
23#11718121—21no—
24C22×Q8×C13—21no—
25C22×C8×C13—21no—
26C22×C8×C13—21no—
27C13×C4⋊Q8—21no—
28C13×C4⋊Q8—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8C2×C412yes—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4×Dic13—21no—
40C22×#1055—21no—
41C22×#1055D411yescharacteristic
42C22×#1055D411yescharacteristic
43C13×C4⋊C8—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8C2×C412yes—
46C13×C4⋊C8C2×C412yes—
47#88075—42no—
48#88075—42no—
49#88071—21no—
50#88057—42no—
51#88055—42no—
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54C4×#1055—21no—
55C4×#1055—21no—
56#9573—131nomaximal, Sylow
57C2×Q8×C13—22no—
58C2×Q8×C13—41no—
59C2×Q8×C13—41no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—41no—
70C2×C8×C13—22no—
71C2×C8×C13—22no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C42×C13C22×C411yescharacteristic
81C42×C13#4111yescharacteristic
82C42×C13#4111yescharacteristic
83C42×C13#4111yescharacteristic
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—81no—
93C4×Dic13—41no—
94C4×Dic13—41no—
95C2×#1055—21no—
96C2×#1055—21no—
97C2×#1055—21no—
98C2×#1055—21no—
99C2×#1055—21no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055SD1612yes—
104#1990—131no—
105#1981—131no—
106#1948—131no—
107#1770—131no—
108C2×#332D1311yescharacteristic
109#1296—131no—
110#1277—131no—
111C23×C13#12111yescharacteristic
112Q8×C13—42no—
113Q8×C13—42no—
114Q8×C13—81no—
115Q8×C13—81no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13—81no—
120C2×C4×C13—81no—
121C2×C4×C13#11711yescharacteristic
122C2×C4×C13C4×D411yescharacteristic
123C2×C4×C13C4×D411yescharacteristic
124C2×C4×C13#12311yescharacteristic
125C2×C4×C13#12411yescharacteristic
126C2×C4×C13#12611yescharacteristic
127C2×C4×C13C2×SD1611yescharacteristic
128C2×C4×C13#13511yescharacteristic
129C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C13#13711yescharacteristic
133C2×C4×C13#13711yescharacteristic
134C2×C4×C13#13711yescharacteristic
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—81no—
142C2×Dic13—81no—
143C2×Dic13—81no—
144C8×C13—42no—
145C8×C13—42no—
146#1055—22no—
147#1055—41no—
148#1055—81no—
149C2×C4⋊Q8C2×D1311yescharacteristic
150C2×#106—261no—
151C2×C4⋊C8—131no—
152C2×C4⋊C8C2×D1311yescharacteristic
153C2×C4⋊C8C2×D1311yescharacteristic
154C2×#103—261no—
155C2×#103—261no—
156C2×#97—261no—
157C2×C4×C8—131no—
158#384—131no—
159C4×C4⋊C4—131no—
160#340—261no—
161#340—261no—
162#340—261no—
163#336—261no—
164#332Dic1314yescomplemented
165C22×C13#38811yescharacteristic
166C22×C13#46111yescharacteristic
167C22×C13#46411yescharacteristic
168C22×C13#46811yescharacteristic
169C22×C13#46911yescharacteristic
170C22×C13#47111yescharacteristic
171C22×C13#47311yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—82no—
175C4×C13C4×SD1611yescharacteristic
176C4×C13#44011yescharacteristic
177C4×C13#44111yescharacteristic
178C4×C13#44211yescharacteristic
179C4×C13#48311yescharacteristic
180C4×C13#48511yescharacteristic
181C4×C13#48911yescharacteristic
182C4×C13#49011yescharacteristic
183Dic13—81no—
184Dic13—81no—
185Dic13—161no—
186C22×Q8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—131no—
190C22×C8—131no—
191C22×C8—261no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8C2×Dic1312yes—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C42—261no—
204C2×C42C22×D1311yescharacteristic
205#106—522no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—261no—
209C4⋊C8—261no—
210C4⋊C8C2×Dic1312yes—
211C4⋊C8C2×Dic1312yes—
212#103—522no—
213#103—522no—
214#97—522no—
215C4×C8—261no—
216C4×C8—261no—
217#95—261no—
218C2×C13#169111yescharacteristic
219C2×C13#169311yescharacteristic
220C2×C13#170011yescharacteristic
221C2×C13#170211yescharacteristic
222C2×C13#192711yescharacteristic
223C2×C13#193011yescharacteristic
224C2×C13#193611yescharacteristic
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—41no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—521no—
235C22×C4#612711yescharacteristic
236C22×C4D4×D1311yescharacteristic
237C22×C4D4×D1311yescharacteristic
238C2×C8—22no—
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—132no—
245C2×C8—261no—
246C2×C8—261no—
247C2×C8—261no—
248C2×C8—261no—
249C2×C8—261no—
250C2×C8—521no—
251C2×C8—521no—
252C2×C8—521no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—1041no—
266C42—521no—
267C42—521no—
268C42#612711yescharacteristic
269C42#612911yescharacteristic
270C42#612911yescharacteristic
271C42C22×Dic1311yescharacteristic
272C13#957311yescharacteristic, complemented, Sylow
273C23#8813811yescharacteristic
274Q8—42no—
275Q8—42no—
276Q8—81no—
277Q8—81no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—521no—
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#8813311yescharacteristic
293C2×C4#8813711yescharacteristic
294C2×C4#8813911yescharacteristic
295C2×C4#8816511yescharacteristic
296C2×C4#8816511yescharacteristic
297C2×C4SD16×D1311yescharacteristic
298C2×C4#8816811yescharacteristic
299C2×C4#8816911yescharacteristic
300C2×C4#8817011yescharacteristic
301C2×C4#8817211yescharacteristic
302C2×C4#8817211yescharacteristic
303C2×C4#8818011yescharacteristic
304C2×C4D4×Dic1311yescharacteristic
305C2×C4D4×Dic1311yescharacteristic
306C8—42no—
307C8—42no—
308C8—262no—
309C8—521no—
310C8—1041no—
311C22#1171841511yescharacteristic
312C22#1171841611yescharacteristic
313C22#1171844111yescharacteristic
314C22#1171844311yescharacteristic
315C22#1171845911yescharacteristic
316C22#1171847911yescharacteristic
317C22#1171861211yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—1041no—
322C4—1041no—
323C4—2081no—
324C4#1171842511yescharacteristic
325C4#1171842611yescharacteristic
326C4#1171846611yescharacteristic
327C4#1171847611yescharacteristic
328C4#1171881311yescharacteristic
329C4SD16×Dic1311yescharacteristic
330C4#1171882511yescharacteristic
331C4#1171884511yescharacteristic
332C2#1311433411yescharacteristic
333C2#1311434811yescharacteristic
334C2#1311439311yescharacteristic
335C2#1311440711yescharacteristic
336C2#1311547211yescharacteristic
337C2#1311549311yescharacteristic
338C2#1311553511yescharacteristic
subgroupG/H
centerC23#88138
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#332C2
socle, prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenterC2×#332D13
hypocenterC13#9573
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
19. C13×#332C4semidirect
164. #332Dic13semidirect
272. C13#9573semidirect

Maximal subgroups

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

subgroupindex
#131157982
#131157602
#131156002
#131147062
#131127202
#131126702
C2×C13×#3322
#957313