Finite Group Databasebeta

← #14649708

Subgroups — #14649708

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078080C211yesmaximal, characteristic
2#13067175C211yesmaximal, characteristic, complemented
3#13067110C211yesmaximal, characteristic, complemented
4#13067007C211yesmaximal, characteristic, complemented
5#13066519C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#2349C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11—21no—
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66985—21no—
11#10623008C2211yescharacteristic
12C11×#389—21no—
13C11×#385—22no—
14C11×#382C2211yescharacteristic
15C11×#380—21no—
16C4×C11×C4⋊C4C2211yescharacteristic
17C2×C11×#95—21no—
18#10622632C412yescomplemented
19#10622629—22no—
20#10622628C412yescomplemented
21#10622579—21no—
22#10622538C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25D4⋊(C11⋊C8)—22no—
26#10622089—21no—
27#10622089—21no—
28#10622089—22no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11—22no—
32C2×#4339—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11—42no—
36C4×D4×C11—42no—
37C4×D4×C11C2×C412yes—
38C4×D4×C11D412yes—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—22no—
45C2×C42×C11—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4324—22no—
48#66985—42no—
49#66985—42no—
50C2×#4323—22no—
51#66983—21no—
52#66983—21no—
53C2×#4318—21no—
54#66928—21no—
55#66927C2×C411yescharacteristic, complemented
56C4×D44—21no—
57C4×D44—21no—
58#66922C2×C411yescharacteristic, complemented
59C11×#95—22no—
60C11×#95—21no—
61C11×#95D411yescharacteristic
62C11×#95D411yescharacteristic
63C11×#95D412yes—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#66874—22no—
67#66873—22no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)C2×C412yescomplemented
72C4×C11⋊C8—21no—
73C4×C11⋊C8—21no—
74#9179—111nomaximal, Sylow
75C24×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11C22⋊C412yes—
80C2×D4×C11D812yes—
81C2×D4×C11SD1612yes—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—44no—
89C22×C4×C11—44no—
90C22×C4×C11—82no—
91C22×C4×C11—82no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—41no—
96#4339—41no—
97#4339—41no—
98#4339—41no—
99#4339—41no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×C4×D11—41no—
104C2×Dic22—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—82no—
110C11×C4⋊C4C22⋊C412yes—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—22no—
113C11×C22⋊C4—44no—
114C42×C11—41no—
115C42×C11—41no—
116C42×C11C22×C411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11#4111yescharacteristic
120#4324—44no—
121#4323—44no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126#4318—41no—
127#4318—41no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131#3036—111no—
132#2349D1111yescharacteristic, complemented
133#1517—111no—
134#1502—111no—
135#1478—111no—
136#1303—111no—
137#1286—111no—
138C23×C11—22no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11#12011yescharacteristic
144C22×D11—41no—
145D4×C11—22no—
146D4×C11—22no—
147D4×C11—22no—
148D4×C11#10214yes—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—82no—
163C2×C4×C11—82no—
164C2×C4×C11—88no—
165C2×C4×C11C2×C22⋊C411yescharacteristic
166C2×C4×C11C4×D411yescharacteristic
167C2×C4×C11C4×D411yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12311yescharacteristic
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×SD1611yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11#13711yescharacteristic
175C22⋊D11—81no—
176C22⋊D11—81no—
177C2×Dic11—41no—
178D44—41no—
179D44—41no—
180D44—81no—
181D44—81no—
182C4×D11—81no—
183C4×D11—81no—
184Dic22—41no—
185Dic22—41no—
186C11⋊C8—42no—
187C11⋊C8—81no—
188C11⋊C8—81no—
189C2×AGL(1,ℤ/8)—221no—
190#532—111no—
191C2×C4×D4—21no—
192C2×C4×D4C2×D1111yescharacteristic
193#463—222no—
194#461—112no—
195#459—112no—
196#431—111no—
197#431—111no—
198#423—111no—
199#417—221no—
200#389—21no—
201#385—22no—
202#382C2×D1111yescharacteristic
203#380—21no—
204C4×C4⋊C4C2×D1111yescharacteristic
205C2×#95—21no—
206#327—221no—
207#327—221no—
208#327—222no—
209D4⋊C8—222no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—24no—
213C22×C11—44no—
214C22×C11—44no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11#38611yescharacteristic
218C22×C11#44711yescharacteristic
219C22×C11#44811yescharacteristic
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—42no—
228C4×C11—42no—
229C4×C11—81no—
230C4×C11—82no—
231C4×C11C2×#10211yescharacteristic
232C4×C11#41711yescharacteristic
233C4×C11#48011yescharacteristic
234C4×C11#48111yescharacteristic
235Dic11—81no—
236C2×#41—221no—
237C22×D4C22⋊D1111yescharacteristic
238C23×C4—21no—
239C23×C4—22no—
240AGL(1,ℤ/8)—442no—
241AGL(1,ℤ/8)—442no—
242C2×SD16—222no—
243C2×D8—222no—
244C2×M16—221no—
245C4⋊Q8—111no—
246#127—111no—
247#124—221no—
248#121—221no—
249#121—221no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—42no—
253C4×D4—42no—
254C4×D4—221no—
255C4×D4—221no—
256C4×D4C4×D1112yes—
257C4×D4D4412yes—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—22no—
264C2×C42—21no—
265C2×C42C22×D1111yescharacteristic
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270#103—222no—
271#102—222no—
272C22⋊C8—221no—
273C22⋊C8—221no—
274C4×C8—221no—
275C4×C8—221no—
276#95—22no—
277#95—21no—
278#95C22⋊D1111yescharacteristic
279#95C22⋊D1111yescharacteristic
280#95C22⋊D1112yes—
281C2×C11—21no—
282C2×C11—21no—
283C2×C11—44no—
284C2×C11#187411yescharacteristic
285C2×C11#190411yescharacteristic
286C2×C11#190611yescharacteristic
287D11—161no—
288C24—21no—
289#41—441no—
290#41—441no—
291#41—441no—
292#41—441no—
293C2×Q8—221no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—441no—
301C2×D4(C2×D11)⋊C412yes—
302C2×D4#432312yes—
303C2×D4#432512yes—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—44no—
311C22×C4—44no—
312C22×C4—82no—
313C22×C4—82no—
314C22×C4—441no—
315C22×C4C2×C22⋊D1111yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318SD16—444no—
319D8—444no—
320M16—441no—
321M16—441no—
322C2×C8—222no—
323C2×C8—441no—
324C2×C8—441no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—82no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4(C2×D11)⋊C412yes—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—44no—
336C22⋊C4—441no—
337C22⋊C4—441no—
338C42—41no—
339C42—41no—
340C42C2×C4×D1111yescharacteristic
341C42C2×D4411yescharacteristic
342C42#433911yescharacteristic
343C42#433911yescharacteristic
344C11#917911yescharacteristic, complemented, Sylow
345C23—22no—
346C23—22no—
347C23—22no—
348C23—42no—
349C23—42no—
350C23—441no—
351C23#6700611yescharacteristic
352Q8—441no—
353Q8—441no—
354D4—22no—
355D4—22no—
356D4—22no—
357D4—441no—
358D4—441no—
359D4—881no—
360D4—881no—
361D4—881no—
362D4—881no—
363D4#6687314yes—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—88no—
380C2×C4—441no—
381C2×C4—881no—
382C2×C4—881no—
383C2×C4C2×(C2×D11)⋊C411yescharacteristic
384C2×C4C4×C22⋊D1111yescharacteristic
385C2×C4C4×C22⋊D1111yescharacteristic
386C2×C4#6698211yescharacteristic
387C2×C4#6698311yescharacteristic
388C2×C4#6698311yescharacteristic
389C2×C4C2×#432311yescharacteristic
390C2×C4#6698511yescharacteristic
391C2×C4C2×#432511yescharacteristic
392C2×C4#6699511yescharacteristic
393C8—442no—
394C8—881no—
395C8—881no—
396C22—21no—
397C22—21no—
398C22—24no—
399C22—44no—
400C22—44no—
401C22—42no—
402C22—42no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22#1062282611yescharacteristic
407C22#1062283011yescharacteristic
408C22#1062284011yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—42no—
414C4—42no—
415C4—82no—
416C4—81no—
417C4—881no—
418C4C2×#6687311yescharacteristic
419C4#1062257911yescharacteristic
420C4#1062258011yescharacteristic
421C4#1062258111yescharacteristic
422C2—21no—
423C2—21no—
424C2—44no—
425C2—1761no—
426C2#1306893311yescharacteristic
427C2#1306910311yescharacteristic
428C2#1306911711yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2349C2
socleC22×C11#386
prime radical#13078080C2
cosocleC2×C42×C11C23
hypercenter#2349D11
hypocenterC11#9179
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2349

Complements

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

NH ≅ G/Ntype
2. #13067175C2semidirect
3. #13067110C2semidirect
4. #13067007C2semidirect
5. #13066519C2semidirect
6. #13066474C2semidirect
7. C11×#2349C2semidirect
18. #10622632C4semidirect
20. #10622628C4semidirect
55. #66927C2×C4semidirect
58. #66922C2×C4semidirect
71. C4⋊(C11⋊C8)C2×C4semidirect
132. #2349D11semidirect
344. C11#9179semidirect

Maximal subgroups

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

subgroupindex
#130780802
#130671752
#130671102
#130670072
#130665192
#130664742
C11×#23492
#917911