Finite Group Databasebeta

← #14653174

Subgroups — #14653174

Order 2816.

440 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079175C211yesmaximal, characteristic
2#13067379C211yesmaximal, characteristic, complemented
3#13067230C211yesmaximal, characteristic, complemented
4#13067226C211yesmaximal, characteristic
5#13067127C211yesmaximal, characteristic, complemented
6#13067123C211yesmaximal, characteristic
7C11×#1726C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×C11×#97—21no—
11C2×C11×#97C2211yescharacteristic
12C2×C4×C8×C11—21no—
13C2×C4×C8×C11C2211yescharacteristic
14C11×#376C2211yescharacteristic
15#10622727—21no—
16#10622727—21no—
17#10622539C2211yescharacteristic
18#10622539C2211yescharacteristic
19#10622307C411yescharacteristic, complemented
20#10622306C411yescharacteristic, complemented
21C4×#4314—21no—
22C4×#4314—21no—
23#10622294C411yescharacteristic, complemented
24#10622293C411yescharacteristic, complemented
25#10622103—22no—
26#10622102—22no—
27#10622096—21no—
28#10622095—21no—
29#10622090—22no—
30#10622089—22no—
31C2×#4339—21no—
32C22×C8×C11—21no—
33C22×C8×C11D411yescharacteristic
34C22×C8×C11D411yescharacteristic
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37#66983—21no—
38#66983—21no—
39#66979—21no—
40#66977—21no—
41#66977—21no—
42C2×#4314—21no—
43C2×#4314—21no—
44#66928—21no—
45#66927C2×C411yescharacteristic
46C4×D44—21no—
47C4×D44—21no—
48#66923—21no—
49#66922C2×C411yescharacteristic
50#66922C2×C411yescharacteristic
51#66922C2×C411yescharacteristic
52C4×Dic22—21no—
53C4×Dic22—21no—
54C11×#97—24no—
55C11×#97—21no—
56C11×#97D412yes—
57C4×C8×C11—24no—
58C4×C8×C11C2×C411yescharacteristic
59C4×C8×C11C2×C411yescharacteristic
60C4×C8×C11D411yescharacteristic
61C4×C8×C11D411yescharacteristic
62C11×#95—21no—
63C11×#95D412yes—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#66885—21no—
67#66885—21no—
68#66881—21no—
69#66881—21no—
70#66880—21no—
71#66880—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74#66867—21no—
75#66867—21no—
76#9761—111nomaximal, Sylow
77C22×C4×C11—22no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×C22⋊D11—41no—
82#4339—82no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×C4×D11—41no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11C22⋊C411yescharacteristic
96C2×C8×C11C22⋊C411yescharacteristic
97C2×C8×C11C22⋊C411yescharacteristic
98C2×C8×C11C22⋊C411yescharacteristic
99C42×C11—22no—
100C42×C11—22no—
101C42×C11C22×C411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105C22⋊Dic11—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114Dic11⋊C4—41no—
115Dic11⋊C4—41no—
116C4×Dic11—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#4314—42no—
120#4314—42no—
121#3167—111no—
122#1726D1111yescharacteristic, complemented
123#1568—111no—
124#1531—111no—
125#1530—111no—
126#1506—111no—
127#1505—111no—
128C23×C11#12111yescharacteristic
129C22×D11—41no—
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—24no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11C2×C22⋊C411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12411yescharacteristic
142C2×C4×C11#12711yescharacteristic
143C22⋊D11—82no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147D44—41no—
148D44—41no—
149D44—81no—
150D44—81no—
151C4×D11—82no—
152Dic22—41no—
153Dic22—41no—
154Dic22—81no—
155Dic22—81no—
156C8×C11—24no—
157C8×C11—21no—
158C8×C11—21no—
159C8×C11#10412yes—
160C8×C11#10412yes—
161C11⋊C8—81no—
162C11⋊C8—81no—
163#533—111no—
164#532—111no—
165#498—111no—
166#492—111no—
167#487—111no—
168#486—111no—
169#465—221no—
170#465—221no—
171C4×SD16—221no—
172C4×SD16—221no—
173#432—111no—
174#432—111no—
175C2×#97—21no—
176C2×#97C2×D1111yescharacteristic
177C2×C4×C8—21no—
178C2×C4×C8C2×D1111yescharacteristic
179#376C2×D1111yescharacteristic
180#335—221no—
181#334—221no—
182#330—222no—
183#329—222no—
184#328—222no—
185#327—222no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11#39011yescharacteristic
189C22×C11#47112yes—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—44no—
199C4×C11C2×#10411yescharacteristic
200C4×C11C2×#10411yescharacteristic
201Dic11—81no—
202Dic11—81no—
203Dic11—81no—
204C2×#41—221no—
205C2×SD16—221no—
206C2×SD16—221no—
207C22×C8—21no—
208C22×C8C22⋊D1111yescharacteristic
209C22×C8C22⋊D1111yescharacteristic
210C4⋊Q8—111no—
211C4⋊Q8—111no—
212C4⋊Q8—111no—
213#127—111no—
214#125—221no—
215#124—221no—
216C22⋊Q8—221no—
217C22⋊Q8—221no—
218#121—221no—
219#121—221no—
220C4×Q8—221no—
221C4×Q8—221no—
222C4×D4—221no—
223C4×D4—221no—
224#117—221no—
225C2×C42—21no—
226C2×C42C22×D1111yescharacteristic
227#106—221no—
228#106—221no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231#103—221no—
232#103—221no—
233#102—221no—
234#102—221no—
235C22⋊C8—221no—
236C22⋊C8—221no—
237#97—24no—
238#97—21no—
239#97—221no—
240#97—221no—
241#97D4412yes—
242C4×C8—24no—
243C4×C8C4×D1111yescharacteristic
244C4×C8C4×D1111yescharacteristic
245C4×C8D4411yescharacteristic
246C4×C8D4411yescharacteristic
247#95—21no—
248#95D4412yes—
249C2×C11—22no—
250C2×C11#196211yescharacteristic
251C2×C11#197611yescharacteristic
252C2×C11#197711yescharacteristic
253D11—161no—
254#41—882no—
255C2×Q8—221no—
256C2×Q8—221no—
257C2×Q8—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—441no—
262C22×C4—22no—
263C22×C4—441no—
264C22×C4C2×D4411yescharacteristic
265C22×C4#433911yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267SD16—442no—
268SD16—442no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—441no—
275C2×C8—441no—
276C2×C8(C2×D11)⋊C411yescharacteristic
277C2×C8(C2×D11)⋊C411yescharacteristic
278C2×C8(C2×D11)⋊C411yescharacteristic
279C2×C8(C2×D11)⋊C411yescharacteristic
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C22⋊C4—441no—
291C42—22no—
292C42—22no—
293C42—441no—
294C42C2×C4×D1111yescharacteristic
295C42C2×D4411yescharacteristic
296C42C2×D4411yescharacteristic
297C42#433911yescharacteristic
298C11#976111yescharacteristic, complemented, Sylow
299C23—441no—
300C23#6698311yescharacteristic
301Q8—441no—
302Q8—441no—
303Q8—881no—
304Q8—881no—
305D4—441no—
306D4—441no—
307D4—881no—
308D4—881no—
309D4—882no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—24no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—882no—
321C2×C4C4×D4411yescharacteristic
322C2×C4C4×D4411yescharacteristic
323C2×C4#6692711yescharacteristic
324C2×C4#6692811yescharacteristic
325C2×C4C2×(C2×D11)⋊C411yescharacteristic
326C2×C4#6698311yescharacteristic
327C8—24no—
328C8—21no—
329C8—21no—
330C8—881no—
331C8—881no—
332C8#6686912yes—
333C8#6686912yes—
334C22—21no—
335C22—21no—
336C22—881no—
337C22—881no—
338C22—881no—
339C22#1062255211yescharacteristic
340C22#1062275412yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—44no—
347C4—881no—
348C4—881no—
349C4—881no—
350C4C2×#6686911yescharacteristic
351C4C2×#6686911yescharacteristic
352C2—22no—
353C2—1761no—
354C2#1306944411yescharacteristic
355C2#1306951411yescharacteristic
356C2#1306951911yescharacteristic
subgroupG/H
centerC22#10622552
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1726C2
socleC22×C11#390
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1726D11
hypocenterC11#9761
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #13067379C2semidirect
3. #13067230C2semidirect
5. #13067127C2semidirect
7. C11×#1726C2semidirect
19. #10622307C4semidirect
20. #10622306C4semidirect
23. #10622294C4semidirect
24. #10622293C4semidirect
122. #1726D11semidirect
298. C11#9761semidirect

Maximal subgroups

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

subgroupindex
#130791752
#130673792
#130672302
#130672262
#130671272
#130671232
C11×#17262
#976111