Finite Group Databasebeta

← #14649265

Subgroups — #14649265

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077639C211yesmaximal, characteristic
2#13071323C211yesmaximal, characteristic
3#13067011C211yesmaximal, characteristic, complemented
4#13066936C211yesmaximal, characteristic
5#13066444C211yesmaximal, characteristic, complemented
6#13066444C211yesmaximal, characteristic, complemented
7C11×#1479C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#67000C411yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622843C411yescharacteristic
14#10622602—22no—
15#10622601C411yescharacteristic
16#10622589C411yescharacteristic
17#10622553—22no—
18#10622545C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622538C2211yescharacteristic
21#10622447—22no—
22D11×C22⋊C8—22no—
23C8×D44—22no—
24C11×Q8⋊C8—22no—
25Q8⋊(C11⋊C8)—22no—
26#10622106—22no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D44C2×C411yescharacteristic
29C22×C4×D11D412yes—
30C4×Q8×C11—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11C2311yescharacteristic
38#67000—22no—
39#67000C814yescomplemented
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4D412yes—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×Dic11⋊C4—22no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C8×D11—24no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C4×D44—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C4×C8×C11—21no—
57C4×C8×C11D412yes—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—22no—
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8D412yes—
68#9099—111nomaximal, Sylow
69C23×D11C22⋊C412yes—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11C2×C812yescomplemented
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11C22⋊C412yes—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44C2×C812yes—
89C2×D44M1612yes—
90C2×C4×D11—22no—
91C2×C4×D11—22no—
92C2×C4×D11—82no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C42×C11—41no—
100C42×C11—41no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11#4111yescharacteristic
104C42×C11#4111yescharacteristic
105(C2×D11)⋊C4—28no—
106(C2×D11)⋊C4—22no—
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—82no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111Dic11⋊C4—82no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115C4×Dic11C2×C812yescomplemented
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118C8×D11—84no—
119#2972—111no—
120#2326—111no—
121#1479—111no—
122#1479D1111yescharacteristic, complemented
123#1460—111no—
124#1274—111no—
125#1274—111no—
126C23×C11C2×C22⋊C411yescharacteristic
127C22×D11—22no—
128C22×D11—22no—
129C22×D11—42no—
130C22×D11—42no—
131C22×D11C22⋊C814yes—
132Q8×C11—22no—
133Q8×C11—22no—
134Q8×C11—41no—
135Q8×C11—41no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11C22×C811yescharacteristic
150C2×C4×C11C2×M1611yescharacteristic
151C2×C4×C11#13111yescharacteristic
152C2×C4×C11#13111yescharacteristic
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—42no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161D44—22no—
162D44—22no—
163D44—22no—
164D44—22no—
165C4×D11—44no—
166C4×D11—82no—
167C8×C11—42no—
168C8×C11—81no—
169C11⋊C8—42no—
170C11⋊C8—81no—
171C2×#124—111no—
172C2×C4×Q8C2×D1111yescharacteristic
173C2×C4×D4—111no—
174C8×D4—222no—
175C8×D4—222no—
176#431—111no—
177#431—111no—
178#431C2×D1111yescharacteristic
179#431C2×D1111yescharacteristic
180C2×C22⋊C8—222no—
181#391—111no—
182#390—111no—
183#388—222no—
184#385—222no—
185#384—111no—
186#376—111no—
187Q8⋊C8—22no—
188Q8⋊C8—222no—
189#323—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11#38611yescharacteristic
193C22×C11C2×C22⋊C811yescharacteristic
194C22×C11#40811yescharacteristic
195C2×D11—24no—
196C2×D11—42no—
197C2×D11—42no—
198C2×D11—44no—
199C2×D11—82no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—42no—
205C4×C11—81no—
206C4×C11C8×D411yescharacteristic
207C4×C11C8×D411yescharacteristic
208C4×C11#43511yescharacteristic
209C4×C11#43511yescharacteristic
210Dic11—42no—
211Dic11—42no—
212Dic11—81no—
213C22×Q8C4×D1111yescharacteristic
214C22×D4—111no—
215C23×C4—112no—
216C22×C8—224no—
217#124—114no—
218#124—222no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×D4—221no—
224C4×D4—221no—
225C4×D4—221no—
226C4×D4—221no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—222no—
230C2×C4⋊C4C4×D1111yescharacteristic
231C2×C22⋊C4—112no—
232C2×C22⋊C4—222no—
233C2×C22⋊C4—222no—
234C2×C42—21no—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42C22×D1111yescharacteristic
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—221no—
241C4⋊C8—221no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8—224no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247C4×C8—21no—
248C4×C8—112no—
249C4×C8—221no—
250C4×C8C22⋊D1112yes—
251#95—222no—
252#95—221no—
253#95—221no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11#186911yescharacteristic
257C2×C11#190911yescharacteristic
258C2×C11#191111yescharacteristic
259D11—44no—
260C24—112no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8C8×D1112yescomplemented
267C2×D4—112no—
268C2×D4—112no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—112no—
276C22×C4—221no—
277C22×C4—222no—
278C22×C4—222no—
279C22×C4—221no—
280C22×C4—882no—
281C22×C4C2×C4×D1111yescharacteristic
282C22×C4D4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—222no—
287C2×C8—441no—
288C2×C8—884no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—882no—
296C22⋊C4—228no—
297C22⋊C4—222no—
298C22⋊C4—222no—
299C22⋊C4—882no—
300C42—41no—
301C42—41no—
302C42—112no—
303C42—221no—
304C42—221no—
305C42—221no—
306C42#433911yescharacteristic
307C42D4×D1111yescharacteristic
308C42#434111yescharacteristic
309C42C2×C22⋊D1111yescharacteristic
310C11#909911yescharacteristic, complemented, Sylow
311C23—114no—
312C23—222no—
313C23—222no—
314C23—442no—
315C23—442no—
316C23C22⋊C4×D1111yescharacteristic
317Q8—22no—
318Q8—22no—
319Q8—41no—
320Q8—41no—
321D4—222no—
322D4—222no—
323D4—222no—
324D4—222no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—222no—
333C2×C4—222no—
334C2×C4—444no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—442no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—882no—
342C2×C4(C22⋊D11)⋊C411yescharacteristic
343C2×C4#6693611yescharacteristic
344C2×C4#6693711yescharacteristic
345C2×C4C2×C8×D1111yescharacteristic
346C2×C4#6695411yescharacteristic
347C2×C4M16×D1111yescharacteristic
348C2×C4#6696011yescharacteristic
349C2×C4C4×C22⋊D1111yescharacteristic
350C2×C4#6699011yescharacteristic
351C2×C4#6699111yescharacteristic
352C8—42no—
353C8—81no—
354C8—442no—
355C8—881no—
356C22—21no—
357C22—21no—
358C22—224no—
359C22—444no—
360C22—442no—
361C22—442no—
362C22—882no—
363C22D11×C22⋊C811yescharacteristic
364C22#1062234011yescharacteristic
365C22#1062256911yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—42no—
371C4—81no—
372C4—442no—
373C4—442no—
374C4—881no—
375C4(C22⋊D11)⋊C811yescharacteristic
376C4#1062234111yescharacteristic
377C4C8×C22⋊D1111yescharacteristic
378C4#1062274011yescharacteristic
379C2—21no—
380C2—21no—
381C2—444no—
382C2#1306890511yescharacteristic
383C2#1306913511yescharacteristic
384C2#1306914511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#1479C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1479D11
hypocenterC11#9099
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
3. #13067011C2semidirect
5. #13066444C2semidirect
6. #13066444C2semidirect
7. C11×#1479C2semidirect
39. #67000C8semidirect
75. C2×Q8×C11C2×C8semidirect
115. C4×Dic11C2×C8semidirect
122. #1479D11semidirect
266. C2×Q8C8×D11semidirect
310. C11#9099semidirect

Maximal subgroups

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

subgroupindex
#130776392
#130713232
#130670112
#130669362
#130664442
C11×#14792
#909911