Finite Group Databasebeta

← #14650474

Subgroups — #14650474

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071342C211yesmaximal, characteristic
2#13069598C211yesmaximal, characteristic, complemented
3#13067284C211yesmaximal, characteristic
4#13067180C211yesmaximal, characteristic, complemented
5#13066475C211yesmaximal, characteristic, complemented
6#13066444C211yesmaximal, characteristic, complemented
7C11×#3208C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×D4×Dic11—21no—
11C11×#492C412yescomplemented
12C11×#486C412yescomplemented
13C11×#460—22no—
14C11×#450—22no—
15C11×#431C2211yescharacteristic
16#10622834—21no—
17#10622833—22no—
18#10622833—22no—
19#10622549C2211yescharacteristic
20#10622545C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622182—22no—
24#10622176—22no—
25#10622170—21no—
26#10622170—21no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11D412yes—
30C23×Dic11—22no—
31C2×C11×SD16—24no—
32C11×C4⋊Q8C2×C411yescharacteristic, complemented
33C11×C4⋊Q8C2×C411yescharacteristic, complemented
34C11×#127—21no—
35C11×#127—21no—
36C11×#127C2×C412yes—
37C11×#127D412yes—
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C11×#117—21no—
44C2×C42×C11C2311yescharacteristic
45C2×C22⋊Dic11—22no—
46C2×C22⋊Dic11—22no—
47C2×C22⋊Dic11—22no—
48D4×Dic11—42no—
49D4×Dic11—42no—
50C2×C4⋊Dic11—21no—
51C2×C4×Dic11D411yescharacteristic
52C2×C4×Dic11D411yescharacteristic
53C2×#4318—21no—
54C11×C4⋊C8—21no—
55C11×#102—24no—
56C11×C22⋊C8—21no—
57C4×C8×C11C2×C412yescomplemented
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95D412yes—
62C22⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67#9295—111nomaximal, Sylow
68C24×C11—22no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—82no—
81C2×D4×C11—82no—
82C2×D4×C11C22⋊C414yes—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—22no—
89C22×Dic11—44no—
90C22×Dic11—82no—
91C22×Dic11—82no—
92C11×SD16—84no—
93C2×C8×C11—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11—41no—
102C42×C11C22×C411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105C42×C11#4111yescharacteristic
106C22⋊Dic11—44no—
107C22⋊Dic11—82no—
108C22⋊Dic11—82no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11SD1612yescomplemented
115#4318—41no—
116#4318—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#3208D1111yescharacteristic
120#2328—111no—
121#1995—111no—
122#1545—111no—
123#1518—111no—
124#1286—111no—
125#1274—111no—
126C23×C11—24no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11#12011yescharacteristic
134Q8×C11—42no—
135Q8×C11—81no—
136D4×C11—44no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—42no—
141D4×C11—82no—
142D4×C11—82no—
143D4×C11—82no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C2×C4×C11C2×SD1611yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C2×Dic11—22no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—88no—
168C8×C11—42no—
169C11⋊C8—81no—
170C11⋊C8—81no—
171#533C2×D1111yescharacteristic
172C2×#127C2×D1111yescharacteristic
173C2×C4×D4—221no—
174#492Dic1112yescomplemented
175#486Dic1112yescomplemented
176#460—22no—
177#450—22no—
178#431—111no—
179#431C2×D1111yescharacteristic
180#423—111no—
181#390—221no—
182#386—222no—
183#386—222no—
184#382—111no—
185#376—111no—
186#339—221no—
187#339—221no—
188#331—222no—
189#328—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—44no—
193C22×C11—44no—
194C22×C11—44no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11#38611yescharacteristic
200C22×C11#45011yescharacteristic
201C22×C11#45211yescharacteristic
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11C4×SD1611yescharacteristic
209C4×C11#44011yescharacteristic
210C4×C11#46111yescharacteristic
211C4×C11#46311yescharacteristic
212Dic11—42no—
213Dic11—81no—
214Dic11—82no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4C22⋊D1112yes—
218C23×C4—222no—
219C2×SD16—24no—
220C2×M16—221no—
221C4⋊Q8C2×Dic1111yescharacteristic, complemented
222C4⋊Q8C2×Dic1111yescharacteristic, complemented
223#127—21no—
224#127—21no—
225#127C2×Dic1112yes—
226#127C22⋊D1112yes—
227#125—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×D4—442no—
233C4×D4—442no—
234#117—21no—
235C2×C4⋊C4—221no—
236C2×C22⋊C4—222no—
237C2×C22⋊C4—222no—
238C2×C22⋊C4—222no—
239C2×C42—111no—
240C2×C42—111no—
241C2×C42C22×D1111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246#102—24no—
247C22⋊C8—21no—
248C22⋊C8—221no—
249C4×C8—221no—
250C4×C8C2×Dic1112yescomplemented
251#95—112no—
252#95—221no—
253#95—221no—
254#95—221no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—84no—
258C2×C11#187711yescharacteristic
259C2×C11#190411yescharacteristic
260C2×C11#191111yescharacteristic
261C24—22no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—82no—
274C2×D4—82no—
275C2×D4C22⋊Dic1114yes—
276C22×C4—221no—
277C22×C4—222no—
278C22×C4—221no—
279C22×C4—444no—
280C22×C4—882no—
281C22×C4—882no—
282C22×C4D4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285SD16—84no—
286M16—441no—
287M16—441no—
288C2×C8—22no—
289C2×C8—441no—
290C2×C8—441no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C22⋊C4—41no—
300C22⋊C4—444no—
301C22⋊C4—882no—
302C22⋊C4—882no—
303C42—41no—
304C42—112no—
305C42—221no—
306C42—221no—
307C42—221no—
308C42#434111yescharacteristic
309C42#434111yescharacteristic
310C42C22×Dic1111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C11#929511yescharacteristic, complemented, Sylow
313C23—24no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23#6699011yescharacteristic
321Q8—42no—
322Q8—81no—
323D4—44no—
324D4—42no—
325D4—42no—
326D4—42no—
327D4—42no—
328D4—82no—
329D4—82no—
330D4—82no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—222no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—441no—
344C2×C4—888no—
345C2×C4SD16×D1111yescharacteristic
346C2×C4#6696711yescharacteristic
347C2×C4#6696811yescharacteristic
348C2×C4#6696911yescharacteristic
349C2×C4D4×Dic1111yescharacteristic
350C2×C4D4×Dic1111yescharacteristic
351C2×C4#6698811yescharacteristic
352C2×C4#6699211yescharacteristic
353C2×C4#6699211yescharacteristic
354C2×C4C2×C22⋊Dic1111yescharacteristic
355C8—42no—
356C8—881no—
357C8—881no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—44no—
362C22—44no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22#1062278211yescharacteristic
368C22#1062278611yescharacteristic
369C22#1062283311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—81no—
375C4—81no—
376C4—442no—
377C4—882no—
378C4—881no—
379C4SD16×Dic1111yescharacteristic
380C4#1062277511yescharacteristic
381C4#1062277711yescharacteristic
382C4#1062277811yescharacteristic
383C2—21no—
384C2—21no—
385C2—84no—
386C2#1306895211yescharacteristic
387C2#1306910511yescharacteristic
388C2#1306914911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3208C2
socleC22×C11#386
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenter#3208D11
hypocenterC11#9295
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
2. #13069598C2semidirect
4. #13067180C2semidirect
5. #13066475C2semidirect
6. #13066444C2semidirect
11. C11×#492C4semidirect
12. C11×#486C4semidirect
32. C11×C4⋊Q8C2×C4semidirect
33. C11×C4⋊Q8C2×C4semidirect
57. C4×C8×C11C2×C4semidirect
114. C4×Dic11SD16semidirect
174. #492Dic11semidirect
175. #486Dic11semidirect
221. C4⋊Q8C2×Dic11semidirect
222. C4⋊Q8C2×Dic11semidirect
250. C4×C8C2×Dic11semidirect
312. C11#9295semidirect

Maximal subgroups

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

subgroupindex
#130713422
#130695982
#130672842
#130671802
#130664752
#130664442
C11×#32082
#929511