Finite Group Databasebeta

← #14650600

Subgroups — #14650600

Order 2816.

428 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077267C211yesmaximal, characteristic, complemented
2#13067227C211yesmaximal, characteristic, complemented
3#13067050C211yesmaximal, characteristic, complemented
4#13067033C211yesmaximal, characteristic, complemented
5#13066514C211yesmaximal, characteristic, complemented
6#13066487C211yesmaximal, characteristic, complemented
7C11×#3115C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C4×C11×#41C2211yescharacteristic
10C11×#482—21no—
11C11×#475C411yescharacteristic
12C11×#474C411yescharacteristic
13C11×#460C411yescharacteristic
14C11×#459C411yescharacteristic
15C11×#449—21no—
16C11×#442—21no—
17C11×#440—21no—
18C11×#432C2211yescharacteristic
19#10622847—21no—
20#10622613—22no—
21#10622612—21no—
22#10622539—22no—
23#10622539C2211yescharacteristic
24#10622538C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26C2×#66867C2211yescharacteristic
27#10622178—22no—
28Q8⋊(C11⋊C8)—21no—
29D4⋊(C11⋊C8)—21no—
30D4⋊(C11⋊C8)—22no—
31C2×C11×#41—21no—
32C2×C11×#41D411yescharacteristic
33C2×C11×SD16—21no—
34C2×C11×D8—21no—
35C11×C4⋊Q8C2×C411yescharacteristic
36C11×#127C2×C411yescharacteristic
37C11×#124—21no—
38C11×#121—21no—
39C11×#121—21no—
40C4×Q8×C11C2×C411yescharacteristic
41C4×Q8×C11D411yescharacteristic
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11C2×C411yescharacteristic
47C4×D4×C11D411yescharacteristic
48C11×#117—21no—
49C11×#117D411yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4318—21no—
53C22×C11⋊C8—21no—
54C11×#107—21no—
55C11×#106—21no—
56C11×C4⋊C8C2×C411yescharacteristic
57C11×C4⋊C8C2×C411yescharacteristic
58C11×#103—21no—
59C11×#102—21no—
60C11×#102—21no—
61C11×#102—21no—
62C11×C22⋊C8—21no—
63C11×#97—21no—
64C22⋊(C11⋊C8)—24no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—24no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70#66867—21no—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75C4×C11⋊C8D412yes—
76#9313—111nomaximal, Sylow
77C11×#41—41no—
78C11×#41—41no—
79C11×#41—82no—
80C2×Q8×C11—21no—
81C2×Q8×C11C22⋊C411yescharacteristic
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C2×D4×C11C22⋊C411yescharacteristic
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C11×SD16—42no—
96C11×D8—42no—
97C2×C8×C11—21no—
98C2×C8×C11—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4C22⋊C411yescharacteristic
104C11×C4⋊C4C22⋊C411yescharacteristic
105C11×C22⋊C4—21no—
106C11×C22⋊C4—21no—
107C11×C22⋊C4—21no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11—21no—
111C42×C11—21no—
112C42×C11—21no—
113C42×C11C22×C411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117#4318—41no—
118#4318—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125#3115D1111yescharacteristic
126#2923—111no—
127#1530—111no—
128#1488—111no—
129#1484—111no—
130#1302—111no—
131#1291—111no—
132C23×C11—21no—
133C23×C11—41no—
134C23×C11#12311yescharacteristic
135Q8×C11—21no—
136Q8×C11—21no—
137Q8×C11—81no—
138D4×C11—21no—
139D4×C11—21no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—41no—
143D4×C11—41no—
144D4×C11—81no—
145D4×C11—82no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11—82no—
158C2×C4×C11C2×C22⋊C411yescharacteristic
159C2×C4×C11C4×D411yescharacteristic
160C2×C4×C11C4×D411yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C8×C11—41no—
165C8×C11—41no—
166C11⋊C8—42no—
167C11⋊C8—42no—
168C11⋊C8—81no—
169C11⋊C8—81no—
170#532C2×D1111yescharacteristic
171C4×#41C2×D1111yescharacteristic
172#482—21no—
173#475Dic1111yescharacteristic
174#474Dic1111yescharacteristic
175#460Dic1111yescharacteristic
176#459Dic1111yescharacteristic
177#449—21no—
178#442—21no—
179#440—21no—
180#433—222no—
181#432—111no—
182#432—222no—
183#432C2×D1111yescharacteristic
184#431—111no—
185#424—221no—
186#408—221no—
187C4×M16—111no—
188C2×#97—111no—
189#329—222no—
190Q8⋊C8—221no—
191D4⋊C8—222no—
192D4⋊C8—221no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11#38611yescharacteristic
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—81no—
212C4×C11#42111yescharacteristic
213C4×C11#42111yescharacteristic
214C2×#41—21no—
215C2×#41C22⋊D1111yescharacteristic
216C2×SD16—21no—
217C2×D8—21no—
218C2×M16—221no—
219C22×C8—221no—
220C4⋊Q8C2×Dic1111yescharacteristic
221#127C2×Dic1111yescharacteristic
222#124—21no—
223#121—21no—
224#121—21no—
225C4×Q8C2×Dic1111yescharacteristic
226C4×Q8C22⋊D1111yescharacteristic
227C4×D4—21no—
228C4×D4—21no—
229C4×D4—21no—
230C4×D4—21no—
231C4×D4C2×Dic1111yescharacteristic
232C4×D4C22⋊D1111yescharacteristic
233#117—21no—
234#117C22⋊D1111yescharacteristic
235C2×C42—21no—
236C2×C42C22×D1111yescharacteristic
237#107—21no—
238#106—21no—
239C4⋊C8—224no—
240C4⋊C8—221no—
241C4⋊C8—221no—
242C4⋊C8C2×Dic1111yescharacteristic
243C4⋊C8C2×Dic1111yescharacteristic
244#103—21no—
245#102—21no—
246#102—21no—
247#102—21no—
248C22⋊C8—21no—
249C22⋊C8—224no—
250C22⋊C8—221no—
251C22⋊C8—221no—
252#97—21no—
253#97—112no—
254#97—221no—
255#97—221no—
256#97—221no—
257C4×C8—112no—
258C4×C8—221no—
259C2×C11—41no—
260C2×C11—81no—
261C2×C11—161no—
262C2×C11#188111yescharacteristic
263C2×C11#189711yescharacteristic
264C2×C11#190311yescharacteristic
265#41—41no—
266#41—41no—
267#41—82no—
268C2×Q8—21no—
269C2×Q8C22⋊Dic1111yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C2×D4C22⋊Dic1111yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4#434111yescharacteristic
281C22×C4#434111yescharacteristic
282C22×C4C2×C22⋊D1111yescharacteristic
283SD16—42no—
284D8—42no—
285M16—441no—
286M16—441no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—222no—
290C2×C8—222no—
291C2×C8—441no—
292C2×C8—441no—
293C2×C8—441no—
294C2×C8—441no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4C22⋊Dic1111yescharacteristic
300C4⋊C4C22⋊Dic1111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42D4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C42C22×Dic1111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C11#931311yescharacteristic, complemented, Sylow
314C23—21no—
315C23—41no—
316C23#6698811yescharacteristic
317Q8—21no—
318Q8—21no—
319Q8—81no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—81no—
327D4—82no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4D4×Dic1111yescharacteristic
341C2×C4D4×Dic1111yescharacteristic
342C2×C4#6699011yescharacteristic
343C2×C4#6699211yescharacteristic
344C2×C4#6699211yescharacteristic
345C2×C4C2×C22⋊Dic1111yescharacteristic
346C8—41no—
347C8—41no—
348C8—442no—
349C8—442no—
350C8—881no—
351C8—881no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22#1062283311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—81no—
371C4#1062284911yescharacteristic
372C4#1062284911yescharacteristic
373C2—41no—
374C2—81no—
375C2—161no—
376C2#1306898011yescharacteristic
377C2#1306906511yescharacteristic
378C2#1306909811yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3115C2
socleC22×C11#386
cosocleC2×C42×C11C23
hypercenter#3115D11
hypocenterC11#9313
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #13077267C2semidirect
2. #13067227C2semidirect
3. #13067050C2semidirect
4. #13067033C2semidirect
5. #13066514C2semidirect
6. #13066487C2semidirect
313. C11#9313semidirect

Maximal subgroups

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

subgroupindex
#130772672
#130672272
#130670502
#130670332
#130665142
#130664872
C11×#31152
#931311