Finite Group Databasebeta

← #14653155

Subgroups — #14653155

Order 2816.

400 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#13078938C211yesmaximal, characteristic
2#13068746C211yesmaximal, characteristic, complemented
3#13067181C211yesmaximal, characteristic, complemented
4#13067179C211yesmaximal, characteristic, complemented
5#13067176C211yesmaximal, characteristic
6#13066900C211yesmaximal, characteristic, complemented
7C11×#1517C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622846—21no—
13#10622846—21no—
14#10622694C411yescharacteristic, complemented
15#10622694C411yescharacteristic, complemented
16#10622683C411yescharacteristic, complemented
17#10622683C411yescharacteristic, complemented
18#10622669—21no—
19#10622669—21no—
20#10622549C2211yescharacteristic
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#327—22no—
24#10622175—22no—
25#10622167—21no—
26#10622167—21no—
27#10622105—22no—
28#10622092—21no—
29C8×C11⋊C8—21no—
30#10622090—22no—
31C2×C11×#41—21no—
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#127C2×C411yescharacteristic
34C11×#124—21no—
35C11×#121—21no—
36C11×#121—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41#66979—21no—
42C2×C4⋊Dic11—21no—
43#66977—21no—
44#66977—21no—
45C22×C11⋊C8D411yescharacteristic
46C22×C11⋊C8D411yescharacteristic
47#66923—21no—
48#66922C2×C411yescharacteristic
49#66922C2×C411yescharacteristic
50C4×Dic22—21no—
51C4×Dic22—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8D412yes—
54C4×C8×C11—21no—
55C11×#95—21no—
56C11×#95—21no—
57#66899—21no—
58#66899—21no—
59#66899—21no—
60#66899—21no—
61#66896—21no—
62#66896—21no—
63#66896—21no—
64#66896—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C22⋊(C11⋊C8)D412yes—
68C4⋊(C11⋊C8)—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8C2×C411yescharacteristic
71C4×C11⋊C8C2×C411yescharacteristic
72C4×C11⋊C8D411yescharacteristic
73C4×C11⋊C8D411yescharacteristic
74#9757—111nomaximal, Sylow
75C11×#41—41no—
76C11×#41—41no—
77C11×#41—41no—
78C11×#41—41no—
79C2×Q8×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—41no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×C8×C11—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11C22×C411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103C22⋊Dic11—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112C4×Dic11—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—21no—
115C2×C11⋊C8—21no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8C22⋊C411yescharacteristic
119C2×C11⋊C8C22⋊C411yescharacteristic
120C2×C11⋊C8C22⋊C411yescharacteristic
121C2×C11⋊C8C22⋊C411yescharacteristic
122#3131—111no—
123#1835—111no—
124#1518—111no—
125#1518—111no—
126#1517—111no—
127#1517D1111yescharacteristic
128#1450—111no—
129C23×C11—41no—
130C23×C11#12711yescharacteristic
131Q8×C11—41no—
132Q8×C11—41no—
133D4×C11—41no—
134D4×C11—41no—
135D4×C11—81no—
136D4×C11—81no—
137D4×C11—81no—
138D4×C11—81no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12411yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162Dic22—81no—
163Dic22—81no—
164C8×C11—42no—
165C11⋊C8—21no—
166C11⋊C8—21no—
167C11⋊C8—21no—
168C11⋊C8—21no—
169C11⋊C8—42no—
170#533—111no—
171#532C2×D1111yescharacteristic
172#488—221no—
173#488—221no—
174#487—111no—
175#487—111no—
176#486—111no—
177#486—111no—
178#431—111no—
179#431C2×D1111yescharacteristic
180#416—221no—
181#416—221no—
182C2×C4×C8—111no—
183#382—111no—
184#382C2×D1111yescharacteristic
185#340—221no—
186#340—221no—
187#328—222no—
188#328—222no—
189#327—22no—
190#327—222no—
191#322—221no—
192C82—221no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11#39011yescharacteristic
199C22×C11#49511yescharacteristic
200C22×C11#49511yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—81no—
206C4×C11—161no—
207C4×C11#41611yescharacteristic
208C4×C11#41611yescharacteristic
209C4×C11#48811yescharacteristic
210C4×C11#48811yescharacteristic
211Dic11—81no—
212Dic11—81no—
213Dic11—161no—
214C2×#41—21no—
215C22×C8—111no—
216C22×C8—111no—
217C4⋊Q8—111no—
218C4⋊Q8—111no—
219C4⋊Q8C4×D1111yescharacteristic
220#127C4×D1111yescharacteristic
221#125—221no—
222#124—21no—
223C22⋊Q8—221no—
224C22⋊Q8—221no—
225#121—21no—
226#121—21no—
227C4×Q8—221no—
228C4×Q8—221no—
229C4×D4—21no—
230C4×D4—21no—
231#117—221no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—221no—
234C2×C42C22×D1111yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—221no—
237#103—221no—
238#103—221no—
239#103—221no—
240#103—221no—
241#102—221no—
242#102—221no—
243#102—221no—
244#102—221no—
245C22⋊C8—112no—
246C22⋊C8C22⋊D1112yes—
247C4×C8—21no—
248C4×C8—111no—
249C4×C8—111no—
250C4×C8—111no—
251C4×C8—111no—
252C4×C8—221no—
253#95—21no—
254#95—21no—
255#95—221no—
256#95—221no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—161no—
260C2×C11#195811yescharacteristic
261C2×C11#197611yescharacteristic
262C2×C11#197611yescharacteristic
263#41—41no—
264#41—41no—
265#41—41no—
266#41—41no—
267C2×Q8—21no—
268C2×Q8—221no—
269C2×Q8—221no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—441no—
277C22×C4D4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280C2×C8—22no—
281C2×C8—111no—
282C2×C8—111no—
283C2×C8—111no—
284C2×C8—111no—
285C2×C8—221no—
286C2×C8—221no—
287C2×C8—221no—
288C2×C8—221no—
289C2×C8—222no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—441no—
305C42—441no—
306C42C2×C4×D1111yescharacteristic
307C42#433911yescharacteristic
308C42D4×D1111yescharacteristic
309C42#434111yescharacteristic
310C11#975711yescharacteristic, complemented, Sylow
311C23—41no—
312C23#6699311yescharacteristic
313Q8—41no—
314Q8—41no—
315Q8—881no—
316Q8—881no—
317D4—41no—
318D4—41no—
319D4—81no—
320D4—81no—
321D4—81no—
322D4—81no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—881no—
334C2×C4—881no—
335C2×C4—881no—
336C2×C4C22⋊C4×D1111yescharacteristic
337C2×C4(C22⋊D11)⋊C411yescharacteristic
338C2×C4#6693711yescharacteristic
339C2×C4#6693811yescharacteristic
340C2×C4#6696511yescharacteristic
341C2×C4#6696511yescharacteristic
342C2×C4#6696911yescharacteristic
343C2×C4#6696911yescharacteristic
344C2×C4C4×C22⋊D1111yescharacteristic
345C2×C4#6699211yescharacteristic
346C8—42no—
347C8—221no—
348C8—221no—
349C8—221no—
350C8—221no—
351C8—442no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1062257011yescharacteristic
358C22#1062276811yescharacteristic
359C22#1062278111yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—161no—
366C4—881no—
367C4—881no—
368C4—1761no—
369C4#1062238111yescharacteristic
370C4#1062238111yescharacteristic
371C4#1062238511yescharacteristic
372C4#1062238511yescharacteristic
373C2—21no—
374C2—21no—
375C2—161no—
376C2#1306942611yescharacteristic
377C2#1306951111yescharacteristic
378C2#1306951311yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1517C2
socleC22×C11#390
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1517D11
hypocenterC11#9757
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #13068746C2semidirect
3. #13067181C2semidirect
4. #13067179C2semidirect
6. #13066900C2semidirect
14. #10622694C4semidirect
15. #10622694C4semidirect
16. #10622683C4semidirect
17. #10622683C4semidirect
310. C11#9757semidirect

Maximal subgroups

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

subgroupindex
#130789382
#130687462
#130671812
#130671792
#130671762
#130669002
C11×#15172
#975711