Finite Group Databasebeta

← #14723917

Subgroups — #14723917

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078625C211yesmaximal, characteristic
2#13077710C211yesmaximal, characteristic, complemented
3#13077639C211yesmaximal, characteristic
4#13067475C212yesmaximal, complemented
5#13067454C212yesmaximal, complemented
6#13067430C212yesmaximal, complemented
7C8×#4314C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067060C211yesmaximal, characteristic
10#13067038C211yesmaximal, characteristic, complemented
11C11×#1453C211yesmaximal, characteristic, complemented
12C2×C4×D44C2211yescharacteristic
13#10623001C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C4×C11×M16C2211yescharacteristic
17#10622539C2211yescharacteristic
18#10622538C2211yescharacteristic
19#10622455C412yes—
20#10622454C412yes—
21#10622447—22no—
22#10622441—22no—
23#10622344C412yes—
24D11×C22⋊C8—22no—
25#10622334C412yes—
26#10622333—22no—
27C4×#4314C2212yes—
28C4×#4314C2212yes—
29C8×D44C2212yes—
30C8×D44C2212yes—
31#10622292C2212yescomplemented
32C8×Dic22C2212yescomplemented
33C11×#322C2211yescharacteristic, complemented
34C11×#322C2211yescharacteristic, complemented
35C11×#322C2211yescharacteristic, complemented
36C82×C11C2211yescharacteristic, complemented
37#10622097C2212yes—
38#10622097C2212yes—
39#10622096C2212yescomplemented
40#10622095C2212yescomplemented
41#10622094C2212yescomplemented
42#10622094C2212yescomplemented
43C22×D44C2×C411yescharacteristic
44C22×C4×D11—21no—
45C2×C11×M16—21no—
46C2×C42×C11C2311yescharacteristic
47C2×(C2×D11)⋊C4—21no—
48#66979—21no—
49C2×C4⋊Dic11C2×C411yescharacteristic
50#66977—21no—
51#66977C2×C412yes—
52C2×#4314C2×C412yes—
53C2×#4314C2×C412yes—
54C2×C8×D11—22no—
55C2×C8×D11—22no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44C2×C412yes—
59C4×D44C2312yes—
60#66923—21no—
61#66922C2×C411yescharacteristic
62#66922C2×C411yescharacteristic
63C4×Dic22—21no—
64C4×Dic22C2312yes—
65C11×C4⋊C8C2×C412yes—
66C11×C4⋊C8D412yes—
67C11×C22⋊C8C2×C412yes—
68C11×C22⋊C8D412yes—
69C11×#97—21no—
70C4×C8×C11C2311yescharacteristic
71C4×C8×C11C2311yescharacteristic
72C4×C8×C11C2311yescharacteristic
73C4×C8×C11C2311yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78#66885C2×C412yes—
79#66885C2×C412yes—
80(C2×D11)⋊C8—22no—
81(C2×D11)⋊C8—22no—
82#66881C2×C412yes—
83#66881C2×C412yes—
84#66880C2×C412yes—
85#66880C2×C412yes—
86#66879—22no—
87Dic11⋊C8—22no—
88Dic11⋊C8—22no—
89C8×Dic11—22no—
90C4⋊(C11⋊C8)C2312yes—
91C4⋊(C11⋊C8)C2312yes—
92#66867—21no—
93C4×C11⋊C8—21no—
94#17924—111nomaximal, Sylow
95C23×D11—21no—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×Dic11—21no—
100C2×D44—24no—
101C2×D44—21no—
102C2×D44C22×C412yes—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—82no—
106C2×Dic22—21no—
107C2×Dic22C22×C412yes—
108C11×M16—42no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11C22×C412yes—
112C2×C8×C11C22×C412yes—
113C2×C8×C11C2×D412yes—
114C2×C8×C11C2×D412yes—
115C42×C11C22×C411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11C2411yescharacteristic
119C22⋊Dic11—22no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11C22×C412yes—
127C4⋊Dic11C22×C412yes—
128Dic11⋊C4—22no—
129Dic11⋊C4—22no—
130C4×Dic11—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133#4314—24no—
134#4314—24no—
135C8×D11—82no—
136C8×D11—82no—
137#3101—111no—
138#2985—111no—
139#2972—111no—
140#1585—112no—
141#1582—112no—
142SD16⋊C8—112no—
143C8×SD16—112no—
144#1572—111no—
145#1490—111no—
146#1485—111no—
147#1453D1111yescharacteristic, complemented
148C23×C11C4×D411yescharacteristic
149C22×D11—22no—
150C22×D11—24no—
151C22×D11—81no—
152C22×D11—81no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C2×#4111yescharacteristic
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—81no—
166D44—24no—
167D44—22no—
168D44#13114yes—
169C4×D11—42no—
170C4×D11—42no—
171C4×D11—82no—
172Dic22—22no—
173Dic22—22no—
174Dic22—81no—
175C8×C11—22no—
176C8×C11—22no—
177C8×C11—22no—
178C8×C11—22no—
179C8×C11—22no—
180C8×C11—41no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183#533—111no—
184C2×C4×D4—111no—
185#483—112no—
186#476—112no—
187#461—112no—
188#450—112no—
189#446—112no—
190#446—222no—
191C8×Q8—112no—
192C4×SD16—112no—
193C4×SD16—112no—
194C8×D4—112no—
195C8×D4—112no—
196C8×D4—222no—
197#433—222no—
198#432—111no—
199#431—111no—
200#431C2×D1111yescharacteristic
201#431C2×D1111yescharacteristic
202C2×C22⋊C8—222no—
203C4×M16C2×D1111yescharacteristic
204#335—112no—
205#334—112no—
206Q8⋊C8—112no—
207Q8⋊C8—112no—
208D4⋊C8—112no—
209D4⋊C8—112no—
210#322C2×D1111yescharacteristic, complemented
211#322C2×D1111yescharacteristic, complemented
212#322C2×D1111yescharacteristic, complemented
213C82C2×D1111yescharacteristic, complemented
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11C2×C4×D411yescharacteristic
218C2×D11—24no—
219C2×D11—42no—
220C2×D11—42no—
221C2×D11—84no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11C2×#13112yes—
227C4×C11#57712yes—
228Dic11—42no—
229Dic11—42no—
230Dic11—42no—
231C22×D4—111no—
232C23×C4—221no—
233C2×SD16—112no—
234C2×SD16—112no—
235C2×M16—21no—
236C22×C8—222no—
237C22×C8—222no—
238C4⋊Q8—111no—
239C4⋊Q8—111no—
240#125—221no—
241C22⋊Q8—112no—
242C22⋊Q8—221no—
243C4×Q8—112no—
244C4×Q8—221no—
245C4×D4—112no—
246C4×D4—112no—
247C4×D4—221no—
248C4×D4—221no—
249#117—221no—
250C2×C4⋊C4—111no—
251C2×C22⋊C4—221no—
252C2×C42C22×D1111yescharacteristic
253#106—112no—
254#106—112no—
255C4⋊C8—112no—
256C4⋊C8—112no—
257C4⋊C8—222no—
258C4⋊C8—222no—
259C4⋊C8C4×D1112yes—
260C4⋊C8D4412yes—
261#103—112no—
262#103—112no—
263#102—112no—
264#102—112no—
265C22⋊C8—221no—
266C22⋊C8—221no—
267C22⋊C8—222no—
268C22⋊C8—222no—
269C22⋊C8C4×D1112yes—
270C22⋊C8D4412yes—
271#97—21no—
272#97—222no—
273#97—221no—
274C4×C8—222no—
275C4×C8—221no—
276C4×C8C22×D1111yescharacteristic
277C4×C8C22×D1111yescharacteristic
278C4×C8C22×D1111yescharacteristic
279C4×C8C22×D1111yescharacteristic
280C4×C8C22×D1111yescharacteristic
281C4×C8C22×D1111yescharacteristic
282C2×C11—41no—
283C2×C11#292911yescharacteristic
284C2×C11#294911yescharacteristic
285C2×C11#295611yescharacteristic
286D11—44no—
287C24—221no—
288C2×Q8—112no—
289C2×Q8—221no—
290C2×D4—112no—
291C2×D4—224no—
292C2×D4—221no—
293C22×C4—221no—
294C22×C4—222no—
295C22×C4—222no—
296C22×C4—882no—
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4C2×D4411yescharacteristic
299C22×C4#433911yescharacteristic
300SD16—224no—
301SD16—224no—
302M16—42no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—222no—
306C2×C8—222no—
307C2×C8—882no—
308C2×C8—882no—
309C2×C8C2×C4×D1112yes—
310C2×C8C2×C4×D1112yes—
311C2×C8C2×D4412yes—
312C2×C8C2×D4412yes—
313C4⋊C4—112no—
314C4⋊C4—112no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C4⋊C4—222no—
319C4⋊C4—221no—
320C4⋊C4—222no—
321C22⋊C4—222no—
322C22⋊C4—222no—
323C22⋊C4—222no—
324C42—222no—
325C42C2×C4×D1111yescharacteristic
326C42C2×D4411yescharacteristic
327C42#433911yescharacteristic
328C42C23×D1111yescharacteristic
329C11#1792411yescharacteristic, complemented, Sylow
330C23—224no—
331C23—222no—
332C23—881no—
333C23—881no—
334C23C4×D4411yescharacteristic
335Q8—222no—
336Q8—222no—
337Q8—881no—
338D4—114no—
339D4—224no—
340D4—222no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—222no—
345C2×C4—222no—
346C2×C4—222no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4—882no—
350C2×C4—881no—
351C2×C4C4×D4411yescharacteristic
352C2×C4C4×D4411yescharacteristic
353C2×C4C4×D4411yescharacteristic
354C2×C4C22×C4×D1111yescharacteristic
355C2×C4C22×D4411yescharacteristic
356C2×C4C2×#433911yescharacteristic
357C8—22no—
358C8—22no—
359C8—22no—
360C8—22no—
361C8—22no—
362C8—41no—
363C8—442no—
364C8—442no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—224no—
369C22—442no—
370C22—442no—
371C22—884no—
372C22C2×C4×D4411yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—442no—
378C4—442no—
379C4—442no—
380C4D11×#13112yes—
381C4#1062328212yes—
382C2—41no—
383C2—444no—
384C2#1307731211yescharacteristic
385C2#1307747711yescharacteristic
386C2#1307752711yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1453C2
socleC22×C11C2×C4×D4
prime radicalC22×D44C2×C4
cosocleC42×C11C24
hypercenter#1453D11
hypocenterC11#17924
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1453

Complements

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

NH ≅ G/Ntype
2. #13077710C2semidirect
4. #13067475C2semidirect
5. #13067454C2semidirect
6. #13067430C2semidirect
7. C8×#4314C2semidirect
8. #13067396C2semidirect
10. #13067038C2semidirect
11. C11×#1453C2semidirect
31. #10622292C22semidirect
32. C8×Dic22C22semidirect
33. C11×#322C22semidirect
34. C11×#322C22semidirect
35. C11×#322C22semidirect
36. C82×C11C22semidirect
39. #10622096C22semidirect
40. #10622095C22semidirect
41. #10622094C22semidirect
42. #10622094C22semidirect
147. #1453D11semidirect
210. #322C2×D11semidirect
211. #322C2×D11semidirect
212. #322C2×D11semidirect
213. C82C2×D11semidirect
329. C11#17924semidirect

Maximal subgroups

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

subgroupindex
#130786252
#130777102
#130776392
#130674752
#130674542
#130674302
C8×#43142
#130673962
#130670602
#130670382
C11×#14532
#1792411