Finite Group Databasebeta

← #14723909

Subgroups — #14723909

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#13078624C211yesmaximal, characteristic
2#13077713C211yesmaximal, characteristic, complemented
3#13077640C211yesmaximal, characteristic
4#13067470C212yesmaximal, complemented
5#13067449C212yesmaximal, complemented
6#13067425C212yesmaximal, complemented
7#13067419C212yesmaximal, complemented
8#13067397C211yesmaximal, characteristic, complemented
9#13067038C211yesmaximal, characteristic, complemented
10#13066913C211yesmaximal, characteristic, complemented
11C11×#1490C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13#10623001C2211yescharacteristic
14C11×#432C2211yescharacteristic
15C4×C11×M16C2211yescharacteristic
16#10622831C412yes—
17C2×C22⋊(C11⋊C8)—22no—
18#10622632C412yes—
19C4×#4324C2212yes—
20C4×#4324C2212yes—
21D4×C11⋊C8—22no—
22D4×C11⋊C8C2212yes—
23D4×C11⋊C8C2212yes—
24#10622621C412yes—
25#10622584C412yes—
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622444C2212yescomplemented
30#10622443C2212yescomplemented
31#10622333—22no—
32#10622314—22no—
33C11×D4⋊C8C2212yes—
34C11×D4⋊C8C2212yes—
35#10622118C2212yescomplemented
36#10622117C2212yescomplemented
37#10622094C2212yescomplemented
38#10622094C2212yescomplemented
39#10622093C2211yescharacteristic, complemented
40#10622092C2211yescharacteristic, complemented
41#10622092C2211yescharacteristic, complemented
42C8×C11⋊C8C2211yescharacteristic, complemented
43C22×D4×C11C2×C411yescharacteristic
44C23×C4×C11—21no—
45C2×C11×M16—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11C2×C412yes—
49C4×D4×C11C2312yes—
50C2×C11×C4⋊C4C2×C411yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4324C2×C412yes—
54C2×#4324C2×C412yes—
55#66979—21no—
56#66977—21no—
57#66977C2×C412yes—
58C22×C11⋊C8—22no—
59C22×C11⋊C8—22no—
60#66923—21no—
61#66922C2×C411yescharacteristic
62#66922C2×C411yescharacteristic
63C4×Dic22—21no—
64C4×Dic22C2312yes—
65C11×C4⋊C8C2312yes—
66C11×C22⋊C8—21no—
67C11×#97—21no—
68C11×#97—21no—
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2311yescharacteristic
71#66896C2×C412yes—
72#66896C2×C412yes—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—22no—
75C22⋊(C11⋊C8)—22no—
76C22⋊(C11⋊C8)C2×C412yes—
77C22⋊(C11⋊C8)D412yes—
78#66879—22no—
79Dic11⋊C8—22no—
80Dic11⋊C8—22no—
81C8×Dic11—22no—
82#66874C2×C412yes—
83#66874C2×C412yes—
84#66872C2×C412yes—
85#66872C2×C412yes—
86C4⋊(C11⋊C8)C2×C412yes—
87C4⋊(C11⋊C8)D412yes—
88C4⋊(C11⋊C8)C2312yes—
89C4×C11⋊C8—21no—
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93C4×C11⋊C8C2311yescharacteristic
94#17924—111nomaximal, Sylow
95C24×C11—21no—
96C2×D4×C11—24no—
97C2×D4×C11—21no—
98C2×D4×C11C22×C412yes—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—82no—
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C2×Dic22—21no—
107C2×Dic22C22×C412yes—
108C11×M16—42no—
109C2×C8×C11—22no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4C22×C412yes—
114C11×C22⋊C4—22no—
115C11×C22⋊C4—22no—
116C42×C11C22×C411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120C22⋊Dic11—22no—
121#4324—24no—
122#4324—24no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11C22×C412yes—
127Dic11⋊C4—22no—
128Dic11⋊C4—22no—
129C4×Dic11—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—82no—
132C2×C11⋊C8—82no—
133C2×C11⋊C8C22×C412yes—
134C2×C11⋊C8C22×C412yes—
135C2×C11⋊C8C2×D412yes—
136C2×C11⋊C8C2×D412yes—
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#1490D1111yescharacteristic
146#1485—111no—
147#1453—111no—
148C23×C11—24no—
149C23×C11—22no—
150C23×C11—81no—
151C23×C11—81no—
152C23×C11C4×D411yescharacteristic
153D4×C11—24no—
154D4×C11—22no—
155D4×C11#13114yes—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—82no—
163C2×C4×C11—81no—
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11C4×D411yescharacteristic
166C2×C4×C11C4×D411yescharacteristic
167C2×C4×C11C23×C411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C2×Dic11—22no—
171C2×Dic11—22no—
172Dic22—22no—
173Dic22—22no—
174Dic22—81no—
175C8×C11—22no—
176C8×C11—41no—
177C8×C11—42no—
178C11⋊C8—22no—
179C11⋊C8—22no—
180C11⋊C8—22no—
181C11⋊C8—22no—
182C11⋊C8—42no—
183#533—111no—
184C2×C4×D4C2×D1111yescharacteristic
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#432C2×D1111yescharacteristic
199#431—111no—
200#431—111no—
201#431—111no—
202C2×C22⋊C8—222no—
203C4×M16C2×D1111yescharacteristic
204#335—112no—
205#334—112no—
206Q8⋊C8—112no—
207Q8⋊C8—112no—
208D4⋊C8C2×D1112yes—
209D4⋊C8C2×D1112yes—
210#322—111no—
211#322—111no—
212#322—111no—
213C82—111no—
214C22×C11—21no—
215C22×C11—24no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11—84no—
221C22×C11C2×C4×D411yescharacteristic
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—42no—
227C4×C11C2×#13112yes—
228C4×C11#57712yes—
229Dic11—42no—
230Dic11—42no—
231C22×D4C4×D1111yescharacteristic
232C23×C4—21no—
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—21no—
246C4×D4—21no—
247C4×D4C4×D1112yes—
248C4×D4C22×D1112yes—
249#117—221no—
250C2×C4⋊C4C4×D1111yescharacteristic
251C2×C22⋊C4—21no—
252C2×C42C22×D1111yescharacteristic
253#106—112no—
254#106—112no—
255C4⋊C8—112no—
256C4⋊C8—112no—
257C4⋊C8—112no—
258C4⋊C8—222no—
259C4⋊C8—222no—
260C4⋊C8C22×D1112yes—
261#103—112no—
262#103—112no—
263#102—112no—
264#102—112no—
265C22⋊C8—21no—
266C22⋊C8—112no—
267C22⋊C8—112no—
268C22⋊C8—222no—
269C22⋊C8—222no—
270C22⋊C8—221no—
271#97—21no—
272#97—21no—
273#97—222no—
274C4×C8—111no—
275C4×C8—111no—
276C4×C8—111no—
277C4×C8—111no—
278C4×C8—222no—
279C4×C8—221no—
280C4×C8C22×D1111yescharacteristic
281C4×C8C22×D1111yescharacteristic
282C2×C11—41no—
283C2×C11—44no—
284C2×C11#292911yescharacteristic
285C2×C11#294911yescharacteristic
286C2×C11#295611yescharacteristic
287C24—21no—
288C2×Q8—112no—
289C2×Q8—221no—
290C2×D4—24no—
291C2×D4—21no—
292C2×D4C2×C4×D1112yes—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—82no—
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299C22×C4#434111yescharacteristic
300SD16—224no—
301SD16—224no—
302M16—42no—
303C2×C8—21no—
304C2×C8—22no—
305C2×C8—21no—
306C2×C8—112no—
307C2×C8—112no—
308C2×C8—112no—
309C2×C8—112no—
310C2×C8—222no—
311C2×C8—882no—
312C2×C8—882no—
313C4⋊C4—21no—
314C4⋊C4—112no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4—222no—
318C4⋊C4—221no—
319C4⋊C4—222no—
320C4⋊C4C2×C4×D1112yes—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—222no—
324C42—222no—
325C42C2×C4×D1111yescharacteristic
326C42D4×D1111yescharacteristic
327C42#434111yescharacteristic
328C42C23×D1111yescharacteristic
329C11#1792411yescharacteristic, complemented, Sylow
330C23—24no—
331C23—22no—
332C23—81no—
333C23—81no—
334C23(C22⋊D11)⋊C411yescharacteristic
335Q8—222no—
336Q8—222no—
337Q8—881no—
338D4—24no—
339D4—22no—
340D4#6696014yes—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—81no—
349C2×C4—222no—
350C2×C4—222no—
351C2×C4(C22⋊D11)⋊C411yescharacteristic
352C2×C4(C22⋊D11)⋊C411yescharacteristic
353C2×C4(C22⋊D11)⋊C411yescharacteristic
354C2×C4C22×C4×D1111yescharacteristic
355C2×C4C2×D4×D1111yescharacteristic
356C2×C4C2×#434111yescharacteristic
357C8—22no—
358C8—41no—
359C8—42no—
360C8—222no—
361C8—222no—
362C8—222no—
363C8—222no—
364C8—442no—
365C22—21no—
366C22—21no—
367C22—24no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—84no—
372C22C2×(C22⋊D11)⋊C411yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—442no—
379C4—442no—
380C4C2×#6696012yes—
381C4#1062330612yes—
382C2—41no—
383C2—44no—
384C2#1307730611yescharacteristic
385C2#1307747811yescharacteristic
386C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1490C2
socleC22×C11C2×C4×D4
prime radicalC22×D4×C11C2×C4
cosocleC42×C11C24
hypercenter#1490D11
hypocenterC11#17924
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #13077713C2semidirect
4. #13067470C2semidirect
5. #13067449C2semidirect
6. #13067425C2semidirect
7. #13067419C2semidirect
8. #13067397C2semidirect
9. #13067038C2semidirect
10. #13066913C2semidirect
29. #10622444C22semidirect
30. #10622443C22semidirect
35. #10622118C22semidirect
36. #10622117C22semidirect
37. #10622094C22semidirect
38. #10622094C22semidirect
39. #10622093C22semidirect
40. #10622092C22semidirect
41. #10622092C22semidirect
42. C8×C11⋊C8C22semidirect
329. C11#17924semidirect

Maximal subgroups

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

subgroupindex
#130786242
#130777132
#130776402
#130674702
#130674492
#130674252
#130674192
#130673972
#130670382
#130669132
C11×#14902
#1792411