Finite Group Databasebeta

← #14739023

Subgroups — #14739023

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078703C211yesmaximal, characteristic
2#13078620C211yesmaximal, characteristic, complemented
3#13077639C211yesmaximal, characteristic, complemented
4#13068050C212yesmaximal, complemented
5#13068022C212yesmaximal, complemented
6#13068012C212yesmaximal, complemented
7#13067988C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067326C211yesmaximal, characteristic, complemented
10#13067278C211yesmaximal, characteristic, complemented
11C11×#3228C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C11×#500C2211yescharacteristic, complemented
16C11×#498C2211yescharacteristic, complemented
17C11×#486C2211yescharacteristic, complemented
18C11×#486C2211yescharacteristic, complemented
19C11×#482—22no—
20C11×#478—22no—
21C11×#431C2211yescharacteristic
22#10622697C2212yes—
23#10622697C2212yes—
24#10622696C2212yes—
25#10622685C2212yes—
26#10622659—21no—
27#10622656—21no—
28#10622649—21no—
29#10622647—21no—
30C4×#4325—22no—
31#10622627—22no—
32#10622539C2211yescharacteristic
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622447—22no—
36D11×C22⋊C8—22no—
37C8×D44C2212yes—
38C8×D44C2212yes—
39#10622185C2212yescomplemented
40#10622184C2212yescomplemented
41#10622184C2212yescomplemented
42#10622182C2212yescomplemented
43#10622096C2212yescomplemented
44#10622095C2212yescomplemented
45C2×C11×#41—21no—
46C22×D44D411yescharacteristic
47C22×C4×D11—21no—
48C11×C4⋊Q8C2311yescharacteristic
49C11×C4⋊Q8C2311yescharacteristic
50C11×C4⋊Q8C2311yescharacteristic
51C11×#127C2311yescharacteristic
52C11×#125—21no—
53C11×#124—21no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8—21no—
56C11×#121—21no—
57C11×#121—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C11×#117—21no—
63C2×C42×C11C2311yescharacteristic
64C2×#4325—22no—
65C2×#4323—22no—
66C2×(C2×D11)⋊C4—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C8×D11—22no—
69C2×C8×D11—22no—
70C4×D44—21no—
71C4×D44—21no—
72C4×D44D412yes—
73C4×D44C2312yes—
74C11×#107—22no—
75C11×#106—22no—
76C11×C4⋊C8D412yes—
77C11×#102—22no—
78C11×#102—22no—
79C11×C22⋊C8D412yes—
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66899—22no—
83#66896—22no—
84C22⋊(C11⋊C8)—21no—
85C22⋊(C11⋊C8)—21no—
86C22⋊(C11⋊C8)—21no—
87(C2×D11)⋊C8—22no—
88(C2×D11)⋊C8—22no—
89#66873—22no—
90#66873—22no—
91#66872—22no—
92#66872—22no—
93C4⋊(C11⋊C8)C2312yes—
94C4⋊(C11⋊C8)C2312yes—
95C4⋊(C11⋊C8)C2312yes—
96#66867—21no—
97C4×C11⋊C8—21no—
98C4×C11⋊C8—21no—
99#19394—111nomaximal, Sylow
100C23×D11—21no—
101C11×#41—82no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×Dic11—21no—
114C2×D44—24no—
115C2×D44—21no—
116C2×D44C2×D412yes—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—82no—
120C2×C8×C11C2×D412yes—
121C2×C8×C11C2×D412yes—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C42×C11—41no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138#4325—44no—
139#4323—44no—
140(C2×D11)⋊C4—22no—
141(C2×D11)⋊C4—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11C2×D412yes—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C8×D11—82no—
148C8×D11—82no—
149#3228D1111yescharacteristic, complemented
150#3109—111no—
151#3101—111no—
152#2972—111no—
153#1681—112no—
154#1677—112no—
155#1675—112no—
156#1671—112no—
157#1572—111no—
158#1554—111no—
159#1543—111no—
160C23×C11—41no—
161C23×C11#12111yescharacteristic
162C22×D11—22no—
163C22×D11—24no—
164C22×D11—81no—
165C22×D11—81no—
166Q8×C11—42no—
167Q8×C11—81no—
168Q8×C11—81no—
169D4×C11—42no—
170D4×C11—42no—
171D4×C11—81no—
172D4×C11—82no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—82no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×Dic11—22no—
187C2×Dic11—81no—
188D44—24no—
189D44—22no—
190D44#13514yes—
191C4×D11—42no—
192C4×D11—42no—
193C4×D11—82no—
194C8×C11—22no—
195C8×C11—22no—
196C11⋊C8—42no—
197C11⋊C8—42no—
198C11⋊C8—42no—
199#533C2×D1111yescharacteristic
200#532C2×D1111yescharacteristic
201C2×C4×D4—111no—
202#500C2×D1111yescharacteristic, complemented
203#498C2×D1111yescharacteristic, complemented
204#486C2×D1111yescharacteristic, complemented
205#486C2×D1111yescharacteristic, complemented
206#483—221no—
207#482—22no—
208#481—221no—
209#478—22no—
210#476—112no—
211#476—112no—
212#461—112no—
213#459—112no—
214#450—221no—
215#447—221no—
216#442—222no—
217C4×SD16—222no—
218C8×D4—112no—
219C8×D4—112no—
220C8×D4—222no—
221#432—111no—
222#431—111no—
223#431—111no—
224#431C2×D1111yescharacteristic
225C2×C22⋊C8—222no—
226#335—112no—
227#334—112no—
228#333—112no—
229#333—112no—
230#332—112no—
231#331—112no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11C2×#12111yescharacteristic
239C2×D11—24no—
240C2×D11—42no—
241C2×D11—42no—
242C2×D11—84no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—81no—
248C4×C11—81no—
249C4×C11—81no—
250C4×C11C2×#13512yes—
251C4×C11#57712yes—
252Dic11—42no—
253C2×#41—21no—
254C22×D4—111no—
255C23×C4—221no—
256C2×SD16—222no—
257C2×D8—222no—
258C22×C8—222no—
259C22×C8—222no—
260C4⋊Q8C22×D1111yescharacteristic
261C4⋊Q8C22×D1111yescharacteristic
262C4⋊Q8C22×D1111yescharacteristic
263#127C22×D1111yescharacteristic
264#125—21no—
265#124—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268#121—21no—
269#121—21no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—112no—
275C4×D4—112no—
276C4×D4—221no—
277C4×D4—221no—
278#117—21no—
279C2×C4⋊C4—111no—
280C2×C22⋊C4—221no—
281C2×C42C22×D1111yescharacteristic
282#107—22no—
283#106—22no—
284#106—222no—
285#106—222no—
286C4⋊C8—112no—
287C4⋊C8—112no—
288C4⋊C8—112no—
289C4⋊C8C22⋊D1112yes—
290#103—222no—
291#102—22no—
292#102—22no—
293#102—222no—
294#102—222no—
295#102—222no—
296C22⋊C8—221no—
297C22⋊C8—221no—
298C22⋊C8—221no—
299C22⋊C8—222no—
300C22⋊C8—222no—
301C22⋊C8C22⋊D1112yes—
302#97—221no—
303C4×C8—221no—
304C4×C8—221no—
305C4×C8C22×D1111yescharacteristic
306C4×C8C22×D1111yescharacteristic
307C2×C11—41no—
308C2×C11—161no—
309C2×C11#304211yescharacteristic
310C2×C11#305011yescharacteristic
311C2×C11#306811yescharacteristic
312D11—44no—
313C24—221no—
314#41—82no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4—112no—
323C2×D4—224no—
324C2×D4—221no—
325C22×C4—41no—
326C22×C4—221no—
327C22×C4—222no—
328C22×C4—222no—
329C22×C4—882no—
330C22×C4D4×D1111yescharacteristic
331C22×C4#434111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—444no—
334D8—444no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—882no—
339C2×C8—882no—
340C2×C8C2×C22⋊D1112yes—
341C2×C8C2×C22⋊D1112yes—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—112no—
351C4⋊C4—221no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—222no—
356C22⋊C4—222no—
357C42—41no—
358C42D4×D1111yescharacteristic
359C42#434111yescharacteristic
360C42C2×C22⋊D1111yescharacteristic
361C42C23×D1111yescharacteristic
362C11#1939411yescharacteristic, complemented, Sylow
363C23—41no—
364C23—224no—
365C23—222no—
366C23—881no—
367C23—881no—
368C23#6699111yescharacteristic
369Q8—42no—
370Q8—81no—
371Q8—81no—
372D4—42no—
373D4—42no—
374D4—81no—
375D4—82no—
376D4—114no—
377D4—224no—
378D4—222no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—82no—
386C2×C4—222no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—882no—
390C2×C4—881no—
391C2×C4#6699111yescharacteristic
392C2×C4#6699111yescharacteristic
393C2×C4#6699111yescharacteristic
394C2×C4C2×D4×D1111yescharacteristic
395C2×C4C2×#434111yescharacteristic
396C2×C4C22×C22⋊D1111yescharacteristic
397C8—22no—
398C8—22no—
399C8—442no—
400C8—442no—
401C8—442no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—224no—
409C22—442no—
410C22—442no—
411C22—884no—
412C22C2×#6699111yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—81no—
418C4—81no—
419C4—81no—
420C4—442no—
421C4D11×#13512yes—
422C4#1062336812yes—
423C2—41no—
424C2—161no—
425C2—444no—
426C2#1307812411yescharacteristic
427C2#1307819311yescharacteristic
428C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3228C2
socleC22×C11C2×#121
prime radical#13078703C2
hypercenter#3228D11
hypocenterC11#19394
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3228

Complements

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

NH ≅ G/Ntype
2. #13078620C2semidirect
3. #13077639C2semidirect
4. #13068050C2semidirect
5. #13068022C2semidirect
6. #13068012C2semidirect
7. #13067988C2semidirect
8. #13067396C2semidirect
9. #13067326C2semidirect
10. #13067278C2semidirect
11. C11×#3228C2semidirect
15. C11×#500C22semidirect
16. C11×#498C22semidirect
17. C11×#486C22semidirect
18. C11×#486C22semidirect
39. #10622185C22semidirect
40. #10622184C22semidirect
41. #10622184C22semidirect
42. #10622182C22semidirect
43. #10622096C22semidirect
44. #10622095C22semidirect
149. #3228D11semidirect
202. #500C2×D11semidirect
203. #498C2×D11semidirect
204. #486C2×D11semidirect
205. #486C2×D11semidirect
362. C11#19394semidirect

Maximal subgroups

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

subgroupindex
#130787032
#130786202
#130776392
#130680502
#130680222
#130680122
#130679882
#130673962
#130673262
#130672782
C11×#32282
#1939411