Finite Group Databasebeta

← #14738968

Subgroups — #14738968

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079572C211yesmaximal, characteristic, complemented
2#13078716C211yesmaximal, characteristic, complemented
3#13078612C211yesmaximal, characteristic
4#13077639C211yesmaximal, characteristic, complemented
5#13068052C212yesmaximal, complemented
6#13068038C212yesmaximal, complemented
7#13067980C212yesmaximal, complemented
8#13067956C212yesmaximal, complemented
9#13067397C211yesmaximal, characteristic, complemented
10#13067280C211yesmaximal, characteristic, complemented
11C11×#1553C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C4×D44C2211yescharacteristic
14#10623001C2211yescharacteristic
15C11×#432C2211yescharacteristic
16C11×#431C2211yescharacteristic
17#10622852—22no—
18#10622705C2211yescharacteristic, complemented
19#10622700C2212yes—
20#10622694C2211yescharacteristic, complemented
21#10622689C2211yescharacteristic, complemented
22#10622685C2212yes—
23#10622683C2211yescharacteristic, complemented
24#10622667—22no—
25#10622649—21no—
26#10622646—21no—
27C4×#4323—22no—
28#10622538C2211yescharacteristic
29#10622538C2211yescharacteristic
30#10622459C2212yes—
31#10622454C2212yes—
32#10622447C2212yes—
33#10622447C2212yes—
34#10622344—21no—
35D11×C22⋊C8—22no—
36#10622335—21no—
37#10622323—22no—
38C8×D44—22no—
39C11×#332C2212yescomplemented
40C11×#331C2212yescomplemented
41#10622124C2212yescomplemented
42#10622120C2212yescomplemented
43#10622118C2212yescomplemented
44#10622117C2212yescomplemented
45C2×C11×#41—21no—
46C22×D44D411yescharacteristic
47C22×C4×D11—21no—
48C11×C4⋊Q8C2311yescharacteristic
49C11×#127C2311yescharacteristic
50C11×#124—21no—
51C11×#121—21no—
52C11×#121—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C2×#4326—22no—
57C2×#4324—22no—
58C2×#4323—22no—
59C2×(C2×D11)⋊C4—21no—
60#66979—21no—
61C2×C4⋊Dic11D411yescharacteristic
62#66977—21no—
63#66977—21no—
64C2×#4314—22no—
65C2×C8×D11—22no—
66C2×C8×D11—22no—
67C4×D44—21no—
68C4×D44—21no—
69C4×D44D412yes—
70C4×D44C2312yes—
71#66923—21no—
72#66922C2311yescharacteristic
73#66922C2311yescharacteristic
74C4×Dic22—21no—
75C4×Dic22—21no—
76C11×C4⋊C8C2312yes—
77C11×C4⋊C8C2312yes—
78C11×C22⋊C8—21no—
79C11×C22⋊C8—21no—
80C11×#97—21no—
81C4×C8×C11—21no—
82#66899—22no—
83#66896—22no—
84#66896—22no—
85C22⋊(C11⋊C8)—21no—
86C22⋊(C11⋊C8)D412yes—
87#66885—22no—
88(C2×D11)⋊C8—22no—
89(C2×D11)⋊C8—22no—
90#66882—22no—
91#66880—22no—
92#66873—22no—
93#66871—22no—
94C4⋊(C11⋊C8)D412yes—
95C4⋊(C11⋊C8)C2312yes—
96C4×C11⋊C8—21no—
97C4×C11⋊C8C2311yescharacteristic
98C4×C11⋊C8C2311yescharacteristic
99#19388—111nomaximal, Sylow
100C23×D11—21no—
101C11×#41—82no—
102C2×Q8×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×Dic11—21no—
112C2×D44—24no—
113C2×D44—21no—
114C2×D44C2×D412yes—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—82no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C42×C11C2411yescharacteristic
130C22⋊Dic11—41no—
131#4326—82no—
132#4324—82no—
133#4323—44no—
134(C2×D11)⋊C4—22no—
135(C2×D11)⋊C4—22no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11C2×D412yes—
142Dic11⋊C4—41no—
143Dic11⋊C4—41no—
144C4×Dic11—41no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8C2×D412yes—
147C2×C11⋊C8C2×D412yes—
148#4314—44no—
149C8×D11—82no—
150C8×D11—82no—
151#3210—111no—
152#3110—111no—
153#3100—111no—
154#2972—111no—
155#1681—112no—
156#1679—112no—
157#1669—112no—
158#1665—112no—
159#1572—111no—
160#1553D1111yescharacteristic, complemented
161#1544—111no—
162C23×C11—41no—
163C23×C11#12111yescharacteristic
164C22×D11—22no—
165C22×D11—24no—
166C22×D11—81no—
167C22×D11—81no—
168Q8×C11—42no—
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—82no—
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×Dic11—22no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—81no—
188D44—24no—
189D44—22no—
190D44#13514yes—
191C4×D11—42no—
192C4×D11—42no—
193C4×D11—82no—
194Dic22—42no—
195Dic22—42no—
196C8×C11—42no—
197C8×C11—42no—
198C11⋊C8—22no—
199C11⋊C8—22no—
200C11⋊C8—42no—
201#533—111no—
202#532C2×D1111yescharacteristic
203C2×C4×D4—111no—
204#494—111no—
205#492—111no—
206#487—111no—
207#486—111no—
208#484—221no—
209#480—221no—
210#474—112no—
211#474—112no—
212#464—222no—
213#461—112no—
214#459—112no—
215#452—222no—
216#450—221no—
217#447—221no—
218#440—222no—
219C4×D8—222no—
220C8×D4—112no—
221C8×D4—112no—
222C8×D4—222no—
223#432C2×D1111yescharacteristic
224#431—111no—
225#431—111no—
226#431C2×D1111yescharacteristic
227C2×C22⋊C8—222no—
228#335—112no—
229#334—112no—
230#332—112no—
231#332—112no—
232#332C2×D1112yescomplemented
233#331C2×D1112yescomplemented
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11C2×#12111yescharacteristic
241C2×D11—24no—
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—84no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—81no—
250C4×C11C2×#13512yes—
251C4×C11#57612yes—
252Dic11—42no—
253Dic11—81no—
254Dic11—81no—
255C2×#41—21no—
256C22×D4—111no—
257C23×C4—221no—
258C2×Q16—222no—
259C2×SD16—222no—
260C2×SD16—222no—
261C2×D8—222no—
262C22×C8—222no—
263C22×C8—222no—
264C4⋊Q8—111no—
265C4⋊Q8—111no—
266C4⋊Q8C22×D1111yescharacteristic
267#127C22×D1111yescharacteristic
268#125—221no—
269#124—21no—
270C22⋊Q8—221no—
271C22⋊Q8—221no—
272#121—21no—
273#121—21no—
274C4×Q8—221no—
275C4×Q8—221no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—112no—
279C4×D4—112no—
280C4×D4—221no—
281C4×D4—221no—
282#117—221no—
283C2×C4⋊C4—111no—
284C2×C22⋊C4—221no—
285C2×C42C22×D1111yescharacteristic
286#107—222no—
287#107—222no—
288C4⋊C8—112no—
289C4⋊C8—112no—
290C4⋊C8C22×D1112yes—
291C4⋊C8C22×D1112yes—
292#103—222no—
293#103—222no—
294#102—222no—
295#102—222no—
296#102—222no—
297#102—222no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—112no—
301C22⋊C8—222no—
302C22⋊C8—222no—
303C22⋊C8—221no—
304#97—21no—
305C4×C8—21no—
306C4×C8—111no—
307C4×C8—111no—
308C4×C8—221no—
309C2×C11—41no—
310C2×C11—161no—
311C2×C11#304111yescharacteristic
312C2×C11#305011yescharacteristic
313C2×C11#306911yescharacteristic
314D11—44no—
315C24—221no—
316#41—82no—
317C2×Q8—21no—
318C2×Q8—221no—
319C2×Q8—221no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—112no—
325C2×D4—224no—
326C2×D4—221no—
327C22×C4—41no—
328C22×C4—221no—
329C22×C4—222no—
330C22×C4—222no—
331C22×C4—882no—
332C22×C4#433911yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4D4×D1111yescharacteristic
335Q16—882no—
336SD16—444no—
337SD16—882no—
338D8—444no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—112no—
342C2×C8—112no—
343C2×C8—222no—
344C2×C8—882no—
345C2×C8—882no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—112no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C4⋊C4—221no—
353C4⋊C4—221no—
354C4⋊C4—441no—
355C4⋊C4—441no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—222no—
359C22⋊C4—222no—
360C22⋊C4—441no—
361C42—441no—
362C42#433911yescharacteristic
363C42D4×D1111yescharacteristic
364C42D4×D1111yescharacteristic
365C42C23×D1111yescharacteristic
366C11#1938811yescharacteristic, complemented, Sylow
367C23—41no—
368C23—224no—
369C23—222no—
370C23—881no—
371C23—881no—
372C23#6693711yescharacteristic
373Q8—42no—
374Q8—442no—
375Q8—442no—
376D4—42no—
377D4—42no—
378D4—81no—
379D4—82no—
380D4—114no—
381D4—224no—
382D4—222no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—82no—
388C2×C4—222no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—882no—
394C2×C4—881no—
395C2×C4#6693711yescharacteristic
396C2×C4#6693711yescharacteristic
397C2×C4#6693711yescharacteristic
398C2×C4C2×#433911yescharacteristic
399C2×C4C2×D4×D1111yescharacteristic
400C2×C4C2×D4×D1111yescharacteristic
401C8—42no—
402C8—42no—
403C8—222no—
404C8—222no—
405C8—442no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—224no—
413C22—442no—
414C22—442no—
415C22—884no—
416C22C2×#6693711yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—81no—
422C4—442no—
423C4—881no—
424C4—881no—
425C4D11×#13512yes—
426C4#1062330512yes—
427C2—41no—
428C2—161no—
429C2—444no—
430C2#1307811811yescharacteristic
431C2#1307819611yescharacteristic
432C2#1307835611yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1553C2
socleC22×C11C2×#121
prime radical#13078612C2
hypercenter#1553D11
hypocenterC11#19388
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1553

Complements

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

NH ≅ G/Ntype
1. #13079572C2semidirect
2. #13078716C2semidirect
4. #13077639C2semidirect
5. #13068052C2semidirect
6. #13068038C2semidirect
7. #13067980C2semidirect
8. #13067956C2semidirect
9. #13067397C2semidirect
10. #13067280C2semidirect
11. C11×#1553C2semidirect
18. #10622705C22semidirect
20. #10622694C22semidirect
21. #10622689C22semidirect
23. #10622683C22semidirect
39. C11×#332C22semidirect
40. C11×#331C22semidirect
41. #10622124C22semidirect
42. #10622120C22semidirect
43. #10622118C22semidirect
44. #10622117C22semidirect
160. #1553D11semidirect
232. #332C2×D11semidirect
233. #331C2×D11semidirect
366. C11#19388semidirect

Maximal subgroups

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

subgroupindex
#130795722
#130787162
#130786122
#130776392
#130680522
#130680382
#130679802
#130679562
#130673972
#130672802
C11×#15532
#1938811