Finite Group Databasebeta

← #14738969

Subgroups — #14738969

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#13079574C211yesmaximal, characteristic, complemented
2#13078715C211yesmaximal, characteristic, complemented
3#13078616C211yesmaximal, characteristic
4#13068053C212yesmaximal, complemented
5#13068039C212yesmaximal, complemented
6#13067981C212yesmaximal, complemented
7#13067957C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067319C211yesmaximal, characteristic, complemented
10#13067280C211yesmaximal, characteristic, complemented
11C11×#2972C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13#10623008C2211yescharacteristic
14#10623001C2211yescharacteristic
15C8×D4×C11—22no—
16C8×D4×C11C2212yes—
17C8×D4×C11C2212yes—
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C2×C11×C22⋊C8—22no—
21#10622831—21no—
22#10622830—21no—
23#10622632C2212yes—
24#10622631—22no—
25#10622628C2212yes—
26C4×#4323—22no—
27#10622620C2212yes—
28#10622620C2212yes—
29#10622583—21no—
30#10622580—21no—
31#10622539C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622458—22no—
34#10622346—22no—
35#10622312C2211yescharacteristic, complemented
36#10622307C2211yescharacteristic, complemented
37#10622306C2211yescharacteristic, complemented
38#10622294C2211yescharacteristic, complemented
39#10622124C2212yescomplemented
40#10622123C2212yescomplemented
41#10622120C2212yescomplemented
42#10622120C2212yescomplemented
43#10622096C2212yescomplemented
44#10622095C2212yescomplemented
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—21no—
47C2×#4339—21no—
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11D412yes—
53C4×D4×C11C2312yes—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C2×#4324—22no—
58C2×#4323—22no—
59#66983—21no—
60#66983—21no—
61#66979—21no—
62#66977—21no—
63#66977—21no—
64C2×Dic44—22no—
65C2×#4314—22no—
66#66928—21no—
67#66927C2311yescharacteristic
68C4×D44—21no—
69C4×D44—21no—
70#66923—21no—
71#66922C2311yescharacteristic
72#66922C2311yescharacteristic
73#66922C2311yescharacteristic
74C4×Dic22—21no—
75C4×Dic22—21no—
76C11×C4⋊C8D412yes—
77C11×C4⋊C8C2312yes—
78C11×C22⋊C8—21no—
79C11×C22⋊C8—22no—
80C11×C22⋊C8—22no—
81C11×C22⋊C8D412yes—
82C4×C8×C11—21no—
83C4×C8×C11C2311yescharacteristic
84C4×C8×C11C2311yescharacteristic
85#66896—22no—
86#66896—22no—
87C22⋊(C11⋊C8)—21no—
88C22⋊(C11⋊C8)—21no—
89#66885—22no—
90#66880—22no—
91#66874—22no—
92#66873—22no—
93#66871—22no—
94#66871—22no—
95C4⋊(C11⋊C8)C2312yes—
96C4⋊(C11⋊C8)C2312yes—
97#66867—21no—
98C4×C11⋊C8—21no—
99#19388—111nomaximal, Sylow
100C24×C11—21no—
101C2×D4×C11—24no—
102C2×D4×C11—21no—
103C2×D4×C11C2×D412yes—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—82no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C2×C22⋊D11—41no—
112#4339—82no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×C4×D11—41no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×C8×C11—22no—
121C2×C8×C11—82no—
122C2×C8×C11—82no—
123C2×C8×C11C2×D412yes—
124C2×C8×C11C2×D412yes—
125C11×C4⋊C4—21no—
126C11×C4⋊C4C2×D412yes—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—22no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C42×C11C2411yescharacteristic
133C22⋊Dic11—41no—
134#4324—44no—
135#4323—44no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144Dic11⋊C4—41no—
145Dic11⋊C4—41no—
146C4×Dic11—41no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149Dic44—82no—
150#4314—82no—
151#3210—111no—
152#3110—111no—
153#3100—111no—
154#2972D1111yescharacteristic, complemented
155#1681—112no—
156#1679—112no—
157#1669—112no—
158#1665—112no—
159#1572—111no—
160#1553—111no—
161#1544—111no—
162C23×C11—24no—
163C23×C11—22no—
164C23×C11—81no—
165C23×C11—81no—
166C23×C11#12111yescharacteristic
167C22×D11—41no—
168D4×C11—24no—
169D4×C11—22no—
170D4×C11#13514yes—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—82no—
178C2×C4×C11—81no—
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C22⋊D11—82no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189D44—42no—
190D44—42no—
191D44—81no—
192C4×D11—82no—
193Dic22—42no—
194Dic22—42no—
195Dic22—42no—
196C8×C11—22no—
197C8×C11—22no—
198C8×C11—42no—
199C11⋊C8—42no—
200C11⋊C8—42no—
201#533—111no—
202#532—111no—
203C2×C4×D4C2×D1111yescharacteristic
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—22no—
221C8×D4C2×D1112yes—
222C8×D4C2×D1112yes—
223#432—111no—
224#431—111no—
225#431C2×D1111yescharacteristic
226#431C2×D1111yescharacteristic
227C2×C22⋊C8—22no—
228#335—112no—
229#334—112no—
230#332—112no—
231#332—112no—
232#332—112no—
233#331—112no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—24no—
237C22×C11—21no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—84no—
241C22×C11C2×#12111yescharacteristic
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—81no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—42no—
250C4×C11C2×#13512yes—
251C4×C11#57612yes—
252Dic11—81no—
253Dic11—81no—
254Dic11—81no—
255C2×#41—221no—
256C22×D4D4411yescharacteristic
257C23×C4—21no—
258C2×Q16—222no—
259C2×SD16—222no—
260C2×SD16—222no—
261C2×D8—222no—
262C22×C8—22no—
263C22×C8—22no—
264C4⋊Q8—111no—
265C4⋊Q8—111no—
266C4⋊Q8—111no—
267#127—111no—
268#125—221no—
269#124—221no—
270C22⋊Q8—221no—
271C22⋊Q8—221no—
272#121—221no—
273#121—221no—
274C4×Q8—221no—
275C4×Q8—221no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—221no—
279C4×D4—221no—
280C4×D4D4412yes—
281C4×D4C22×D1112yes—
282#117—221no—
283C2×C4⋊C4D4411yescharacteristic
284C2×C22⋊C4—21no—
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—22no—
300C22⋊C8—22no—
301C22⋊C8—221no—
302C22⋊C8—221no—
303C22⋊C8C22⋊D1112yes—
304#97—221no—
305C4×C8—21no—
306C4×C8—221no—
307C4×C8C22×D1111yescharacteristic
308C4×C8C22×D1111yescharacteristic
309C2×C11—41no—
310C2×C11—44no—
311C2×C11#304111yescharacteristic
312C2×C11#305011yescharacteristic
313C2×C11#306911yescharacteristic
314D11—161no—
315C24—21no—
316#41—882no—
317C2×Q8—221no—
318C2×Q8—221no—
319C2×Q8—221no—
320C2×D4—24no—
321C2×D4—21no—
322C2×D4—221no—
323C2×D4—221no—
324C2×D4—221no—
325C2×D4—441no—
326C2×D4C2×D4412yes—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—82no—
331C22×C4—441no—
332C22×C4C2×D4411yescharacteristic
333C22×C4#433911yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335Q16—882no—
336SD16—444no—
337SD16—882no—
338D8—444no—
339C2×C8—22no—
340C2×C8—82no—
341C2×C8—82no—
342C2×C8—222no—
343C2×C8—222no—
344C2×C8C2×C22⋊D1112yes—
345C2×C8C2×C22⋊D1112yes—
346C4⋊C4—21no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C4⋊C4—221no—
353C4⋊C4—441no—
354C4⋊C4—441no—
355C4⋊C4C2×D4412yes—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—441no—
359C22⋊C4—441no—
360C22⋊C4—441no—
361C42—441no—
362C42C2×D4411yescharacteristic
363C42#433911yescharacteristic
364C42C2×C22⋊D1111yescharacteristic
365C42C23×D1111yescharacteristic
366C11#1938811yescharacteristic, complemented, Sylow
367C23—24no—
368C23—22no—
369C23—81no—
370C23—81no—
371C23—441no—
372C23#6698311yescharacteristic
373Q8—442no—
374Q8—442no—
375Q8—442no—
376D4—24no—
377D4—22no—
378D4—442no—
379D4—442no—
380D4—881no—
381D4—882no—
382D4#6695714yes—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—82no—
390C2×C4—81no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—882no—
395C2×C4#6698311yescharacteristic
396C2×C4#6698311yescharacteristic
397C2×C4#6698311yescharacteristic
398C2×C4C22×D4411yescharacteristic
399C2×C4C2×#433911yescharacteristic
400C2×C4C22×C22⋊D1111yescharacteristic
401C8—22no—
402C8—22no—
403C8—42no—
404C8—442no—
405C8—442no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—24no—
410C22—42no—
411C22—42no—
412C22—84no—
413C22—881no—
414C22—881no—
415C22—881no—
416C22C2×#6698311yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—881no—
423C4—881no—
424C4—881no—
425C4C2×#6695712yes—
426C4#1062336612yes—
427C2—41no—
428C2—44no—
429C2—1761no—
430C2#1307811911yescharacteristic
431C2#1307819711yescharacteristic
432C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2972C2
socleC22×C11C2×#121
prime radical#13078616C2
hypercenter#2972D11
hypocenterC11#19388
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
1. #13079574C2semidirect
2. #13078715C2semidirect
4. #13068053C2semidirect
5. #13068039C2semidirect
6. #13067981C2semidirect
7. #13067957C2semidirect
8. #13067396C2semidirect
9. #13067319C2semidirect
10. #13067280C2semidirect
11. C11×#2972C2semidirect
35. #10622312C22semidirect
36. #10622307C22semidirect
37. #10622306C22semidirect
38. #10622294C22semidirect
39. #10622124C22semidirect
40. #10622123C22semidirect
41. #10622120C22semidirect
42. #10622120C22semidirect
43. #10622096C22semidirect
44. #10622095C22semidirect
154. #2972D11semidirect
366. C11#19388semidirect

Maximal subgroups

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

subgroupindex
#130795742
#130787152
#130786162
#130680532
#130680392
#130679812
#130679572
#130673962
#130673192
#130672802
C11×#29722
#1938811