Finite Group Databasebeta

← #14739027

Subgroups — #14739027

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#13079754C211yesmaximal, characteristic, complemented
2#13078707C211yesmaximal, characteristic
3#13078624C211yesmaximal, characteristic, complemented
4#13068053C212yesmaximal, complemented
5#13068025C212yesmaximal, complemented
6#13068015C212yesmaximal, complemented
7#13067991C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067324C211yesmaximal, characteristic, complemented
10#13067276C211yesmaximal, 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—
24C4×#4324—22no—
25#10622628C2212yes—
26#10622627—22no—
27#10622621C2212yes—
28#10622621C2212yes—
29#10622584—21no—
30#10622581—21no—
31#10622539C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622460—22no—
34#10622350—22no—
35#10622307C2211yescharacteristic, complemented
36#10622307C2211yescharacteristic, complemented
37#10622295C2211yescharacteristic, complemented
38#10622293C2211yescharacteristic, complemented
39#10622124C2212yescomplemented
40#10622123C2212yescomplemented
41#10622119C2212yescomplemented
42#10622119C2212yescomplemented
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—
64#66928—21no—
65#66927C2311yescharacteristic
66C4×D44—21no—
67C4×D44—21no—
68#66923—21no—
69#66922C2311yescharacteristic
70#66922C2311yescharacteristic
71#66922C2311yescharacteristic
72C4×Dic22—21no—
73C4×Dic22—21no—
74C11×C4⋊C8D412yes—
75C11×C4⋊C8C2312yes—
76C11×C22⋊C8—21no—
77C11×C22⋊C8—22no—
78C11×C22⋊C8—22no—
79C11×C22⋊C8D412yes—
80C4×C8×C11—21no—
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66896—22no—
84#66896—22no—
85C22⋊(C11⋊C8)—21no—
86C22⋊(C11⋊C8)—21no—
87#66885—22no—
88#66885—22no—
89#66882—22no—
90#66881—22no—
91#66874—22no—
92#66873—22no—
93#66872—22no—
94#66872—22no—
95C4⋊(C11⋊C8)C2312yes—
96C4⋊(C11⋊C8)C2312yes—
97#66867—21no—
98C4×C11⋊C8—21no—
99#19394—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—
149#3228—111no—
150#3109—111no—
151#3101—111no—
152#2972D1111yescharacteristic, complemented
153#1681—112no—
154#1677—112no—
155#1675—112no—
156#1671—112no—
157#1572—111no—
158#1554—111no—
159#1543—111no—
160C23×C11—24no—
161C23×C11—22no—
162C23×C11—81no—
163C23×C11—81no—
164C23×C11#12111yescharacteristic
165C22×D11—41no—
166D4×C11—24no—
167D4×C11—22no—
168D4×C11#13514yes—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—82no—
176C2×C4×C11—81no—
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C22⋊D11—82no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187D44—42no—
188D44—42no—
189D44—81no—
190C4×D11—82no—
191Dic22—42no—
192Dic22—81no—
193Dic22—81no—
194C8×C11—22no—
195C8×C11—22no—
196C8×C11—42no—
197C11⋊C8—42no—
198C11⋊C8—42no—
199#533—111no—
200#532—111no—
201C2×C4×D4C2×D1111yescharacteristic
202#500—111no—
203#498—111no—
204#486—111no—
205#486—111no—
206#483—221no—
207#482—222no—
208#481—221no—
209#478—222no—
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—22no—
219C8×D4C2×D1112yes—
220C8×D4C2×D1112yes—
221#432—111no—
222#431—111no—
223#431C2×D1111yescharacteristic
224#431C2×D1111yescharacteristic
225C2×C22⋊C8—22no—
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—24no—
235C22×C11—21no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—84no—
239C22×C11C2×#12111yescharacteristic
240C2×D11—81no—
241C2×D11—81no—
242C2×D11—81no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—42no—
248C4×C11C2×#13512yes—
249C4×C11#57712yes—
250Dic11—81no—
251Dic11—81no—
252Dic11—81no—
253C2×#41—221no—
254C22×D4D4411yescharacteristic
255C23×C4—21no—
256C2×SD16—222no—
257C2×D8—222no—
258C22×C8—22no—
259C22×C8—22no—
260C4⋊Q8—111no—
261C4⋊Q8—111no—
262C4⋊Q8—111no—
263#127—111no—
264#125—221no—
265#124—221no—
266C22⋊Q8—221no—
267C22⋊Q8—221no—
268#121—221no—
269#121—221no—
270C4×Q8—221no—
271C4×Q8—221no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—221no—
275C4×D4—221no—
276C4×D4D4412yes—
277C4×D4C22×D1112yes—
278#117—221no—
279C2×C4⋊C4D4411yescharacteristic
280C2×C22⋊C4—21no—
281C2×C42C22×D1111yescharacteristic
282#107—222no—
283#106—222no—
284#106—222no—
285#106—222no—
286C4⋊C8—112no—
287C4⋊C8—112no—
288C4⋊C8C22⋊D1112yes—
289C4⋊C8C22×D1112yes—
290#103—222no—
291#102—222no—
292#102—222no—
293#102—222no—
294#102—222no—
295#102—222no—
296C22⋊C8—21no—
297C22⋊C8—22no—
298C22⋊C8—22no—
299C22⋊C8—221no—
300C22⋊C8—221no—
301C22⋊C8C22⋊D1112yes—
302#97—221no—
303C4×C8—21no—
304C4×C8—221no—
305C4×C8C22×D1111yescharacteristic
306C4×C8C22×D1111yescharacteristic
307C2×C11—41no—
308C2×C11—44no—
309C2×C11#304211yescharacteristic
310C2×C11#305011yescharacteristic
311C2×C11#306811yescharacteristic
312D11—161no—
313C24—21no—
314#41—882no—
315C2×Q8—221no—
316C2×Q8—221no—
317C2×Q8—221no—
318C2×D4—24no—
319C2×D4—21no—
320C2×D4—221no—
321C2×D4—221no—
322C2×D4—221no—
323C2×D4—441no—
324C2×D4C2×D4412yes—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—82no—
329C22×C4—441no—
330C22×C4C2×D4411yescharacteristic
331C22×C4#433911yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—444no—
334D8—444no—
335C2×C8—22no—
336C2×C8—82no—
337C2×C8—82no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8C2×C22⋊D1112yes—
341C2×C8C2×C22⋊D1112yes—
342C4⋊C4—21no—
343C4⋊C4—221no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4—441no—
350C4⋊C4—441no—
351C4⋊C4C2×D4412yes—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C22⋊C4—441no—
357C42—441no—
358C42C2×D4411yescharacteristic
359C42#433911yescharacteristic
360C42C2×C22⋊D1111yescharacteristic
361C42C23×D1111yescharacteristic
362C11#1939411yescharacteristic, complemented, Sylow
363C23—24no—
364C23—22no—
365C23—81no—
366C23—81no—
367C23—441no—
368C23#6698311yescharacteristic
369Q8—442no—
370Q8—881no—
371Q8—881no—
372D4—24no—
373D4—22no—
374D4—442no—
375D4—442no—
376D4—881no—
377D4—882no—
378D4#6695714yes—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—82no—
386C2×C4—81no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—882no—
391C2×C4#6698311yescharacteristic
392C2×C4#6698311yescharacteristic
393C2×C4#6698311yescharacteristic
394C2×C4C22×D4411yescharacteristic
395C2×C4C2×#433911yescharacteristic
396C2×C4C22×C22⋊D1111yescharacteristic
397C8—22no—
398C8—22no—
399C8—42no—
400C8—442no—
401C8—442no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—24no—
406C22—42no—
407C22—42no—
408C22—84no—
409C22—881no—
410C22—881no—
411C22—881no—
412C22C2×#6698311yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—42no—
418C4—881no—
419C4—881no—
420C4—881no—
421C4C2×#6695712yes—
422C4#1062336712yes—
423C2—41no—
424C2—44no—
425C2—1761no—
426C2#1307812811yescharacteristic
427C2#1307819711yescharacteristic
428C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2972C2
socleC22×C11C2×#121
prime radical#13078707C2
hypercenter#2972D11
hypocenterC11#19394
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. #13079754C2semidirect
3. #13078624C2semidirect
4. #13068053C2semidirect
5. #13068025C2semidirect
6. #13068015C2semidirect
7. #13067991C2semidirect
8. #13067396C2semidirect
9. #13067324C2semidirect
10. #13067276C2semidirect
11. C11×#2972C2semidirect
35. #10622307C22semidirect
36. #10622307C22semidirect
37. #10622295C22semidirect
38. #10622293C22semidirect
39. #10622124C22semidirect
40. #10622123C22semidirect
41. #10622119C22semidirect
42. #10622119C22semidirect
43. #10622096C22semidirect
44. #10622095C22semidirect
152. #2972D11semidirect
362. C11#19394semidirect

Maximal subgroups

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

subgroupindex
#130797542
#130787072
#130786242
#130680532
#130680252
#130680152
#130679912
#130673962
#130673242
#130672762
C11×#29722
#1939411