Finite Group Databasebeta

← #14739024

Subgroups — #14739024

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#13079752C211yesmaximal, characteristic, complemented
2#13078707C211yesmaximal, characteristic
3#13077640C211yesmaximal, characteristic, complemented
4#13068055C212yesmaximal, complemented
5#13068027C212yesmaximal, complemented
6#13068013C212yesmaximal, complemented
7#13067989C212yesmaximal, complemented
8#13067394C211yesmaximal, characteristic, complemented
9#13067326C211yesmaximal, characteristic, complemented
10#13067276C211yesmaximal, characteristic, complemented
11C11×#3101C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#483—21no—
16C11×#476C2212yes—
17C11×#461C2212yes—
18C11×#450—21no—
19C4×C11×SD16—22no—
20C11×#431C2211yescharacteristic
21#10622830—21no—
22C2×C22⋊(C11⋊C8)—22no—
23#10622701C2211yescharacteristic, complemented
24#10622701C2211yescharacteristic, complemented
25#10622692C2211yescharacteristic, complemented
26#10622691C2211yescharacteristic, complemented
27#10622679—22no—
28#10622628C2212yes—
29#10622627—22no—
30D4×C11⋊C8—22no—
31D4×C11⋊C8C2212yes—
32D4×C11⋊C8C2212yes—
33#10622621C2212yes—
34#10622616—22no—
35#10622581—21no—
36#10622539C2211yescharacteristic
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622185C2212yescomplemented
40#10622184C2212yescomplemented
41#10622123C2212yescomplemented
42#10622119C2212yescomplemented
43#10622118C2212yescomplemented
44#10622117C2212yescomplemented
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—21no—
47C2×#4339—21no—
48C2×C11×SD16—22no—
49C11×C4⋊Q8C2311yescharacteristic
50C11×C4⋊Q8C2311yescharacteristic
51C11×#125—21no—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11D412yes—
59C4×D4×C11C2312yes—
60C11×#117—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64C2×#4323—22no—
65#66983—21no—
66#66983—21no—
67C22×C11⋊C8—22no—
68C22×C11⋊C8—22no—
69#66928—21no—
70#66927C2311yescharacteristic
71C4×D44—21no—
72C4×D44—21no—
73#66922C2311yescharacteristic
74C11×#106—22no—
75C11×C4⋊C8C2312yes—
76C11×#103—22no—
77C11×#102—22no—
78C11×C22⋊C8—21no—
79C4×C8×C11—21no—
80#66896—22no—
81C22⋊(C11⋊C8)—21no—
82C22⋊(C11⋊C8)—21no—
83C22⋊(C11⋊C8)—22no—
84C22⋊(C11⋊C8)—22no—
85C22⋊(C11⋊C8)D412yes—
86#66873—22no—
87#66873—22no—
88#66873—22no—
89#66872—22no—
90#66872—22no—
91#66871—22no—
92C4⋊(C11⋊C8)D412yes—
93C4⋊(C11⋊C8)C2312yes—
94C4⋊(C11⋊C8)C2312yes—
95#66867—21no—
96C4×C11⋊C8—21no—
97C4×C11⋊C8C2311yescharacteristic
98C4×C11⋊C8C2311yescharacteristic
99#19394—111nomaximal, Sylow
100C24×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×D4×C11—24no—
104C2×D4×C11—21no—
105C2×D4×C11C2×D412yes—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—82no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—41no—
114#4339—82no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×C4×D11—41no—
119C2×Dic22—21no—
120C11×SD16—44no—
121C2×C8×C11—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4C2×D412yes—
130C11×C22⋊C4—22no—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—41no—
133C42×C11—41no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138#4323—44no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—82no—
146C2×C11⋊C8—82no—
147C2×C11⋊C8C2×D412yes—
148C2×C11⋊C8C2×D412yes—
149#3228—111no—
150#3109—111no—
151#3101D1111yescharacteristic, complemented
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—24no—
161C23×C11—22no—
162C23×C11—81no—
163C23×C11—81no—
164C23×C11#12111yescharacteristic
165C22×D11—41no—
166Q8×C11—42no—
167Q8×C11—81no—
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—41no—
178C2×C4×C11—41no—
179C2×C4×C11—82no—
180C2×C4×C11—81no—
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C22⋊D11—82no—
188C2×Dic11—41no—
189D44—42no—
190D44—42no—
191D44—81no—
192C4×D11—82no—
193Dic22—81no—
194C8×C11—42no—
195C11⋊C8—22no—
196C11⋊C8—22no—
197C11⋊C8—42no—
198C11⋊C8—42no—
199#533C2×D1111yescharacteristic
200#532—111no—
201C2×C4×D4C2×D1111yescharacteristic
202#500—111no—
203#498—111no—
204#486—111no—
205#486—111no—
206#483—21no—
207#482—222no—
208#481—221no—
209#478—222no—
210#476—112no—
211#476C2×D1112yes—
212#461C2×D1112yes—
213#459—112no—
214#450—21no—
215#447—221no—
216#442—222no—
217C4×SD16—22no—
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—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×C11—81no—
249C4×C11—81no—
250C4×C11C2×#13512yes—
251C4×C11#57712yes—
252Dic11—81no—
253C2×#41—221no—
254C22×D4C22⋊D1111yescharacteristic
255C23×C4—21no—
256C2×SD16—22no—
257C2×D8—222no—
258C22×C8—222no—
259C22×C8—222no—
260C4⋊Q8—111no—
261C4⋊Q8C22×D1111yescharacteristic
262C4⋊Q8C22×D1111yescharacteristic
263#127—111no—
264#125—21no—
265#124—221no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268#121—221no—
269#121—221no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—221no—
275C4×D4—221no—
276C4×D4C22⋊D1112yes—
277C4×D4C22×D1112yes—
278#117—21no—
279C2×C4⋊C4C22⋊D1111yescharacteristic
280C2×C22⋊C4—21no—
281C2×C42C22×D1111yescharacteristic
282#107—222no—
283#106—22no—
284#106—222no—
285#106—222no—
286C4⋊C8—112no—
287C4⋊C8—112no—
288C4⋊C8—112no—
289C4⋊C8C22×D1112yes—
290#103—22no—
291#102—22no—
292#102—222no—
293#102—222no—
294#102—222no—
295#102—222no—
296C22⋊C8—21no—
297C22⋊C8—112no—
298C22⋊C8—222no—
299C22⋊C8—222no—
300C22⋊C8—221no—
301C22⋊C8—221no—
302#97—221no—
303C4×C8—21no—
304C4×C8—111no—
305C4×C8—111no—
306C4×C8—221no—
307C2×C11—41no—
308C2×C11—44no—
309C2×C11#304211yescharacteristic
310C2×C11#305011yescharacteristic
311C2×C11#306811yescharacteristic
312D11—161no—
313C24—21no—
314#41—882no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—221no—
318C2×D4—24no—
319C2×D4—21no—
320C2×D4—221no—
321C2×D4—221no—
322C2×D4—221no—
323C2×D4—441no—
324C2×D4C2×C22⋊D1112yes—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—82no—
329C22×C4—441no—
330C22×C4D4×D1111yescharacteristic
331C22×C4#434111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—44no—
334D8—444no—
335C2×C8—22no—
336C2×C8—112no—
337C2×C8—112no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—882no—
341C2×C8—882no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4C2×C22⋊D1112yes—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—41no—
355C22⋊C4—441no—
356C22⋊C4—441no—
357C42—41no—
358C42D4×D1111yescharacteristic
359C42#434111yescharacteristic
360C42C2×C22⋊D1111yescharacteristic
361C42C23×D1111yescharacteristic
362C11#1939411yescharacteristic, complemented, Sylow
363C23—24no—
364C23—22no—
365C23—81no—
366C23—81no—
367C23—441no—
368C23#6699211yescharacteristic
369Q8—42no—
370Q8—81no—
371Q8—881no—
372D4—24no—
373D4—22no—
374D4—442no—
375D4—442no—
376D4—881no—
377D4—882no—
378D4#6700314yes—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—82no—
388C2×C4—81no—
389C2×C4—441no—
390C2×C4—882no—
391C2×C4#6699211yescharacteristic
392C2×C4#6699211yescharacteristic
393C2×C4#6699211yescharacteristic
394C2×C4C2×D4×D1111yescharacteristic
395C2×C4C2×#434111yescharacteristic
396C2×C4C22×C22⋊D1111yescharacteristic
397C8—42no—
398C8—222no—
399C8—222no—
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×#6699211yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—42no—
418C4—81no—
419C4—81no—
420C4—881no—
421C4#1062329312yes—
422C4C2×#6700312yes—
423C2—41no—
424C2—44no—
425C2—1761no—
426C2#1307812511yescharacteristic
427C2#1307819411yescharacteristic
428C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3101C2
socleC22×C11C2×#121
prime radical#13078707C2
hypercenter#3101D11
hypocenterC11#19394
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
1. #13079752C2semidirect
3. #13077640C2semidirect
4. #13068055C2semidirect
5. #13068027C2semidirect
6. #13068013C2semidirect
7. #13067989C2semidirect
8. #13067394C2semidirect
9. #13067326C2semidirect
10. #13067276C2semidirect
11. C11×#3101C2semidirect
23. #10622701C22semidirect
24. #10622701C22semidirect
25. #10622692C22semidirect
26. #10622691C22semidirect
39. #10622185C22semidirect
40. #10622184C22semidirect
41. #10622123C22semidirect
42. #10622119C22semidirect
43. #10622118C22semidirect
44. #10622117C22semidirect
151. #3101D11semidirect
362. C11#19394semidirect

Maximal subgroups

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

subgroupindex
#130797522
#130787072
#130776402
#130680552
#130680272
#130680132
#130679892
#130673942
#130673262
#130672762
C11×#31012
#1939411