Finite Group Databasebeta

← #14737341

Subgroups — #14737341

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic, complemented
2#13079066C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13068098C212yesmaximal, complemented
5#13068086C212yesmaximal, complemented
6#13067974C212yesmaximal, complemented
7#13067962C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067263C211yesmaximal, characteristic, complemented
10C2×#10622182C211yesmaximal, characteristic, complemented
11C11×#3208C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×#66985—21no—
15C2×#66985—21no—
16#10623008C2211yescharacteristic
17C11×#492—21no—
18C11×#486—21no—
19C11×#460C2212yes—
20C11×#460C2212yes—
21C11×#450—22no—
22C11×#431C2211yescharacteristic
23#10622697—21no—
24#10622696—21no—
25#10622689C2212yes—
26#10622687—22no—
27#10622686C2212yes—
28#10622661—22no—
29#10622640C2212yescomplemented
30#10622637—22no—
31#10622637C2212yescomplemented
32Q8×C11⋊C8C2212yescomplemented
33#10622633C2212yescomplemented
34#10622612—21no—
35#10622610—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622182C2212yes—
40#10622182C2212yes—
41#10622124C2211yescharacteristic, complemented
42#10622124C2211yescharacteristic, complemented
43#10622123C2211yescharacteristic, complemented
44#10622123C2211yescharacteristic, complemented
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C2×#4339—21no—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×#127—21no—
56C11×#127—21no—
57C11×#127—21no—
58C11×#127C2312yes—
59C11×#125—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8D412yes—
62C4×Q8×C11—21no—
63C4×Q8×C11C2312yes—
64C11×#117—21no—
65C2×C42×C11C2311yescharacteristic
66C2×#4325—22no—
67C2×#4324—22no—
68C2×#4324—22no—
69#66985—44no—
70#66985—44no—
71C2×#4323—22no—
72C2×#4323—22no—
73#66983—21no—
74#66983—21no—
75C2×#4318D411yescharacteristic
76C2×#4318D411yescharacteristic
77C22×C11⋊C8—21no—
78C22×C11⋊C8—21no—
79#66928—21no—
80#66927C2311yescharacteristic
81C4×D44—21no—
82C4×D44—21no—
83#66922C2311yescharacteristic
84C11×C4⋊C8C2311yescharacteristic
85C11×C4⋊C8C2311yescharacteristic
86C11×#102—22no—
87C11×#102—22no—
88C11×C22⋊C8—21no—
89C4×C8×C11—21no—
90#66899—22no—
91#66873—22no—
92#66872—22no—
93C4⋊(C11⋊C8)—21no—
94C4⋊(C11⋊C8)—21no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)—22no—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100#66867—22no—
101#66867D412yes—
102C4×C11⋊C8—22no—
103C4×C11⋊C8C2312yes—
104#19238—111nomaximal, Sylow
105C24×C11—41no—
106C2×Q8×C11—21no—
107C2×Q8×C11C2×D412yes—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—41no—
112C2×D4×C11—41no—
113C2×D4×C11—41no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—81no—
117C2×D4×C11—81no—
118C2×D4×C11—82no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C2×C22⋊D11—41no—
123#4339—42no—
124#4339—42no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C11×SD16—82no—
131C11×SD16—82no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—22no—
141C42×C11—22no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C42×C11C2411yescharacteristic
146#4325—82no—
147#4324—44no—
148#4324—44no—
149#4323—44no—
150#4323—44no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155#4318—22no—
156#4318SD1614yescomplemented
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—42no—
161C2×C11⋊C8—81no—
162C2×C11⋊C8C2×D412yes—
163C2×C11⋊C8C2×D412yes—
164#3246—111no—
165#3208D1111yescharacteristic, complemented
166#3151—111no—
167#2962—111no—
168#1688—112no—
169#1686—112no—
170#1668—112no—
171#1666—112no—
172#1565—111no—
173#1540—111no—
174C2×#331—111no—
175C23×C11—42no—
176C23×C11—82no—
177C23×C11—82no—
178C23×C11—82no—
179C23×C11#12111yescharacteristic
180C22×D11—41no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—81no—
184D4×C11—42no—
185D4×C11—42no—
186D4×C11—42no—
187D4×C11—42no—
188D4×C11—82no—
189D4×C11—82no—
190D4×C11—82no—
191D4×C11—82no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11C2×SD1612yes—
201C2×C4×C11AGL(1,ℤ/8)12yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C22⋊D11—82no—
206C2×Dic11—41no—
207D44—41no—
208D44—41no—
209D44—41no—
210D44—41no—
211D44—81no—
212C4×D11—82no—
213Dic22—41no—
214Dic22—41no—
215C8×C11—41no—
216C8×C11—41no—
217C11⋊C8—22no—
218C11⋊C8—41no—
219C11⋊C8—41no—
220C11⋊C8—42no—
221C11⋊C8C2×SD1614yes—
222C2×AGL(1,ℤ/8)—221no—
223C2×AGL(1,ℤ/8)—221no—
224#533C2×D1111yescharacteristic
225#532—111no—
226C2×#127C2×D1111yescharacteristic
227#496—222no—
228#493—112no—
229#492—21no—
230#492—112no—
231#486—21no—
232#476—221no—
233#475—112no—
234#465—222no—
235#461—221no—
236#460—112no—
237#460C2×D1112yes—
238#460C2×D1112yes—
239#450—22no—
240#446—112no—
241#446—222no—
242C8×Q8—112no—
243#431C2×D1111yescharacteristic
244#424—221no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8—111no—
247#405—221no—
248C4×M16—111no—
249#335—112no—
250#334—112no—
251#332—111no—
252#332—111no—
253#331—112no—
254#331—112no—
255#331—111no—
256#331—111no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11—164no—
263C22×C11#46012yes—
264C22×C11C2×#12111yescharacteristic
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11#46012yes—
274C4×C11C22×SD1611yescharacteristic
275C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
276C4×C11#57611yescharacteristic
277C4×C11#57711yescharacteristic
278Dic11—81no—
279C2×#41—221no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283AGL(1,ℤ/8)—444no—
284AGL(1,ℤ/8)—444no—
285C2×SD16—22no—
286C2×SD16—22no—
287C2×SD16—222no—
288C2×SD16—222no—
289C2×SD16—222no—
290C2×D8—222no—
291C2×D8—222no—
292C2×M16—111no—
293C2×M16—111no—
294C22×C8—221no—
295C22×C8—221no—
296C4⋊Q8—111no—
297C4⋊Q8C22⋊D1111yescharacteristic
298C4⋊Q8C22⋊D1111yescharacteristic
299#127—21no—
300#127—21no—
301#127—21no—
302#127—111no—
303#127C22×D1112yes—
304#125—21no—
305#124—221no—
306C22⋊Q8—21no—
307C22⋊Q8C22⋊D1112yes—
308#121—221no—
309#121—221no—
310C4×Q8—21no—
311C4×Q8C22×D1112yes—
312C4×D4—221no—
313C4×D4—221no—
314#117—21no—
315C2×C42C22×D1111yescharacteristic
316#106—222no—
317C4⋊C8—111no—
318C4⋊C8—111no—
319C4⋊C8—112no—
320C4⋊C8—222no—
321C4⋊C8—222no—
322C4⋊C8—221no—
323C4⋊C8—221no—
324C4⋊C8C22×D1111yescharacteristic
325C4⋊C8C22×D1111yescharacteristic
326#103—222no—
327#102—22no—
328#102—22no—
329#102—222no—
330C22⋊C8—21no—
331#97—112no—
332#97—222no—
333C4×C8—21no—
334C4×C8—112no—
335C4×C8—222no—
336C2×C11—22no—
337C2×C11—162no—
338C2×C11C2×#46011yescharacteristic
339C2×C11#306211yescharacteristic
340C2×C11#306811yescharacteristic
341D11—161no—
342C24—41no—
343#41—442no—
344#41—442no—
345C2×Q8—21no—
346C2×Q8—221no—
347C2×Q8C2×C22⋊D1112yes—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—81no—
357C2×D4—81no—
358C2×D4—82no—
359C2×D4—221no—
360C2×D4—221no—
361C2×D4—221no—
362C2×D4—441no—
363C22×C4—441no—
364C22×C4D4×D1111yescharacteristic
365C22×C4#434111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367SD16—82no—
368SD16—82no—
369SD16—444no—
370SD16—444no—
371SD16—882no—
372D8—444no—
373D8—444no—
374M16—114no—
375M16—222no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—112no—
379C2×C8—112no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8—222no—
383C2×C8—442no—
384C2×C8—881no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4C2×C22⋊D1112yes—
393C22⋊C4—22no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C42—22no—
397C42D4×D1111yescharacteristic
398C42#434111yescharacteristic
399C42C2×C22⋊D1111yescharacteristic
400C42C23×D1111yescharacteristic
401C11#1923811yescharacteristic, complemented, Sylow
402C23—42no—
403C23—82no—
404C23—82no—
405C23—82no—
406C23—441no—
407C23#6699211yescharacteristic
408Q8—22no—
409Q8—22no—
410Q8—81no—
411Q8—441no—
412Q8—441no—
413D4—42no—
414D4—42no—
415D4—42no—
416D4—42no—
417D4—82no—
418D4—82no—
419D4—82no—
420D4—82no—
421D4—441no—
422D4—441no—
423D4—441no—
424D4—441no—
425D4—881no—
426D4—882no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—441no—
433C2×C4—882no—
434C2×C4SD16×D1112yes—
435C2×C4#6696712yes—
436C2×C4#6699211yescharacteristic
437C2×C4#6699211yescharacteristic
438C2×C4#6699211yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C2×C4C2×#434111yescharacteristic
441C2×C4C22×C22⋊D1111yescharacteristic
442C8—41no—
443C8—41no—
444C8—114no—
445C8—222no—
446C8—441no—
447C8—441no—
448C8—442no—
449C22—21no—
450C22—21no—
451C22—82no—
452C22—82no—
453C22—82no—
454C22—164no—
455C22—881no—
456C22—881no—
457C22—881no—
458C22#1062277612yes—
459C22C2×#6699211yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—42no—
465C4—881no—
466C4#1062277612yes—
467C4C2×SD16×D1111yescharacteristic
468C4C2×#6696711yescharacteristic
469C4#1062336611yescharacteristic
470C4#1062336711yescharacteristic
471C2—22no—
472C2—162no—
473C2—1761no—
474C2C2×#1062277611yescharacteristic
475C2#1307829211yescharacteristic
476C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3208C2
socleC22×C11C2×#121
prime radical#13079066C2
hypercenter#3208D11
hypocenterC11#19238
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #13079928C2semidirect
3. #13077565C2semidirect
4. #13068098C2semidirect
5. #13068086C2semidirect
6. #13067974C2semidirect
7. #13067962C2semidirect
8. #13067369C2semidirect
9. #13067263C2semidirect
10. C2×#10622182C2semidirect
11. C11×#3208C2semidirect
29. #10622640C22semidirect
31. #10622637C22semidirect
32. Q8×C11⋊C8C22semidirect
33. #10622633C22semidirect
41. #10622124C22semidirect
42. #10622124C22semidirect
43. #10622123C22semidirect
44. #10622123C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
156. #4318SD16semidirect
165. #3208D11semidirect
401. C11#19238semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130790662
#130775652
#130680982
#130680862
#130679742
#130679622
#130673692
#130672632
C2×#106221822
C11×#32082
#1923811