Finite Group Databasebeta

← #14737345

Subgroups — #14737345

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#13079554C211yesmaximal, characteristic, complemented
3#13079068C211yesmaximal, characteristic
4#13068100C212yesmaximal, complemented
5#13068088C212yesmaximal, complemented
6#13067976C212yesmaximal, complemented
7#13067964C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067266C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#2962C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×#66961—21no—
14C2×#66961—21no—
15#10623008C2211yescharacteristic
16C2×#66927C2211yescharacteristic
17C11×#446—22no—
18C11×#446C2212yescomplemented
19C8×Q8×C11C2212yescomplemented
20C11×#424—21no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C11×#405—21no—
23C4×C11×M16C2211yescharacteristic
24#10622701—21no—
25#10622698—21no—
26#10622697—21no—
27#10622696—21no—
28#10622661—22no—
29#10622659—22no—
30#10622640C2212yes—
31#10622640C2212yes—
32#10622640C2212yescomplemented
33#10622633C2212yescomplemented
34#10622538C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622325—22no—
37#10622308C2212yes—
38#10622306C2212yes—
39#10622123C2212yes—
40#10622123C2212yes—
41#10622123C2211yescharacteristic, complemented
42#10622123C2211yescharacteristic, complemented
43#10622120C2211yescharacteristic, complemented
44#10622120C2211yescharacteristic, complemented
45#10622096C2212yescomplemented
46#10622095C2212yescomplemented
47C2×#4339—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C2×C11×M16D411yescharacteristic
52C2×C11×M16D411yescharacteristic
53C22×C8×C11—21no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×#125—21no—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8D412yes—
59C4×Q8×C11—21no—
60C4×Q8×C11C2312yes—
61C11×#117—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4325—22no—
64C2×#4325—22no—
65C2×#4325—22no—
66#66983—21no—
67#66983—21no—
68C22×C11⋊C8—21no—
69#66961—44no—
70#66961—44no—
71C2×D88—22no—
72C2×D88—22no—
73C2×#4314—22no—
74C2×#4314—22no—
75#66928—21no—
76#66927—21no—
77#66927—21no—
78#66927—21no—
79#66927C2312yes—
80#66927C2311yescharacteristic
81C4×D44—21no—
82C4×D44—21no—
83#66922C2311yescharacteristic
84C11×C4⋊C8—22no—
85C11×C4⋊C8—22no—
86C11×C4⋊C8—21no—
87C11×C4⋊C8C2311yescharacteristic
88C11×C4⋊C8C2311yescharacteristic
89C11×#97—22no—
90C11×#97D412yes—
91C4×C8×C11—22no—
92C4×C8×C11C2312yes—
93#66899—22no—
94C22⋊(C11⋊C8)—21no—
95#66873—22no—
96#66873—22no—
97#66873—22no—
98#66872—22no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4×C11⋊C8—21no—
104#19238—111nomaximal, Sylow
105C23×D11—41no—
106C2×Q8×C11—21no—
107C2×Q8×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C2×C22⋊D11—41no—
112#4339—42no—
113#4339—42no—
114C2×D44—21no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—22no—
120C2×D44—41no—
121C2×D44—41no—
122C2×D44—41no—
123C2×D44—42no—
124C2×D44—42no—
125C2×D44—81no—
126C2×D44—81no—
127C2×D44—82no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C11×M16—22no—
131C11×M16SD1614yescomplemented
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—42no—
135C2×C8×C11C2×D412yes—
136C2×C8×C11C2×D412yes—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4C2×D412yes—
143C11×C22⋊C4—22no—
144C42×C11—22no—
145C42×C11C2×D411yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11#4111yescharacteristic
148C42×C11C2411yescharacteristic
149#4325—82no—
150#4325—82no—
151#4325—82no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—81no—
160D88—44no—
161D88—44no—
162#4314—44no—
163#4314—44no—
164#3246—111no—
165#3208—111no—
166#3151—111no—
167#2962D1111yescharacteristic, complemented
168#1688—112no—
169#1686—112no—
170#1668—112no—
171#1666—112no—
172#1565—111no—
173#1540—111no—
174C2×#331—111no—
175C23×C11#12111yescharacteristic
176C22×D11—41no—
177C22×D11—42no—
178C22×D11—82no—
179C22×D11—82no—
180C22×D11—82no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—81no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—41no—
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11C2×SD1612yes—
193C2×C4×C11AGL(1,ℤ/8)12yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C22⋊D11—82no—
198C2×Dic11—41no—
199D44—42no—
200D44—41no—
201D44—42no—
202D44—41no—
203D44—41no—
204D44—42no—
205D44—42no—
206D44—41no—
207D44—81no—
208D44—82no—
209D44—82no—
210D44—82no—
211D44—82no—
212C4×D11—82no—
213Dic22—41no—
214Dic22—41no—
215C8×C11—22no—
216C8×C11—41no—
217C8×C11—41no—
218C8×C11C2×SD1614yes—
219C11⋊C8—42no—
220C11⋊C8—41no—
221C11⋊C8—41no—
222C2×AGL(1,ℤ/8)—221no—
223C2×AGL(1,ℤ/8)—221no—
224#533C2×D1111yescharacteristic
225#532—111no—
226C2×#127—111no—
227#496—222no—
228#493—112no—
229#492—112no—
230#492—221no—
231#486—221no—
232#476—221no—
233#475—112no—
234#465—222no—
235#461—221no—
236#460—112no—
237#460—112no—
238#460—112no—
239#450—222no—
240#446—22no—
241#446C2×D1112yescomplemented
242C8×Q8C2×D1112yescomplemented
243#431—111no—
244#424—21no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8C2×D1111yescharacteristic
247#405—21no—
248C4×M16C2×D1111yescharacteristic
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#46012yes—
260C22×C11C2×#12111yescharacteristic
261C2×D11—82no—
262C2×D11—81no—
263C2×D11—82no—
264C2×D11—81no—
265C2×D11—82no—
266C2×D11—81no—
267C2×D11—164no—
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—221no—
281C22×D4—221no—
282C22×D4—221no—
283AGL(1,ℤ/8)—444no—
284AGL(1,ℤ/8)—444no—
285C2×SD16—222no—
286C2×SD16—222no—
287C2×SD16—222no—
288C2×SD16—222no—
289C2×SD16—222no—
290C2×D8—222no—
291C2×D8—222no—
292C2×M16C22⋊D1111yescharacteristic
293C2×M16C22⋊D1111yescharacteristic
294C22×C8—21no—
295C22×C8—221no—
296C4⋊Q8—111no—
297C4⋊Q8D4411yescharacteristic
298C4⋊Q8D4411yescharacteristic
299#127—112no—
300#127—111no—
301#127—221no—
302#127—221no—
303#127—221no—
304#125—21no—
305#124—221no—
306C22⋊Q8—21no—
307C22⋊Q8D4412yes—
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—22no—
318C4⋊C8—22no—
319C4⋊C8—21no—
320C4⋊C8—112no—
321C4⋊C8—111no—
322C4⋊C8—111no—
323C4⋊C8—221no—
324C4⋊C8C22×D1111yescharacteristic
325C4⋊C8C22×D1111yescharacteristic
326#103—222no—
327#102—222no—
328#102—222no—
329#102—222no—
330C22⋊C8—221no—
331#97—22no—
332#97C22⋊D1112yes—
333C4×C8—22no—
334C4×C8—221no—
335C4×C8C22×D1112yes—
336C2×C11—22no—
337C2×C11C2×#46011yescharacteristic
338C2×C11#306211yescharacteristic
339C2×C11#306811yescharacteristic
340D11—161no—
341D11—162no—
342C24—441no—
343#41—442no—
344#41—442no—
345C2×Q8—21no—
346C2×Q8—221no—
347C2×Q8C2×D4412yes—
348C2×D4—221no—
349C2×D4—222no—
350C2×D4—221no—
351C2×D4—222no—
352C2×D4—221no—
353C2×D4—222no—
354C2×D4—441no—
355C2×D4—441no—
356C2×D4—441no—
357C2×D4—441no—
358C2×D4—442no—
359C2×D4—442no—
360C2×D4—881no—
361C2×D4—881no—
362C2×D4—882no—
363C22×C4—441no—
364C22×C4C2×D4411yescharacteristic
365C22×C4#433911yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367SD16—444no—
368SD16—444no—
369SD16—882no—
370SD16—882no—
371SD16—882no—
372D8—444no—
373D8—444no—
374M16—22no—
375M16#432514yescomplemented
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—42no—
379C2×C8—221no—
380C2×C8—221no—
381C2×C8—222no—
382C2×C8—881no—
383C2×C8C2×C22⋊D1112yes—
384C2×C8C2×C22⋊D1112yes—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4C2×D4412yes—
393C22⋊C4—22no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C42—22no—
397C42C2×D4411yescharacteristic
398C42#433911yescharacteristic
399C42C2×C22⋊D1111yescharacteristic
400C42C23×D1111yescharacteristic
401C11#1923811yescharacteristic, complemented, Sylow
402C23—441no—
403C23—442no—
404C23—882no—
405C23—882no—
406C23—882no—
407C23#6698311yescharacteristic
408Q8—22no—
409Q8—22no—
410Q8—81no—
411Q8—441no—
412Q8—441no—
413D4—442no—
414D4—441no—
415D4—441no—
416D4—442no—
417D4—441no—
418D4—442no—
419D4—441no—
420D4—442no—
421D4—882no—
422D4—881no—
423D4—882no—
424D4—882no—
425D4—882no—
426D4—882no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—441no—
433C2×C4—882no—
434C2×C4#6698311yescharacteristic
435C2×C4#6698311yescharacteristic
436C2×C4#6698311yescharacteristic
437C2×C4C2×#432512yes—
438C2×C4#6700212yes—
439C2×C4C22×D4411yescharacteristic
440C2×C4C2×#433911yescharacteristic
441C2×C4C22×C22⋊D1111yescharacteristic
442C8—22no—
443C8—41no—
444C8—41no—
445C8—441no—
446C8—442no—
447C8—441no—
448C8C2×#432514yes—
449C22—21no—
450C22—21no—
451C22—882no—
452C22—881no—
453C22—881no—
454C22—882no—
455C22—882no—
456C22—881no—
457C22—1764no—
458C22#1062264012yes—
459C22C2×#6698311yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—42no—
465C4—881no—
466C4#1062264012yes—
467C4#1062328211yescharacteristic
468C4#1062328311yescharacteristic
469C4C22×#432511yescharacteristic
470C4C2×#6700211yescharacteristic
471C2—22no—
472C2—1762no—
473C2—1761no—
474C2C2×#1062264011yescharacteristic
475C2#1307829611yescharacteristic
476C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2962C2
socleC22×C11C2×#121
prime radical#13079068C2
hypercenter#2962D11
hypocenterC11#19238
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
1. #13079928C2semidirect
2. #13079554C2semidirect
4. #13068100C2semidirect
5. #13068088C2semidirect
6. #13067976C2semidirect
7. #13067964C2semidirect
8. #13067368C2semidirect
9. #13067266C2semidirect
10. C2×#10622123C2semidirect
11. C11×#2962C2semidirect
18. C11×#446C22semidirect
19. C8×Q8×C11C22semidirect
32. #10622640C22semidirect
33. #10622633C22semidirect
41. #10622123C22semidirect
42. #10622123C22semidirect
43. #10622120C22semidirect
44. #10622120C22semidirect
45. #10622096C22semidirect
46. #10622095C22semidirect
131. C11×M16SD16semidirect
167. #2962D11semidirect
241. #446C2×D11semidirect
242. C8×Q8C2×D11semidirect
375. M16#4325semidirect
401. C11#19238semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130795542
#130790682
#130681002
#130680882
#130679762
#130679642
#130673682
#130672662
C2×#106221232
C11×#29622
#1923811