Finite Group Databasebeta

← #14737346

Subgroups — #14737346

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#13079933C211yesmaximal, characteristic, complemented
2#13079559C211yesmaximal, characteristic, complemented
3#13079068C211yesmaximal, characteristic
4#13077563C211yesmaximal, characteristic, complemented
5#13068101C212yesmaximal, complemented
6#13068089C212yesmaximal, complemented
7#13067977C212yesmaximal, complemented
8#13067965C212yesmaximal, complemented
9#13067263C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#1565C211yesmaximal, characteristic, complemented
12C2×#66961—21no—
13C2×#66961—21no—
14#10623008C2211yescharacteristic
15C2×#66927C2211yescharacteristic
16#10623001C2211yescharacteristic
17C11×#431C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C4×C11×M16C2211yescharacteristic
20#10622735—21no—
21#10622732—21no—
22#10622727—22no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622464C2212yescomplemented
25#10622461C2212yes—
26#10622461C2212yes—
27#10622461C2212yescomplemented
28#10622455—21no—
29#10622454—21no—
30#10622344—22no—
31#10622325—22no—
32#10622314—22no—
33#10622308C2212yes—
34#10622307—21no—
35#10622306—21no—
36#10622306C2212yes—
37#10622292C2212yescomplemented
38C8×Dic22C2212yescomplemented
39C11×#335C2212yescomplemented
40C11×#334C2212yescomplemented
41#10622124C2211yescharacteristic, complemented
42#10622124C2211yescharacteristic, complemented
43#10622123C2212yes—
44#10622123C2212yes—
45#10622123C2211yescharacteristic, complemented
46#10622123C2211yescharacteristic, complemented
47C2×#4339—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C2×C11×M16D411yescharacteristic
52C2×C11×M16D411yescharacteristic
53C22×C8×C11—21no—
54C2×C42×C11C2311yescharacteristic
55#66983—21no—
56#66983—21no—
57#66979—21no—
58#66977—21no—
59#66977D412yes—
60C22×C11⋊C8—21no—
61#66961—44no—
62#66961—44no—
63C2×D88—22no—
64C2×D88—22no—
65C2×#4314—22no—
66C2×#4314—22no—
67C2×#4314—22no—
68C2×#4314—22no—
69C2×#4314—22no—
70#66928—21no—
71#66927—21no—
72#66927—21no—
73#66927—21no—
74#66927C2312yes—
75#66927C2311yescharacteristic
76C4×D44—21no—
77C4×D44—21no—
78#66923—21no—
79#66922D411yescharacteristic
80#66922D411yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22C2312yes—
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2312yes—
86C11×C4⋊C8C2311yescharacteristic
87C11×C4⋊C8C2311yescharacteristic
88C11×C22⋊C8—21no—
89C11×#97D412yes—
90C4×C8×C11—21no—
91C4×C8×C11C2312yes—
92#66885—22no—
93#66885—22no—
94#66885—22no—
95#66881—22no—
96#66880—22no—
97#66879—22no—
98Dic11⋊C8—22no—
99Dic11⋊C8—22no—
100C8×Dic11—22no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4⋊(C11⋊C8)C2311yescharacteristic
104#19238—111nomaximal, Sylow
105C23×D11—41no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C2×C22⋊D11—41no—
110#4339—42no—
111#4339—42no—
112C2×D44—21no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—22no—
118C2×D44—41no—
119C2×D44—41no—
120C2×D44—41no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44—81no—
124C2×D44—81no—
125C2×D44—82no—
126C2×C4×D11—41no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C2×Dic22C2×D412yes—
130C11×M16—22no—
131C11×M16SD1614yescomplemented
132C2×C8×C11—22no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—81no—
136C2×C8×C11C2×D412yes—
137C2×C8×C11C2×D412yes—
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11#4111yescharacteristic
141C42×C11C2411yescharacteristic
142C22⋊Dic11—22no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11C2×D412yes—
151Dic11⋊C4—22no—
152Dic11⋊C4—22no—
153C4×Dic11—22no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—42no—
157D88—44no—
158D88—44no—
159#4314—44no—
160#4314—44no—
161#4314—82no—
162#4314—82no—
163#4314—82no—
164#3246—111no—
165#3208—111no—
166#3151—111no—
167#2962—111no—
168#1688—112no—
169#1686—112no—
170#1668—112no—
171#1666—112no—
172#1565D1111yescharacteristic, complemented
173#1540—111no—
174C2×#331—111no—
175C23×C11#12111yescharacteristic
176C22×D11—41no—
177C22×D11—42no—
178C22×D11—82no—
179C22×D11—82no—
180C22×D11—82no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11C2×SD1612yes—
188C2×C4×C11AGL(1,ℤ/8)12yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C22⋊D11—82no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—41no—
196D44—42no—
197D44—41no—
198D44—42no—
199D44—41no—
200D44—41no—
201D44—42no—
202D44—42no—
203D44—41no—
204D44—81no—
205D44—82no—
206D44—82no—
207D44—82no—
208D44—82no—
209C4×D11—82no—
210Dic22—22no—
211Dic22—22no—
212Dic22—41no—
213Dic22—41no—
214Dic22—81no—
215C8×C11—22no—
216C8×C11—41no—
217C8×C11—42no—
218C8×C11—41no—
219C8×C11C2×SD1614yes—
220C11⋊C8—41no—
221C11⋊C8—41no—
222C2×AGL(1,ℤ/8)—221no—
223C2×AGL(1,ℤ/8)—221no—
224#533—111no—
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—112no—
241#446—222no—
242C8×Q8—112no—
243#431C2×D1111yescharacteristic
244#424—221no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8C2×D1111yescharacteristic
247#405—221no—
248C4×M16C2×D1111yescharacteristic
249#335C2×D1112yescomplemented
250#334C2×D1112yescomplemented
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#46012yes—
272C4×C11C22×SD1611yescharacteristic
273C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
274C4×C11#57611yescharacteristic
275C4×C11#57711yescharacteristic
276Dic11—42no—
277Dic11—42no—
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×M16D4411yescharacteristic
293C2×M16D4411yescharacteristic
294C22×C8—21no—
295C22×C8—221no—
296C4⋊Q8—111no—
297C4⋊Q8—111no—
298C4⋊Q8—111no—
299#127—112no—
300#127—111no—
301#127—221no—
302#127—221no—
303#127—221no—
304#125—221no—
305#124—221no—
306C22⋊Q8—112no—
307C22⋊Q8—221no—
308#121—221no—
309#121—221no—
310C4×Q8—112no—
311C4×Q8—221no—
312C4×D4—221no—
313C4×D4—221no—
314#117—221no—
315C2×C42C22×D1111yescharacteristic
316#106—222no—
317C4⋊C8—21no—
318C4⋊C8—111no—
319C4⋊C8—111no—
320C4⋊C8—222no—
321C4⋊C8—222no—
322C4⋊C8—221no—
323C4⋊C8C22×D1112yes—
324C4⋊C8C22×D1111yescharacteristic
325C4⋊C8C22×D1111yescharacteristic
326#103—222no—
327#102—222no—
328#102—222no—
329#102—222no—
330C22⋊C8—21no—
331#97—222no—
332#97D4412yes—
333C4×C8—21no—
334C4×C8—222no—
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—112no—
346C2×Q8—221no—
347C2×Q8—221no—
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×C4D4×D1111yescharacteristic
366C22×C4#434311yescharacteristic
367SD16—444no—
368SD16—444no—
369SD16—882no—
370SD16—882no—
371SD16—882no—
372D8—444no—
373D8—444no—
374M16—22no—
375M16#431414yescomplemented
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—81no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8—442no—
383C2×C8C2×D4412yes—
384C2×C8C2×D4412yes—
385C4⋊C4—112no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—222no—
389C4⋊C4—221no—
390C4⋊C4—222no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C22⋊C4—222no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C42—222no—
397C42C2×D4411yescharacteristic
398C42D4×D1111yescharacteristic
399C42#434311yescharacteristic
400C42C23×D1111yescharacteristic
401C11#1923811yescharacteristic, complemented, Sylow
402C23—441no—
403C23—442no—
404C23—882no—
405C23—882no—
406C23—882no—
407C23#6694811yescharacteristic
408Q8—222no—
409Q8—222no—
410Q8—441no—
411Q8—441no—
412Q8—881no—
413D4—441no—
414D4—442no—
415D4—441no—
416D4—442no—
417D4—441no—
418D4—442no—
419D4—442no—
420D4—441no—
421D4—882no—
422D4—881no—
423D4—882no—
424D4—882no—
425D4—882no—
426D4—882no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—441no—
433C2×C4—882no—
434C2×C4#6694811yescharacteristic
435C2×C4#6694811yescharacteristic
436C2×C4#6694811yescharacteristic
437C2×C4C2×#431412yes—
438C2×C4#6696112yes—
439C2×C4C22×D4411yescharacteristic
440C2×C4C2×D4×D1111yescharacteristic
441C2×C4C2×#434311yescharacteristic
442C8—22no—
443C8—42no—
444C8—41no—
445C8—41no—
446C8—441no—
447C8—441no—
448C8C2×#431414yes—
449C22—21no—
450C22—21no—
451C22—882no—
452C22—881no—
453C22—881no—
454C22—882no—
455C22—882no—
456C22—881no—
457C22—1764no—
458C22#1062246112yes—
459C22C2×#6694811yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—442no—
464C4—442no—
465C4—881no—
466C4#1062246112yes—
467C4C22×#431411yescharacteristic
468C4C2×#6696111yescharacteristic
469C4#1062330511yescharacteristic
470C4#1062330911yescharacteristic
471C2—22no—
472C2—1762no—
473C2—1761no—
474C2C2×#1062246111yescharacteristic
475C2#1307829711yescharacteristic
476C2#1307834511yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1565C2
socleC22×C11C2×#121
prime radical#13079068C2
hypercenter#1565D11
hypocenterC11#19238
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
1. #13079933C2semidirect
2. #13079559C2semidirect
4. #13077563C2semidirect
5. #13068101C2semidirect
6. #13068089C2semidirect
7. #13067977C2semidirect
8. #13067965C2semidirect
9. #13067263C2semidirect
10. C2×#10622123C2semidirect
11. C11×#1565C2semidirect
24. #10622464C22semidirect
27. #10622461C22semidirect
37. #10622292C22semidirect
38. C8×Dic22C22semidirect
39. C11×#335C22semidirect
40. C11×#334C22semidirect
41. #10622124C22semidirect
42. #10622124C22semidirect
45. #10622123C22semidirect
46. #10622123C22semidirect
131. C11×M16SD16semidirect
172. #1565D11semidirect
249. #335C2×D11semidirect
250. #334C2×D11semidirect
375. M16#4314semidirect
401. C11#19238semidirect

Maximal subgroups

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

subgroupindex
#130799332
#130795592
#130790682
#130775632
#130681012
#130680892
#130679772
#130679652
#130672632
C2×#106221232
C11×#15652
#1923811