Finite Group Databasebeta

← #14737392

Subgroups — #14737392

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079958C211yesmaximal, characteristic, complemented
2#13079559C211yesmaximal, characteristic
3#13078992C211yesmaximal, characteristic
4#13077559C211yesmaximal, characteristic, complemented
5#13068187C212yesmaximal, complemented
6#13068159C212yesmaximal, complemented
7#13068063C212yesmaximal, complemented
8#13068035C212yesmaximal, complemented
9#13067369C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic
11C11×#1542C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×#66927C2211yescharacteristic
14#10623001C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17#10622715—21no—
18#10622714—21no—
19#10622704C2212yescomplemented
20#10622703C2212yescomplemented
21#10622701C2212yes—
22#10622701C2212yes—
23#10622680—22no—
24#10622664—22no—
25#10622644—21no—
26#10622634—21no—
27#10622614—21no—
28#10622614—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C4×#4318C2211yescharacteristic
31#10622461C2212yes—
32#10622461C2212yes—
33#10622444C2212yescomplemented
34#10622443C2212yescomplemented
35#10622441—22no—
36#10622344—22no—
37#10622307—21no—
38#10622306—21no—
39C11×#333C2211yescharacteristic, complemented
40C11×#333C2211yescharacteristic, complemented
41C11×#332C2211yescharacteristic, complemented
42C11×#332C2211yescharacteristic, complemented
43#10622123C2212yes—
44#10622123C2212yes—
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47C22×D44—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×C8×C11—21no—
51C11×C4⋊Q8C2311yescharacteristic
52C11×C4⋊Q8C2311yescharacteristic
53C11×#125—21no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11—21no—
58C11×#117—21no—
59C2×C42×C11C2311yescharacteristic
60C2×#4326—22no—
61#66979—21no—
62#66977—21no—
63#66977D412yes—
64C2×#4318D411yescharacteristic
65C2×#4318D411yescharacteristic
66C22×C11⋊C8—21no—
67C2×#4314—22no—
68C2×#4314—22no—
69#66927—21no—
70#66927—21no—
71#66927—21no—
72#66927C2312yes—
73#66923—21no—
74#66922D411yescharacteristic
75#66922D411yescharacteristic
76C4×Dic22—21no—
77C4×Dic22C2312yes—
78C11×C4⋊C8—21no—
79C11×C4⋊C8C2311yescharacteristic
80C11×C4⋊C8C2311yescharacteristic
81C11×C4⋊C8C2311yescharacteristic
82C11×C4⋊C8C2311yescharacteristic
83C11×C22⋊C8—21no—
84C4×C8×C11—21no—
85#66899—22no—
86#66885—22no—
87#66885—22no—
88#66879—22no—
89Dic11⋊C8—22no—
90Dic11⋊C8—22no—
91C8×Dic11—22no—
92#66874—22no—
93#66873—22no—
94#66873—22no—
95#66873—22no—
96#66873—22no—
97#66871—22no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2312yes—
100#66867D412yes—
101C4×C11⋊C8C2312yes—
102#19242—111nomaximal, Sylow
103C23×D11—41no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—41no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—42no—
116C2×D44—42no—
117C2×D44—81no—
118C2×D44—81no—
119C2×D44—82no—
120C2×Dic22—21no—
121C2×Dic22C2×D412yes—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—42no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C42×C11—41no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11#4111yescharacteristic
138C42×C11C2411yescharacteristic
139C22⋊Dic11—22no—
140#4326—82no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11C2×D412yes—
145Dic11⋊C4—22no—
146Dic11⋊C4—22no—
147C4×Dic11—22no—
148#4318—22no—
149#4318—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—81no—
152C2×C11⋊C8C2×D412yes—
153C2×C11⋊C8C2×D412yes—
154#4314—82no—
155#4314—82no—
156#3249—111no—
157#3208—111no—
158#3138—111no—
159#2962—111no—
160#1702—112no—
161#1698—112no—
162#1682—112no—
163#1678—112no—
164#1565—111no—
165#1542D1111yescharacteristic, complemented
166C2×#331—111no—
167C23×C11#12111yescharacteristic
168C22×D11—42no—
169C22×D11—82no—
170C22×D11—82no—
171C22×D11—82no—
172Q8×C11—41no—
173Q8×C11—41no—
174Q8×C11—81no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#13512yes—
184C2×C4×C11#13712yes—
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×Dic11—22no—
189C2×Dic11—22no—
190D44—42no—
191D44—42no—
192D44—42no—
193D44—42no—
194D44—82no—
195D44—82no—
196D44—82no—
197D44—82no—
198Dic22—22no—
199Dic22—22no—
200Dic22—81no—
201C8×C11—41no—
202C8×C11—41no—
203C8×C11—41no—
204C8×C11—41no—
205C11⋊C8—22no—
206C11⋊C8—22no—
207C11⋊C8—42no—
208#533—111no—
209#533C2×D1111yescharacteristic
210C2×#127—111no—
211#492—221no—
212#490—222no—
213#486—112no—
214#486—112no—
215#486—221no—
216#477—112no—
217#477—221no—
218#467—222no—
219#462—112no—
220#462—221no—
221#460—112no—
222#460—112no—
223#450—222no—
224#446—112no—
225#446—222no—
226C8×Q8—112no—
227#431C2×D1111yescharacteristic
228#424—221no—
229C2×C4⋊C8—111no—
230C2×C4⋊C8C2×D1111yescharacteristic
231#418—221no—
232#418—221no—
233#405—221no—
234C4×M16—111no—
235#335—112no—
236#334—112no—
237#333C2×D1111yescharacteristic, complemented
238#333C2×D1111yescharacteristic, complemented
239#332C2×D1111yescharacteristic, complemented
240#332C2×D1111yescharacteristic, complemented
241#331—112no—
242#331—112no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11#46412yes—
246C22×C11C2×#12111yescharacteristic
247C2×D11—82no—
248C2×D11—82no—
249C2×D11—82no—
250C2×D11—164no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—81no—
255C4×C11—81no—
256C4×C11#46412yes—
257C4×C11C2×#13511yescharacteristic
258C4×C11C2×#13711yescharacteristic
259C4×C11#57611yescharacteristic
260C4×C11#57711yescharacteristic
261Dic11—42no—
262Dic11—42no—
263C22×D4—221no—
264C22×D4—221no—
265C22×D4—221no—
266C2×Q16—222no—
267C2×SD16—222no—
268C2×SD16—222no—
269C2×M16—111no—
270C2×M16—111no—
271C22×C8—21no—
272C22×C8—221no—
273C4⋊Q8—111no—
274C4⋊Q8—111no—
275C4⋊Q8C22×D1111yescharacteristic
276C4⋊Q8C22×D1111yescharacteristic
277#127—112no—
278#127—221no—
279#127—221no—
280#127—221no—
281#125—21no—
282#125—221no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8—112no—
286C22⋊Q8—221no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8—112no—
290C4×Q8—221no—
291#117—21no—
292#117—221no—
293C2×C42C22×D1111yescharacteristic
294#107—222no—
295C4⋊C8—21no—
296C4⋊C8—112no—
297C4⋊C8—222no—
298C4⋊C8—222no—
299C4⋊C8—221no—
300C4⋊C8C22×D1111yescharacteristic
301C4⋊C8C22×D1111yescharacteristic
302C4⋊C8C22×D1111yescharacteristic
303C4⋊C8C22×D1111yescharacteristic
304#103—222no—
305#103—222no—
306#102—222no—
307#102—222no—
308#102—222no—
309#102—222no—
310#102—222no—
311#102—222no—
312C22⋊C8—21no—
313#97—112no—
314#97—222no—
315C4×C8—21no—
316C4×C8—112no—
317C4×C8—222no—
318C2×C11—22no—
319C2×C11C2×#46411yescharacteristic
320C2×C11#306211yescharacteristic
321C2×C11#306811yescharacteristic
322D11—162no—
323C24—441no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—112no—
327C2×Q8—221no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—441no—
332C2×D4—441no—
333C2×D4—441no—
334C2×D4—442no—
335C2×D4—442no—
336C2×D4—881no—
337C2×D4—881no—
338C2×D4—882no—
339C22×C4#433911yescharacteristic
340C22×C4D4×D1111yescharacteristic
341C22×C4D4×D1111yescharacteristic
342Q16—882no—
343SD16—882no—
344SD16—882no—
345M16—222no—
346M16—222no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—42no—
352C2×C8—112no—
353C2×C8—112no—
354C2×C8—222no—
355C2×C8—881no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—112no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C4⋊C4—222no—
366C4⋊C4—221no—
367C4⋊C4—222no—
368C22⋊C4—41no—
369C22⋊C4—222no—
370C42—41no—
371C42—222no—
372C42#433911yescharacteristic
373C42D4×D1111yescharacteristic
374C42D4×D1111yescharacteristic
375C42C23×D1111yescharacteristic
376C11#1924211yescharacteristic, complemented, Sylow
377C23—442no—
378C23—882no—
379C23—882no—
380C23—882no—
381C23#6693711yescharacteristic
382Q8—41no—
383Q8—41no—
384Q8—81no—
385Q8—222no—
386Q8—222no—
387Q8—881no—
388D4—442no—
389D4—442no—
390D4—442no—
391D4—442no—
392D4—882no—
393D4—882no—
394D4—882no—
395D4—882no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—222no—
402C2×C4—222no—
403C2×C4#6693711yescharacteristic
404C2×C4#6693711yescharacteristic
405C2×C4#6693711yescharacteristic
406C2×C4#6696912yes—
407C2×C4#6697112yes—
408C2×C4C2×#433911yescharacteristic
409C2×C4C2×D4×D1111yescharacteristic
410C2×C4C2×D4×D1111yescharacteristic
411C8—41no—
412C8—41no—
413C8—41no—
414C8—41no—
415C8—222no—
416C8—222no—
417C8—442no—
418C22—21no—
419C22—21no—
420C22—882no—
421C22—882no—
422C22—882no—
423C22—1764no—
424C22#1062241112yes—
425C22C2×#6693711yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—81no—
430C4—81no—
431C4—442no—
432C4—442no—
433C4#1062241112yes—
434C4C2×#6696911yescharacteristic
435C4C2×#6697111yescharacteristic
436C4#1062330011yescharacteristic
437C4#1062330111yescharacteristic
438C2—22no—
439C2—1762no—
440C2C2×#1062241111yescharacteristic
441C2#1307829911yescharacteristic
442C2#1307834711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#1542D11
hypocenterC11#19242
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #13079958C2semidirect
4. #13077559C2semidirect
5. #13068187C2semidirect
6. #13068159C2semidirect
7. #13068063C2semidirect
8. #13068035C2semidirect
9. #13067369C2semidirect
11. C11×#1542C2semidirect
19. #10622704C22semidirect
20. #10622703C22semidirect
33. #10622444C22semidirect
34. #10622443C22semidirect
39. C11×#333C22semidirect
40. C11×#333C22semidirect
41. C11×#332C22semidirect
42. C11×#332C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
165. #1542D11semidirect
237. #333C2×D11semidirect
238. #333C2×D11semidirect
239. #332C2×D11semidirect
240. #332C2×D11semidirect
376. C11#19242semidirect

Maximal subgroups

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

subgroupindex
#130799582
#130795592
#130789922
#130775592
#130681872
#130681592
#130680632
#130680352
#130673692
C2×#106221232
C11×#15422
#1924211