Finite Group Databasebeta

← #14737383

Subgroups — #14737383

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#13079557C211yesmaximal, characteristic
3#13077563C211yesmaximal, characteristic, complemented
4#13068181C212yesmaximal, complemented
5#13068153C212yesmaximal, complemented
6#13068057C212yesmaximal, complemented
7#13068029C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067273C211yesmaximal, characteristic, complemented
10C2×#10622182C211yesmaximal, characteristic
11C11×#3138C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14#10623001C2211yescharacteristic
15C11×#490—22no—
16C11×#486C2212yes—
17C11×#486C2212yes—
18C11×#418—21no—
19C11×#418—21no—
20C4×C11×M16C2211yescharacteristic
21#10622831—22no—
22#10622735—21no—
23#10622732—21no—
24#10622704C2212yescomplemented
25#10622703C2212yescomplemented
26#10622689—21no—
27#10622688C2212yes—
28#10622688C2212yes—
29#10622683—21no—
30#10622664—22no—
31#10622644—21no—
32#10622634—21no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622314—22no—
37#10622292C2212yescomplemented
38C8×Dic22C2212yescomplemented
39#10622185C2211yescharacteristic, complemented
40#10622185C2211yescharacteristic, complemented
41#10622184C2211yescharacteristic, complemented
42#10622184C2211yescharacteristic, complemented
43#10622182C2212yes—
44#10622182C2212yes—
45#10622096C2212yescomplemented
46#10622095C2212yescomplemented
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C2×C11×M16D411yescharacteristic
51C2×C11×M16D411yescharacteristic
52C11×C4⋊Q8C2311yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×#127—21no—
55C11×#127—21no—
56C11×#127—21no—
57C11×#127C2312yes—
58C11×#125—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C11×#117—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4326—22no—
66C2×#4324—22no—
67C2×#4324—22no—
68#66979—21no—
69#66977—21no—
70#66977D412yes—
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73#66923—21no—
74#66922D411yescharacteristic
75#66922D411yescharacteristic
76C4×Dic22—21no—
77C4×Dic22C2312yes—
78C11×#102—22no—
79C11×#102—22no—
80C11×#102—22no—
81C11×#102—22no—
82C11×#97D412yes—
83C4×C8×C11C2312yes—
84#66899—22no—
85#66896—22no—
86#66896—22no—
87C22⋊(C11⋊C8)—21no—
88#66879—22no—
89Dic11⋊C8—22no—
90Dic11⋊C8—22no—
91C8×Dic11—22no—
92#66874—22no—
93#66871—22no—
94C4⋊(C11⋊C8)—21no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)C2311yescharacteristic
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4×C11⋊C8—21no—
102#19242—111nomaximal, Sylow
103C24×C11—41no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11—81no—
115C2×D4×C11—81no—
116C2×D4×C11—82no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×Dic22—21no—
121C2×Dic22C2×D412yes—
122C11×M16—22no—
123C11×M16—22no—
124C2×C8×C11C2×D412yes—
125C2×C8×C11C2×D412yes—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—41no—
133C42×C11—41no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138C22⋊Dic11—22no—
139#4326—82no—
140#4324—82no—
141#4324—82no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11C2×D412yes—
146Dic11⋊C4—22no—
147Dic11⋊C4—22no—
148C4×Dic11—22no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—42no—
155C2×C11⋊C8—81no—
156#3249—111no—
157#3208—111no—
158#3138D1111yescharacteristic
159#2962—111no—
160#1702—112no—
161#1698—112no—
162#1682—112no—
163#1678—112no—
164#1565—111no—
165#1542—111no—
166C2×#331—111no—
167C23×C11—42no—
168C23×C11—82no—
169C23×C11—82no—
170C23×C11—82no—
171C23×C11#12111yescharacteristic
172Q8×C11—41no—
173Q8×C11—41no—
174Q8×C11—81no—
175D4×C11—42no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—42no—
179D4×C11—82no—
180D4×C11—82no—
181D4×C11—82no—
182D4×C11—82no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#13512yes—
192C2×C4×C11#13712yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—22no—
198Dic22—22no—
199Dic22—22no—
200Dic22—81no—
201C8×C11—22no—
202C8×C11—22no—
203C11⋊C8—41no—
204C11⋊C8—41no—
205C11⋊C8—42no—
206C11⋊C8—41no—
207C11⋊C8—41no—
208#533—111no—
209#533C2×D1111yescharacteristic
210C2×#127C2×D1111yescharacteristic
211#492—221no—
212#490—22no—
213#486—221no—
214#486C2×D1112yes—
215#486C2×D1112yes—
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#431—111no—
228#424—221no—
229C2×C4⋊C8—111no—
230C2×C4⋊C8—111no—
231#418—21no—
232#418—21no—
233#405—221no—
234C4×M16C2×D1111yescharacteristic
235#335—112no—
236#334—112no—
237#333—111no—
238#333—111no—
239#332—111no—
240#332—111no—
241#331—112no—
242#331—112no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11—82no—
248C22×C11—164no—
249C22×C11#46412yes—
250C22×C11C2×#12111yescharacteristic
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—21no—
264C22×D4—21no—
265C22×D4—21no—
266C2×Q16—222no—
267C2×SD16—222no—
268C2×SD16—222no—
269C2×M16C22⋊D1111yescharacteristic
270C2×M16C22⋊D1111yescharacteristic
271C22×C8—221no—
272C22×C8—221no—
273C4⋊Q8—111no—
274C4⋊Q8—111no—
275C4⋊Q8C22×D1111yescharacteristic
276C4⋊Q8C22×D1111yescharacteristic
277#127—21no—
278#127—21no—
279#127—21no—
280#127C22×D1112yes—
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—111no—
296C4⋊C8—111no—
297C4⋊C8—112no—
298C4⋊C8—111no—
299C4⋊C8—111no—
300C4⋊C8—222no—
301C4⋊C8—222no—
302C4⋊C8—221no—
303C4⋊C8—221no—
304#103—222no—
305#103—222no—
306#102—22no—
307#102—22no—
308#102—22no—
309#102—22no—
310#102—222no—
311#102—222no—
312C22⋊C8—221no—
313#97—222no—
314#97C22⋊D1112yes—
315C4×C8—222no—
316C4×C8—221no—
317C4×C8C22×D1112yes—
318C2×C11—22no—
319C2×C11—162no—
320C2×C11C2×#46411yescharacteristic
321C2×C11#306211yescharacteristic
322C2×C11#306811yescharacteristic
323C24—41no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—112no—
327C2×Q8—221no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—81no—
337C2×D4—81no—
338C2×D4—82no—
339C22×C4D4×D1111yescharacteristic
340C22×C4#434111yescharacteristic
341C22×C4C2×C22⋊D1111yescharacteristic
342Q16—882no—
343SD16—882no—
344SD16—882no—
345M16—22no—
346M16—22no—
347C2×C8—221no—
348C2×C8—221no—
349C2×C8—222no—
350C2×C8—221no—
351C2×C8—221no—
352C2×C8—442no—
353C2×C8—881no—
354C2×C8C2×C22⋊D1112yes—
355C2×C8C2×C22⋊D1112yes—
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—
372C42D4×D1111yescharacteristic
373C42#434111yescharacteristic
374C42C2×C22⋊D1111yescharacteristic
375C42C23×D1111yescharacteristic
376C11#1924211yescharacteristic, complemented, Sylow
377C23—42no—
378C23—82no—
379C23—82no—
380C23—82no—
381C23#6699111yescharacteristic
382Q8—41no—
383Q8—41no—
384Q8—81no—
385Q8—222no—
386Q8—222no—
387Q8—881no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—82no—
393D4—82no—
394D4—82no—
395D4—82no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—222no—
402C2×C4—222no—
403C2×C4#6699111yescharacteristic
404C2×C4#6699111yescharacteristic
405C2×C4#6699111yescharacteristic
406C2×C4#6700312yes—
407C2×C4#6700412yes—
408C2×C4C2×D4×D1111yescharacteristic
409C2×C4C2×#434111yescharacteristic
410C2×C4C22×C22⋊D1111yescharacteristic
411C8—22no—
412C8—22no—
413C8—442no—
414C8—441no—
415C8—441no—
416C8—441no—
417C8—441no—
418C22—21no—
419C22—21no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22—164no—
424C22#1062266712yes—
425C22C2×#6699111yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—81no—
430C4—81no—
431C4—442no—
432C4—442no—
433C4#1062266712yes—
434C4#1062330511yescharacteristic
435C4#1062330611yescharacteristic
436C4C2×#6700311yescharacteristic
437C4C2×#6700411yescharacteristic
438C2—22no—
439C2—162no—
440C2C2×#1062266711yescharacteristic
441C2#1307829011yescharacteristic
442C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3138C2
socleC22×C11C2×#121
prime radicalC2×C11×#127C22
hypercenter#3138D11
hypocenterC11#19242
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
1. #13079958C2semidirect
3. #13077563C2semidirect
4. #13068181C2semidirect
5. #13068153C2semidirect
6. #13068057C2semidirect
7. #13068029C2semidirect
8. #13067368C2semidirect
9. #13067273C2semidirect
24. #10622704C22semidirect
25. #10622703C22semidirect
37. #10622292C22semidirect
38. C8×Dic22C22semidirect
39. #10622185C22semidirect
40. #10622185C22semidirect
41. #10622184C22semidirect
42. #10622184C22semidirect
45. #10622096C22semidirect
46. #10622095C22semidirect
376. C11#19242semidirect

Maximal subgroups

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

subgroupindex
#130799582
#130795572
#130775632
#130681812
#130681532
#130680572
#130680292
#130673682
#130672732
C2×#106221822
C11×#31382
#1924211