Finite Group Databasebeta

← #14729938

Subgroups — #14729938

Order 2816.

940 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#13079012C211yesmaximal, characteristic, complemented
2#13078738C211yesmaximal, characteristic, complemented
3#13078707C211yesmaximal, characteristic
4#13067788C214yesmaximal, complemented
5#13067726C214yesmaximal, complemented
6#13067333C211yesmaximal, characteristic, complemented
7#13067063C211yesmaximal, characteristic, complemented
8#13067059C211yesmaximal, characteristic, complemented
9C2×C11×#556C211yesmaximal, characteristic, complemented
10C11×#556—22no—
11C11×#556—22no—
12C11×#556—22no—
13C11×#556C2214yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22#10623008C2211yescharacteristic
23#10622840—21no—
24#10622830—21no—
25#10622706C2212yescomplemented
26#10622702—22no—
27#10622701C2212yescomplemented
28#10622640C2212yescomplemented
29#10622639—22no—
30#10622634C2212yescomplemented
31#10622628C2212yes—
32#10622627—22no—
33#10622621C2212yes—
34#10622581—21no—
35#10622580—21no—
36#10622579—22no—
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40#10622185C2214yescomplemented
41Q8⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yes—
43C22×Q8×C11—21no—
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—21no—
47C2×#4339—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8D412yes—
51C11×C4⋊Q8C2312yes—
52C11×#126—28no—
53C11×#126—28no—
54C11×#124—24no—
55C11×#124—24no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—24no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11D412yes—
63C4×Q8×C11C2312yes—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11D412yes—
67C4×D4×C11C2312yes—
68C11×#117—24no—
69C11×#117—24no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D412yes—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—22no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4325—22no—
83C2×#4323—22no—
84#66983—21no—
85#66983—21no—
86C2×#4318—21no—
87#66928—21no—
88#66927C2311yescharacteristic
89C4×D44—21no—
90C4×D44—21no—
91#66922C2311yescharacteristic
92#66899—22no—
93#66896—22no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)—21no—
96#66874—24no—
97#66873—24no—
98#66873—22no—
99#66873—22no—
100#66872—22no—
101#66871—22no—
102C4⋊(C11⋊C8)C2312yes—
103C4⋊(C11⋊C8)C2312yes—
104#66867—21no—
105#66867—21no—
106#66867—21no—
107C4×C11⋊C8C2312yes—
108#18536—111nomaximal, Sylow
109C24×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—42no—
114C2×Q8×C11—44no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—21no—
117C2×D4×C11—42no—
118C2×D4×C11C2×D412yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—44no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11—41no—
130#4339—44no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×C4×D11—41no—
135C2×Dic22—21no—
136C11×C4⋊C4—28no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4C2×D412yes—
145C11×C4⋊C4C2×D412yes—
146C11×C4⋊C4C2×D414yes—
147C11×C22⋊C4—28no—
148C11×C22⋊C4—28no—
149C11×C22⋊C4—22no—
150C11×C22⋊C4—22no—
151C42×C11—28no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2411yescharacteristic
158#4325—44no—
159#4323—44no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164#4318—42no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×#556D1111yescharacteristic, complemented
169#3141—111no—
170#3112—111no—
171#3109—111no—
172#1638—114no—
173#1628—114no—
174#1556—111no—
175#1491—111no—
176#1490—111no—
177C23×C11—22no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11#12011yescharacteristic
182C22×D11—41no—
183Q8×C11—22no—
184Q8×C11—22no—
185Q8×C11—42no—
186Q8×C11—44no—
187Q8×C11—44no—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—42no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—44no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—44no—
202C2×C4×C11—42no—
203C2×C4×C11—44no—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C22⋊D11—82no—
211C2×Dic11—41no—
212D44—42no—
213D44—42no—
214D44—42no—
215C4×D11—82no—
216Dic22—42no—
217C11⋊C8—42no—
218C11⋊C8—42no—
219C11⋊C8—42no—
220#556—22no—
221#556—22no—
222#556—22no—
223#556C2×D1114yes—
224#532—111no—
225C2×C4⋊Q8C2×D1111yescharacteristic
226C2×#126—22no—
227C2×#124—21no—
228C2×C22⋊Q8—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8C2×D1111yescharacteristic
231C2×C4×D4C2×D1111yescharacteristic
232C2×#117—21no—
233#489—222no—
234#487—112no—
235#486—112no—
236#481—221no—
237#480—221no—
238#477—112no—
239#476—112no—
240#460—112no—
241#459—112no—
242#448—221no—
243#447—221no—
244#442—222no—
245#440—222no—
246#432—111no—
247#432—111no—
248#417—222no—
249C4×M16—111no—
250#332—114no—
251Q8⋊C8—114no—
252D4⋊C8—114no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—84no—
259C22×C11#45412yes—
260C22×C11C2×#12011yescharacteristic
261C2×D11—81no—
262C2×D11—81no—
263C2×D11—81no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—44no—
271C4×C11—42no—
272C4×C11#57512yes—
273C4×C11#57512yes—
274Dic11—81no—
275C2×#41—221no—
276C22×Q8—21no—
277C22×Q8C22⋊D1111yescharacteristic
278C22×D4C22⋊D1111yescharacteristic
279C23×C4—21no—
280C2×SD16—222no—
281C2×D8—222no—
282C2×M16—221no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—111no—
286C4⋊Q8C22⋊D1112yes—
287C4⋊Q8C22×D1112yes—
288#127—111no—
289#126—28no—
290#126—28no—
291#124—24no—
292#124—24no—
293#124—221no—
294C22⋊Q8—24no—
295C22⋊Q8—24no—
296#121—221no—
297#121—221no—
298C4×Q8—24no—
299C4×Q8—24no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8C22⋊D1112yes—
303C4×Q8C22×D1112yes—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—221no—
307C4×D4—221no—
308C4×D4C22⋊D1112yes—
309C4×D4C22×D1112yes—
310#117—24no—
311#117—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4C22⋊D1111yescharacteristic
316C2×C4⋊C4C22⋊D1111yescharacteristic
317C2×C4⋊C4C22⋊D1112yes—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—21no—
321C2×C42—22no—
322C2×C42—21no—
323C2×C42C22×D1111yescharacteristic
324#107—222no—
325#106—222no—
326C4⋊C8—112no—
327C4⋊C8—112no—
328#103—222no—
329#103—224no—
330#102—222no—
331#102—224no—
332#102—222no—
333#102—222no—
334C22⋊C8—221no—
335C22⋊C8—221no—
336#97—221no—
337#97—221no—
338#97—221no—
339C4×C8—112no—
340C2×C11—22no—
341C2×C11—82no—
342C2×C11#300511yescharacteristic
343C2×C11#300511yescharacteristic
344C2×C11C2×#45411yescharacteristic
345D11—161no—
346C24—21no—
347#41—444no—
348C2×Q8—21no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—42no—
352C2×Q8—44no—
353C2×Q8—221no—
354C2×Q8C2×C22⋊D1112yes—
355C2×D4—21no—
356C2×D4—42no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—221no—
360C2×D4—441no—
361C2×D4C2×C22⋊D1112yes—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—44no—
369C22×C4—441no—
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C2×C22⋊D1111yescharacteristic
372C22×C4C2×C22⋊D1111yescharacteristic
373SD16—444no—
374D8—444no—
375M16—442no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8—222no—
379C4⋊C4—28no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4C2×C22⋊D1114yes—
390C4⋊C4C2×C22⋊D1112yes—
391C4⋊C4C2×C22⋊D1112yes—
392C22⋊C4—28no—
393C22⋊C4—28no—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C42—28no—
399C42—22no—
400C42—22no—
401C42C2×C22⋊D1111yescharacteristic
402C42C2×C22⋊D1111yescharacteristic
403C42C2×C22⋊D1111yescharacteristic
404C42C23×D1111yescharacteristic
405C11#1853611yescharacteristic, complemented, Sylow
406C23—22no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—441no—
411C23#6700611yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—42no—
415Q8—44no—
416Q8—44no—
417Q8—442no—
418D4—22no—
419D4—22no—
420D4—42no—
421D4—442no—
422D4—442no—
423D4—442no—
424D4—882no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—441no—
439C2×C4—882no—
440C2×C4#6700611yescharacteristic
441C2×C4#6700611yescharacteristic
442C2×C4#6700611yescharacteristic
443C2×C4C22×C22⋊D1111yescharacteristic
444C2×C4C22×C22⋊D1111yescharacteristic
445C2×C4C22×C22⋊D1111yescharacteristic
446C8—442no—
447C8—442no—
448C8—442no—
449C22—21no—
450C22—21no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—881no—
456C22—881no—
457C22—881no—
458C22#1062285812yes—
459C22C2×#6700611yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—42no—
465C4—42no—
466C4—44no—
467C4—42no—
468C4—881no—
469C4#1062335312yes—
470C4#1062335312yes—
471C2—22no—
472C2—82no—
473C2—1761no—
474C2#1307785811yescharacteristic
475C2#1307785811yescharacteristic
476C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#556C2
socleC22×C11C2×#120
prime radical#13078707C2
hypercenterC2×#556D11
hypocenterC11#18536
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #13079012C2semidirect
2. #13078738C2semidirect
4. #13067788C2semidirect
5. #13067726C2semidirect
6. #13067333C2semidirect
7. #13067063C2semidirect
8. #13067059C2semidirect
9. C2×C11×#556C2semidirect
25. #10622706C22semidirect
27. #10622701C22semidirect
28. #10622640C22semidirect
30. #10622634C22semidirect
40. #10622185C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
168. C2×#556D11semidirect
405. C11#18536semidirect

Maximal subgroups

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

subgroupindex
#130790122
#130787382
#130787072
#130677882
#130677262
#130673332
#130670632
#130670592
C2×C11×#5562
#1853611