Finite Group Databasebeta

← #14765621

Subgroups — #14765621

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078525C211yesmaximal, characteristic
2C2×#10622715C211yesmaximal, characteristic, complemented
3#13069361C212yesmaximal, complemented
4#13069323C212yesmaximal, complemented
5#13069215C212yesmaximal, complemented
6#13068919C211yesmaximal, characteristic
7#13068891C212yesmaximal, complemented
8#13068820C211yesmaximal, characteristic, complemented
9#13068713C211yesmaximal, characteristic, complemented
10C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C11×#2929C211yesmaximal, characteristic
12C2×C11×#131C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#525C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C11×#435—21no—
18C11×#435—21no—
19C8×D4×C11—21no—
20C8×D4×C11—21no—
21C11×#424C2211yescharacteristic
22C11×#408C2211yescharacteristic
23C11×#407C2211yescharacteristic
24C11×#405C2211yescharacteristic
25C2×#66901C2212yes—
26#10622846C2212yes—
27C4×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66886C2212yes—
30#10622715—21no—
31#10622715—21no—
32#10622715C2212yes—
33#10622715C2212yes—
34C2×Dic11⋊C8—21no—
35C2×Dic11⋊C8—21no—
36C2×C8×Dic11C2212yes—
37#10622658C412yescomplemented
38#10622657C411yescharacteristic, complemented
39#10622656C411yescharacteristic, complemented
40#10622648C412yescomplemented
41#10622647C411yescharacteristic, complemented
42#10622646C411yescharacteristic, complemented
43#10622611C2212yes—
44#10622196C2212yes—
45#10622193C2212yes—
46#10622193C2212yes—
47#10622188C2212yes—
48#10622170C2212yes—
49C2×C11×#41C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C11×#131—42no—
52C2×C11×M16—21no—
53C2×C11×M16C2311yescharacteristic
54C2×C11×M16C2311yescharacteristic
55C22×C8×C11—21no—
56C22×C8×C11—42no—
57C22×C8×C11D411yescharacteristic
58C22×C8×C11D411yescharacteristic
59C22×C8×C11D411yescharacteristic
60C22×C8×C11D411yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#123—21no—
64C11×C22⋊Q8C2×C411yescharacteristic
65C11×C22⋊Q8C2×C411yescharacteristic
66C11×#121C2×C411yescharacteristic
67C11×#121C2×C411yescharacteristic
68C11×#120—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C11×#117C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74#66979—21no—
75#66979—21no—
76#66979C2×C412yes—
77#66979C2312yes—
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×C4×Dic11—21no—
81C2×C4×Dic11C2312yes—
82C2×#4318—21no—
83C2×#4318—42no—
84C2×#4318C2312yes—
85C22×C11⋊C8—21no—
86C22×C11⋊C8C2312yes—
87C11×C4⋊C8—21no—
88C11×C4⋊C8—21no—
89C11×C22⋊C8—21no—
90C11×C22⋊C8—21no—
91C11×C22⋊C8—21no—
92C11×C22⋊C8—21no—
93C11×#97—21no—
94C4×C8×C11—21no—
95#66901—42no—
96#66899C2×C412yes—
97#66899C2×C412yes—
98#66896C2×C412yes—
99#66896C2×C412yes—
100C11⋊#95—21no—
101C22⋊(C11⋊C8)C2×C411yescharacteristic
102C22⋊(C11⋊C8)C2×C411yescharacteristic
103C22⋊(C11⋊C8)C2×C412yes—
104#66886—42no—
105Dic11⋊C8—22no—
106Dic11⋊C8—22no—
107Dic11⋊C8—22no—
108Dic11⋊C8—22no—
109C8×Dic11—42no—
110#66872C2×C412yes—
111#66872C2×C412yes—
112#66871C2×C412yes—
113#66871C2×C412yes—
114#22095—111nomaximal, Sylow
115C24×C11#4111yescharacteristic
116C11×#41—22no—
117C11×#41—22no—
118C2×Q8×C11C22×C411yescharacteristic
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11C22×C411yescharacteristic
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C11×M16—22no—
136C11×M16—22no—
137C11×M16—42no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—41no—
143C2×C8×C11—41no—
144C2×C8×C11—41no—
145C2×C8×C11—41no—
146C2×C8×C11—42no—
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2×D411yescharacteristic
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4C22×C411yescharacteristic
154C11×C4⋊C4C22×C411yescharacteristic
155C11×C22⋊C4—21no—
156C11×C22⋊C4—21no—
157C11×C22⋊C4—21no—
158C11×C22⋊C4—21no—
159C11×C22⋊C4—21no—
160C42×C11—21no—
161C22⋊Dic11—24no—
162C22⋊Dic11—22no—
163C22⋊Dic11—22no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11C22×C412yes—
167C4⋊Dic11C22×C412yes—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C4×Dic11—22no—
171C4×Dic11—22no—
172#4318—22no—
173#4318—22no—
174#4318—42no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—42no—
179C2×C11⋊C8C22×C412yes—
180C2×C11⋊C8C22×C412yes—
181#3091—111no—
182#2929D1111yescharacteristic
183C2×#424—111no—
184#1945—112no—
185#1937—112no—
186#1922—112no—
187#1871—111no—
188#1866—112no—
189#1855—111no—
190#1826—111no—
191C8×C22⋊C4—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—21no—
195C23×C11—41no—
196C23×C11C4×D411yescharacteristic
197C23×C11C4×D411yescharacteristic
198C23×C11C2×#4111yescharacteristic
199Q8×C11—22no—
200D4×C11—22no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—42no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11C4×D411yescharacteristic
217C2×C4×C11C4×D411yescharacteristic
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11H(5,𝔽2)12yes—
221C2×C4×C112−1+412yes—
222C2×Dic11—24no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C8×C11—21no—
230C8×C11—21no—
231C8×C11—21no—
232C8×C11—21no—
233C8×C11—41no—
234C8×C11—41no—
235C11⋊C8—22no—
236C11⋊C8—22no—
237C11⋊C8—42no—
238C2×#131C2×D1111yescharacteristic
239C22×M16—111no—
240C23×C8C2×D1111yescharacteristic
241#525C2×D1111yescharacteristic
242C2×#117—111no—
243#485—112no—
244#484—111no—
245#483—111no—
246#482—112no—
247#481—111no—
248#480—111no—
249#435—21no—
250#435—21no—
251C8×D4—21no—
252C8×D4—21no—
253C2×#108—112no—
254#427—112no—
255#424—112no—
256#424—112no—
257#424—221no—
258#424—221no—
259#424C2×D1111yescharacteristic
260C2×C4⋊C8—221no—
261C2×C4⋊C8—221no—
262C2×#104—112no—
263#416—112no—
264#408C2×D1111yescharacteristic
265#407C2×D1111yescharacteristic
266C2×C22⋊C8—111no—
267#405C2×D1111yescharacteristic
268C2×C4×C8—112no—
269C4×C22⋊C4—111no—
270#341—112no—
271#339—112no—
272#339—112no—
273#339—112no—
274#336—112no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—44no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11#44312yes—
287C22×C11C2×C4×D411yescharacteristic
288C22×C11#53912yes—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—41no—
292C4×C11—41no—
293C4×C11—41no—
294C4×C11#52012yes—
295C4×C11#53411yescharacteristic
296C4×C11#53611yescharacteristic
297Dic11—44no—
298Dic11—42no—
299Dic11—42no—
300C2×#41C22×D1111yescharacteristic
301C23×C4C22×D1111yescharacteristic
302#131—42no—
303C2×M16—21no—
304C2×M16—112no—
305C2×M16—221no—
306C2×M16—442no—
307C2×M16C22×D1111yescharacteristic
308C2×M16C22×D1111yescharacteristic
309C22×C8—21no—
310C22×C8—42no—
311C22×C8—112no—
312C22×C8—221no—
313C22×C8C22⋊D1111yescharacteristic
314C22×C8C22⋊D1111yescharacteristic
315C22×C8C22⋊D1111yescharacteristic
316C22×C8C22⋊D1111yescharacteristic
317C22×C8C22×D1111yescharacteristic
318C22×C8C22×D1111yescharacteristic
319#123—21no—
320C22⋊Q8C4×D1111yescharacteristic
321C22⋊Q8C4×D1111yescharacteristic
322#121C4×D1111yescharacteristic
323#121C4×D1111yescharacteristic
324#120—21no—
325C4×D4—21no—
326C4×D4—21no—
327#117—112no—
328#117—112no—
329#117—221no—
330#117—221no—
331#117C22×D1111yescharacteristic
332C2×C4⋊C4—111no—
333C2×C4⋊C4—111no—
334C2×C22⋊C4—221no—
335C2×C22⋊C4—221no—
336C2×C42—112no—
337C2×C42—221no—
338#108—442no—
339#107—112no—
340#107—112no—
341#106—112no—
342#106—112no—
343C4⋊C8—21no—
344C4⋊C8—21no—
345C4⋊C8—222no—
346C4⋊C8—222no—
347C4⋊C8—222no—
348C4⋊C8—222no—
349#104—442no—
350#103—112no—
351#103—112no—
352#102—112no—
353#102—112no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—111no—
359C22⋊C8—111no—
360C22⋊C8—112no—
361#97—21no—
362C4×C8—21no—
363C4×C8—442no—
364#95—221no—
365C2×C11—22no—
366C2×C11—22no—
367C2×C11—41no—
368C2×C11—81no—
369C2×C11#232211yescharacteristic
370C2×C11C2×#44311yescharacteristic
371C2×C11#295511yescharacteristic
372C24#433911yescharacteristic
373#41—22no—
374#41—22no—
375C2×Q8C2×C4×D1111yescharacteristic
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4C2×C4×D1111yescharacteristic
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—222no—
386C22×C4C2×C4×D1111yescharacteristic
387C22×C4C2×C4×D1111yescharacteristic
388C22×C4#433911yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392M16—22no—
393M16—22no—
394M16—42no—
395M16—222no—
396M16—222no—
397M16—442no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—41no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—42no—
407C2×C8—112no—
408C2×C8—112no—
409C2×C8—222no—
410C2×C8—222no—
411C2×C8—222no—
412C2×C8—442no—
413C2×C8C2×C22⋊D1111yescharacteristic
414C2×C8C2×C22⋊D1111yescharacteristic
415C2×C8C2×C22⋊D1111yescharacteristic
416C2×C8C2×C22⋊D1111yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—112no—
420C4⋊C4—112no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4C2×C4×D1111yescharacteristic
424C4⋊C4C2×C4×D1111yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—224no—
431C22⋊C4—222no—
432C22⋊C4—222no—
433C42—21no—
434C42—222no—
435C42—222no—
436C42—222no—
437C42—222no—
438C11#2209511yescharacteristic, complemented, Sylow
439C23—22no—
440C23—22no—
441C23—21no—
442C23—41no—
443C23C4×C22⋊D1111yescharacteristic
444C23C4×C22⋊D1111yescharacteristic
445C23C2×#433911yescharacteristic
446Q8—22no—
447D4—22no—
448D4—42no—
449D4—42no—
450D4—42no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—224no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4C4×C22⋊D1111yescharacteristic
471C2×C4C4×C22⋊D1111yescharacteristic
472C2×C4C22×C4×D1111yescharacteristic
473C2×C4#6703712yes—
474C2×C4#6704312yes—
475C2×C4C22×C22⋊D1111yescharacteristic
476C8—21no—
477C8—21no—
478C8—21no—
479C8—21no—
480C8—41no—
481C8—41no—
482C8—222no—
483C8—222no—
484C8—442no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—44no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22#1062275712yes—
497C22#1062309512yes—
498C22C2×C4×C22⋊D1111yescharacteristic
499C4—21no—
500C4—21no—
501C4—41no—
502C4—41no—
503C4—41no—
504C4—444no—
505C4—442no—
506C4—442no—
507C4#1062307712yes—
508C4#1062333511yescharacteristic
509C4#1062335611yescharacteristic
510C2—22no—
511C2—22no—
512C2—41no—
513C2—81no—
514C2#1307128111yescharacteristic
515C2C2×#1062275711yescharacteristic
516C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2929C2
socleC22×C11C2×C4×D4
prime radicalC11×#525C22
cosocleC22×C4×C11C24
hypercenter#2929D11
hypocenterC11#22095
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. C2×#10622715C2semidirect
3. #13069361C2semidirect
4. #13069323C2semidirect
5. #13069215C2semidirect
7. #13068891C2semidirect
8. #13068820C2semidirect
9. #13068713C2semidirect
10. C8×C22⋊Dic11C2semidirect
37. #10622658C4semidirect
38. #10622657C4semidirect
39. #10622656C4semidirect
40. #10622648C4semidirect
41. #10622647C4semidirect
42. #10622646C4semidirect
438. C11#22095semidirect

Maximal subgroups

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

subgroupindex
#130785252
C2×#106227152
#130693612
#130693232
#130692152
#130689192
#130688912
#130688202
#130687132
C8×C22⋊Dic112
C11×#29292
#2209511