Finite Group Databasebeta

← #14765641

Subgroups — #14765641

Order 2816.

726 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
2#13077311C211yesmaximal, characteristic
3C2×#10622732C211yesmaximal, characteristic, complemented
4#13069368C212yesmaximal, complemented
5#13069324C212yesmaximal, complemented
6#13069213C212yesmaximal, complemented
7#13068889C212yesmaximal, complemented
8#13068821C211yesmaximal, characteristic, complemented
9#13068716C211yesmaximal, characteristic, complemented
10#13068394C211yesmaximal, characteristic, complemented
11C11×#1871C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C11×#525C2211yescharacteristic
14C2×#67001C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C2×C11×#104C2212yes—
18C4×C11×C22⋊C4C2211yescharacteristic
19#10622847C2211yescharacteristic
20#10622846C2212yes—
21#10622820C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×#66886C2212yes—
24#10622732—21no—
25#10622732—21no—
26#10622732C2212yes—
27#10622732C2212yes—
28C2×Dic11⋊C8—21no—
29C2×Dic11⋊C8—21no—
30#10622658C412yescomplemented
31#10622657C411yescharacteristic, complemented
32#10622656C411yescharacteristic, complemented
33#10622648C412yescomplemented
34#10622647C411yescharacteristic, complemented
35#10622646C411yescharacteristic, complemented
36#10622624—21no—
37#10622624—21no—
38D4×C11⋊C8—21no—
39D4×C11⋊C8—21no—
40#10622612C2211yescharacteristic
41#10622611C2212yes—
42#10622610C2211yescharacteristic
43C2×#66867C2212yes—
44C11×#339C2212yes—
45#10622196C2212yes—
46#10622162C2212yes—
47#10622161C2212yes—
48#10622161C2212yes—
49C2×C11×#41C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C2×C11×M16—21no—
52C2×C11×M16—42no—
53C2×C11×M16C2312yes—
54C22×C8×C11—21no—
55C11×#123—21no—
56C11×C22⋊Q8C2×C411yescharacteristic
57C11×C22⋊Q8C2×C411yescharacteristic
58C11×#121C2×C411yescharacteristic
59C11×#121C2×C411yescharacteristic
60C11×#120—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C11×#117C2311yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C42×C11C2312yes—
66C2×C22⋊Dic11—21no—
67#67001—42no—
68#66979—21no—
69#66979—21no—
70#66979C2×C412yes—
71#66979C2312yes—
72C2×C4⋊Dic11C2×C411yescharacteristic
73C2×C4⋊Dic11C2×C411yescharacteristic
74C2×C4×Dic11—21no—
75C2×#4318—21no—
76C2×#4318C2311yescharacteristic
77C2×#4318C2311yescharacteristic
78C22×C11⋊C8—21no—
79C22×C11⋊C8—42no—
80C22×C11⋊C8D411yescharacteristic
81C22×C11⋊C8D411yescharacteristic
82C22×C11⋊C8D411yescharacteristic
83C22×C11⋊C8D411yescharacteristic
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C11×#104—42no—
88C11×#95—21no—
89#66899C2×C412yes—
90#66899C2×C412yes—
91#66896C2×C412yes—
92#66896C2×C412yes—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)C2×C411yescharacteristic
98C22⋊(C11⋊C8)C2×C411yescharacteristic
99C22⋊(C11⋊C8)C2×C412yes—
100#66886—42no—
101Dic11⋊C8—22no—
102Dic11⋊C8—22no—
103Dic11⋊C8—22no—
104Dic11⋊C8—22no—
105#66872C2×C412yes—
106#66872C2×C412yes—
107#66871C2×C412yes—
108#66871C2×C412yes—
109C4⋊(C11⋊C8)—21no—
110C4⋊(C11⋊C8)—21no—
111#66867—21no—
112#66867—42no—
113C4×C11⋊C8—21no—
114#22096—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×C11—22no—
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—21no—
134C22×Dic11—21no—
135C11×M16—22no—
136C11×M16—22no—
137C11×M16—42no—
138C2×C8×C11—22no—
139C2×C8×C11—42no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4C22×C411yescharacteristic
143C11×C4⋊C4C22×C411yescharacteristic
144C11×C22⋊C4—21no—
145C11×C22⋊C4—21no—
146C11×C22⋊C4—21no—
147C11×C22⋊C4—21no—
148C11×C22⋊C4—21no—
149C11×C22⋊C4—42no—
150C42×C11—21no—
151C42×C11—22no—
152C42×C11—22no—
153C22⋊Dic11—22no—
154C22⋊Dic11—22no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11C22×C412yes—
158C4⋊Dic11C22×C412yes—
159C4×Dic11—22no—
160C4×Dic11—22no—
161#4318—22no—
162#4318—22no—
163#4318—42no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—41no—
171C2×C11⋊C8—41no—
172C2×C11⋊C8—41no—
173C2×C11⋊C8—41no—
174C2×C11⋊C8—42no—
175C2×C11⋊C8C22×C412yes—
176C2×C11⋊C8C22×C412yes—
177C2×C11⋊C8C2×D411yescharacteristic
178C2×C11⋊C8C2×D411yescharacteristic
179C2×C11⋊C8C2×D411yescharacteristic
180C2×C11⋊C8C2×D411yescharacteristic
181#3091—111no—
182#2929—111no—
183C2×#424—111no—
184#1946—112no—
185#1938—112no—
186#1922—112no—
187#1871D1111yescharacteristic
188#1866—112no—
189#1855—111no—
190#1826—111no—
191#1752—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×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11C4×D411yescharacteristic
220C2×C4×C11C4×D411yescharacteristic
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11H(5,𝔽2)12yes—
224C2×C4×C112−1+412yes—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C8×C11—42no—
230C11⋊C8—22no—
231C11⋊C8—22no—
232C11⋊C8—21no—
233C11⋊C8—21no—
234C11⋊C8—21no—
235C11⋊C8—21no—
236C11⋊C8—41no—
237C11⋊C8—41no—
238C2×#131—111no—
239C22×M16C2×D1111yescharacteristic
240C23×C8—111no—
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—221no—
250#435—221no—
251C8×D4—221no—
252C8×D4—221no—
253C2×#108—112no—
254#427—112no—
255#424—112no—
256#424—112no—
257#424—111no—
258#424—221no—
259#424—221no—
260C2×C4⋊C8—221no—
261C2×C4⋊C8—221no—
262C2×#104C2×D1112yes—
263#416—112no—
264#408—111no—
265#407—111no—
266C2×C22⋊C8—111no—
267#405—111no—
268C2×#97—112no—
269C4×C22⋊C4C2×D1111yescharacteristic
270#341—112no—
271#339—112no—
272#339—112no—
273#339C2×D1112yes—
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#44412yes—
287C22×C11C2×C4×D411yescharacteristic
288C22×C11#53912yes—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—41no—
292C4×C11—41no—
293C4×C11—41no—
294C4×C11—82no—
295C4×C11#52012yes—
296C4×C11#53411yescharacteristic
297C4×C11#53611yescharacteristic
298Dic11—42no—
299Dic11—42no—
300C2×#41C22×D1111yescharacteristic
301C23×C4C22×D1111yescharacteristic
302#131—442no—
303C2×M16—21no—
304C2×M16—42no—
305C2×M16—111no—
306C2×M16—111no—
307C2×M16—221no—
308C2×M16C22×D1112yes—
309C22×C8—21no—
310C22×C8—111no—
311C22×C8—111no—
312C22×C8—112no—
313C22×C8—111no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8—111no—
317C22×C8—221no—
318C22×C8—442no—
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—21no—
335C2×C22⋊C4—221no—
336C2×C42—221no—
337C2×C42C22×D1112yes—
338#108—442no—
339#107—112no—
340#107—112no—
341#106—112no—
342#106—112no—
343C4⋊C8—221no—
344C4⋊C8—221no—
345C4⋊C8—222no—
346C4⋊C8—222no—
347C4⋊C8—222no—
348C4⋊C8—222no—
349#104—42no—
350#103—112no—
351#103—112no—
352#102—112no—
353#102—112no—
354C22⋊C8—111no—
355C22⋊C8—111no—
356C22⋊C8—112no—
357C22⋊C8—221no—
358C22⋊C8—221no—
359C22⋊C8—221no—
360C22⋊C8—221no—
361#97—221no—
362#97—442no—
363C4×C8—221no—
364#95—21no—
365C2×C11—22no—
366C2×C11—22no—
367C2×C11—41no—
368C2×C11—81no—
369C2×C11#232211yescharacteristic
370C2×C11C2×#44411yescharacteristic
371C2×C11#295511yescharacteristic
372C24#434111yescharacteristic
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—22no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4C2×C4×D1111yescharacteristic
387C22×C4C2×C4×D1111yescharacteristic
388C22×C4D4×D1111yescharacteristic
389C22×C4D4×D1111yescharacteristic
390C22×C4#434111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392M16—22no—
393M16—22no—
394M16—42no—
395M16—222no—
396M16—222no—
397M16—442no—
398C2×C8—22no—
399C2×C8—42no—
400C2×C8—112no—
401C2×C8—112no—
402C2×C8—111no—
403C2×C8—111no—
404C2×C8—111no—
405C2×C8—111no—
406C2×C8—222no—
407C2×C8—222no—
408C2×C8—222no—
409C2×C8—222no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8—441no—
413C2×C8—441no—
414C2×C8—441no—
415C2×C8—441no—
416C2×C8—442no—
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—42no—
431C22⋊C4—222no—
432C22⋊C4—222no—
433C42—21no—
434C42—22no—
435C42—22no—
436C42—222no—
437C42—222no—
438C11#2209611yescharacteristic, complemented, Sylow
439C23—22no—
440C23—22no—
441C23—21no—
442C23—41no—
443C23(C22⋊D11)⋊C411yescharacteristic
444C23(C22⋊D11)⋊C411yescharacteristic
445C23C2×#434111yescharacteristic
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—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4(C22⋊D11)⋊C411yescharacteristic
471C2×C4(C22⋊D11)⋊C411yescharacteristic
472C2×C4C22×C4×D1111yescharacteristic
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4#6703712yes—
475C2×C4#6704312yes—
476C8—42no—
477C8—222no—
478C8—222no—
479C8—221no—
480C8—221no—
481C8—221no—
482C8—221no—
483C8—441no—
484C8—441no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—44no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22#1062243612yes—
497C22C2×(C22⋊D11)⋊C411yescharacteristic
498C22#1062313312yes—
499C4—21no—
500C4—21no—
501C4—41no—
502C4—41no—
503C4—41no—
504C4—82no—
505C4—442no—
506C4—442no—
507C4#1062307712yes—
508C4#1062312011yescharacteristic
509C4#1062317911yescharacteristic
510C2—22no—
511C2—22no—
512C2—41no—
513C2—81no—
514C2#1307129011yescharacteristic
515C2C2×#1062243611yescharacteristic
516C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1871C2
socleC22×C11C2×C4×D4
prime radicalC11×#525C22
cosocleC22×C4×C11C24
hypercenter#1871D11
hypocenterC11#22096
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
3. C2×#10622732C2semidirect
4. #13069368C2semidirect
5. #13069324C2semidirect
6. #13069213C2semidirect
7. #13068889C2semidirect
8. #13068821C2semidirect
9. #13068716C2semidirect
10. #13068394C2semidirect
30. #10622658C4semidirect
31. #10622657C4semidirect
32. #10622656C4semidirect
33. #10622648C4semidirect
34. #10622647C4semidirect
35. #10622646C4semidirect
438. C11#22096semidirect

Maximal subgroups

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

subgroupindex
#130785252
#130773112
C2×#106227322
#130693682
#130693242
#130692132
#130688892
#130688212
#130687162
#130683942
C11×#18712
#2209611