Finite Group Databasebeta

← #14765624

Subgroups — #14765624

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#13078531C211yesmaximal, characteristic
2#13077306C211yesmaximal, characteristic
3C2×#10622732C211yesmaximal, characteristic, complemented
4#13069362C212yesmaximal, complemented
5#13069318C212yesmaximal, complemented
6#13069214C212yesmaximal, complemented
7#13068918C211yesmaximal, characteristic
8#13068888C212yesmaximal, complemented
9#13068713C211yesmaximal, characteristic, complemented
10#13068390C211yesmaximal, characteristic, complemented
11C11×#1855C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13#10623322C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×#66960C2211yescharacteristic
17C2×C11×#108C2212yes—
18C11×#407C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C4×C22⋊Dic11C2211yescharacteristic
21C2×#66889C2212yes—
22#10622742C2211yescharacteristic
23#10622735C2211yescharacteristic
24#10622732—21no—
25#10622732—21no—
26#10622732C2212yes—
27#10622732C2211yescharacteristic
28#10622732C2212yes—
29#10622726C2212yes—
30#10622719C2212yes—
31C2×Dic11⋊C8—21no—
32C2×Dic11⋊C8—21no—
33C2×C8×Dic11C2212yes—
34#10622350C412yescomplemented
35#10622349C411yescharacteristic, complemented
36#10622348C411yescharacteristic, complemented
37#10622343—21no—
38#10622343—21no—
39(C22⋊D11)⋊C8—21no—
40(C22⋊D11)⋊C8—21no—
41#10622336C412yescomplemented
42#10622335C411yescharacteristic, complemented
43#10622334C411yescharacteristic, complemented
44C11×#341C2212yes—
45#10622193C2212yes—
46#10622193C2212yes—
47#10622193C2212yes—
48#10622188C2212yes—
49C23×C4×C11C2311yescharacteristic
50C2×#4339C2311yescharacteristic
51C2×C11×M16—21no—
52C2×C11×M16—42no—
53C2×C11×M16C2312yes—
54C2×C11×M16C2311yescharacteristic
55C2×C11×M16C2311yescharacteristic
56C22×C8×C11—21no—
57C22×C8×C11C2312yes—
58#67006—21no—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—21no—
61#66983C2×C411yescharacteristic
62#66983C2×C411yescharacteristic
63#66982—21no—
64C4×C22⋊D11—21no—
65C4×C22⋊D11—21no—
66#66979—21no—
67#66979—21no—
68#66979C2×C412yes—
69#66979C2312yes—
70#66979C2311yescharacteristic
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×C4⋊Dic11C2×C411yescharacteristic
73#66977C2×C411yescharacteristic
74#66977C2×C411yescharacteristic
75C2×C4×Dic11—21no—
76C2×C4×Dic11C2312yes—
77C22×C11⋊C8—42no—
78C22×C11⋊C8D411yescharacteristic
79C22×C11⋊C8D411yescharacteristic
80C22×C11⋊C8D411yescharacteristic
81C22×C11⋊C8D411yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84#66960—42no—
85C2×#4313—21no—
86C2×C8×D11—21no—
87C11×#108—42no—
88C11×C22⋊C8—21no—
89C11×C22⋊C8—21no—
90C11×C22⋊C8C2×C411yescharacteristic
91C11×C22⋊C8C2×C411yescharacteristic
92C11×C22⋊C8C2×C412yes—
93C11⋊#95—21no—
94#66889—42no—
95#66885C2×C412yes—
96#66885C2×C412yes—
97(C2×D11)⋊C8—21no—
98(C2×D11)⋊C8—21no—
99#66882C2×C412yes—
100#66882C2×C412yes—
101#66881C2×C412yes—
102#66881C2×C412yes—
103#66880C2×C412yes—
104#66880C2×C412yes—
105#66879—21no—
106Dic11⋊C8—22no—
107Dic11⋊C8—22no—
108Dic11⋊C8—22no—
109Dic11⋊C8—22no—
110Dic11⋊C8—21no—
111Dic11⋊C8—21no—
112C8×Dic11—21no—
113C8×Dic11—42no—
114#22095—111nomaximal, Sylow
115C24×C11#4111yescharacteristic
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—21no—
125C2×C22⋊D11—21no—
126C2×C22⋊D11—21no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130#4339—22no—
131#4339—22no—
132C2×D44C22×C411yescharacteristic
133C2×C4×D11—21no—
134C2×Dic22C22×C411yescharacteristic
135C11×M16—22no—
136C11×M16—22no—
137C11×M16—22no—
138C11×M16—22no—
139C11×M16—42no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—42no—
146C2×C8×C11C22×C412yes—
147C2×C8×C11C22×C412yes—
148C22⋊Dic11—24no—
149C22⋊Dic11—21no—
150C22⋊Dic11—21no—
151C22⋊Dic11—22no—
152C22⋊Dic11—22no—
153C22⋊Dic11—21no—
154(C2×D11)⋊C4—21no—
155(C2×D11)⋊C4—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11C22×C412yes—
159C4⋊Dic11C22×C412yes—
160C4⋊Dic11C22×C411yescharacteristic
161C4⋊Dic11C22×C411yescharacteristic
162Dic11⋊C4—21no—
163Dic11⋊C4—21no—
164C4×Dic11—22no—
165C4×Dic11—21no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168C4×Dic11—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—41no—
172C2×C11⋊C8—41no—
173C2×C11⋊C8—41no—
174C2×C11⋊C8—41no—
175C2×C11⋊C8C2×D411yescharacteristic
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178C2×C11⋊C8C2×D411yescharacteristic
179#4313—42no—
180C8×D11—42no—
181#3091—111no—
182#2929—111no—
183C2×#424—111no—
184#1945—112no—
185#1937—112no—
186#1922—112no—
187#1871—111no—
188#1866—112no—
189#1855D1111yescharacteristic, complemented
190#1826—111no—
191C8×C22⋊C4—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—41no—
195C23×C11C4×D411yescharacteristic
196C23×C11C4×D411yescharacteristic
197C23×C11C2×#4111yescharacteristic
198C22×D11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11C4×D411yescharacteristic
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11H(5,𝔽2)12yes—
211C2×C4×C112−1+412yes—
212C22⋊D11—42no—
213C22⋊D11—42no—
214C22⋊D11—42no—
215C2×Dic11—24no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225D44—22no—
226C4×D11—41no—
227C4×D11—41no—
228Dic22—22no—
229C8×C11—22no—
230C8×C11—22no—
231C8×C11—41no—
232C8×C11—42no—
233C8×C11—41no—
234C11⋊C8—21no—
235C11⋊C8—21no—
236C11⋊C8—21no—
237C11⋊C8—21no—
238C2×#131—111no—
239C22×M16C2×D1111yescharacteristic
240C23×C8—111no—
241#525—111no—
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×#108C2×D1112yes—
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×#104—112no—
263#416—112no—
264#408—111no—
265#407C2×D1111yescharacteristic
266C2×C22⋊C8C2×D1111yescharacteristic
267#405—111no—
268C2×C4×C8—112no—
269C4×C22⋊C4—111no—
270#341C2×D1112yes—
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#44312yes—
284C22×C11C2×C4×D411yescharacteristic
285C22×C11#53912yes—
286C2×D11—41no—
287C2×D11—41no—
288C2×D11—41no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11#52012yes—
292C4×C11#53411yescharacteristic
293C4×C11#53611yescharacteristic
294Dic11—44no—
295Dic11—41no—
296Dic11—42no—
297Dic11—41no—
298Dic11—42no—
299Dic11—41no—
300C2×#41—111no—
301C23×C4C22×D1111yescharacteristic
302#131—442no—
303C2×M16—21no—
304C2×M16—42no—
305C2×M16—221no—
306C2×M16C22×D1112yes—
307C2×M16C22×D1111yescharacteristic
308C2×M16C22×D1111yescharacteristic
309C22×C8—21no—
310C22×C8—111no—
311C22×C8—111no—
312C22×C8—111no—
313C22×C8—111no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8—221no—
317C22×C8—442no—
318C22×C8C22×D1112yes—
319#123—221no—
320C22⋊Q8—111no—
321C22⋊Q8—111no—
322#121—111no—
323#121—111no—
324#120—221no—
325C4×D4—221no—
326C4×D4—221no—
327#117—112no—
328#117—112no—
329#117—111no—
330#117—221no—
331#117—221no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—111no—
334C2×C22⋊C4—221no—
335C2×C22⋊C4—221no—
336C2×C42—112no—
337C2×C42—221no—
338#108—42no—
339#107—112no—
340#107—112no—
341#106—112no—
342#106—112no—
343C4⋊C8—222no—
344C4⋊C8—222no—
345C4⋊C8—222no—
346C4⋊C8—222no—
347C4⋊C8—221no—
348C4⋊C8—221no—
349#104—442no—
350#103—112no—
351#103—112no—
352#102—112no—
353#102—112no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—221no—
357C22⋊C8—221no—
358C22⋊C8C4×D1111yescharacteristic
359C22⋊C8C4×D1111yescharacteristic
360C22⋊C8C4×D1112yes—
361#97—221no—
362C4×C8—221no—
363C4×C8—442no—
364#95—221no—
365C2×C11—22no—
366C2×C11—22no—
367C2×C11—41no—
368C2×C11#232211yescharacteristic
369C2×C11C2×#44311yescharacteristic
370C2×C11#295511yescharacteristic
371D11—81no—
372C24#434311yescharacteristic
373#41—222no—
374#41—222no—
375C2×Q8—111no—
376C2×D4—111no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—221no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—222no—
385C22×C4—221no—
386C22×C4C2×C4×D1111yescharacteristic
387C22×C4C2×C4×D1111yescharacteristic
388C22×C4D4×D1111yescharacteristic
389C22×C4D4×D1111yescharacteristic
390C22×C4#434311yescharacteristic
391C22×C4C23×D1111yescharacteristic
392M16—22no—
393M16—22no—
394M16—22no—
395M16—22no—
396M16—42no—
397M16—442no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8—42no—
404C2×C8—111no—
405C2×C8—111no—
406C2×C8—111no—
407C2×C8—111no—
408C2×C8—222no—
409C2×C8—222no—
410C2×C8—442no—
411C2×C8—441no—
412C2×C8—441no—
413C2×C8—441no—
414C2×C8—441no—
415C2×C8C2×C4×D1112yes—
416C2×C8C2×C4×D1112yes—
417C4⋊C4—112no—
418C4⋊C4—112no—
419C4⋊C4—111no—
420C4⋊C4—111no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C22⋊C4—224no—
426C22⋊C4—222no—
427C22⋊C4—221no—
428C22⋊C4—221no—
429C22⋊C4—222no—
430C22⋊C4—221no—
431C22⋊C4—221no—
432C22⋊C4—221no—
433C42—222no—
434C42—221no—
435C42—222no—
436C42—222no—
437C42—222no—
438C11#2209511yescharacteristic, complemented, Sylow
439C23—22no—
440C23—22no—
441C23—41no—
442C23—221no—
443C23#6694611yescharacteristic
444C23#6694611yescharacteristic
445C23C2×#434311yescharacteristic
446Q8—222no—
447D4—222no—
448D4—442no—
449D4—442no—
450D4—442no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—224no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4#6694611yescharacteristic
471C2×C4#6694611yescharacteristic
472C2×C4C22×C4×D1111yescharacteristic
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4#6703712yes—
475C2×C4#6704312yes—
476C8—22no—
477C8—22no—
478C8—42no—
479C8—41no—
480C8—41no—
481C8—221no—
482C8—221no—
483C8—221no—
484C8—221no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—44no—
493C22—441no—
494C22—441no—
495C22—441no—
496C22#1062250812yes—
497C22C2×#6694611yescharacteristic
498C22#1062317612yes—
499C4—21no—
500C4—21no—
501C4—444no—
502C4—442no—
503C4—441no—
504C4—442no—
505C4—441no—
506C4—441no—
507C4#1062307712yes—
508C4#1062312011yescharacteristic
509C4#1062317911yescharacteristic
510C2—22no—
511C2—22no—
512C2—41no—
513C2—881no—
514C2#1307128411yescharacteristic
515C2C2×#1062250811yescharacteristic
516C2#1307751811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1855C2
socleC22×C11C2×C4×D4
prime radical#10623322C22
cosocleC22×C4×C11C24
hypercenter#1855D11
hypocenterC11#22095
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
3. C2×#10622732C2semidirect
4. #13069362C2semidirect
5. #13069318C2semidirect
6. #13069214C2semidirect
8. #13068888C2semidirect
9. #13068713C2semidirect
10. #13068390C2semidirect
11. C11×#1855C2semidirect
34. #10622350C4semidirect
35. #10622349C4semidirect
36. #10622348C4semidirect
41. #10622336C4semidirect
42. #10622335C4semidirect
43. #10622334C4semidirect
189. #1855D11semidirect
438. C11#22095semidirect

Maximal subgroups

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

subgroupindex
#130785312
#130773062
C2×#106227322
#130693622
#130693182
#130692142
#130689182
#130688882
#130687132
#130683902
C11×#18552
#2209511