Finite Group Databasebeta

← #14764015

Subgroups — #14764015

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622739C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic
3#13070997C211yesmaximal, characteristic
4#13068801C211yesmaximal, characteristic, complemented
5#13068800C212yesmaximal, complemented
6#13068799C211yesmaximal, characteristic, complemented
7#13068798C211yesmaximal, characteristic, complemented
8#13068797C212yesmaximal, complemented
9#13068599C212yesmaximal, complemented
10#13068597C212yesmaximal, complemented
11C11×#1851C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4313C2211yescharacteristic
16C22×#4313C2211yescharacteristic
17C2×#66925C2212yes—
18C2×C11×C4⋊C8C2212yescomplemented
19C2×C11×C22⋊C8C2211yescharacteristic
20C4×C11×C22⋊C4C2211yescharacteristic
21C4×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23#10622739—24no—
24C2×(C2×D11)⋊C8C2212yes—
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2212yes—
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2212yescomplemented
29C2×Dic11⋊C8C2212yescomplemented
30#10622568C412yes—
31#10622555C412yes—
32C4×(C2×D11)⋊C4C2212yes—
33C2×C4⋊(C11⋊C8)C2212yescomplemented
34#10622339—24no—
35#10622280C411yescharacteristic
36#10622280C411yescharacteristic
37#10622277C411yescharacteristic
38#10622277C411yescharacteristic
39C11×#336C2212yescomplemented
40#10622188C2212yescomplemented
41#10622188C2212yescomplemented
42#10622162C2212yescomplemented
43C24×D11C2×C411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2×C411yescharacteristic
46C22×C4×D11—42no—
47C22×C4×D11—42no—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11D414yes—
51C22×C4×D11Q814yes—
52C22×C4×D11C2311yescharacteristic
53C22×C4×D11C2311yescharacteristic
54C2×C11×M16—22no—
55C2×C11×M16—42no—
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C2×C11×C22⋊C4C2×C412yes—
60C2×C42×C11C2312yes—
61C2×C22⋊Dic11C2×C412yes—
62C2×(C2×D11)⋊C4C2×C412yes—
63C2×(C2×D11)⋊C4C2×C412yes—
64C2×(C2×D11)⋊C4C2×C412yes—
65C2×(C2×D11)⋊C4C2×C412yes—
66C2×Dic11⋊C4C2×C412yes—
67C2×Dic11⋊C4C2×C412yes—
68C2×C4×Dic11C2312yes—
69C2×#4318—22no—
70C2×#4318—42no—
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C2×#4313—22no—
75C2×#4313—22no—
76C2×#4313—42no—
77C2×#4313—42no—
78#66925—42no—
79#66925—42no—
80C11×C4⋊C8—42no—
81C11×C22⋊C8—22no—
82C11×#95C2×C411yescharacteristic
83C11×#95C2×C411yescharacteristic
84C11⋊#95C2×C411yescharacteristic
85C11⋊#95C2×C411yescharacteristic
86C11⋊#95C2×C412yes—
87C11⋊#95C2×C412yes—
88C22⋊(C11⋊C8)—22no—
89(C2×D11)⋊C8—24no—
90(C2×D11)⋊C8—24no—
91(C2×D11)⋊C8—22no—
92(C2×D11)⋊C8—22no—
93Dic11⋊C8—42no—
94Dic11⋊C8—42no—
95C4⋊(C11⋊C8)—42no—
96#21935—111nomaximal, Sylow
97C24×C11C22×C411yescharacteristic
98C23×D11—42no—
99C23×D11—41no—
100C23×D11—41no—
101C23×D11—42no—
102C23×D11C4⋊C414yes—
103C23×D11C22×C411yescharacteristic
104C23×D11C22×C411yescharacteristic
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×Q812yes—
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—42no—
114C22×Dic11C4⋊C414yes—
115C22×Dic11C22×C412yes—
116C22×Dic11C22×C412yes—
117C22×Dic11C22×C411yescharacteristic
118C22×Dic11C22×C411yescharacteristic
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×C4×D11—44no—
126C2×C4×D11—44no—
127C2×C4×D11—48no—
128C2×C4×D11C4⋊C414yes—
129C2×C4×D11C4⋊C414yes—
130C2×C4×D11C2×D412yes—
131C2×C4×D11C2×D412yes—
132C2×C4×D11C2×Q812yes—
133C2×C4×D11C2×Q812yes—
134C11×M16—44no—
135C2×C8×C11—22no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C11×C22⋊C4—42no—
143C42×C11—22no—
144C42×C11—22no—
145C22⋊Dic11—42no—
146(C2×D11)⋊C4—42no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—42no—
149(C2×D11)⋊C4—42no—
150Dic11⋊C4—42no—
151Dic11⋊C4—42no—
152C4×Dic11—22no—
153C4×Dic11—22no—
154#4318—44no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162#4313—44no—
163#4313—44no—
164C2×#407—111no—
165C2×#407—111no—
166#2280—111no—
167#1851—112no—
168#1851—111no—
169#1851—111no—
170#1851—112no—
171#1851—111no—
172#1851D1111yescharacteristic, complemented
173#1798—112no—
174#1798—112no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11C2×C4⋊C412yes—
180C23×C11C23×C411yescharacteristic
181C22×D11—22no—
182C22×D11—22no—
183C22×D11—21no—
184C22×D11—21no—
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—21no—
188C22×D11—21no—
189C22×D11—44no—
190C22×D11—44no—
191C22×D11—44no—
192C22×D11—48no—
193C22×D11—48no—
194C22×D11C2×C4⋊C412yes—
195C22×D11C2×C4⋊C412yes—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11C2×C4⋊C412yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×Q811yescharacteristic
209C2×C4×C11H(5,𝔽2)12yes—
210C2×C4×C11H(5,𝔽2)12yes—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—44no—
220C2×Dic11C2×C4⋊C412yes—
221C2×Dic11C2×C4⋊C412yes—
222C4×D11—22no—
223C4×D11—22no—
224C4×D11—22no—
225C4×D11—22no—
226C4×D11—24no—
227C4×D11—24no—
228C4×D11—44no—
229C4×D11—44no—
230C8×C11—41no—
231C8×C11—41no—
232C8×C11—42no—
233C11⋊C8—41no—
234C11⋊C8—41no—
235C11⋊C8—42no—
236C24×C4—111no—
237C22×M16—111no—
238C22×M16—111no—
239C22×M16—111no—
240C22×M16C2×D1111yescharacteristic
241C2×#117—112no—
242C2×C4⋊C8—112no—
243C2×C4⋊C8—112no—
244C2×C4⋊C8—112no—
245C2×C4⋊C8C2×D1112yescomplemented
246#407—224no—
247#407—224no—
248C2×C22⋊C8—111no—
249C2×C22⋊C8—111no—
250C2×C22⋊C8—111no—
251C2×C22⋊C8—112no—
252C2×C22⋊C8—112no—
253C2×C22⋊C8C2×D1111yescharacteristic
254#381—111no—
255#381—111no—
256#380—112no—
257#380—111no—
258#380—111no—
259#379—112no—
260C4×C22⋊C4—111no—
261C4×C22⋊C4—112no—
262C4×C22⋊C4C2×D1111yescharacteristic
263#336—112no—
264#336—112no—
265#336—112no—
266#336C2×D1112yescomplemented
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11C22×C4⋊C411yescharacteristic
273C22×C11#51812yes—
274C22×C11#56812yes—
275C22×C11#56811yescharacteristic
276C22×C11#56811yescharacteristic
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—22no—
283C2×D11—416no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—42no—
287C2×D11—42no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11#53411yescharacteristic
292C4×C11#53411yescharacteristic
293C4×C11#54312yes—
294Dic11—22no—
295Dic11—22no—
296Dic11—42no—
297Dic11—42no—
298C25—111no—
299C23×C4—111no—
300C23×C4—111no—
301C23×C4—111no—
302C23×C4—111no—
303C23×C4—111no—
304C23×C4—114no—
305C23×C4—114no—
306C23×C4—442no—
307C23×C4—442no—
308C23×C4C22×D1111yescharacteristic
309C2×M16—22no—
310C2×M16—42no—
311C2×M16—222no—
312C2×M16—222no—
313C2×M16—222no—
314C2×M16—442no—
315C2×M16—442no—
316C2×M16—442no—
317C22×C8—111no—
318C22×C8—112no—
319C22×C8—111no—
320C22×C8C22×D1111yescharacteristic
321C22×C8C22×D1111yescharacteristic
322C22×C8C22×D1112yes—
323#117—442no—
324#117—442no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—112no—
327C2×C22⋊C4—112no—
328C2×C22⋊C4—112no—
329C2×C22⋊C4—112no—
330C2×C22⋊C4—112no—
331C2×C22⋊C4—112no—
332C2×C22⋊C4C4×D1112yes—
333C2×C42—112no—
334C2×C42C22×D1112yes—
335C4⋊C8—42no—
336C4⋊C8—442no—
337C4⋊C8—442no—
338C4⋊C8—442no—
339C22⋊C8—22no—
340C22⋊C8—222no—
341C22⋊C8—222no—
342C22⋊C8—224no—
343C22⋊C8—224no—
344C22⋊C8—222no—
345#95—112no—
346#95—112no—
347#95—111no—
348#95—111no—
349#95C4×D1111yescharacteristic
350#95C4×D1111yescharacteristic
351C2×C11—42no—
352C2×C11#231511yescharacteristic
353C2×C11#290511yescharacteristic
354C2×C11#290511yescharacteristic
355C2×C11#297812yes—
356C2×C11#297812yes—
357D11—42no—
358D11—42no—
359C24—111no—
360C24—111no—
361C24—114no—
362C24—442no—
363C24—442no—
364C24—441no—
365C24—441no—
366C24C2×C4×D1111yescharacteristic
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—114no—
372C22×C4—112no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—114no—
377C22×C4—114no—
378C22×C4—112no—
379C22×C4—112no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—444no—
385C22×C4—448no—
386C22×C4—444no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4C2×C4×D1112yes—
391C22×C4C2×C4×D1112yes—
392C22×C4C2×C4×D1111yescharacteristic
393C22×C4D4×D1112yes—
394C22×C4Q8×D1112yes—
395C22×C4C23×D1111yescharacteristic
396M16—44no—
397M16—444no—
398M16—444no—
399M16—444no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—221no—
408C2×C8—222no—
409C2×C8—221no—
410C2×C8—222no—
411C2×C8—222no—
412C2×C8—222no—
413C2×C8—222no—
414C4⋊C4—442no—
415C4⋊C4—442no—
416C22⋊C4—42no—
417C22⋊C4—442no—
418C22⋊C4—442no—
419C22⋊C4—442no—
420C22⋊C4—442no—
421C22⋊C4—442no—
422C42—22no—
423C42—22no—
424C42—222no—
425C42—222no—
426C11#2193511yescharacteristic, complemented, Sylow
427C23—22no—
428C23—21no—
429C23—21no—
430C23—22no—
431C23—112no—
432C23—112no—
433C23—222no—
434C23—222no—
435C23—221no—
436C23—221no—
437C23—221no—
438C23—221no—
439C23—222no—
440C23—222no—
441C23—444no—
442C23—444no—
443C23—444no—
444C23—448no—
445C23—448no—
446C23C4⋊C4×D1112yes—
447C23C22×C4×D1111yescharacteristic
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—112no—
459C2×C4—112no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—444no—
475C2×C4—444no—
476C2×C4—444no—
477C2×C4C4⋊C4×D1112yes—
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4#6703712yes—
480C2×C4C2×Q8×D1111yescharacteristic
481C2×C4#6704212yes—
482C8—42no—
483C8—41no—
484C8—41no—
485C8—441no—
486C8—441no—
487C8—442no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—42no—
492C22—42no—
493C22—222no—
494C22—222no—
495C22—222no—
496C22—222no—
497C22—222no—
498C22—222no—
499C22—4416no—
500C22—442no—
501C22—442no—
502C22—442no—
503C22—442no—
504C22C2×C4⋊C4×D1111yescharacteristic
505C22#1062307612yes—
506C22#1062327612yes—
507C22#1062328111yescharacteristic
508C22#1062328111yescharacteristic
509C4—22no—
510C4—42no—
511C4—42no—
512C4—222no—
513C4—222no—
514C4—442no—
515C4—442no—
516C4#1062312011yescharacteristic
517C4#1062316512yes—
518C4#1062318411yescharacteristic
519C2—42no—
520C2—442no—
521C2—442no—
522C2#1307122711yescharacteristic
523C2#1307717711yescharacteristic
524C2#1307717811yescharacteristic
525C2#1307767312yes—
526C2#1307767512yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1851C2
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1851D11
hypocenterC11#21935
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
4. #13068801C2semidirect
5. #13068800C2semidirect
6. #13068799C2semidirect
7. #13068798C2semidirect
8. #13068797C2semidirect
9. #13068599C2semidirect
10. #13068597C2semidirect
11. C11×#1851C2semidirect
18. C2×C11×C4⋊C8C22semidirect
28. C2×Dic11⋊C8C22semidirect
29. C2×Dic11⋊C8C22semidirect
33. C2×C4⋊(C11⋊C8)C22semidirect
39. C11×#336C22semidirect
40. #10622188C22semidirect
41. #10622188C22semidirect
42. #10622162C22semidirect
172. #1851D11semidirect
245. C2×C4⋊C8C2×D11semidirect
266. #336C2×D11semidirect
426. C11#21935semidirect

Maximal subgroups

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

subgroupindex
C2×#106227392
C2×#106223392
#130709972
#130688012
#130688002
#130687992
#130687982
#130687972
#130685992
#130685972
C11×#18512
#2193511