Finite Group Databasebeta

← #14764284

Subgroups — #14764284

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622331C211yesmaximal, characteristic
2#13071018C211yesmaximal, characteristic
3C2×#10622589C211yesmaximal, characteristic
4#13069378C212yesmaximal, complemented
5#13069376C212yesmaximal, complemented
6#13068811C211yesmaximal, characteristic
7#13068809C211yesmaximal, characteristic
8#13068808C211yesmaximal, characteristic
9#13068771C212yesmaximal, complemented
10#13068742C212yesmaximal, complemented
11C11×#1853C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4—21no—
15C22×Dic11⋊C4—21no—
16C22×C4×Dic11C2211yescharacteristic
17C2×#66930—21no—
18C2×C11×#106C2212yes—
19C2×C11×C22⋊C8C2211yescharacteristic
20C11×#380C2211yescharacteristic
21#10622825C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×#66881C2212yes—
24C2×Dic11⋊C8C2212yes—
25C2×C8×Dic11C2212yes—
26#10622589—21no—
27#10622589—21no—
28#10622589C2212yes—
29#10622589C2212yes—
30#10622589C2211yescharacteristic
31#10622589C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C2×#66872C2212yes—
35C2×#66872C2212yes—
36#10622555—21no—
37#10622331C418yescomplemented
38#10622263—21no—
39#10622262—21no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11D411yescharacteristic
48C23×Dic11D411yescharacteristic
49C22×C8×C11C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—42no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C22⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—42no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×Dic11⋊C4—21no—
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—44no—
71C2×Dic11⋊C4—44no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11C2×C414yes—
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11Q814yes—
78C2×C4×Dic11C2311yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C22×C11⋊C8C2312yes—
81#66930—44no—
82C11×#106—42no—
83C11×C22⋊C8C2×C414yes—
84C11×#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88C22⋊(C11⋊C8)C2×C414yes—
89#66881—42no—
90Dic11⋊C8C2×C418yescomplemented
91C8×Dic11C2×C418yescomplemented
92#66872—42no—
93#66872—42no—
94#21981—111nomaximal, Sylow
95C24×C11C2×D411yescharacteristic
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×Q812yes—
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—42no—
114C22×Dic11—42no—
115C22×Dic11—42no—
116C22×Dic11C4⋊C414yes—
117C22×Dic11C4⋊C414yes—
118C22×Dic11SD1614yes—
119C22×Dic11SD1614yes—
120C22×Dic11C2×D411yescharacteristic
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123C22×Dic11C2×D411yescharacteristic
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11C22×C414yes—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—42no—
132C11×C22⋊C4—42no—
133C22⋊Dic11—42no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—42no—
139Dic11⋊C4—44no—
140Dic11⋊C4—42no—
141Dic11⋊C4—42no—
142Dic11⋊C4—44no—
143Dic11⋊C4—44no—
144Dic11⋊C4—42no—
145Dic11⋊C4—44no—
146Dic11⋊C4—42no—
147C4×Dic11—42no—
148C4×Dic11—42no—
149C4×Dic11C4⋊C414yes—
150C4×Dic11C4⋊C414yes—
151C4×Dic11C22×C412yes—
152C4×Dic11C22×C412yes—
153C4×Dic11C2×Q812yes—
154C4×Dic11C2×Q812yes—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8C22×C414yes—
158C2×#431—111no—
159#2285—111no—
160C2×#384—111no—
161#1948—112no—
162#1948—112no—
163#1853—111no—
164#1853—111no—
165#1853—111no—
166#1853D1111yescharacteristic
167#1844—112no—
168#1834—112no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11C2×C4⋊C412yes—
174C23×C11C2×SD1612yes—
175C23×C11C2×SD1612yes—
176C23×C11C22×D411yescharacteristic
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—84no—
191C2×C4×C11C2×C4⋊C412yes—
192C2×C4×C11C23×C411yescharacteristic
193C2×C4×C11C22×Q811yescharacteristic
194C2×C4×C11H(5,𝔽2)12yes—
195C2×C4×C112−1+412yes—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—28no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—84no—
209C2×Dic11#106116yescomplemented
210C2×Dic11C2×C4⋊C412yes—
211C2×Dic11C2×C4⋊C412yes—
212C2×Dic11C2×C4⋊C412yes—
213C2×Dic11C2×C4⋊C412yes—
214C2×Dic11C2×SD1612yes—
215C2×Dic11C2×SD1612yes—
216C2×Dic11C2×SD1612yes—
217C2×Dic11C2×SD1612yes—
218C2×Dic11AGL(1,ℤ/8)12yes—
219C2×Dic11#13712yes—
220C8×C11—24no—
221C11⋊C8—24no—
222C2×#117—221no—
223C22×C4⋊C4—111no—
224C22×C4⋊C4—221no—
225C22×C4⋊C4—221no—
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C42—111no—
228#431—118no—
229C2×#106—112no—
230C2×#106—112no—
231C2×#106—112no—
232C2×#106C2×D1112yes—
233C2×C4⋊C8—112no—
234C2×C22⋊C8—111no—
235C2×C22⋊C8C2×D1111yescharacteristic
236C2×C4×C8—112no—
237#384—111no—
238#384—112no—
239#384—111no—
240#384—112no—
241#384—221no—
242#384—221no—
243#382—221no—
244#380—111no—
245#380—221no—
246#380C2×D1111yescharacteristic
247C4×C4⋊C4—111no—
248C4×C4⋊C4—111no—
249C4×C4⋊C4—221no—
250#340—112no—
251#340—112no—
252#340—112no—
253#340C2×D1112yes—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11C2×#10614yes—
261C22×C11C22×C4⋊C411yescharacteristic
262C22×C11#53511yescharacteristic
263C22×C11#53611yescharacteristic
264C22×C11C22×SD1611yescharacteristic
265C22×C11C22×SD1611yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C4×C11—22no—
269C4×C11—81no—
270C4×C11—82no—
271C4×C11—81no—
272C4×C11#52012yes—
273C4×C11#54412yes—
274Dic11—22no—
275Dic11—81no—
276Dic11—82no—
277Dic11—81no—
278Dic11C2×#10614yes—
279Dic11C2×#10614yes—
280Dic11#42814yes—
281C23×C4—21no—
282C23×C4—111no—
283C23×C4—111no—
284C23×C4—221no—
285C23×C4C22×D1111yescharacteristic
286C22×C8—112no—
287C22×C8C22×D1112yes—
288#117—444no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—442no—
304C2×C4⋊C4—444no—
305C2×C4⋊C4—444no—
306C2×C4⋊C4C22×D1112yes—
307C2×C4⋊C4C22×D1111yescharacteristic
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—221no—
311C2×C42—114no—
312C2×C42—111no—
313C2×C42—111no—
314C2×C42—114no—
315C2×C42—111no—
316C2×C42—111no—
317C2×C42—221no—
318C2×C42—221no—
319#106—42no—
320#106—442no—
321#106—442no—
322#106—442no—
323C4⋊C8—118no—
324C22⋊C8—114no—
325C22⋊C8C4×D1114yes—
326C4×C8—118no—
327#95—21no—
328#95—221no—
329#95—221no—
330#95—221no—
331C2×C11—24no—
332C2×C11#231711yescharacteristic
333C2×C11C22×#10611yescharacteristic
334C2×C11C2×#42811yescharacteristic
335C2×C11#320611yescharacteristic
336C2×C11#320811yescharacteristic
337C2×C11#322711yescharacteristic
338C2×C11#322911yescharacteristic
339C24D4×D1111yescharacteristic
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—114no—
349C22×C4—114no—
350C22×C4—114no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—111no—
354C22×C4—114no—
355C22×C4—111no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—222no—
361C22×C4—442no—
362C22×C4—442no—
363C22×C4—442no—
364C22×C4C2×C4×D1112yes—
365C22×C4D4×D1111yescharacteristic
366C22×C4Q8×D1112yes—
367C22×C4C23×D1111yescharacteristic
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—114no—
371C2×C8—222no—
372C2×C8—222no—
373C2×C8C2×C4×D1114yes—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—42no—
379C4⋊C4—222no—
380C4⋊C4—222no—
381C4⋊C4—222no—
382C4⋊C4—222no—
383C4⋊C4—442no—
384C4⋊C4—444no—
385C4⋊C4—444no—
386C4⋊C4—444no—
387C4⋊C4—442no—
388C4⋊C4—442no—
389C4⋊C4—442no—
390C4⋊C4—442no—
391C4⋊C4—444no—
392C22⋊C4—42no—
393C22⋊C4—442no—
394C42—114no—
395C42—114no—
396C42—112no—
397C42—112no—
398C42—112no—
399C42—112no—
400C42—442no—
401C42—442no—
402C11#2198111yescharacteristic, complemented, Sylow
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23C4⋊C4×D1112yes—
408C23SD16×D1112yes—
409C23SD16×D1112yes—
410C23C2×D4×D1111yescharacteristic
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—84no—
425C2×C4—1116no—
426C2×C4—112no—
427C2×C4—112no—
428C2×C4—112no—
429C2×C4—112no—
430C2×C4—112no—
431C2×C4—112no—
432C2×C4—112no—
433C2×C4—112no—
434C2×C4—112no—
435C2×C4—112no—
436C2×C4—228no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—442no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—884no—
449C2×C4C4⋊C4×D1112yes—
450C2×C4C22×C4×D1111yescharacteristic
451C2×C4#6703712yes—
452C2×C4C2×Q8×D1111yescharacteristic
453C2×C4#6704312yes—
454C8—24no—
455C8—224no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22D11×#10614yes—
463C22C2×C4⋊C4×D1111yescharacteristic
464C22#1062312311yescharacteristic
465C22#1062317911yescharacteristic
466C22C2×SD16×D1111yescharacteristic
467C22C2×SD16×D1111yescharacteristic
468C22D11×AGL(1,ℤ/8)11yescharacteristic
469C22D11×#13711yescharacteristic
470C4—22no—
471C4—82no—
472C4—81no—
473C4—81no—
474C4—114no—
475C4—114no—
476C4—114no—
477C4—222no—
478C4—882no—
479C4—881no—
480C4—881no—
481C4#1062307712yes—
482C4#1062315412yes—
483C2—24no—
484C2#1307123511yescharacteristic
485C2C2×D11×#10611yescharacteristic
486C2D11×#42811yescharacteristic
487C2#1307953911yescharacteristic
488C2#1307955511yescharacteristic
489C2#1307974211yescharacteristic
490C2#1307975811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1853C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1853D11
hypocenterC11#21981
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
4. #13069378C2semidirect
5. #13069376C2semidirect
9. #13068771C2semidirect
10. #13068742C2semidirect
37. #10622331C4semidirect
90. Dic11⋊C8C2×C4semidirect
91. C8×Dic11C2×C4semidirect
209. C2×Dic11#106semidirect
402. C11#21981semidirect

Maximal subgroups

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

subgroupindex
C2×#106223312
#130710182
C2×#106225892
#130693782
#130693762
#130688112
#130688092
#130688082
#130687712
#130687422
C11×#18532
#2198111