Finite Group Databasebeta

← #14656767

Subgroups — #14656767

Order 2816.

640 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#13074589C211yesmaximal, characteristic
2#13068552C211yesmaximal, characteristic
3#13068550C211yesmaximal, characteristic
4#13066886C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic
6#13066458C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C23×Dic22C2211yescharacteristic
9C2×C11×C22⋊C8C2211yescharacteristic
10C11×#380C2211yescharacteristic
11C2×C11×#95C2211yescharacteristic
12#10622825C2211yescharacteristic
13C2×C11⋊#95—21no—
14C2×C11⋊#95—21no—
15C2×C11⋊#95C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66880—21no—
18C2×#66880—21no—
19#10622599—21no—
20#10622597—21no—
21C2×#66874—21no—
22C2×#66874—21no—
23#10622563—21no—
24#10622559—21no—
25#10622274—21no—
26#10622273—21no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×Dic22—21no—
33C22×Dic22—21no—
34C22×Dic22—21no—
35C22×Dic22—21no—
36C22×Dic22—21no—
37C22×Dic22—42no—
38C22×Dic22—42no—
39C22×Dic22Q812yes—
40C22×C8×C11—21no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C22⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C22×C11⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—42no—
65C11⋊#95—42no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#66880—42no—
69#66880—42no—
70#66874—42no—
71#66874—42no—
72#10345—111nomaximal, Sylow
73C24×C11C2×D411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×Q811yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—22no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C22×Dic11—41no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11—41no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—41no—
117C2×Dic22—41no—
118C2×Dic22—41no—
119C2×Dic22—41no—
120C2×Dic22—44no—
121C2×Dic22—44no—
122C2×Dic22—44no—
123C2×Dic22—44no—
124C2×Dic22—41no—
125C2×Dic22—41no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C2×C8×C11—41no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C22⋊Dic11—41no—
134C22⋊Dic11—41no—
135C4⋊Dic11—41no—
136C4⋊Dic11—41no—
137C4⋊Dic11—81no—
138C4⋊Dic11—81no—
139Dic11⋊C4—81no—
140Dic11⋊C4—81no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144#2646—111no—
145#1787—111no—
146#1787—111no—
147#1446—111no—
148#1294—111no—
149#1294D1111yescharacteristic
150#1280—111no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11#12011yescharacteristic
156C23×C11C22⋊Q811yescharacteristic
157C23×C11#12411yescharacteristic
158C23×C11#13511yescharacteristic
159C23×C11#13511yescharacteristic
160C23×C11#13711yescharacteristic
161C23×C11#13711yescharacteristic
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11C22⋊Q811yescharacteristic
184C2×C4×C11C22⋊Q811yescharacteristic
185C2×C4×C11#12411yescharacteristic
186C2×C4×C11#12411yescharacteristic
187C2×Dic11—24no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—81no—
209C2×Dic11—81no—
210Dic22—24no—
211Dic22—24no—
212Dic22—42no—
213Dic22—42no—
214Dic22—42no—
215Dic22—42no—
216Dic22—42no—
217Dic22—42no—
218C8×C11—81no—
219C11⋊C8—81no—
220C23×Q8—111no—
221C2×#103—221no—
222C2×#103—221no—
223C2×#103—221no—
224C2×#103—221no—
225C2×C22⋊C8—111no—
226C2×C22⋊C8C2×D1111yescharacteristic
227#400—221no—
228#400—221no—
229#398—221no—
230#398—221no—
231#385—221no—
232#385—221no—
233#380—111no—
234#380C2×D1111yescharacteristic
235C2×#95—111no—
236C2×#95—221no—
237C2×#95—221no—
238C2×#95C2×D1111yescharacteristic
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11#39311yescharacteristic
252C22×C11#45211yescharacteristic
253C22×C11#45211yescharacteristic
254C22×C11#45511yescharacteristic
255C22×C11#45611yescharacteristic
256C22×C11B(4,𝔽2)11yescharacteristic
257C22×C11B(4,𝔽2)11yescharacteristic
258C22×C11#47911yescharacteristic
259C22×C11#47911yescharacteristic
260C22×C11#48811yescharacteristic
261C22×C11#49111yescharacteristic
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—82no—
267C4×C11—81no—
268C4×C11—81no—
269Dic11—44no—
270Dic11—81no—
271Dic11—81no—
272Dic11—81no—
273Dic11—81no—
274C22×Q8—112no—
275C22×Q8—221no—
276C22×Q8—221no—
277C22×Q8—221no—
278C22×Q8—221no—
279C22×Q8—221no—
280C22×Q8—442no—
281C22×Q8—442no—
282C23×C4—21no—
283C23×C4—111no—
284C23×C4—111no—
285C23×C4—221no—
286C23×C4C22×D1111yescharacteristic
287C22×C8—21no—
288C22×C8—221no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4D4411yescharacteristic
296C2×C4⋊C4D4411yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—221no—
299#103—442no—
300#103—442no—
301#103—442no—
302#103—442no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—221no—
306C22⋊C8—221no—
307#95—21no—
308#95—21no—
309#95—21no—
310#95—221no—
311#95—221no—
312#95—221no—
313#95—221no—
314#95—221no—
315#95—221no—
316#95—221no—
317#95—442no—
318#95—442no—
319C2×C11—21no—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11#160311yescharacteristic
324C2×C11#160311yescharacteristic
325C2×C11#160611yescharacteristic
326C2×C11#160611yescharacteristic
327C2×C11#202611yescharacteristic
328C2×C11#202811yescharacteristic
329C2×C11#202911yescharacteristic
330C24D4×D1111yescharacteristic
331C2×Q8—222no—
332C2×Q8—222no—
333C2×Q8—222no—
334C2×Q8—222no—
335C2×Q8—222no—
336C2×Q8—222no—
337C2×Q8—441no—
338C2×Q8—441no—
339C2×Q8—441no—
340C2×Q8—441no—
341C2×Q8—444no—
342C2×Q8—444no—
343C2×Q8—444no—
344C2×Q8—444no—
345C2×Q8—441no—
346C2×Q8—441no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4—441no—
376C22×C4—441no—
377C22×C4C2×D4411yescharacteristic
378C22×C4#433911yescharacteristic
379C22×C4#433911yescharacteristic
380C22×C4D4×D1111yescharacteristic
381C22×C4#434111yescharacteristic
382C22×C4Q8×D1111yescharacteristic
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—441no—
387C2×C8—441no—
388C2×C8—441no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—881no—
394C4⋊C4—881no—
395C4⋊C4—881no—
396C4⋊C4—881no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C11#1034511yescharacteristic, complemented, Sylow
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23#6693511yescharacteristic
407C23#6693811yescharacteristic
408C23#6694911yescharacteristic
409C23#6696511yescharacteristic
410C23#6696811yescharacteristic
411C23#6696911yescharacteristic
412C23#6697111yescharacteristic
413Q8—224no—
414Q8—224no—
415Q8—442no—
416Q8—442no—
417Q8—442no—
418Q8—442no—
419Q8—442no—
420Q8—442no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—224no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—881no—
464C2×C4—881no—
465C2×C4#6692811yescharacteristic
466C2×C4#6693811yescharacteristic
467C2×C4#6694911yescharacteristic
468C2×C4#6695011yescharacteristic
469C8—81no—
470C8—881no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22#1062228611yescharacteristic
484C22#1062235411yescharacteristic
485C22#1062235411yescharacteristic
486C22#1062238111yescharacteristic
487C22#1062239611yescharacteristic
488C22#1062241011yescharacteristic
489C22#1062242311yescharacteristic
490C22#1062243811yescharacteristic
491C22#1062243911yescharacteristic
492C22#1062247011yescharacteristic
493C22#1062249011yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—82no—
499C4—81no—
500C4—81no—
501C4—444no—
502C4—881no—
503C4—881no—
504C4—881no—
505C4—881no—
506C2—21no—
507C2—21no—
508C2—21no—
509C2—21no—
510C2#1306758011yescharacteristic
511C2#1306758211yescharacteristic
512C2#1306759711yescharacteristic
513C2#1306759911yescharacteristic
514C2#1306976611yescharacteristic
515C2#1306977611yescharacteristic
516C2#1306978111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1294D11
hypocenterC11#10345
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
401. C11#10345semidirect

Maximal subgroups

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

subgroupindex
#130745892
#130685522
#130685502
#130668862
#130664952
#130664582
C11×#12942
#1034511