Finite Group Databasebeta

← #14656747

Subgroups — #14656747

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074733C211yesmaximal, characteristic
2#13068552C211yesmaximal, characteristic
3#13068550C211yesmaximal, characteristic
4#13066886C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic
6#13066458C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C23×Dic22C2211yescharacteristic
9C2×#66931—21no—
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12C2×C11×#95C2211yescharacteristic
13#10622825C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×#66880—21no—
19C2×#66880—21no—
20#10622597—21no—
21#10622592—21no—
22C2×#66874—21no—
23C2×#66874—21no—
24#10622555—21no—
25#10622270—21no—
26#10622269—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—21no—
38C22×Dic22—42no—
39C22×Dic22—42no—
40C22×Dic22Q812yescomplemented
41C22×C8×C11—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C22⋊C4—21no—
45C2×C22⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—21no—
53C22×C11⋊C8—21no—
54#66931—42no—
55#66931—42no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66880—42no—
71#66880—42no—
72#66874—42no—
73#66874—42no—
74#10341—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C22×C4×C11—22no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
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×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×Q811yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—22no—
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—
110C22×Dic11SD1612yes—
111C22×Dic11Q1612yes—
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—41no—
119C2×Dic22—41no—
120C2×Dic22—41no—
121C2×Dic22—41no—
122C2×Dic22—44no—
123C2×Dic22—44no—
124C2×Dic22—44no—
125C2×Dic22—44no—
126C2×Dic22—42no—
127C2×Dic22—41no—
128C2×Dic22—41no—
129C2×Dic22—81no—
130C2×Dic22—81no—
131C2×C8×C11—41no—
132C2×C8×C11—41no—
133C2×C8×C11—41no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C4⋊Dic11—41no—
141C4⋊Dic11—41no—
142C4⋊Dic11—42no—
143Dic11⋊C4—42no—
144Dic11⋊C4—42no—
145Dic11⋊C4—81no—
146Dic11⋊C4—81no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149C2×C11⋊C8—41no—
150#2659—111no—
151#1787—111no—
152#1787—111no—
153#1446—111no—
154#1294—111no—
155#1294D1111yescharacteristic
156#1280—111no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11#12011yescharacteristic
162C23×C11C22⋊Q811yescharacteristic
163C23×C11#12411yescharacteristic
164C23×C11C2×SD1611yescharacteristic
165C23×C11C2×Q1611yescharacteristic
166C23×C11AGL(1,ℤ/8)11yescharacteristic
167C23×C11#13711yescharacteristic
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11C22⋊Q811yescharacteristic
190C2×C4×C11C22⋊Q811yescharacteristic
191C2×C4×C11#12411yescharacteristic
192C2×C4×C11#12411yescharacteristic
193C2×Dic11—24no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—81no—
215C2×Dic11—81no—
216Dic22—24no—
217Dic22—24no—
218Dic22—42no—
219Dic22—42no—
220Dic22—42no—
221Dic22—42no—
222Dic22—42no—
223Dic22—42no—
224Dic22—84no—
225C8×C11—81no—
226C11⋊C8—81no—
227C23×Q8—111no—
228C2×C22⋊Q8—221no—
229C2×#103—221no—
230C2×#103—221no—
231C2×#103—221no—
232C2×#103—221no—
233C2×C22⋊C8—111no—
234C2×C22⋊C8C2×D1111yescharacteristic
235#398—221no—
236#398—221no—
237#395—221no—
238#395—221no—
239#380—111no—
240#380—221no—
241#380C2×D1111yescharacteristic
242C2×#95—111no—
243C2×#95—221no—
244C2×#95—221no—
245C2×#95C2×D1111yescharacteristic
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11#39311yescharacteristic
259C22×C11#45011yescharacteristic
260C22×C11#45111yescharacteristic
261C22×C11#45511yescharacteristic
262C22×C11#45611yescharacteristic
263C22×C11B(4,𝔽2)11yescharacteristic
264C22×C11B(4,𝔽2)11yescharacteristic
265C22×C11#47511yescharacteristic
266C22×C11#47711yescharacteristic
267C22×C11#48711yescharacteristic
268C22×C11#48911yescharacteristic
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—82no—
274C4×C11—81no—
275C4×C11—81no—
276Dic11—42no—
277Dic11—42no—
278Dic11—44no—
279Dic11—81no—
280Dic11—81no—
281C22×Q8—112no—
282C22×Q8—221no—
283C22×Q8—221no—
284C22×Q8—221no—
285C22×Q8—221no—
286C22×Q8—221no—
287C22×Q8—221no—
288C22×Q8—442no—
289C22×Q8—442no—
290C23×C4—21no—
291C23×C4—111no—
292C23×C4—111no—
293C23×C4—221no—
294C23×C4C22×D1111yescharacteristic
295C22×C8—21no—
296C22×C8—221no—
297C22⋊Q8—442no—
298C22⋊Q8—442no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4D4411yescharacteristic
307C2×C4⋊C4D4411yescharacteristic
308C2×C22⋊C4—21no—
309C2×C22⋊C4—221no—
310#103—442no—
311#103—442no—
312#103—442no—
313#103—442no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—221no—
317C22⋊C8—221no—
318#95—21no—
319#95—21no—
320#95—21no—
321#95—221no—
322#95—221no—
323#95—221no—
324#95—221no—
325#95—221no—
326#95—442no—
327#95—442no—
328C2×C11—21no—
329C2×C11—21no—
330C2×C11—21no—
331C2×C11—21no—
332C2×C11#160111yescharacteristic
333C2×C11#160211yescharacteristic
334C2×C11#160411yescharacteristic
335C2×C11#160511yescharacteristic
336C2×C11#202411yescharacteristic
337C2×C11#202811yescharacteristic
338C2×C11#202911yescharacteristic
339C24D4×D1111yescharacteristic
340C2×Q8—222no—
341C2×Q8—222no—
342C2×Q8—222no—
343C2×Q8—222no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8—441no—
347C2×Q8—441no—
348C2×Q8—441no—
349C2×Q8—441no—
350C2×Q8—444no—
351C2×Q8—444no—
352C2×Q8—442no—
353C2×Q8—444no—
354C2×Q8—444no—
355C2×Q8—441no—
356C2×Q8—441no—
357C2×Q8—881no—
358C2×Q8—881no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—112no—
371C22×C4—112no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—222no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—441no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4C2×D4411yescharacteristic
390C22×C4#433911yescharacteristic
391C22×C4#433911yescharacteristic
392C22×C4D4×D1111yescharacteristic
393C22×C4#434111yescharacteristic
394C22×C4Q8×D1111yescharacteristic
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—41no—
398C2×C8—441no—
399C2×C8—441no—
400C2×C8—441no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—441no—
404C4⋊C4—441no—
405C4⋊C4—442no—
406C4⋊C4—442no—
407C4⋊C4—442no—
408C4⋊C4—881no—
409C4⋊C4—881no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C11#1034111yescharacteristic, complemented, Sylow
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23#6693511yescharacteristic
420C23#6693811yescharacteristic
421C23#6694911yescharacteristic
422C23#6696411yescharacteristic
423C23SD16×D1111yescharacteristic
424C23#6696811yescharacteristic
425C23Q16×D1111yescharacteristic
426Q8—224no—
427Q8—224no—
428Q8—442no—
429Q8—442no—
430Q8—442no—
431Q8—442no—
432Q8—442no—
433Q8—442no—
434Q8—884no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—224no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—441no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—881no—
478C2×C4—881no—
479C2×C4#6692811yescharacteristic
480C2×C4#6693811yescharacteristic
481C2×C4#6694911yescharacteristic
482C2×C4#6695011yescharacteristic
483C8—81no—
484C8—881no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22#1062228611yescharacteristic
498C22#1062235411yescharacteristic
499C22#1062235411yescharacteristic
500C22#1062237811yescharacteristic
501C22#1062238911yescharacteristic
502C22#1062240511yescharacteristic
503C22#1062242111yescharacteristic
504C22#1062243811yescharacteristic
505C22#1062243911yescharacteristic
506C22#1062246711yescharacteristic
507C22#1062248811yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—82no—
513C4—81no—
514C4—81no—
515C4—442no—
516C4—442no—
517C4—444no—
518C4—881no—
519C4—881no—
520C2—21no—
521C2—21no—
522C2—21no—
523C2—21no—
524C2#1306756911yescharacteristic
525C2#1306757411yescharacteristic
526C2#1306758611yescharacteristic
527C2#1306759111yescharacteristic
528C2#1306975611yescharacteristic
529C2#1306977611yescharacteristic
530C2#1306978111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1294D11
hypocenterC11#10341
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
40. C22×Dic22Q8semidirect
414. C11#10341semidirect

Maximal subgroups

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

subgroupindex
#130747332
#130685522
#130685502
#130668862
#130664952
#130664582
C11×#12942
#1034111