Finite Group Databasebeta

← #14656746

Subgroups — #14656746

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#13068551C211yesmaximal, characteristic
3#13066887C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic
5#13066494C211yesmaximal, characteristic
6#13066458C211yesmaximal, characteristic
7C11×#1787C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C2×#66931—21no—
10C2×C11×#103—21no—
11C2×C11×#103—21no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C2×#66899—21no—
15C2×#66899—21no—
16#10622825C2211yescharacteristic
17C2×C11⋊#95—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2211yescharacteristic
20C2×C11⋊#95C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22#10622597—21no—
23#10622592—21no—
24#10622555—21no—
25#10622270—21no—
26#10622269—21no—
27C22×Q8×C11—21no—
28C22×Q8×C11—21no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11—21no—
32C22×Q8×C11—42no—
33C22×Q8×C11—42no—
34C22×Q8×C11Q812yescomplemented
35C23×C4×C11—21no—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11—21no—
38C23×Dic11D411yescharacteristic
39C23×Dic11D411yescharacteristic
40C22×Dic22—21no—
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×#103—42no—
57C11×#103—42no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61#66899—42no—
62#66899—42no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#10341—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—22no—
79C2×Q8×C11—22no—
80C2×Q8×C11—22no—
81C2×Q8×C11—22no—
82C2×Q8×C11—44no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—44no—
88C2×Q8×C11—44no—
89C2×Q8×C11—44no—
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×Q811yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×Dic11—22no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C22×Dic11SD1612yes—
127C22×Dic11Q1612yes—
128C2×Dic22—42no—
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#1787D1111yescharacteristic
153#1446—111no—
154#1294—111no—
155#1294—111no—
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
168Q8×C11—24no—
169Q8×C11—24no—
170Q8×C11—42no—
171Q8×C11—42no—
172Q8×C11—42no—
173Q8×C11—42no—
174Q8×C11—42no—
175Q8×C11—42no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—24no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11C22⋊Q811yescharacteristic
198C2×C4×C11C22⋊Q811yescharacteristic
199C2×C4×C11#12411yescharacteristic
200C2×C4×C11#12411yescharacteristic
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—81no—
219C2×Dic11—81no—
220C2×Dic11—81no—
221C2×Dic11—81no—
222C2×Dic11—81no—
223C2×Dic11—81no—
224Dic22—84no—
225C8×C11—81no—
226C11⋊C8—81no—
227C23×Q8C2×D1111yescharacteristic
228C2×C22⋊Q8—221no—
229C2×#103—21no—
230C2×#103—21no—
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—111no—
244C2×#95—221no—
245C2×#95—221no—
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—44no—
274C4×C11—81no—
275C4×C11—81no—
276Dic11—42no—
277Dic11—42no—
278Dic11—82no—
279Dic11—81no—
280Dic11—81no—
281C22×Q8—21no—
282C22×Q8—21no—
283C22×Q8—21no—
284C22×Q8—21no—
285C22×Q8—21no—
286C22×Q8—42no—
287C22×Q8—42no—
288C22×Q8—221no—
289C22×Q8Dic2212yescomplemented
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⋊C4C22⋊D1111yescharacteristic
307C2×C4⋊C4C22⋊D1111yescharacteristic
308C2×C22⋊C4—21no—
309C2×C22⋊C4—221no—
310#103—42no—
311#103—42no—
312#103—442no—
313#103—442no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—221no—
317C22⋊C8—221no—
318#95—21no—
319#95—221no—
320#95—221no—
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—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—44no—
347C2×Q8—41no—
348C2×Q8—41no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×Q8—44no—
352C2×Q8—44no—
353C2×Q8—44no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×Q8—442no—
357C2×Q8—881no—
358C2×Q8—881no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
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—221no—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—222no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—441no—
380C22×C4—441no—
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×Dic2211yescharacteristic
390C22×C4#433911yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4#434111yescharacteristic
393C22×C4#434111yescharacteristic
394C22×C4C2×C22⋊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#6693111yescharacteristic
420C23#6693811yescharacteristic
421C23SD16×D1111yescharacteristic
422C23#6696711yescharacteristic
423C23Q16×D1111yescharacteristic
424C23#6697111yescharacteristic
425C23#6699011yescharacteristic
426Q8—24no—
427Q8—24no—
428Q8—42no—
429Q8—42no—
430Q8—42no—
431Q8—42no—
432Q8—42no—
433Q8—42no—
434Q8—884no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—24no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—881no—
474C2×C4—881no—
475C2×C4—881no—
476C2×C4—881no—
477C2×C4—881no—
478C2×C4—881no—
479C2×C4#6693111yescharacteristic
480C2×C4#6693811yescharacteristic
481C2×C4#6697711yescharacteristic
482C2×C4#6698911yescharacteristic
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#1062240411yescharacteristic
498C22#1062240511yescharacteristic
499C22#1062240711yescharacteristic
500C22#1062240811yescharacteristic
501C22#1062256011yescharacteristic
502C22#1062264511yescharacteristic
503C22#1062264511yescharacteristic
504C22#1062278211yescharacteristic
505C22#1062279911yescharacteristic
506C22#1062281511yescharacteristic
507C22#1062281811yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—44no—
513C4—81no—
514C4—81no—
515C4—442no—
516C4—442no—
517C4—882no—
518C4—881no—
519C4—881no—
520C2—21no—
521C2—21no—
522C2—21no—
523C2—21no—
524C2#1306756611yescharacteristic
525C2#1306757111yescharacteristic
526C2#1306758311yescharacteristic
527C2#1306758811yescharacteristic
528C2#1306975511yescharacteristic
529C2#1306977511yescharacteristic
530C2#1306978011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1787C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1787D11
hypocenterC11#10341
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
34. C22×Q8×C11Q8semidirect
289. C22×Q8Dic22semidirect
414. C11#10341semidirect

Maximal subgroups

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

subgroupindex
#130747332
#130685512
#130668872
#130664962
#130664942
#130664582
C11×#17872
#1034111