Finite Group Databasebeta

← #14657119

Subgroups — #14657119

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074732C211yesmaximal, characteristic
2#13068923C211yesmaximal, characteristic
3C2×#10622105C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic
5#13066879C211yesmaximal, characteristic
6#13066458C211yesmaximal, characteristic
7C11×#1872C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C22×Dic11⋊C4—21no—
12C2×C11×#103—21no—
13C2×C11×C22⋊C8C2211yescharacteristic
14#10622842—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19#10622596—21no—
20#10622593—21no—
21#10622592—21no—
22C2×#66874—21no—
23#10622555—21no—
24#10622555—21no—
25C11×#340—21no—
26#10622176—22no—
27#10622167—21no—
28#10622105—22no—
29C22×Q8×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—21no—
33C23×Dic11D411yescharacteristic
34C23×Dic11D411yescharacteristic
35C22×Dic22D411yescharacteristic
36C22×C8×C11—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—42no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C22⋊Dic11—21no—
48C2×C4⋊Dic11D411yescharacteristic
49#66977—21no—
50#66977—21no—
51#66977—21no—
52#66977—21no—
53C2×Dic11⋊C4—21no—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C2×Dic11⋊C4—42no—
59C2×Dic11⋊C4—42no—
60C2×Dic11⋊C4—42no—
61C22×C11⋊C8—21no—
62C11×#103—42no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—42no—
73C11⋊#95D412yes—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76#66874—42no—
77#10406—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—22no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11SD1612yes—
118C22×Dic11Q1612yes—
119C2×Dic22—21no—
120C2×Dic22—21no—
121C2×Dic22—41no—
122C2×Dic22—41no—
123C2×C8×C11—41no—
124C2×C8×C11—41no—
125C2×C8×C11—41no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140Dic11⋊C4—48no—
141Dic11⋊C4—41no—
142Dic11⋊C4—41no—
143Dic11⋊C4—81no—
144Dic11⋊C4—81no—
145Dic11⋊C4—81no—
146Dic11⋊C4—81no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149C2×C11⋊C8—41no—
150#2659—111no—
151#1872—111no—
152#1872D1111yescharacteristic
153C2×#328—111no—
154C2×#328—111no—
155#1444—111no—
156#1280—111no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11#12011yescharacteristic
162C23×C11#12111yescharacteristic
163C23×C11#12411yescharacteristic
164C23×C11C2×SD1611yescharacteristic
165C23×C11C2×Q1611yescharacteristic
166C23×C11#13711yescharacteristic
167C23×C11#13711yescharacteristic
168Q8×C11—42no—
169Q8×C11—81no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11—81no—
190C2×C4×C11—81no—
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12311yescharacteristic
194C2×C4×C11#12311yescharacteristic
195C2×Dic11—24no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—81no—
217C2×Dic11—81no—
218Dic22—42no—
219Dic22—81no—
220C8×C11—81no—
221C11⋊C8—81no—
222C2×C22⋊Q8—111no—
223C2×C22⋊Q8C2×D1111yescharacteristic
224C22×C4⋊C4—221no—
225C22×C4⋊C4C2×D1111yescharacteristic
226C2×#103—21no—
227C2×#103—221no—
228C2×C22⋊C8—111no—
229C2×C22⋊C8C2×D1111yescharacteristic
230#398—221no—
231#398—221no—
232#395—221no—
233#395—221no—
234#380—221no—
235#380—221no—
236C2×#95—111no—
237C2×#95—111no—
238C2×#95—221no—
239#340—21no—
240#340—221no—
241#328—222no—
242#328—222no—
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—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11#39411yescharacteristic
256C22×C11#44811yescharacteristic
257C22×C11#45111yescharacteristic
258C22×C11#45311yescharacteristic
259C22×C11#45611yescharacteristic
260C22×C11B(4,𝔽2)11yescharacteristic
261C22×C11#45811yescharacteristic
262C22×C11#46111yescharacteristic
263C22×C11#46211yescharacteristic
264C22×C11#48711yescharacteristic
265C22×C11#49111yescharacteristic
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—82no—
271C4×C11—81no—
272C4×C11—81no—
273Dic11—44no—
274Dic11—42no—
275Dic11—42no—
276Dic11—81no—
277Dic11—81no—
278C22×Q8—111no—
279C22×Q8C22⋊D1111yescharacteristic
280C23×C4—21no—
281C23×C4—111no—
282C23×C4—111no—
283C23×C4—221no—
284C23×C4C22×D1111yescharacteristic
285C22×C8—21no—
286C22×C8—221no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—221no—
292C22⋊Q8—221no—
293C22⋊Q8—221no—
294C22⋊Q8—221no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—442no—
306C2×C4⋊C4—442no—
307C2×C4⋊C4—442no—
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—221no—
311#103—42no—
312#103—442no—
313C22⋊C8—21no—
314C22⋊C8—21no—
315C22⋊C8—221no—
316C22⋊C8—221no—
317#95—112no—
318#95—221no—
319#95—221no—
320#95—221no—
321#95—221no—
322#95—221no—
323#95—221no—
324#95—221no—
325#95—442no—
326C2×C11—21no—
327C2×C11—21no—
328C2×C11—21no—
329C2×C11—21no—
330C2×C11#159611yescharacteristic
331C2×C11#160511yescharacteristic
332C2×C11#161111yescharacteristic
333C2×C11#161411yescharacteristic
334C2×C11#203911yescharacteristic
335C2×C11#204311yescharacteristic
336C2×C11#204411yescharacteristic
337C24D4×D1111yescharacteristic
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8—221no—
343C2×Q8—221no—
344C2×Q8—441no—
345C2×Q8—441no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—112no—
358C22×C4—112no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—441no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4—441no—
376C22×C4#433911yescharacteristic
377C22×C4#433911yescharacteristic
378C22×C4D4×D1111yescharacteristic
379C22×C4D4×D1111yescharacteristic
380C22×C4#434111yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—441no—
386C2×C8—441no—
387C2×C8—441no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C4⋊C4—448no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4—881no—
402C4⋊C4—881no—
403C4⋊C4—881no—
404C4⋊C4—881no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C11#1040611yescharacteristic, complemented, Sylow
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23#6693711yescharacteristic
415C23#6693811yescharacteristic
416C23SD16×D1111yescharacteristic
417C23#6696811yescharacteristic
418C23Q16×D1111yescharacteristic
419C23#6697111yescharacteristic
420C23#6699011yescharacteristic
421Q8—42no—
422Q8—81no—
423Q8—442no—
424Q8—881no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—224no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—881no—
468C2×C4—881no—
469C2×C4#6693611yescharacteristic
470C2×C4#6693711yescharacteristic
471C2×C4#6698211yescharacteristic
472C2×C4#6699211yescharacteristic
473C8—81no—
474C8—881no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22#1062240511yescharacteristic
488C22#1062240611yescharacteristic
489C22#1062241011yescharacteristic
490C22#1062243111yescharacteristic
491C22#1062257211yescharacteristic
492C22#1062264511yescharacteristic
493C22#1062266611yescharacteristic
494C22#1062278311yescharacteristic
495C22#1062279911yescharacteristic
496C22#1062281111yescharacteristic
497C22#1062281811yescharacteristic
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—81no—
503C4—82no—
504C4—81no—
505C4—444no—
506C4—442no—
507C4—442no—
508C4—881no—
509C4—881no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—21no—
514C2#1306753711yescharacteristic
515C2#1306758811yescharacteristic
516C2#1306762211yescharacteristic
517C2#1306763911yescharacteristic
518C2#1306983811yescharacteristic
519C2#1306986011yescharacteristic
520C2#1306986511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1872C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1872D11
hypocenterC11#10406
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
409. C11#10406semidirect

Maximal subgroups

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

subgroupindex
#130747322
#130689232
C2×#106221052
C2×#106221762
#130668792
#130664582
C11×#18722
#1040611