Finite Group Databasebeta

← #14654013

Subgroups — #14654013

Order 2816.

856 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622348C211yesmaximal, characteristic, complemented
2#13074350C211yesmaximal, characteristic
3C2×#10622562C211yesmaximal, characteristic, complemented
4#13068707C211yesmaximal, characteristic, complemented
5C2×#10622108C211yesmaximal, characteristic, complemented
6#13066496C211yesmaximal, characteristic, complemented
7C2×C11×#323C211yesmaximal, characteristic, complemented
8C22×C11×C22⋊C4C2211yescharacteristic
9C2×#67006—21no—
10C22×C22⋊Dic11—21no—
11C2×#66983C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4—21no—
14C2×C11×C22⋊C8C2211yescharacteristic
15C2×C11×C22⋊C8C2211yescharacteristic
16#10622826—21no—
17#10622825C2211yescharacteristic
18C2×C11⋊#95C2211yescharacteristic
19C2×#66885—21no—
20C2×#66881—21no—
21#10622574—22no—
22#10622573—21no—
23#10622566—21no—
24#10622562—22no—
25#10622562—22no—
26#10622348—22no—
27#10622348—22no—
28C11×#323—22no—
29#10622189—22no—
30#10622108—22no—
31C25×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C22×C22⋊D11—22no—
36C23×Dic11—21no—
37C23×Dic11—21no—
38C22×D44D411yescharacteristic
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47#67006—42no—
48#67006—42no—
49C2×C22⋊Dic11—24no—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—44no—
53#66983—21no—
54#66983—21no—
55#66983—21no—
56#66983—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11D412yes—
66C2×C4⋊Dic11D412yescomplemented
67C2×Dic11⋊C4—24no—
68C2×Dic11⋊C4—44no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8D412yescomplemented
73C11⋊#95—22no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95D412yescomplemented
77#66885—24no—
78#66881—24no—
79#9920—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11—21no—
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—42no—
87C24×C11—42no—
88C24×C11SD1612yes—
89C24×C11C2×D411yescharacteristic
90C23×D11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C2×C22⋊D11—44no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—41no—
107C2×C22⋊D11—41no—
108C2×C22⋊D11—41no—
109C2×C22⋊D11—82no—
110C2×C22⋊D11—82no—
111C22×Dic11—24no—
112C22×Dic11—22no—
113C22×Dic11—21no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—42no—
117C22×Dic11—42no—
118C22×Dic11—42no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—42no—
126C2×C8×C11—22no—
127C2×C8×C11—42no—
128C2×C8×C11—42no—
129C2×C8×C11—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C22⋊Dic11—44no—
135C22⋊Dic11—48no—
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—82no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11—42no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
148Dic11⋊C4—48no—
149C2×#481—111no—
150#2617—111no—
151C2×#399—111no—
152#1824—111no—
153C2×#327—111no—
154C2×#323D1111yescharacteristic, complemented
155#1294—111no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—44no—
162C23×C11—42no—
163C23×C11—44no—
164C23×C11—42no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—41no—
171C23×C11—82no—
172C23×C11—82no—
173C23×C11—81no—
174C23×C11—81no—
175C23×C11#12011yescharacteristic
176C23×C11#12011yescharacteristic
177C23×C11#12111yescharacteristic
178C23×C11C2×SD1611yescharacteristic
179C23×C11#13511yescharacteristic
180C23×C11AGL(1,ℤ/8)11yescharacteristic
181C23×C11#13711yescharacteristic
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—42no—
186C22×D11—42no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—81no—
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12711yescharacteristic
201C22⋊D11—88no—
202C22⋊D11—81no—
203C22⋊D11—81no—
204C22⋊D11—81no—
205C22⋊D11—81no—
206C2×Dic11—24no—
207C2×Dic11—44no—
208C2×Dic11—44no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—82no—
221C2×Dic11—82no—
222D44—42no—
223D44—81no—
224C8×C11—42no—
225C8×C11—81no—
226C2×#121—111no—
227C2×#120—221no—
228C22×C4⋊C4—111no—
229C22×C4⋊C4—221no—
230C22×C22⋊C4—221no—
231C22×C22⋊C4C2×D1111yescharacteristic
232#481—222no—
233#481—222no—
234C2×#106—221no—
235C2×#102—221no—
236C2×C22⋊C8C2×D1111yescharacteristic
237C2×C22⋊C8C2×D1111yescharacteristic
238#399—222no—
239#399—222no—
240#397—221no—
241#394—222no—
242#392—221no—
243#386—221no—
244#380—111no—
245C2×#95—111no—
246#340—222no—
247#327—222no—
248#323—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—44no—
258C22×C11—44no—
259C22×C11—42no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11—82no—
263C22×C11—82no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11#39211yescharacteristic
267C22×C11#44811yescharacteristic
268C22×C11#44911yescharacteristic
269C22×C11#45011yescharacteristic
270C22×C11#45211yescharacteristic
271C22×C11#45312yes—
272C22×C11#45812yes—
273C22×C11#46511yescharacteristic
274C22×C11#46811yescharacteristic
275C2×D11—82no—
276C2×D11—82no—
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—81no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—81no—
285Dic11—44no—
286Dic11—82no—
287Dic11—81no—
288Dic11—82no—
289C25D4411yescharacteristic
290C22×D4—111no—
291C22×D4—221no—
292C22×D4—222no—
293C23×C4—221no—
294C23×C4—221no—
295C23×C4D4411yescharacteristic
296C23×C4C22×D1111yescharacteristic
297C22×C8—21no—
298C22×C8—21no—
299#121—221no—
300#121—221no—
301#121—221no—
302#121—221no—
303#120—442no—
304#120—442no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—112no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—224no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—444no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—224no—
322C2×C22⋊C4—222no—
323C2×C22⋊C4—221no—
324C2×C22⋊C4—221no—
325C2×C22⋊C4—222no—
326C2×C22⋊C4—444no—
327#106—224no—
328#102—224no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C22⋊C8C22⋊D1112yescomplemented
333#95—112no—
334#95—222no—
335#95—221no—
336#95—221no—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—82no—
342C2×C11#161312yes—
343C2×C11#161812yes—
344C2×C11#200011yescharacteristic
345C2×C11#200211yescharacteristic
346C2×C11#202211yescharacteristic
347D11—161no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—42no—
355C24—42no—
356C24—221no—
357C24#431412yes—
358C24C2×D4411yescharacteristic
359C2×D4—221no—
360C2×D4—221no—
361C2×D4—442no—
362C2×D4—444no—
363C2×D4—441no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—441no—
367C2×D4—441no—
368C2×D4—441no—
369C2×D4—882no—
370C2×D4—882no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—224no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—221no—
380C22×C4—222no—
381C22×C4—442no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—442no—
385C22×C4—442no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4#433911yescharacteristic
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4D4×D1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394C2×C8—22no—
395C2×C8—42no—
396C2×C8—42no—
397C2×C8—41no—
398C4⋊C4—222no—
399C4⋊C4—221no—
400C4⋊C4—222no—
401C4⋊C4—221no—
402C4⋊C4—442no—
403C4⋊C4—448no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—448no—
411C22⋊C4—444no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C22⋊C4—441no—
416C22⋊C4—882no—
417C11#992011yescharacteristic, complemented, Sylow
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—44no—
424C23—42no—
425C23—44no—
426C23—42no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—42no—
432C23—42no—
433C23—82no—
434C23—81no—
435C23—82no—
436C23—81no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—442no—
441C23—442no—
442C23#6693511yescharacteristic
443C23#6693511yescharacteristic
444C23C2×#431411yescharacteristic
445C23#6695711yescharacteristic
446C23#6696111yescharacteristic
447C23#6696211yescharacteristic
448C23#6698311yescharacteristic
449D4—442no—
450D4—881no—
451D4—888no—
452D4—881no—
453D4—881no—
454D4—881no—
455D4—881no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—81no—
466C2×C4—224no—
467C2×C4—444no—
468C2×C4—444no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—442no—
475C2×C4—441no—
476C2×C4—442no—
477C2×C4—441no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—882no—
481C2×C4—882no—
482C2×C4#6693711yescharacteristic
483C2×C4#6693711yescharacteristic
484C2×C4#6699011yescharacteristic
485C2×C4#6699311yescharacteristic
486C8—42no—
487C8—81no—
488C22—21no—
489C22—21no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—21no—
495C22—21no—
496C22—44no—
497C22—42no—
498C22—44no—
499C22—82no—
500C22—82no—
501C22—82no—
502C22—81no—
503C22—82no—
504C22—81no—
505C22—881no—
506C22—881no—
507C22—882no—
508C22—882no—
509C22—881no—
510C22#1062234411yescharacteristic
511C22#1062234611yescharacteristic
512C22#1062234711yescharacteristic
513C22#1062235111yescharacteristic
514C22#1062235512yes—
515C22#1062236012yes—
516C22#1062257311yescharacteristic
517C22#1062272711yescharacteristic
518C22#1062274711yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—81no—
524C4—444no—
525C4—881no—
526C4—882no—
527C4—882no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—82no—
533C2—1761no—
534C2#1306763812yes—
535C2#1306766612yes—
536C2#1306962111yescharacteristic
537C2#1306963311yescharacteristic
538C2#1306974611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC2×C11×#323C2
socleC23×C11#120
prime radical#13074350C2
hypercenterC2×#323D11
hypocenterC11#9920
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
1. C2×#10622348C2semidirect
3. C2×#10622562C2semidirect
4. #13068707C2semidirect
5. C2×#10622108C2semidirect
6. #13066496C2semidirect
7. C2×C11×#323C2semidirect
66. C2×C4⋊Dic11D4semidirect
72. C11×C22⋊C8D4semidirect
76. C11⋊#95D4semidirect
154. C2×#323D11semidirect
332. C22⋊C8C22⋊D11semidirect
417. C11#9920semidirect

Maximal subgroups

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

subgroupindex
C2×#106223482
#130743502
C2×#106225622
#130687072
C2×#106221082
#130664962
C2×C11×#3232
#992011