Finite Group Databasebeta

← #14657072

Subgroups — #14657072

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074424C211yesmaximal, characteristic
2#13068921C211yesmaximal, characteristic, complemented
3#13068808C211yesmaximal, characteristic, complemented
4C2×#10622090C211yesmaximal, characteristic, complemented
5C2×#10622106C211yesmaximal, characteristic
6#13066862C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic, complemented
8C22×(C2×D11)⋊C4—21no—
9C22×(C2×D11)⋊C4C2211yescharacteristic
10C22×C4⋊Dic11C2211yescharacteristic
11C2×#66977C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66880—21no—
18#10622607—21no—
19#10622607—21no—
20C2×#66872—21no—
21#10622568—21no—
22#10622563—21no—
23#10622290—21no—
24#10622286—21no—
25#10622189—21no—
26#10622167—21no—
27#10622106—22no—
28#10622090—22no—
29C24×D11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—21no—
33C23×Dic11D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C22×C8×C11—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C22⋊Dic11—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—42no—
51C2×(C2×D11)⋊C4—42no—
52C2×(C2×D11)⋊C4—42no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—42no—
58C2×C4⋊Dic11D411yescharacteristic
59#66977—21no—
60#66977—21no—
61#66977—21no—
62#66977—21no—
63C2×Dic11⋊C4—21no—
64C22×C11⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C11×#95—21no—
68C11×#95—21no—
69C11×#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—42no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)D412yes—
75#66880—42no—
76#66872—42no—
77#10398—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C23×D11—21no—
80C23×D11—21no—
81C23×D11—21no—
82C23×D11—21no—
83C23×D11—21no—
84C23×D11—21no—
85C23×D11—41no—
86C23×D11—41no—
87C23×D11—41no—
88C23×D11—41no—
89C23×D11SD1612yes—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C2×Dic22—21no—
122C2×Dic22—21no—
123C2×Dic22—41no—
124C2×Dic22—41no—
125C2×C8×C11—41no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C22⋊Dic11—41no—
133C22⋊Dic11—41no—
134(C2×D11)⋊C4—48no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—81no—
140(C2×D11)⋊C4—81no—
141(C2×D11)⋊C4—81no—
142(C2×D11)⋊C4—81no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—41no—
148C4⋊Dic11—41no—
149C4⋊Dic11—81no—
150C4⋊Dic11—81no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—41no—
155C2×C11⋊C8—41no—
156#2626—111no—
157#1872—111no—
158#1853—111no—
159C2×#328—111no—
160C2×#323—111no—
161#1439—111no—
162#1294D1111yescharacteristic, complemented
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11#12011yescharacteristic
168C23×C11#12111yescharacteristic
169C23×C11#12311yescharacteristic
170C23×C11C2×SD1611yescharacteristic
171C23×C11#13511yescharacteristic
172C23×C11#13711yescharacteristic
173C23×C11#13711yescharacteristic
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—81no—
192C22×D11—81no—
193C22×D11—81no—
194C22×D11—81no—
195C22×D11—81no—
196C22×D11—81no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—81no—
215C2×C4×C11—81no—
216C2×C4×C11—81no—
217C2×C4×C11—81no—
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11#12311yescharacteristic
221C2×C4×C11#12411yescharacteristic
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—42no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—81no—
236C2×Dic11—81no—
237C2×Dic11—81no—
238C2×Dic11—81no—
239C2×Dic11—81no—
240Dic22—42no—
241Dic22—81no—
242C8×C11—81no—
243C11⋊C8—42no—
244C2×C22⋊Q8—111no—
245C22×C4⋊C4—111no—
246C22×C22⋊C4—111no—
247C22×C22⋊C4—221no—
248C2×#106—221no—
249C2×#103—221no—
250C2×C22⋊C8—111no—
251C2×C22⋊C8C2×D1111yescharacteristic
252#399—221no—
253#396—221no—
254#396—221no—
255#393—221no—
256#385—221no—
257#380C2×D1111yescharacteristic
258#379—221no—
259C2×#95—221no—
260C2×#95C2×D1111yescharacteristic
261#340—221no—
262#340—221no—
263#328—222no—
264#323—222no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11#39411yescharacteristic
278C22×C11#44811yescharacteristic
279C22×C11#45211yescharacteristic
280C22×C11#45311yescharacteristic
281C22×C11#45511yescharacteristic
282C22×C11B(4,𝔽2)11yescharacteristic
283C22×C11#45811yescharacteristic
284C22×C11#46511yescharacteristic
285C22×C11#47011yescharacteristic
286C22×C11#48311yescharacteristic
287C22×C11#48511yescharacteristic
288C2×D11—44no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—82no—
293C2×D11—82no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—82no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—82no—
304C4×C11—81no—
305C4×C11—81no—
306Dic11—82no—
307Dic11—81no—
308Dic11—81no—
309Dic11—81no—
310C25—111no—
311C22×Q8—111no—
312C23×C4—21no—
313C23×C4—111no—
314C23×C4—221no—
315C23×C4C22×D1111yescharacteristic
316C22×C8—21no—
317C22×C8—221no—
318C22⋊Q8—221no—
319C22⋊Q8—221no—
320C22⋊Q8—221no—
321C22⋊Q8—221no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—442no—
329C2×C4⋊C4D4411yescharacteristic
330C2×C4⋊C4D4411yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—221no—
334C2×C22⋊C4—221no—
335C2×C22⋊C4—221no—
336C2×C22⋊C4—221no—
337C2×C22⋊C4—221no—
338C2×C22⋊C4—221no—
339C2×C22⋊C4—221no—
340C2×C22⋊C4—221no—
341C2×C22⋊C4—221no—
342C2×C22⋊C4—221no—
343C2×C22⋊C4—442no—
344C2×C22⋊C4—442no—
345C2×C22⋊C4—442no—
346#106—442no—
347#103—442no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—112no—
351C22⋊C8—221no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—221no—
356#95—221no—
357#95—442no—
358C2×C11—21no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11#159611yescharacteristic
363C2×C11#160611yescharacteristic
364C2×C11#160811yescharacteristic
365C2×C11#161811yescharacteristic
366C2×C11#203511yescharacteristic
367C2×C11#203711yescharacteristic
368C2×C11#204411yescharacteristic
369D11—82no—
370C24—112no—
371C24—221no—
372C24—221no—
373C24—221no—
374C24—221no—
375C24—221no—
376C24—221no—
377C24—441no—
378C24—441no—
379C24—441no—
380C24—441no—
381C24D4×D1111yescharacteristic
382C2×Q8—221no—
383C2×Q8—221no—
384C2×Q8—441no—
385C2×Q8—441no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—222no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—441no—
404C22×C4—441no—
405C22×C4—441no—
406C22×C4—441no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4—441no—
410C22×C4—441no—
411C22×C4C2×D4411yescharacteristic
412C22×C4#433911yescharacteristic
413C22×C4#433911yescharacteristic
414C22×C4D4×D1111yescharacteristic
415C22×C4D4×D1111yescharacteristic
416C22×C4#434311yescharacteristic
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—41no—
420C2×C8—222no—
421C2×C8—441no—
422C2×C8—441no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—222no—
426C4⋊C4—222no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C4⋊C4—881no—
434C4⋊C4—881no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—448no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C22⋊C4—441no—
441C22⋊C4—441no—
442C22⋊C4—441no—
443C22⋊C4—441no—
444C22⋊C4—881no—
445C22⋊C4—881no—
446C22⋊C4—881no—
447C22⋊C4—881no—
448C11#1039811yescharacteristic, complemented, Sylow
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—222no—
454C23—222no—
455C23—222no—
456C23—442no—
457C23—442no—
458C23—442no—
459C23—442no—
460C23—442no—
461C23—442no—
462C23—441no—
463C23—441no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23—441no—
469C23—441no—
470C23—881no—
471C23—881no—
472C23—881no—
473C23—881no—
474C23—881no—
475C23—881no—
476C23#6693511yescharacteristic
477C23#6693711yescharacteristic
478C23#6694711yescharacteristic
479C23#6696511yescharacteristic
480C23SD16×D1111yescharacteristic
481C23#6696811yescharacteristic
482C23#6697111yescharacteristic
483Q8—442no—
484Q8—881no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—442no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—881no—
520C2×C4—881no—
521C2×C4—881no—
522C2×C4—881no—
523C2×C4—881no—
524C2×C4#6692811yescharacteristic
525C2×C4#6693711yescharacteristic
526C2×C4#6694711yescharacteristic
527C2×C4#6694811yescharacteristic
528C8—81no—
529C8—442no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—444no—
543C22—442no—
544C22—442no—
545C22—442no—
546C22—882no—
547C22—882no—
548C22—882no—
549C22—881no—
550C22—881no—
551C22—881no—
552C22—881no—
553C22#1062228511yescharacteristic
554C22#1062235411yescharacteristic
555C22#1062235511yescharacteristic
556C22#1062239111yescharacteristic
557C22#1062239611yescharacteristic
558C22#1062241911yescharacteristic
559C22#1062242911yescharacteristic
560C22#1062243511yescharacteristic
561C22#1062243811yescharacteristic
562C22#1062247511yescharacteristic
563C22#1062250111yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—82no—
569C4—81no—
570C4—81no—
571C4—881no—
572C4—881no—
573C4—882no—
574C4—881no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—882no—
580C2#1306754011yescharacteristic
581C2#1306759711yescharacteristic
582C2#1306760811yescharacteristic
583C2#1306766511yescharacteristic
584C2#1306981511yescharacteristic
585C2#1306982911yescharacteristic
586C2#1306986811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11#120
prime radicalC24×D11D4
hypercenter#1294D11
hypocenterC11#10398
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
2. #13068921C2semidirect
3. #13068808C2semidirect
4. C2×#10622090C2semidirect
7. C11×#1294C2semidirect
162. #1294D11semidirect
448. C11#10398semidirect

Maximal subgroups

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

subgroupindex
#130744242
#130689212
#130688082
C2×#106220902
C2×#106221062
#130668622
C11×#12942
#1039811