Finite Group Databasebeta

← #14657096

Subgroups — #14657096

Order 2816.

760 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074720C211yesmaximal, characteristic
2#13068934C211yesmaximal, characteristic, complemented
3#13068931C211yesmaximal, characteristic, complemented
4C2×#10622089C211yesmaximal, characteristic, complemented
5#13066881C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C2×C11×#327C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×#66992—21no—
10C2×#66992—21no—
11C2×#66983C2211yescharacteristic
12C22×C4⋊Dic11—21no—
13C22×C4⋊Dic11C2211yescharacteristic
14C2×C11×C22⋊C8C2211yescharacteristic
15C2×C11×#95C2211yescharacteristic
16#10622836—21no—
17C2×#66896—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21C2×#66885—21no—
22#10622605—21no—
23#10622573—21no—
24#10622562—21no—
25C11×#327—22no—
26#10622189—21no—
27#10622167—21no—
28#10622089—22no—
29C22×D4×C11—21no—
30C22×D4×C11D411yescharacteristic
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C22×C22⋊D11—21no—
35C22×C22⋊D11—21no—
36C23×Dic11—21no—
37C23×Dic11D411yescharacteristic
38C23×Dic11D411yescharacteristic
39C22×D44D411yescharacteristic
40C22×C8×C11—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49#66992—42no—
50#66992—42no—
51#66992—42no—
52#66992—42no—
53#66983—21no—
54#66983—21no—
55#66983—21no—
56#66983—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—42no—
63C2×C4⋊Dic11—42no—
64C2×C4⋊Dic11—42no—
65C2×C4⋊Dic11—42no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C22×C11⋊C8—21no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8—21no—
72C11×#95—21no—
73C11×#95D412yescomplemented
74#66896—42no—
75C11⋊#95—21no—
76C11⋊#95—21no—
77C11⋊#95—42no—
78C22⋊(C11⋊C8)—21no—
79C22⋊(C11⋊C8)—21no—
80#66885—42no—
81#10402—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11C2×D411yescharacteristic
84C23×D11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C2×C22⋊D11—42no—
112C2×C22⋊D11—42no—
113C2×C22⋊D11—41no—
114C2×C22⋊D11—41no—
115C2×C22⋊D11—41no—
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C2×C22⋊D11—81no—
120C2×C22⋊D11—81no—
121C2×C22⋊D11—81no—
122C2×C22⋊D11—81no—
123C22×Dic11—22no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11—41no—
133C22×Dic11—41no—
134C22×Dic11—41no—
135C22×Dic11—41no—
136C22×Dic11—41no—
137C22×Dic11—41no—
138C22×Dic11—41no—
139C22×Dic11D812yes—
140C22×Dic11SD1612yes—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—41no—
144C2×D44—41no—
145C2×C8×C11—41no—
146C2×C8×C11—41no—
147C2×C8×C11—41no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—41no—
152C22⋊Dic11—42no—
153C22⋊Dic11—42no—
154(C2×D11)⋊C4—42no—
155(C2×D11)⋊C4—42no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—41no—
163C4⋊Dic11—41no—
164C4⋊Dic11—48no—
165Dic11⋊C4—42no—
166Dic11⋊C4—42no—
167C2×C11⋊C8—41no—
168C2×C11⋊C8—41no—
169C2×C11⋊C8—41no—
170#2656—111no—
171#1874—111no—
172#1874—111no—
173C2×#327—111no—
174C2×#327D1111yescharacteristic, complemented
175#1444—111no—
176#1280—111no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11#12011yescharacteristic
189C23×C11#12111yescharacteristic
190C23×C11#12411yescharacteristic
191C23×C11C2×D811yescharacteristic
192C23×C11C2×SD1611yescharacteristic
193C23×C11AGL(1,ℤ/8)11yescharacteristic
194C23×C11AGL(1,ℤ/8)11yescharacteristic
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202D4×C11—42no—
203D4×C11—81no—
204D4×C11—81no—
205D4×C11—81no—
206D4×C11—81no—
207D4×C11—81no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11#12111yescharacteristic
227C2×C4×C11#12111yescharacteristic
228C2×C4×C11#12311yescharacteristic
229C2×C4×C11#12311yescharacteristic
230C22⋊D11—84no—
231C22⋊D11—84no—
232C22⋊D11—81no—
233C22⋊D11—81no—
234C22⋊D11—81no—
235C22⋊D11—81no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—42no—
250C2×Dic11—81no—
251C2×Dic11—81no—
252C2×Dic11—81no—
253C2×Dic11—81no—
254C2×Dic11—81no—
255C2×Dic11—81no—
256D44—42no—
257D44—81no—
258C8×C11—81no—
259C11⋊C8—81no—
260C2×#121—111no—
261C2×#121—221no—
262C2×#121—221no—
263C2×#121C2×D1111yescharacteristic
264C22×C4⋊C4—111no—
265C22×C4⋊C4—221no—
266C2×#102—221no—
267C2×#102—221no—
268C2×C22⋊C8—111no—
269C2×C22⋊C8C2×D1111yescharacteristic
270#399—221no—
271#399—221no—
272#392—221no—
273#392—221no—
274C2×#95—111no—
275C2×#95—221no—
276C2×#95C2×D1111yescharacteristic
277#340—221no—
278#340—221no—
279#327—22no—
280#327—222no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11#39411yescharacteristic
301C22×C11#44711yescharacteristic
302C22×C11#45011yescharacteristic
303C22×C11#45311yescharacteristic
304C22×C11#45611yescharacteristic
305C22×C11B(4,𝔽2)11yescharacteristic
306C22×C11#45811yescharacteristic
307C22×C11#45911yescharacteristic
308C22×C11#46011yescharacteristic
309C22×C11#48611yescharacteristic
310C22×C11#49011yescharacteristic
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—81no—
318C4×C11—21no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—44no—
323C4×C11—81no—
324Dic11—42no—
325Dic11—42no—
326Dic11—82no—
327Dic11—81no—
328C22×D4—21no—
329C22×D4—111no—
330C22×D4—221no—
331C22×D4—221no—
332C22×D4—221no—
333C22×D4D4411yescharacteristic
334C23×C4—21no—
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—221no—
338C23×C4C22×D1111yescharacteristic
339C22×C8—21no—
340C22×C8—221no—
341#121—21no—
342#121—21no—
343#121—21no—
344#121—21no—
345#121—221no—
346#121—221no—
347#121—221no—
348#121—221no—
349#121—442no—
350#121—442no—
351#121—442no—
352#121—442no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—442no—
359C2×C4⋊C4—442no—
360C2×C4⋊C4—442no—
361C2×C4⋊C4—442no—
362C2×C4⋊C4D4411yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4—221no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—221no—
369#102—442no—
370#102—442no—
371C22⋊C8—21no—
372C22⋊C8—21no—
373C22⋊C8—221no—
374C22⋊C8—221no—
375#95—21no—
376#95—221no—
377#95—221no—
378#95—442no—
379#95C22⋊D1112yescomplemented
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—21no—
384C2×C11—161no—
385C2×C11#159511yescharacteristic
386C2×C11#160411yescharacteristic
387C2×C11#161011yescharacteristic
388C2×C11#161311yescharacteristic
389C2×C11#203911yescharacteristic
390C2×C11#204111yescharacteristic
391C2×C11#204411yescharacteristic
392D11—161no—
393C24—21no—
394C24—221no—
395C24D4×D1111yescharacteristic
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—221no—
407C2×D4—221no—
408C2×D4—441no—
409C2×D4—441no—
410C2×D4—442no—
411C2×D4—442no—
412C2×D4—441no—
413C2×D4—441no—
414C2×D4—441no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4—881no—
419C2×D4—881no—
420C2×D4—881no—
421C2×D4—881no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—222no—
439C22×C4—221no—
440C22×C4—441no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4—441no—
444C22×C4—441no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4—441no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4C2×D4411yescharacteristic
451C22×C4#433911yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4#434111yescharacteristic
454C22×C4#434111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—41no—
459C2×C8—441no—
460C2×C8—441no—
461C2×C8—441no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—222no—
465C4⋊C4—222no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—441no—
469C4⋊C4—441no—
470C4⋊C4—442no—
471C4⋊C4—442no—
472C4⋊C4—448no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—442no—
476C22⋊C4—442no—
477C22⋊C4—442no—
478C22⋊C4—442no—
479C22⋊C4—441no—
480C22⋊C4—441no—
481C11#1040211yescharacteristic, complemented, Sylow
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—441no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23#6693511yescharacteristic
501C23#6693811yescharacteristic
502C23D8×D1111yescharacteristic
503C23#6696411yescharacteristic
504C23SD16×D1111yescharacteristic
505C23#6696711yescharacteristic
506C23#6699211yescharacteristic
507D4—42no—
508D4—81no—
509D4—81no—
510D4—81no—
511D4—81no—
512D4—81no—
513D4—442no—
514D4—881no—
515D4—884no—
516D4—884no—
517D4—881no—
518D4—881no—
519D4—881no—
520D4—881no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—441no—
550C2×C4—442no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—881no—
554C2×C4—881no—
555C2×C4—881no—
556C2×C4—881no—
557C2×C4—881no—
558C2×C4—881no—
559C2×C4#6693611yescharacteristic
560C2×C4#6693911yescharacteristic
561C2×C4#6698311yescharacteristic
562C2×C4#6699111yescharacteristic
563C8—81no—
564C8—881no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—881no—
585C22—881no—
586C22—881no—
587C22—881no—
588C22—881no—
589C22—881no—
590C22—881no—
591C22#1062235411yescharacteristic
592C22#1062235511yescharacteristic
593C22#1062237311yescharacteristic
594C22#1062237711yescharacteristic
595C22#1062238611yescharacteristic
596C22#1062238911yescharacteristic
597C22#1062243511yescharacteristic
598C22#1062243911yescharacteristic
599C22#1062257411yescharacteristic
600C22#1062276311yescharacteristic
601C22#1062277611yescharacteristic
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—44no—
607C4—81no—
608C4—442no—
609C4—442no—
610C4—882no—
611C4—881no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—161no—
617C2—1761no—
618C2#1306753511yescharacteristic
619C2#1306758611yescharacteristic
620C2#1306762011yescharacteristic
621C2#1306763711yescharacteristic
622C2#1306983911yescharacteristic
623C2#1306984911yescharacteristic
624C2#1306986611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC2×C11×#327C2
socleC23×C11#120
prime radical#13074720C2
hypercenterC2×#327D11
hypocenterC11#10402
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #13068934C2semidirect
3. #13068931C2semidirect
4. C2×#10622089C2semidirect
5. #13066881C2semidirect
6. #13066458C2semidirect
7. C2×C11×#327C2semidirect
73. C11×#95D4semidirect
174. C2×#327D11semidirect
379. #95C22⋊D11semidirect
481. C11#10402semidirect

Maximal subgroups

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

subgroupindex
#130747202
#130689342
#130689312
C2×#106220892
#130668812
#130664582
C2×C11×#3272
#1040211