Finite Group Databasebeta

← #14657073

Subgroups — #14657073

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#13068924C211yesmaximal, characteristic, complemented
2#13068803C211yesmaximal, characteristic, complemented
3C2×#10622176C211yesmaximal, characteristic, complemented
4C2×#10622163C211yesmaximal, characteristic
5#13066861C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic, complemented
7C11×#2626C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11—21no—
11C22×C4⋊Dic11C2211yescharacteristic
12C11×#399—21no—
13C11×#396—21no—
14C11×#396—21no—
15C11×#393—21no—
16C11×#385—21no—
17C11×#380C2211yescharacteristic
18C11×#379—21no—
19C2×#66899—21no—
20C2×C11⋊#95—21no—
21C2×C11⋊#95C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×#66871—21no—
25#10622176—22no—
26#10622167—21no—
27#10622167—21no—
28#10622163—22no—
29C25×C11D411yescharacteristic
30C22×Q8×C11D411yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—21no—
34C23×Dic11—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C22⋊Dic11—42no—
58C2×C22⋊Dic11—42no—
59C2×C22⋊Dic11—42no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—42no—
63C22×C11⋊C8—21no—
64C22×C11⋊C8—21no—
65C11×#95—21no—
66C11×#95—21no—
67C11×#95—21no—
68#66899—42no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—42no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)D412yes—
76#66871—42no—
77#10399—111nomaximal, Sylow
78C24×C11—21no—
79C24×C11—21no—
80C24×C11—21no—
81C24×C11—21no—
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—41no—
85C24×C11—41no—
86C24×C11—41no—
87C24×C11—41no—
88C24×C11Q1612yes—
89C24×C11C2×D411yescharacteristic
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—41no—
93C2×Q8×C11—41no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
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
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
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—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—81no—
132C11×C4⋊C4—81no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—81no—
142C11×C22⋊C4—81no—
143C11×C22⋊C4—81no—
144C11×C22⋊C4—81no—
145C22⋊Dic11—48no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—41no—
152C2×C11⋊C8—41no—
153C2×C11⋊C8—41no—
154C2×C11⋊C8—41no—
155C2×C11⋊C8—41no—
156#2626D1111yescharacteristic
157#1872—111no—
158#1852—111no—
159C2×#328—111no—
160C2×#323—111no—
161#1439—111no—
162#1294—111no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—81no—
185C23×C11—81no—
186C23×C11—81no—
187C23×C11—81no—
188C23×C11—81no—
189C23×C11—81no—
190C23×C11#12011yescharacteristic
191C23×C11#12111yescharacteristic
192C23×C11#12311yescharacteristic
193C23×C11C2×Q1611yescharacteristic
194C23×C11#13511yescharacteristic
195C23×C11AGL(1,ℤ/8)11yescharacteristic
196C23×C11#13711yescharacteristic
197Q8×C11—42no—
198Q8×C11—81no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
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—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—81no—
224C2×C4×C11#12111yescharacteristic
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11#12311yescharacteristic
227C2×C4×C11#12411yescharacteristic
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—81no—
235C2×Dic11—81no—
236C2×Dic11—81no—
237C2×Dic11—81no—
238C2×Dic11—81no—
239C2×Dic11—81no—
240C2×Dic11—81no—
241C2×Dic11—81no—
242C11⋊C8—42no—
243C11⋊C8—81no—
244C2×C22⋊Q8C2×D1111yescharacteristic
245C22×C4⋊C4—111no—
246C22×C22⋊C4—221no—
247C22×C22⋊C4C2×D1111yescharacteristic
248C2×#107—221no—
249C2×#103—221no—
250C2×C22⋊C8—111no—
251C2×C22⋊C8—111no—
252#399—21no—
253#396—21no—
254#396—21no—
255#393—21no—
256#385—21no—
257#380C2×D1111yescharacteristic
258#379—21no—
259C2×#95—111no—
260C2×#95—221no—
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—44no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11—82no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11#39411yescharacteristic
289C22×C11#44911yescharacteristic
290C22×C11#45111yescharacteristic
291C22×C11#45311yescharacteristic
292C22×C11#45511yescharacteristic
293C22×C11B(4,𝔽2)11yescharacteristic
294C22×C11#45811yescharacteristic
295C22×C11#46711yescharacteristic
296C22×C11#46811yescharacteristic
297C22×C11#48411yescharacteristic
298C22×C11#48511yescharacteristic
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11—81no—
307C4×C11—81no—
308Dic11—82no—
309Dic11—82no—
310C25C22⋊D1111yescharacteristic
311C22×Q8C22⋊D1111yescharacteristic
312C23×C4—221no—
313C23×C4—221no—
314C23×C4C22⋊D1111yescharacteristic
315C23×C4C22×D1111yescharacteristic
316C22×C8—221no—
317C22×C8—221no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—442no—
328C2×C4⋊C4C22⋊D1111yescharacteristic
329C2×C4⋊C4C22⋊D1111yescharacteristic
330C2×C4⋊C4C22⋊D1111yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—442no—
344C2×C22⋊C4—442no—
345C2×C22⋊C4—442no—
346#107—442no—
347#103—442no—
348C22⋊C8—112no—
349C22⋊C8—221no—
350C22⋊C8—221no—
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—82no—
363C2×C11#160011yescharacteristic
364C2×C11#160211yescharacteristic
365C2×C11#161211yescharacteristic
366C2×C11#161411yescharacteristic
367C2×C11#203611yescharacteristic
368C2×C11#203711yescharacteristic
369C2×C11#204411yescharacteristic
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24#432612yes—
381C24C2×C22⋊D1111yescharacteristic
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—41no—
385C2×Q8—41no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—441no—
402C22×C4—441no—
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×C4D4×D1111yescharacteristic
412C22×C4#434111yescharacteristic
413C22×C4#434111yescharacteristic
414C22×C4#434111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417C2×C8—222no—
418C2×C8—441no—
419C2×C8—441no—
420C2×C8—441no—
421C2×C8—441no—
422C2×C8—441no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—81no—
430C4⋊C4—81no—
431C4⋊C4—222no—
432C4⋊C4—222no—
433C4⋊C4—441no—
434C4⋊C4—441no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—81no—
444C22⋊C4—81no—
445C22⋊C4—81no—
446C22⋊C4—81no—
447C22⋊C4—448no—
448C11#1039911yescharacteristic, complemented, Sylow
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—81no—
471C23—81no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—81no—
476C23#6698811yescharacteristic
477C23#6699211yescharacteristic
478C23#6699511yescharacteristic
479C23C2×#432611yescharacteristic
480C23#6700211yescharacteristic
481C23#6700311yescharacteristic
482C23#6700611yescharacteristic
483Q8—42no—
484Q8—81no—
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—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—81no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—881no—
517C2×C4—881no—
518C2×C4—881no—
519C2×C4—881no—
520C2×C4—881no—
521C2×C4—881no—
522C2×C4—881no—
523C2×C4—881no—
524C2×C4#6698811yescharacteristic
525C2×C4#6698911yescharacteristic
526C2×C4#6699111yescharacteristic
527C2×C4#6699211yescharacteristic
528C8—442no—
529C8—881no—
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—44no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22#1062265711yescharacteristic
554C22#1062265811yescharacteristic
555C22#1062266211yescharacteristic
556C22#1062266411yescharacteristic
557C22#1062283511yescharacteristic
558C22#1062284111yescharacteristic
559C22#1062285111yescharacteristic
560C22#1062285411yescharacteristic
561C22#1062285511yescharacteristic
562C22#1062285611yescharacteristic
563C22#1062285711yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—882no—
574C4—882no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—82no—
580C2#1306756211yescharacteristic
581C2#1306757311yescharacteristic
582C2#1306763011yescharacteristic
583C2#1306764111yescharacteristic
584C2#1306981611yescharacteristic
585C2#1306982311yescharacteristic
586C2#1306986411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2626C2
socleC23×C11#120
prime radicalC25×C11D4
hypercenter#2626D11
hypocenterC11#10399
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2626

Complements

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

NH ≅ G/Ntype
1. #13068924C2semidirect
2. #13068803C2semidirect
3. C2×#10622176C2semidirect
6. #13066494C2semidirect
448. C11#10399semidirect

Maximal subgroups

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

subgroupindex
#130689242
#130688032
C2×#106221762
C2×#106221632
#130668612
#130664942
C11×#26262
#1039911