Finite Group Databasebeta

← #14814813

Subgroups — #14814813

Order 2816.

860 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072056C211yesmaximal, characteristic
2#13071565C211yesmaximal, characteristic, complemented
3#13070175C211yesmaximal, characteristic, complemented
4#13070049C211yesmaximal, characteristic, complemented
5#13070021C211yesmaximal, characteristic, complemented
6#13069806C211yesmaximal, characteristic, complemented
7#13069244C211yesmaximal, characteristic, complemented
8#13069195C211yesmaximal, characteristic, complemented
9#13069054C211yesmaximal, characteristic, complemented
10#13068936C211yesmaximal, characteristic, complemented
11#13068936C211yesmaximal, characteristic, complemented
12#13068811C211yesmaximal, characteristic, complemented
13#13068712C211yesmaximal, characteristic, complemented
14#13068336C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66992—21no—
19C2×#66983C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622834—21no—
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37#10622607—21no—
38C4⋊C4×Dic11—21no—
39#10622574—21no—
40#10622571—21no—
41#10622564—21no—
42#10622564—21no—
43#10622552C2211yescharacteristic
44#10622548C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D4×C11D411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×C22⋊D11—21no—
64C23×Dic11—21no—
65C22×D44C2311yescharacteristic
66C2×C11×M16—22no—
67C2×C11×M16—41no—
68C2×C11×M16—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84#66992—44no—
85#66983—22no—
86#66983—22no—
87#66983—22no—
88#66983—41no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93#66979—22no—
94#66979—22no—
95#66979—41no—
96#66979—41no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—41no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×Dic11⋊C4—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—41no—
115C11×C22⋊C8—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66885—22no—
122#66885—41no—
123#66885—41no—
124#66885—41no—
125#66881—22no—
126#66881—41no—
127#26229—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C24×C11C2×D411yescharacteristic
130C23×D11—21no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—41no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4112yes—
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—42no—
152C2×C22⋊D11—42no—
153C2×C22⋊D11—42no—
154C2×C22⋊D11—42no—
155C2×C22⋊D11—42no—
156C2×C22⋊D11—81no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—42no—
165C22×Dic11—42no—
166C22×Dic11—81no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C11×M16—44no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C11×C4⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C42×C11—21no—
190C42×C11—21no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—81no—
195C22⋊Dic11—81no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—81no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—42no—
213C4⋊Dic11—42no—
214C4⋊Dic11—81no—
215C4⋊Dic11#4112yes—
216C4⋊Dic11#4112yes—
217Dic11⋊C4—42no—
218C4×Dic11—42no—
219C4×Dic11—42no—
220C4×Dic11—42no—
221#2416—111no—
222#2354—111no—
223#2099—111no—
224#2077—111no—
225#2071—111no—
226#2034—111no—
227#1926—111no—
228#1919—111no—
229#1895—111no—
230#1875—111no—
231#1875—111no—
232#1870D1111yescharacteristic, complemented
233#1853—111no—
234#1825—111no—
235#1736—111no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11#12312yes—
250C23×C11C22×D411yescharacteristic
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258D4×C11—44no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11#12312yes—
278C2×C4×C11AGL(1,ℤ/8)12yes—
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C22⋊D11—84no—
286C22⋊D11—84no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—84no—
309D44—41no—
310D44—41no—
311D44—41no—
312D44—41no—
313C8×C11—41no—
314C8×C11—41no—
315C8×C11—41no—
316C8×C11—41no—
317C22×M16C2×D1111yescharacteristic
318C2×#121—111no—
319C2×#121—111no—
320C2×#121—221no—
321C2×C4×D4C2×D1111yescharacteristic
322C2×#117—111no—
323C2×#117—111no—
324C22×C4⋊C4—111no—
325C2×#106—111no—
326C2×#106—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×C22⋊C8C2×D1111yescharacteristic
332C2×C22⋊C8C2×D1111yescharacteristic
333C2×C22⋊C8C2×D1111yescharacteristic
334#396—221no—
335#394—221no—
336#390—111no—
337#390—221no—
338#389—111no—
339#388—221no—
340#388—221no—
341#386—221no—
342#384—111no—
343#380—111no—
344#380—111no—
345#380—111no—
346C4×C4⋊C4—111no—
347C4×C4⋊C4—221no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#336C2×D1111yescharacteristic
359#336C2×D1111yescharacteristic
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11C2×#12311yescharacteristic
375C22×C11#54611yescharacteristic
376C22×C11#54611yescharacteristic
377C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C11#57511yescharacteristic
379C22×C11#57711yescharacteristic
380C22×C11#57711yescharacteristic
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C2×D11—81no—
388C4×C11—22no—
389C4×C11—22no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11#52911yescharacteristic
393C4×C11#53811yescharacteristic
394C4×C11#55311yescharacteristic
395C4×C11#55311yescharacteristic
396Dic11—42no—
397Dic11—42no—
398Dic11—81no—
399Dic11—81no—
400Dic11—81no—
401Dic11—81no—
402Dic11—81no—
403C22×D4—111no—
404C22×D4—221no—
405C22×D4—221no—
406C22×D4D4411yescharacteristic
407C23×C4—221no—
408C23×C4C22×D1111yescharacteristic
409C23×C4C22×D1111yescharacteristic
410C2×M16—22no—
411C2×M16—41no—
412C2×M16—41no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417#121—222no—
418#121—222no—
419#121—222no—
420#121—441no—
421#121—444no—
422C4×D4—22no—
423C4×D4—22no—
424#117—222no—
425#117—222no—
426#117—441no—
427#117—441no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—441no—
441C2×C4⋊C4D4411yescharacteristic
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4D4411yescharacteristic
452C2×C22⋊C4D4411yescharacteristic
453C2×C42—221no—
454C2×C42—221no—
455C2×C42—221no—
456C2×C42C22×D1111yescharacteristic
457#106—222no—
458#106—441no—
459#102—222no—
460#102—441no—
461#102—441no—
462#102—441no—
463C22⋊C8—22no—
464C22⋊C8—41no—
465C22⋊C8—41no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471C2×C11—42no—
472C2×C11—81no—
473C2×C11#244411yescharacteristic
474C2×C11#309411yescharacteristic
475C2×C11#309911yescharacteristic
476C2×C11#330711yescharacteristic
477C2×C11#332111yescharacteristic
478C2×C11#332411yescharacteristic
479C2×C11#333211yescharacteristic
480D11—161no—
481C24—221no—
482C24C2×D4411yescharacteristic
483C24C2×D4411yescharacteristic
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—41no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—442no—
494C2×D4—442no—
495C2×D4—442no—
496C2×D4—442no—
497C2×D4—442no—
498C2×D4—881no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—881no—
519C22×C4C2×D4411yescharacteristic
520C22×C4C2×D4411yescharacteristic
521C22×C4C2×D4411yescharacteristic
522C22×C4C2×D4411yescharacteristic
523C22×C4#434112yes—
524C22×C4#434112yes—
525C22×C4C23×D1111yescharacteristic
526M16—44no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C4⋊C4—22no—
540C4⋊C4—112no—
541C4⋊C4—112no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—442no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—881no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C22⋊C4—442no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C22⋊C4—881no—
567C22⋊C4—881no—
568C22⋊C4—881no—
569C42—21no—
570C42—21no—
571C42—442no—
572C42—442no—
573C42—442no—
574C11#2622911yescharacteristic, complemented, Sylow
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23—441no—
592C23—441no—
593C23—441no—
594C23—441no—
595C23#6693912yes—
596C23C22×D4411yescharacteristic
597D4—44no—
598D4—441no—
599D4—441no—
600D4—441no—
601D4—441no—
602D4—884no—
603D4—884no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—884no—
644C2×C4#6693912yes—
645C2×C4#6696112yes—
646C2×C4C2×#434111yescharacteristic
647C2×C4C2×#434111yescharacteristic
648C2×C4#6703711yescharacteristic
649C2×C4#6703711yescharacteristic
650C2×C4#41×D1111yescharacteristic
651C2×C4#41×D1111yescharacteristic
652C8—41no—
653C8—41no—
654C8—41no—
655C8—41no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—881no—
671C22—881no—
672C22—881no—
673C22—881no—
674C22—881no—
675C22—881no—
676C22—881no—
677C22C2×#6693911yescharacteristic
678C22#1062308511yescharacteristic
679C22#1062308511yescharacteristic
680C22C2×#6696111yescharacteristic
681C22#1062327911yescharacteristic
682C22#1062328211yescharacteristic
683C22#1062328211yescharacteristic
684C4—22no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—442no—
689C4—442no—
690C4—881no—
691C4—881no—
692C4—881no—
693C4—881no—
694C4—881no—
695C4#1062312411yescharacteristic
696C4#1062313211yescharacteristic
697C4#1062313211yescharacteristic
698C4#1062318011yescharacteristic
699C2—42no—
700C2—81no—
701C2—1761no—
702C2#1307236411yescharacteristic
703C2#1307855711yescharacteristic
704C2#1307860711yescharacteristic
705C2#1308059411yescharacteristic
706C2#1308080411yescharacteristic
707C2#1308084811yescharacteristic
708C2#1308094411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1870C2
socleC23×C11C22×D4
prime radical#13072056C2
hypercenter#1870D11
hypocenterC11#26229
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #13071565C2semidirect
3. #13070175C2semidirect
4. #13070049C2semidirect
5. #13070021C2semidirect
6. #13069806C2semidirect
7. #13069244C2semidirect
8. #13069195C2semidirect
9. #13069054C2semidirect
10. #13068936C2semidirect
11. #13068936C2semidirect
12. #13068811C2semidirect
13. #13068712C2semidirect
14. #13068336C2semidirect
15. C11×#1870C2semidirect
232. #1870D11semidirect
574. C11#26229semidirect

Maximal subgroups

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

subgroupindex
#130720562
#130715652
#130701752
#130700492
#130700212
#130698062
#130692442
#130691952
#130690542
#130689362
#130688112
#130687122
#130683362
C11×#18702
#2622911