Finite Group Databasebeta

← #14803910

Subgroups — #14803910

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622404C211yesmaximal, characteristic, complemented
2C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic
3#13073610C211yesmaximal, characteristic
4#13073535C211yesmaximal, characteristic
5#13070054C211yesmaximal, characteristic, complemented
6#13070049C211yesmaximal, characteristic, complemented
7#13069810C211yesmaximal, characteristic, complemented
8#13069575C211yesmaximal, characteristic, complemented
9#13069376C211yesmaximal, characteristic, complemented
10#13069040C211yesmaximal, characteristic, complemented
11#13069036C211yesmaximal, characteristic, complemented
12#13068639C211yesmaximal, characteristic, complemented
13#13068638C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#2035C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×#66941C2211yescharacteristic
23C2×#66938—21no—
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31#10622825C2211yescharacteristic
32#10622825C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622607—21no—
38#10622600C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622600C2211yescharacteristic
41#10622589C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622585—21no—
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46#10622570—21no—
47#10622565—21no—
48#10622561—21no—
49#10622404—24no—
50(C22⋊D11)⋊C8—24no—
51#10622288—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×Dic22—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11D411yescharacteristic
79#66999—22no—
80#66999—41no—
81Q8×Dic11—22no—
82Q8×Dic11—22no—
83C4×C22⋊D11—22no—
84C4×C22⋊D11—22no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4D411yescharacteristic
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8—22no—
104C22×C11⋊C8—22no—
105C22×C11⋊C8—41no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C2×C8×D11—22no—
109C2×C8×D11—22no—
110C2×C8×D11—41no—
111#66941—22no—
112#66941—22no—
113#66938—44no—
114C11×#106—41no—
115C11×#103—22no—
116C11×#103—22no—
117C11×C22⋊C8—22no—
118C11×#95—21no—
119#66899—22no—
120#66899—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127(C2×D11)⋊C8—22no—
128#66881—22no—
129Dic11⋊C8D414yes—
130C8×Dic11—22no—
131#66872—22no—
132#66872—41no—
133#25341—111nomaximal, Sylow
134C24×C11C2×D411yescharacteristic
135C23×D11C2×D411yescharacteristic
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11#4112yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—22no—
155C2×C22⋊D11—22no—
156C2×C22⋊D11SD1614yes—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×Dic22—42no—
171C2×Dic22—42no—
172C2×Dic22—42no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C2×D412yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C22⋊Dic11—22no—
189C22⋊Dic11—42no—
190C22⋊Dic11—81no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205Dic11⋊C4—22no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—81no—
210C4×Dic11—42no—
211C4×Dic11—42no—
212C4×Dic11C2×D412yes—
213C4×Dic11#4112yes—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—44no—
219C2×C11⋊C8C2×D412yes—
220C2×C11⋊C8#4112yes—
221C8×D11—44no—
222C2×#475—111no—
223C2×C8×D4—111no—
224#2547—111no—
225#2538—111no—
226#2077—111no—
227#2077—111no—
228#2035—111no—
229#2035D1111yescharacteristic, complemented
230#1990—111no—
231#1948—111no—
232#1892—111no—
233#1892—111no—
234#1807—111no—
235#1807—111no—
236C4×#103—111no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11C2×SD1612yes—
244C23×C11C22×D411yescharacteristic
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11C2×SD1612yes—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—41no—
255Q8×C11—41no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C112−1+411yescharacteristic
281C22⋊D11—28no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—41no—
288C2×Dic11—41no—
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#12112yes—
300C2×Dic11#12112yes—
301C2×Dic11C2×SD1612yes—
302C2×Dic11#13512yes—
303C4×D11—41no—
304C4×D11—41no—
305C4×D11—41no—
306C4×D11—41no—
307Dic22—84no—
308C8×C11—22no—
309C8×C11—41no—
310C11⋊C8—22no—
311C11⋊C8—22no—
312C23×C8—111no—
313C23×C8—111no—
314C2×C4⋊Q8—111no—
315C2×#124—221no—
316C2×C22⋊Q8—111no—
317C2×C22⋊Q8C2×D1111yescharacteristic
318C2×C4×Q8—111no—
319C2×C4×D4—111no—
320#475—224no—
321C8×D4—224no—
322C2×#106—111no—
323C2×#106—111no—
324C2×#106—111no—
325C2×#106C2×D1111yescharacteristic
326C2×C4⋊C8—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103C2×D1111yescharacteristic
330C2×#103C2×D1111yescharacteristic
331C2×C22⋊C8—111no—
332C2×C22⋊C8C2×D1111yescharacteristic
333C2×C4×C8—111no—
334#397—221no—
335#397—221no—
336#396—221no—
337#396—221no—
338#391—221no—
339#390—221no—
340#389—221no—
341#384—111no—
342#380—111no—
343#380—111no—
344#380—111no—
345#380—111no—
346#380—111no—
347#380C2×D1111yescharacteristic
348C4×C4⋊C4—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340C2×D1111yescharacteristic
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11C2×#12111yescharacteristic
365C22×C11#54611yescharacteristic
366C22×C11#54711yescharacteristic
367C22×C11C22×SD1611yescharacteristic
368C22×C11C2×#13511yescharacteristic
369C22×C11#57711yescharacteristic
370C22×C11#57811yescharacteristic
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—41no—
378C4×C11—41no—
379C4×C11—42no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11#52911yescharacteristic
384C4×C11#54211yescharacteristic
385C4×C11#54611yescharacteristic
386C4×C11#54811yescharacteristic
387Dic11—22no—
388Dic11—41no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392Dic11—81no—
393Dic11#46514yes—
394C22×Q8—221no—
395C22×Q8C22×D1111yescharacteristic
396C22×D4—111no—
397C23×C4—111no—
398C23×C4C22×D1111yescharacteristic
399C22×C8—111no—
400C22×C8—111no—
401C22×C8—222no—
402C22×C8—222no—
403C22×C8—222no—
404C22×C8—222no—
405C22×C8—441no—
406C22×C8—441no—
407C22×C8C22×D1111yescharacteristic
408C22×C8C22×D1111yescharacteristic
409C4⋊Q8—222no—
410C4⋊Q8—222no—
411#124—444no—
412C22⋊Q8—22no—
413C22⋊Q8—41no—
414C22⋊Q8—222no—
415C22⋊Q8—441no—
416C4×Q8—222no—
417C4×Q8—222no—
418C4×D4—222no—
419C4×D4—222no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—111no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C42—111no—
445C2×C42—221no—
446C2×C42—221no—
447#106—41no—
448#106—222no—
449#106—222no—
450#106—441no—
451C4⋊C8—114no—
452#103—22no—
453#103—22no—
454#103—222no—
455#103—222no—
456C22⋊C8—22no—
457C22⋊C8—222no—
458C4×C8—222no—
459#95—21no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466C2×C11—42no—
467C2×C11#242711yescharacteristic
468C2×C11C2×#46511yescharacteristic
469C2×C11#306311yescharacteristic
470C2×C11#329811yescharacteristic
471C2×C11#330411yescharacteristic
472C2×C11#333511yescharacteristic
473C2×C11#334211yescharacteristic
474D11—42no—
475C24—111no—
476C24D4×D1111yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—442no—
483C2×Q8—442no—
484C2×Q8—442no—
485C2×Q8#434112yes—
486C2×D4—114no—
487C2×D4—222no—
488C2×D4—222no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4D4×D1111yescharacteristic
513C22×C4C23×D1111yescharacteristic
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—112no—
520C2×C8—112no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—444no—
526C2×C8—444no—
527C2×C8D4×D1112yes—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—222no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4—442no—
548C4⋊C4—881no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—222no—
552C22⋊C4—222no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—881no—
558C22⋊C4—881no—
559C42—112no—
560C42—112no—
561C42—442no—
562C42—442no—
563C11#2534111yescharacteristic, complemented, Sylow
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—112no—
571C23—221no—
572C23—221no—
573C23—221no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23SD16×D1112yes—
578C23C2×D4×D1111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583Q8—884no—
584D4—228no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—112no—
605C2×C4—112no—
606C2×C4—112no—
607C2×C4—112no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4C2×D4×D1111yescharacteristic
630C2×C4C2×#434111yescharacteristic
631C2×C4#6703711yescharacteristic
632C2×C4#41×D1111yescharacteristic
633C2×C4#41×D1111yescharacteristic
634C2×C4#6704311yescharacteristic
635C8—22no—
636C8—41no—
637C8—222no—
638C8—222no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—222no—
647C22—222no—
648C22—222no—
649C22—441no—
650C22—441no—
651C22—441no—
652C22—441no—
653C22#1062312211yescharacteristic
654C22D11×#12111yescharacteristic
655C22#1062318611yescharacteristic
656C22C2×SD16×D1111yescharacteristic
657C22D11×#13511yescharacteristic
658C22#1062330911yescharacteristic
659C22#1062331011yescharacteristic
660C4—41no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—114no—
666C4—222no—
667C4—441no—
668C4—881no—
669C4—881no—
670C4—881no—
671C4—881no—
672C4#1062312911yescharacteristic
673C4#1062314111yescharacteristic
674C4#1062318011yescharacteristic
675C4#1062320011yescharacteristic
676C2—42no—
677C2—442no—
678C2#1307218611yescharacteristic
679C2D11×#46511yescharacteristic
680C2#1307830411yescharacteristic
681C2#1308047411yescharacteristic
682C2#1308054811yescharacteristic
683C2#1308096611yescharacteristic
684C2#1308104111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2035C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenter#2035D11
hypocenterC11#25341
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
1. C2×#10622404C2semidirect
5. #13070054C2semidirect
6. #13070049C2semidirect
7. #13069810C2semidirect
8. #13069575C2semidirect
9. #13069376C2semidirect
10. #13069040C2semidirect
11. #13069036C2semidirect
12. #13068639C2semidirect
13. #13068638C2semidirect
14. #103×Dic11C2semidirect
15. C11×#2035C2semidirect
229. #2035D11semidirect
563. C11#25341semidirect

Maximal subgroups

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

subgroupindex
C2×#106224042
C2×(C22⋊D11)⋊C82
#130736102
#130735352
#130700542
#130700492
#130698102
#130695752
#130693762
#130690402
#130690362
#130686392
#130686382
#103×Dic112
C11×#20352
#2534111