Finite Group Databasebeta

← #14814499

Subgroups — #14814499

Order 2816.

886 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072058C211yesmaximal, characteristic
2#13071546C211yesmaximal, characteristic, complemented
3#13070188C211yesmaximal, characteristic, complemented
4#13070047C211yesmaximal, characteristic, complemented
5#13070033C211yesmaximal, characteristic, complemented
6#13069799C211yesmaximal, characteristic, complemented
7#13069234C211yesmaximal, characteristic, complemented
8#13069207C211yesmaximal, characteristic, complemented
9#13069043C211yesmaximal, characteristic, complemented
10#13068938C211yesmaximal, characteristic, complemented
11#13068932C211yesmaximal, characteristic, complemented
12#13068905C211yesmaximal, characteristic, complemented
13#13068805C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#1825C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66948C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×#66937—21no—
24C2×C11×C22⋊C8C2211yescharacteristic
25C11×#380C2211yescharacteristic
26#10622825C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32#10622601C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622590C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622586C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622572—21no—
41#10622569—21no—
42#10622558—21no—
43C4×(C2×D11)⋊C4—21no—
44#10622546—21no—
45#10622289—21no—
46#10622278—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11D411yescharacteristic
62C22×D44—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#117—22no—
70C11×#117—41no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11D411yescharacteristic
80#66983—22no—
81#66983—41no—
82C4×C22⋊D11—22no—
83C4×C22⋊D11—22no—
84C2×(C2×D11)⋊C4—21no—
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⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4D411yescharacteristic
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×C8×D11—22no—
102C2×C8×D11—41no—
103C2×C8×D11—41no—
104#66948—22no—
105#66948—22no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—22no—
108C4⋊C4×D11—41no—
109C4⋊C4×D11—41no—
110#66937—44no—
111C11×C22⋊C8—41no—
112C11×#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C22⋊(C11⋊C8)—41no—
120#66885—41no—
121#66885—41no—
122(C2×D11)⋊C8—22no—
123#66882—22no—
124#66873—22no—
125#66873—41no—
126#66871—41no—
127#26208—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C23×D11C2×D411yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C2×C22⋊D11—22no—
144C2×C22⋊D11—22no—
145C2×C22⋊D11—22no—
146C2×C22⋊D11—42no—
147C2×C22⋊D11—42no—
148C2×C22⋊D11—81no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—42no—
162C2×D44—42no—
163C2×D44—42no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—81no—
173C2×C4×D11—81no—
174C2×C4×D11#4112yes—
175C2×C4×D11#4112yes—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4#4112yes—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—42no—
192C42×C11—42no—
193C22⋊Dic11—22no—
194C22⋊Dic11—81no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—81no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11#4112yes—
207Dic11⋊C4—22no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—81no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C8×D11—44no—
221#2416—111no—
222#2352—111no—
223#2101—111no—
224#2076—111no—
225#2073—111no—
226#2033—111no—
227#1925—111no—
228#1921—111no—
229#1893—111no—
230#1875—111no—
231#1874—111no—
232#1869—111no—
233#1852—111no—
234#1825D1111yescharacteristic, complemented
235C2×#340—111no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11C22×D411yescharacteristic
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11#12312yes—
256C22×D11#13512yes—
257C22×D11AGL(1,ℤ/8)12yes—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
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×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C22⋊D11—44no—
284C22⋊D11—84no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—22no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
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#12312yes—
303D44—41no—
304D44—41no—
305D44—41no—
306D44—41no—
307D44—84no—
308C4×D11—22no—
309C4×D11—22no—
310C4×D11—22no—
311C4×D11—22no—
312C4×D11—84no—
313C4×D11—84no—
314C8×C11—41no—
315C8×C11—41no—
316C11⋊C8—41no—
317C11⋊C8—41no—
318C23×C8—111no—
319C2×#121—111no—
320C2×#121—111no—
321C2×#121—221no—
322C2×C4×D4—111no—
323C2×#117C2×D1111yescharacteristic
324C22×C4⋊C4—111no—
325C22×C4⋊C4—111no—
326C2×#107—111no—
327C2×#107—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×C22⋊C8—111no—
333C2×C22⋊C8—111no—
334C2×C22⋊C8C2×D1111yescharacteristic
335#396—221no—
336#394—221no—
337#390—111no—
338#389—111no—
339#388—221no—
340#387—221no—
341#386—221no—
342#386—221no—
343#382—111no—
344#380—111no—
345#380—111no—
346#380C2×D1111yescharacteristic
347C4×C4⋊C4—111no—
348C4×C22⋊C4—221no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340C2×D1111yescharacteristic
356#340C2×D1111yescharacteristic
357#340C2×D1111yescharacteristic
358#340C2×D1111yescharacteristic
359#336—111no—
360#336—111no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11C2×#12311yescharacteristic
369C22×C11#54611yescharacteristic
370C22×C11#54611yescharacteristic
371C22×C11C2×#13511yescharacteristic
372C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C11#57611yescharacteristic
374C22×C11#57811yescharacteristic
375C2×D11—22no—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—22no—
380C2×D11—22no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C2×D11—81no—
388C2×D11#48214yes—
389C4×C11—41no—
390C4×C11—42no—
391C4×C11—81no—
392C4×C11—81no—
393C4×C11—81no—
394C4×C11#52911yescharacteristic
395C4×C11#53811yescharacteristic
396C4×C11#55311yescharacteristic
397C4×C11#55311yescharacteristic
398Dic11—22no—
399Dic11—41no—
400Dic11—41no—
401Dic11—42no—
402Dic11—81no—
403Dic11—81no—
404C22×D4—111no—
405C22×D4—111no—
406C22×D4—221no—
407C22×D4—221no—
408C23×C4—111no—
409C23×C4—221no—
410C23×C4—221no—
411C23×C4C22×D1111yescharacteristic
412C22×C8—111no—
413C22×C8—111no—
414C22×C8—222no—
415C22×C8—441no—
416C22×C8—441no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419#121—222no—
420#121—222no—
421#121—222no—
422#121—444no—
423#121—441no—
424C4×D4—222no—
425C4×D4—222no—
426#117—22no—
427#117—41no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—222no—
433C2×C4⋊C4—222no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—441no—
438C2×C4⋊C4—441no—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C4⋊C4C22×D1111yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—111no—
446C2×C22⋊C4—111no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C42—21no—
454C2×C42—111no—
455C2×C42—221no—
456#107—222no—
457#107—441no—
458#102—222no—
459#102—441no—
460#102—441no—
461#102—441no—
462C22⋊C8—41no—
463C22⋊C8—222no—
464C22⋊C8—441no—
465#95—21no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472C2×C11—81no—
473C2×C11#244411yescharacteristic
474C2×C11C2×#48211yescharacteristic
475C2×C11#309811yescharacteristic
476C2×C11#329711yescharacteristic
477C2×C11#330011yescharacteristic
478C2×C11#330811yescharacteristic
479C2×C11#331811yescharacteristic
480D11—24no—
481D11—161no—
482C24—111no—
483C24—221no—
484C24D4×D1111yescharacteristic
485C2×D4—222no—
486C2×D4—222no—
487C2×D4—222no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—442no—
495C2×D4—442no—
496C2×D4—442no—
497C2×D4—442no—
498C2×D4—442no—
499C2×D4—881no—
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—21no—
510C22×C4—111no—
511C22×C4—112no—
512C22×C4—112no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—442no—
523C22×C4—442no—
524C22×C4—442no—
525C22×C4—442no—
526C22×C4—881no—
527C22×C4—881no—
528C22×C4D4×D1111yescharacteristic
529C22×C4C23×D1111yescharacteristic
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—444no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—112no—
551C4⋊C4—222no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—442no—
558C4⋊C4—442no—
559C4⋊C4—442no—
560C4⋊C4#433912yes—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—222no—
564C22⋊C4—222no—
565C22⋊C4—442no—
566C22⋊C4—442no—
567C22⋊C4—442no—
568C22⋊C4—442no—
569C22⋊C4—881no—
570C22⋊C4—881no—
571C42—42no—
572C42—221no—
573C42—221no—
574C42—881no—
575C11#2620811yescharacteristic, complemented, Sylow
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—112no—
584C23—112no—
585C23—112no—
586C23—221no—
587C23—221no—
588C23—221no—
589C23—221no—
590C23—441no—
591C23—441no—
592C23—441no—
593C23—441no—
594C23—441no—
595C23—441no—
596C23—441no—
597C23C2×D4×D1111yescharacteristic
598D4—444no—
599D4—441no—
600D4—441no—
601D4—441no—
602D4—441no—
603D4—884no—
604D4—884no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—112no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—221no—
637C2×C4—222no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—884no—
647C2×C4—884no—
648C2×C4C2×#433911yescharacteristic
649C2×C4#6703711yescharacteristic
650C2×C4#41×D1111yescharacteristic
651C2×C4#41×D1111yescharacteristic
652C2×C4#41×D1111yescharacteristic
653C2×C4#6704211yescharacteristic
654C8—41no—
655C8—41no—
656C8—441no—
657C8—441no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—114no—
666C22—222no—
667C22—222no—
668C22—222no—
669C22—222no—
670C22—222no—
671C22—222no—
672C22—881no—
673C22—881no—
674C22—881no—
675C22—881no—
676C22—881no—
677C22—881no—
678C22—881no—
679C22#1062302111yescharacteristic
680C22D11×#12311yescharacteristic
681C22#1062318511yescharacteristic
682C22D11×#13511yescharacteristic
683C22#1062330011yescharacteristic
684C22D11×AGL(1,ℤ/8)11yescharacteristic
685C22#1062331011yescharacteristic
686C4—42no—
687C4—41no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—222no—
692C4—441no—
693C4—442no—
694C4—441no—
695C4—881no—
696C4—881no—
697C4#1062305911yescharacteristic
698C4#1062306111yescharacteristic
699C4#1062318811yescharacteristic
700C4#1062319211yescharacteristic
701C2—81no—
702C2—224no—
703C2—1761no—
704C2#1307236511yescharacteristic
705C2D11×#48211yescharacteristic
706C2#1307859711yescharacteristic
707C2#1308046711yescharacteristic
708C2#1308050611yescharacteristic
709C2#1308060811yescharacteristic
710C2#1308076011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radical#13072058C2
hypercenter#1825D11
hypocenterC11#26208
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
2. #13071546C2semidirect
3. #13070188C2semidirect
4. #13070047C2semidirect
5. #13070033C2semidirect
6. #13069799C2semidirect
7. #13069234C2semidirect
8. #13069207C2semidirect
9. #13069043C2semidirect
10. #13068938C2semidirect
11. #13068932C2semidirect
12. #13068905C2semidirect
13. #13068805C2semidirect
14. D11×#340C2semidirect
15. C11×#1825C2semidirect
234. #1825D11semidirect
575. C11#26208semidirect

Maximal subgroups

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

subgroupindex
#130720582
#130715462
#130701882
#130700472
#130700332
#130697992
#130692342
#130692072
#130690432
#130689382
#130689322
#130689052
#130688052
D11×#3402
C11×#18252
#2620811