Finite Group Databasebeta

← #14814815

Subgroups — #14814815

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#13072050C211yesmaximal, characteristic
2#13071566C211yesmaximal, characteristic, complemented
3#13070177C211yesmaximal, characteristic, complemented
4#13070055C211yesmaximal, characteristic, complemented
5#13070023C211yesmaximal, characteristic, complemented
6#13069808C211yesmaximal, characteristic, complemented
7#13069241C211yesmaximal, characteristic, complemented
8#13069197C211yesmaximal, characteristic, complemented
9#13069054C211yesmaximal, characteristic, complemented
10#13068938C211yesmaximal, characteristic, complemented
11#13068937C211yesmaximal, characteristic, complemented
12#13068913C211yesmaximal, characteristic, complemented
13#13068809C211yesmaximal, characteristic, complemented
14#13068709C211yesmaximal, characteristic, complemented
15C11×#1736C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983—21no—
20C2×#66983C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×#66948C2211yescharacteristic
23C2×#66945C2211yescharacteristic
24#10622826—21no—
25#10622825C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31#10622607—21no—
32#10622604—21no—
33#10622601C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622589C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43#10622570—21no—
44#10622557—21no—
45#10622553—21no—
46C4×Dic11⋊C4—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C22×C22⋊D11D411yescharacteristic
63C22×D44—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C2×C11×M16—22no—
67C2×C11×M16—41no—
68C2×C11×M16—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#117—22no—
72C11×#117—41no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84#66983—22no—
85#66983—22no—
86#66983—44no—
87C4×C22⋊D11—22no—
88C4×C22⋊D11—22no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4D411yescharacteristic
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4D411yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66948—22no—
110#66948—41no—
111#66945—22no—
112#66945—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)—22no—
119#66885—41no—
120#66885—41no—
121(C2×D11)⋊C8—41no—
122(C2×D11)⋊C8—41no—
123#66873—22no—
124#66873—41no—
125#66872—22no—
126#66872—41no—
127#26229—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—42no—
140C22×C4×C11—42no—
141C22×C4×C11—81no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11#4112yes—
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—22no—
147C2×C22⋊D11—22no—
148C2×C22⋊D11—41no—
149C2×C22⋊D11—42no—
150C2×C22⋊D11—42no—
151C2×C22⋊D11—42no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—42no—
165C2×D44—42no—
166C2×D44—81no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—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—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4#4112yes—
188C11×C4⋊C4#4112yes—
189C11×C22⋊C4—42no—
190C42×C11—42no—
191C22⋊Dic11—22no—
192C22⋊Dic11—81no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—81no—
200(C2×D11)⋊C4—81no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—42no—
208Dic11⋊C4—22no—
209Dic11⋊C4—42no—
210Dic11⋊C4—81no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
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#1870—111no—
233#1853—111no—
234#1825—111no—
235#1736D1111yescharacteristic, complemented
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11#12312yes—
243C23×C11C22×D411yescharacteristic
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
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—84no—
277C2×C4×C11#12312yes—
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C22⋊D11—44no—
285C22⋊D11—84no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
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—41no—
303C2×Dic11AGL(1,ℤ/8)12yes—
304D44—41no—
305D44—41no—
306D44—41no—
307D44—41no—
308D44—84no—
309C4×D11—41no—
310C4×D11—41no—
311C4×D11—41no—
312C4×D11—41no—
313C8×C11—41no—
314C8×C11—41no—
315C11⋊C8—41no—
316C11⋊C8—41no—
317C22×M16C2×D1111yescharacteristic
318C2×#121—111no—
319C2×#121—111no—
320C2×#121—221no—
321C2×C4×D4—111no—
322C2×#117—111no—
323C2×#117C2×D1111yescharacteristic
324C22×C4⋊C4C2×D1111yescharacteristic
325C2×#106—111no—
326C2×#106—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×C22⋊C8—111no—
332C2×C22⋊C8—111no—
333C2×C22⋊C8—111no—
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#340C2×D1111yescharacteristic
355#340C2×D1111yescharacteristic
356#340C2×D1111yescharacteristic
357#340C2×D1111yescharacteristic
358#336—111no—
359#336—111no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11C2×#12311yescharacteristic
368C22×C11#54611yescharacteristic
369C22×C11#54611yescharacteristic
370C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C11#57511yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57711yescharacteristic
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—41no—
378C2×D11—41no—
379C2×D11—41no—
380C2×D11—41no—
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—42no—
390C4×C11—42no—
391C4×C11—81no—
392C4×C11—81no—
393C4×C11#52911yescharacteristic
394C4×C11#53811yescharacteristic
395C4×C11#55311yescharacteristic
396C4×C11#55311yescharacteristic
397Dic11—22no—
398Dic11—41no—
399Dic11—41no—
400Dic11—81no—
401Dic11—81no—
402Dic11—81no—
403C22×D4—111no—
404C22×D4—111no—
405C22×D4—221no—
406C22×D4—221no—
407C23×C4—21no—
408C23×C4—111no—
409C23×C4C22×D1111yescharacteristic
410C2×M16—22no—
411C2×M16—41no—
412C2×M16—41no—
413C22×C8—111no—
414C22×C8—111no—
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417#121—222no—
418#121—222no—
419#121—222no—
420#121—441no—
421#121—444no—
422C4×D4—222no—
423C4×D4—222no—
424#117—22no—
425#117—41no—
426#117—222no—
427#117—441no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—111no—
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⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C42—21no—
454C2×C42—111no—
455C2×C42—221no—
456C2×C42—221no—
457#106—222no—
458#106—441no—
459#102—222no—
460#102—441no—
461#102—441no—
462#102—441no—
463C22⋊C8—222no—
464C22⋊C8—441no—
465C22⋊C8—441no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471C2×C11—42no—
472C2×C11#244411yescharacteristic
473C2×C11#309411yescharacteristic
474C2×C11#309911yescharacteristic
475C2×C11#330711yescharacteristic
476C2×C11#332111yescharacteristic
477C2×C11#332411yescharacteristic
478C2×C11#333211yescharacteristic
479D11—81no—
480D11—161no—
481C24—111no—
482C24—221no—
483C24D4×D1111yescharacteristic
484C2×D4—222no—
485C2×D4—222no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—442no—
493C2×D4—442no—
494C2×D4—441no—
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—42no—
508C22×C4—42no—
509C22×C4—81no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4#433912yes—
523C22×C4D4×D1111yescharacteristic
524C22×C4#434312yes—
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—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—222no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—442no—
554C4⋊C4—442no—
555C4⋊C4—881no—
556C4⋊C4#433912yes—
557C4⋊C4#433912yes—
558C22⋊C4—42no—
559C22⋊C4—222no—
560C22⋊C4—222no—
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—42no—
570C42—221no—
571C42—221no—
572C42—442no—
573C42—442no—
574C11#2622911yescharacteristic, complemented, Sylow
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—221no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23—221no—
587C23—221no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23—441no—
592C23—441no—
593C23—441no—
594C23—441no—
595C23#6694712yes—
596C23C2×D4×D1111yescharacteristic
597D4—444no—
598D4—441no—
599D4—441no—
600D4—441no—
601D4—441no—
602D4—884no—
603D4—884no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
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—84no—
623C2×C4—112no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
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—441no—
644C2×C4—441no—
645C2×C4#6694712yes—
646C2×C4C2×#433911yescharacteristic
647C2×C4C2×#433911yescharacteristic
648C2×C4C2×#433911yescharacteristic
649C2×C4#6703711yescharacteristic
650C2×C4#6703711yescharacteristic
651C2×C4C2×#434311yescharacteristic
652C8—41no—
653C8—41no—
654C8—441no—
655C8—441no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—441no—
664C22—441no—
665C22—441no—
666C22—441no—
667C22—441no—
668C22—441no—
669C22—441no—
670C22—881no—
671C22—881no—
672C22—881no—
673C22—881no—
674C22—881no—
675C22—881no—
676C22—881no—
677C22#1062302111yescharacteristic
678C22#1062302111yescharacteristic
679C22C2×#6694711yescharacteristic
680C22D11×AGL(1,ℤ/8)11yescharacteristic
681C22#1062330611yescharacteristic
682C22#1062330811yescharacteristic
683C22#1062330911yescharacteristic
684C4—22no—
685C4—42no—
686C4—42no—
687C4—81no—
688C4—81no—
689C4—222no—
690C4—441no—
691C4—441no—
692C4—881no—
693C4—881no—
694C4—881no—
695C4#1062301011yescharacteristic
696C4#1062302511yescharacteristic
697C4#1062304511yescharacteristic
698C4#1062304511yescharacteristic
699C2—42no—
700C2—881no—
701C2—1761no—
702C2#1307236611yescharacteristic
703C2#1307855811yescharacteristic
704C2#1307860911yescharacteristic
705C2#1308059311yescharacteristic
706C2#1308080311yescharacteristic
707C2#1308084311yescharacteristic
708C2#1308093911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radical#13072050C2
hypercenter#1736D11
hypocenterC11#26229
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. #13071566C2semidirect
3. #13070177C2semidirect
4. #13070055C2semidirect
5. #13070023C2semidirect
6. #13069808C2semidirect
7. #13069241C2semidirect
8. #13069197C2semidirect
9. #13069054C2semidirect
10. #13068938C2semidirect
11. #13068937C2semidirect
12. #13068913C2semidirect
13. #13068809C2semidirect
14. #13068709C2semidirect
15. C11×#1736C2semidirect
235. #1736D11semidirect
574. C11#26229semidirect

Maximal subgroups

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

subgroupindex
#130720502
#130715662
#130701772
#130700552
#130700232
#130698082
#130692412
#130691972
#130690542
#130689382
#130689372
#130689132
#130688092
#130687092
C11×#17362
#2622911