Finite Group Databasebeta

← #14756807

Subgroups — #14756807

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622398C211yesmaximal, characteristic
2#13071078C211yesmaximal, characteristic, complemented
3C4×#66946C211yesmaximal, characteristic, complemented
4#13069238C211yesmaximal, characteristic, complemented
5#13069199C211yesmaximal, characteristic, complemented
6#13069194C211yesmaximal, characteristic, complemented
7#13068967C211yesmaximal, characteristic
8#13068961C211yesmaximal, characteristic
9#13068874C211yesmaximal, characteristic, complemented
10#13068866C211yesmaximal, characteristic, complemented
11#13068516C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068363C211yesmaximal, characteristic, complemented
15C11×#1926C211yesmaximal, characteristic, complemented
16C2×D4×Dic11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×#66930—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C42×D11—21no—
23C2×C11×#106C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41#10622558—21no—
42#10622557—21no—
43C22⋊C4×Dic11—21no—
44C4×(C2×D11)⋊C4—21no—
45C42×Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622398C418yescomplemented
48#10622279—21no—
49#10622279—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78D4×Dic11—22no—
79D4×Dic11C2×C414yescomplemented
80C2×#4323—22no—
81C2×#4323—22no—
82C2×#4323C2×C414yes—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11D411yescharacteristic
97C2×C4×Dic11D411yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66946—22no—
103#66946—22no—
104#66946—22no—
105#66946C2×C414yes—
106#66930—44no—
107C4×D44—22no—
108C4×D44—22no—
109C42×D11—44no—
110C11×#106—22no—
111C11×#102—22no—
112C11×#102C2×C414yescomplemented
113C11×#95—21no—
114#66896—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66885—22no—
121#66885C2×C414yes—
122#66882—22no—
123#66879—22no—
124#66879C2×C414yescomplemented
125#66873—22no—
126#66872C2×C414yescomplemented
127#21122—111nomaximal, Sylow
128C24×C11—21no—
129C23×D11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11C22×C412yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—24no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C22×C412yes—
156C2×D44#4112yes—
157C2×D44#4112yes—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C22×C412yes—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C22×C412yes—
178C11×C4⋊C4#4112yes—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184C22⋊Dic11—24no—
185C22⋊Dic11—42no—
186C22⋊Dic11—42no—
187#4323—28no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11C22×C412yes—
196C4⋊Dic11#4112yes—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199C4×Dic11—22no—
200C4×Dic11—22no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—41no—
204C4×Dic11—41no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208C4×Dic11C22×C412yes—
209C4×Dic11#4112yes—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C22×C412yes—
216C2×#442—111no—
217#2293—111no—
218C42×D4—111no—
219#1926D1111yescharacteristic, complemented
220#1925—111no—
221#1920—111no—
222#1919—111no—
223#1879—111no—
224#1879—111no—
225#1864—111no—
226#1862—111no—
227#1776—111no—
228#1762—111no—
229#1762—111no—
230#1745—111no—
231C23×C11—22no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C22×D411yescharacteristic
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—41no—
249D4×C11—41no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11AGL(1,ℤ/8)12yes—
265C2×C4×C11C23×C411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—48no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11C4×D412yes—
291C2×Dic11C4×D412yes—
292C2×Dic11AGL(1,ℤ/8)12yes—
293D44—22no—
294D44—22no—
295D44—22no—
296D44#11714yescomplemented
297C4×D11—48no—
298C4×D11—48no—
299C4×D11—48no—
300C8×C11—22no—
301C8×C11—41no—
302C11⋊C8—22no—
303C11⋊C8—41no—
304C22×D8—111no—
305C2×C4×D4—111no—
306C2×C4×D4—111no—
307C2×C4×D4—111no—
308C2×C4×D4—111no—
309C2×#117—221no—
310C22×C42—221no—
311#442—118no—
312C2×#107—111no—
313C2×#106—111no—
314C2×#106C2×D1111yescharacteristic
315C2×#102—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102C2×D1111yescharacteristic
320C2×#102C2×D1111yescharacteristic
321C2×#97—111no—
322C2×#97—111no—
323#390—111no—
324#390C2×D1111yescharacteristic
325#389—111no—
326#389—111no—
327#388—221no—
328#388—221no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—111no—
332C4×C4⋊C4C2×D1111yescharacteristic
333C4×C22⋊C4—221no—
334C4×C22⋊C4—221no—
335C4×C22⋊C4—221no—
336C4×C22⋊C4—221no—
337C43—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#336—111no—
345#336—111no—
346#336—111no—
347#336C2×D1111yescharacteristic
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11C2×C4×D411yescharacteristic
356C22×C11#52511yescharacteristic
357C22×C11#52511yescharacteristic
358C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C11#57511yescharacteristic
361C22×C11#57511yescharacteristic
362C2×D11—24no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—42no—
369C4×C11—22no—
370C4×C11—41no—
371C4×C11—42no—
372C4×C11—42no—
373C4×C11—81no—
374C4×C11C2×#11711yescharacteristic
375C4×C11C4×#4111yescharacteristic
376C4×C11#52911yescharacteristic
377C4×C11#52911yescharacteristic
378Dic11—22no—
379Dic11—22no—
380Dic11—22no—
381Dic11—42no—
382Dic11—41no—
383Dic11—42no—
384Dic11—81no—
385C22×D4—111no—
386C22×D4C22×D1111yescharacteristic
387C23×C4—221no—
388C23×C4—221no—
389C23×C4—221no—
390C23×C4—221no—
391C2×D8—114no—
392C2×D8—222no—
393C2×D8—222no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398C4×D4—114no—
399C4×D4—114no—
400C4×D4—222no—
401C4×D4—222no—
402C4×D4—222no—
403C4×D4—222no—
404C4×D4—222no—
405C4×D4—222no—
406#117—444no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C42—21no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42—444no—
434C2×C42C22×D1111yescharacteristic
435#107—222no—
436#106—22no—
437#106—114no—
438#102—22no—
439#102—114no—
440#102—222no—
441#102—222no—
442#102—222no—
443#102C4×D1114yescomplemented
444#97—114no—
445#97—222no—
446#95—21no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452C2×C11—82no—
453C2×C11#229011yescharacteristic
454C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
455C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
456C2×C11#310911yescharacteristic
457C2×C11#311111yescharacteristic
458C2×C11#311411yescharacteristic
459C2×C11#311511yescharacteristic
460D11—44no—
461C24—21no—
462C24—221no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—112no—
469C2×D4—112no—
470C2×D4—112no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4C2×C4×D1112yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4D4×D1111yescharacteristic
498C22×C4D4×D1111yescharacteristic
499C22×C4C23×D1111yescharacteristic
500D8—228no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—112no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8C2×C4×D1112yes—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—112no—
518C4⋊C4—112no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4C2×C4×D1112yes—
526C4⋊C4#434112yes—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—224no—
530C22⋊C4—224no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C42—21no—
536C42—21no—
537C42—42no—
538C42—112no—
539C42—112no—
540C42—222no—
541C42—222no—
542C42—221no—
543C42—221no—
544C42—441no—
545C42—441no—
546C42—442no—
547C42—442no—
548C42—442no—
549C11#2112211yescharacteristic, complemented, Sylow
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—222no—
558C23—222no—
559C23—222no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23C2×D4×D1111yescharacteristic
565D4—22no—
566D4—22no—
567D4—41no—
568D4—41no—
569D4—114no—
570D4—222no—
571D4—222no—
572D4—222no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—112no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—222no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—448no—
602C2×C4—448no—
603C2×C4—448no—
604C2×C4—448no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4#6696712yes—
613C2×C4C22×C4×D1111yescharacteristic
614C2×C4C2×#434111yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C2×C4#41×D1111yescharacteristic
619C8—22no—
620C8—41no—
621C8—222no—
622C8—441no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—224no—
631C22—442no—
632C22—442no—
633C22—442no—
634C22—442no—
635C22—442no—
636C22—442no—
637C22C4×D4×D1111yescharacteristic
638C22#1062313711yescharacteristic
639C22#1062318711yescharacteristic
640C22C2×#6696711yescharacteristic
641C22#1062329911yescharacteristic
642C22D11×AGL(1,ℤ/8)11yescharacteristic
643C22#1062330411yescharacteristic
644C4—22no—
645C4—42no—
646C4—41no—
647C4—42no—
648C4—81no—
649C4—222no—
650C4—222no—
651C4—222no—
652C4—442no—
653C4—442no—
654C4—441no—
655C4—881no—
656C4D11×#11711yescharacteristic
657C4C4×#434111yescharacteristic
658C4#1062321111yescharacteristic
659C4#1062323711yescharacteristic
660C2—82no—
661C2—444no—
662C2#1307105811yescharacteristic
663C2C4×#6696711yescharacteristic
664C2#1307742711yescharacteristic
665C2#1307870411yescharacteristic
666C2#1307872011yescharacteristic
667C2#1307875311yescharacteristic
668C2#1307876611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1926C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#1926D11
hypocenterC11#21122
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. #13071078C2semidirect
3. C4×#66946C2semidirect
4. #13069238C2semidirect
5. #13069199C2semidirect
6. #13069194C2semidirect
9. #13068874C2semidirect
10. #13068866C2semidirect
11. #13068516C2semidirect
12. #13068443C2semidirect
13. #13068440C2semidirect
14. #13068363C2semidirect
15. C11×#1926C2semidirect
47. #10622398C4semidirect
79. D4×Dic11C2×C4semidirect
112. C11×#102C2×C4semidirect
124. #66879C2×C4semidirect
126. #66872C2×C4semidirect
219. #1926D11semidirect
296. D44#117semidirect
443. #102C4×D11semidirect
549. C11#21122semidirect

Maximal subgroups

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

subgroupindex
C2×#106223982
#130710782
C4×#669462
#130692382
#130691992
#130691942
#130689672
#130689612
#130688742
#130688662
#130685162
#130684432
#130684402
#130683632
C11×#19262
#2112211