Finite Group Databasebeta

← #14680419

Subgroups — #14680419

Order 2816.

1978 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic
2C2×#10622280C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4#13066867C212yesmaximal, complemented
5#13066864C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7#13066856C212yesmaximal
8#13066854C211yesmaximal, characteristic, complemented
9#13066852C211yesmaximal, characteristic, complemented
10#13066848C211yesmaximal, characteristic, complemented
11C11×#1436C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26C2×#66947—24no—
27C2×#66947—24no—
28C2×#66947C418yescomplemented
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C4×(C2×D11)⋊C4—24no—
39#10622280—24no—
40C24×D11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—42no—
54C22×D44—42no—
55C22×D44C2×C414yes—
56C22×C4×D11—42no—
57C22×C4×D11—42no—
58C22×C4×D11C2×C414yes—
59C22×C4×D11D414yes—
60C22×C4×D11D414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2×C414yes—
64C2×C42×C11—22no—
65C2×C42×C11—42no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4—42no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4C2×C414yes—
85C2×(C2×D11)⋊C4C2×C414yes—
86C2×(C2×D11)⋊C4C2×C414yes—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—42no—
91C2×Dic11⋊C4—42no—
92C2×Dic11⋊C4C2×C414yes—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—42no—
95#66947—232no—
96C11×#95—22no—
97C11×#95—24no—
98C11×#95—42no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#14287—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—21no—
114C23×D11—21no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11C22×C412yes—
122C23×D11C22×C412yes—
123C23×D11C2×D412yes—
124C23×D11C2×D412yes—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11C22×C412yes—
149C22×C4×C11C22×C412yes—
150C22×C4×C11C22×C412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11#4114yes—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11C22×C412yes—
174C22×Dic11C22×C412yes—
175C22×Dic11C2×D412yes—
176C22×Dic11C2×D412yes—
177C22×Dic11#4114yes—
178C2×D44—28no—
179C2×D44—48no—
180C2×D44—44no—
181C2×D44—48no—
182C2×D44—44no—
183C2×C4×D11—48no—
184C2×C4×D11—44no—
185C2×C4×D11—44no—
186C2×C4×D11—48no—
187C2×C4×D11C22⋊C4116yescomplemented
188C11×C4⋊C4—28no—
189C42×C11—44no—
190(C2×D11)⋊C4—216no—
191(C2×D11)⋊C4—28no—
192(C2×D11)⋊C4—28no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—48no—
195(C2×D11)⋊C4—48no—
196(C2×D11)⋊C4—48no—
197Dic11⋊C4—28no—
198Dic11⋊C4—48no—
199C4×Dic11—44no—
200C22×#123—111no—
201C2×#380—111no—
202C2×C4×C22⋊C4—111no—
203#1441—112no—
204#1440—112no—
205#1439—112no—
206#1438—112no—
207#1437—111no—
208#1437—111no—
209#1436—111no—
210#1436D1111yescharacteristic, complemented
211C23×C11C23×C411yescharacteristic
212C23×C11C22×D411yescharacteristic
213C23×C11C22×D411yescharacteristic
214C23×C11C2×#4112yes—
215C23×C11C2×#4112yes—
216C23×C11H(5,𝔽2)12yes—
217C23×C11H(5,𝔽2)12yes—
218C23×C11H(5,𝔽2)12yes—
219C23×C112−1+412yes—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—22no—
227C22×D11—24no—
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—24no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11—42no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—41no—
248C22×D11—42no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—42no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11—42no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11C2×C22⋊C414yes—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—41no—
278C2×C4×C11—42no—
279C2×C4×C11—41no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11C2×C22⋊C414yes—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—24no—
297C2×Dic11—24no—
298C2×Dic11—24no—
299C2×Dic11—24no—
300C2×Dic11—42no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—42no—
311C2×Dic11—42no—
312C2×Dic11—42no—
313C2×Dic11—42no—
314C2×Dic11C2×C22⋊C414yes—
315D44—416no—
316C4×D11—416no—
317C23×D4—111no—
318C24×C4—111no—
319C2×#123—118no—
320C2×#123—224no—
321C2×#123—224no—
322C22×C4⋊C4—111no—
323C22×C4⋊C4—112no—
324C22×C4⋊C4C2×D1111yescharacteristic
325C22×C22⋊C4—111no—
326C22×C22⋊C4—111no—
327C22×C22⋊C4—111no—
328C22×C22⋊C4—112no—
329C22×C22⋊C4—112no—
330C22×C22⋊C4—112no—
331C22×C22⋊C4—112no—
332C22×C42—111no—
333C22×C42C2×D1111yescharacteristic
334#380—224no—
335C4×C22⋊C4—224no—
336C2×#95—111no—
337C2×#95—112no—
338C2×#95—112no—
339C2×#95—112no—
340C2×#95—112no—
341C2×#95—112no—
342C2×#95C2×D1111yescharacteristic
343C2×#95C2×D1112yes—
344C2×#95C2×D1112yes—
345C22×C11C22×C22⋊C411yescharacteristic
346C22×C11C4×#4111yescharacteristic
347C22×C11C4×#4111yescharacteristic
348C22×C11#51812yes—
349C22×C11#52012yes—
350C22×C11#52512yes—
351C22×C11#53212yes—
352C22×C11#53411yescharacteristic
353C22×C11#53412yes—
354C22×C11#53411yescharacteristic
355C22×C11#53511yescharacteristic
356C22×C11#53611yescharacteristic
357C22×C11#53712yes—
358C22×C11#53812yes—
359C22×C11#53812yes—
360C22×C11#53912yes—
361C22×C11#53912yes—
362C22×C11#54012yes—
363C22×C11#54012yes—
364C22×C11#54212yes—
365C22×C11#54212yes—
366C2×D11—24no—
367C2×D11—24no—
368C2×D11—24no—
369C2×D11—44no—
370C2×D11—44no—
371C2×D11—44no—
372C2×D11—44no—
373C2×D11—44no—
374C2×D11—44no—
375C2×D11—42no—
376C2×D11—42no—
377C2×D11—44no—
378C2×D11—44no—
379C2×D11—42no—
380C2×D11—82no—
381C2×D11—82no—
382C2×D11—82no—
383C2×D11—82no—
384C4×C11—24no—
385C4×C11—42no—
386C4×C11—44no—
387C4×C11—42no—
388C4×C11—82no—
389Dic11—24no—
390Dic11—42no—
391Dic11—44no—
392Dic11—82no—
393C25—111no—
394C25—111no—
395C22×D4—114no—
396C22×D4—222no—
397C22×D4—222no—
398C22×D4—442no—
399C22×D4—442no—
400C23×C4—111no—
401C23×C4—114no—
402C23×C4—114no—
403C23×C4—114no—
404C23×C4—111no—
405C23×C4—112no—
406C23×C4—112no—
407C23×C4—442no—
408C23×C4—442no—
409C23×C4C22×D1112yes—
410C23×C4C22×D1111yescharacteristic
411C23×C4C22×D1111yescharacteristic
412C23×C4C22×D1112yes—
413C23×C4C22×D1111yescharacteristic
414#123—2232no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—114no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—224no—
421C2×C4⋊C4—442no—
422C2×C4⋊C4—442no—
423C2×C4⋊C4C4×D1114yes—
424C2×C22⋊C4—114no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—114no—
427C2×C22⋊C4—222no—
428C2×C22⋊C4—222no—
429C2×C22⋊C4—224no—
430C2×C22⋊C4—222no—
431C2×C22⋊C4—222no—
432C2×C22⋊C4—224no—
433C2×C22⋊C4—224no—
434C2×C22⋊C4—222no—
435C2×C22⋊C4—222no—
436C2×C22⋊C4—224no—
437C2×C22⋊C4—224no—
438C2×C22⋊C4—224no—
439C2×C22⋊C4—442no—
440C2×C22⋊C4—442no—
441C2×C22⋊C4—442no—
442C2×C22⋊C4—442no—
443C2×C22⋊C4—442no—
444C2×C22⋊C4—442no—
445C2×C42—22no—
446C2×C42—42no—
447C2×C42—222no—
448C2×C42—442no—
449#95—24no—
450#95—22no—
451#95—42no—
452#95—224no—
453#95—224no—
454#95—222no—
455#95—442no—
456#95—442no—
457#95—442no—
458C2×C11#229711yescharacteristic
459C2×C11#230811yescharacteristic
460C2×C11#231111yescharacteristic
461C2×C11#233512yes—
462C2×C11#233512yes—
463C2×C11#263012yes—
464C2×C11#263012yes—
465C2×C11#266112yes—
466C2×C11#266312yes—
467D11—44no—
468D11—82no—
469C24—112no—
470C24—112no—
471C24—112no—
472C24—112no—
473C24—222no—
474C24—222no—
475C24—222no—
476C24—222no—
477C24—222no—
478C24—222no—
479C24—222no—
480C24—221no—
481C24—221no—
482C24—222no—
483C24—222no—
484C24—222no—
485C24—222no—
486C24—222no—
487C24C23×D1111yescharacteristic
488C2×D4—228no—
489C2×D4—448no—
490C2×D4—444no—
491C2×D4—448no—
492C2×D4—444no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—112no—
517C22×C4—112no—
518C22×C4—112no—
519C22×C4—1116no—
520C22×C4—112no—
521C22×C4—114no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—222no—
529C22×C4—222no—
530C22×C4—222no—
531C22×C4—222no—
532C22×C4—222no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—222no—
540C22×C4—222no—
541C22×C4—448no—
542C22×C4—444no—
543C22×C4—448no—
544C22×C4—444no—
545C22×C4C2×C4×D1112yes—
546C22×C4C2×C4×D1112yes—
547C22×C4C2×C4×D1112yes—
548C22×C4#433914yes—
549C22×C4D4×D1112yes—
550C22×C4D4×D1112yes—
551C4⋊C4—28no—
552C4⋊C4—228no—
553C4⋊C4—448no—
554C22⋊C4—228no—
555C22⋊C4—228no—
556C22⋊C4—2216no—
557C22⋊C4—228no—
558C22⋊C4—448no—
559C22⋊C4—448no—
560C22⋊C4—448no—
561C42—44no—
562C42—444no—
563C11#1428711yescharacteristic, complemented, Sylow
564C23—114no—
565C23—222no—
566C23—222no—
567C23—222no—
568C23—224no—
569C23—224no—
570C23—224no—
571C23—224no—
572C23—222no—
573C23—224no—
574C23—224no—
575C23—222no—
576C23—222no—
577C23—222no—
578C23—222no—
579C23—222no—
580C23—224no—
581C23—224no—
582C23—442no—
583C23—442no—
584C23—442no—
585C23—442no—
586C23—442no—
587C23—442no—
588C23—442no—
589C23—442no—
590C23—442no—
591C23—441no—
592C23—442no—
593C23—442no—
594C23—442no—
595C23—442no—
596C23—442no—
597C23—442no—
598C23—441no—
599C23—442no—
600C23—442no—
601C23—442no—
602C23—441no—
603C23—442no—
604C23—441no—
605C23—442no—
606C23C22×C4×D1111yescharacteristic
607C23C2×#433912yes—
608C23C2×D4×D1111yescharacteristic
609C23C2×D4×D1111yescharacteristic
610C23#6703712yes—
611C23#6704012yes—
612C23#41×D1112yes—
613C23#6704212yes—
614C23#6704212yes—
615D4—4416no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—114no—
645C2×C4—224no—
646C2×C4—222no—
647C2×C4—224no—
648C2×C4—222no—
649C2×C4—224no—
650C2×C4—222no—
651C2×C4—224no—
652C2×C4—224no—
653C2×C4—224no—
654C2×C4—4416no—
655C2×C4—441no—
656C2×C4—442no—
657C2×C4—442no—
658C2×C4—442no—
659C2×C4—442no—
660C2×C4—442no—
661C2×C4—441no—
662C2×C4—442no—
663C2×C4—442no—
664C2×C4—442no—
665C2×C4—442no—
666C2×C4—442no—
667C2×C4—442no—
668C2×C4—442no—
669C2×C4C22⋊C4×D1114yes—
670C22—224no—
671C22—224no—
672C22—224no—
673C22—444no—
674C22—444no—
675C22—444no—
676C22—444no—
677C22—444no—
678C22—444no—
679C22—444no—
680C22—444no—
681C22—442no—
682C22—442no—
683C22—442no—
684C22—882no—
685C22—882no—
686C22—882no—
687C22—882no—
688C22C4×#433911yescharacteristic
689C22C2×C22⋊C4×D1111yescharacteristic
690C22#1062304612yes—
691C22#1062305311yescharacteristic
692C22#1062306612yes—
693C22#1062307612yes—
694C22#1062307812yes—
695C22#1062307912yes—
696C22#1062309112yes—
697C22#1062310512yes—
698C22#1062311312yes—
699C22#1062312011yescharacteristic
700C22#1062313612yes—
701C22#1062316012yes—
702C22#1062317112yes—
703C22#1062318411yescharacteristic
704C22#1062319412yes—
705C22#1062320511yescharacteristic
706C22#1062322312yes—
707C22#1062323512yes—
708C22#1062325511yescharacteristic
709C4—24no—
710C4—44no—
711C4—42no—
712C4—42no—
713C4—82no—
714C4—224no—
715C4—444no—
716C4—442no—
717C4—882no—
718C2—444no—
719C2—882no—
720C2#1307110211yescharacteristic
721C2#1307119011yescharacteristic
722C2#1307120711yescharacteristic
723C2#1307140012yes—
724C2#1307141212yes—
725C2#1307446112yes—
726C2#1307446512yes—
727C2#1307474812yes—
728C2#1307477012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14287
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622280C2semidirect
3. C2×C4×(C2×D11)⋊C4C2semidirect
4. #13066867C2semidirect
5. #13066864C2semidirect
6. #13066860C2semidirect
8. #13066854C2semidirect
9. #13066852C2semidirect
10. #13066848C2semidirect
11. C11×#1436C2semidirect
28. C2×#66947C4semidirect
187. C2×C4×D11C22⋊C4semidirect
210. #1436D11semidirect
563. C11#14287semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
C2×#106222802
C2×C4×(C2×D11)⋊C42
#130668672
#130668642
#130668602
#130668562
#130668542
#130668522
#130668482
C11×#14362
#1428711