Finite Group Databasebeta

← C2×D11×#397 #14919977

Subgroups — C2×D11×#397 #14919977

Order 2816.

5230 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D11C212yesmaximal
3C22×C22⋊C4×D11C211yesmaximal, characteristic
4C2×#10622288C212yesmaximal, complemented
5C2×#10622565C212yesmaximal, complemented
6C2×#10622287C211yesmaximal, characteristic, complemented
7C2×#10622606C211yesmaximal, characteristic, complemented
8C2×#10622566C211yesmaximal, characteristic, complemented
9D11×#397C2116yesmaximal, direct product factor
10C2×D11×#95C211yesmaximal, characteristic, complemented
11C2×D11×#95C212yesmaximal, complemented
12C2×C11×#397C211yesmaximal, characteristic, complemented
13C25×D11C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2212yes—
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic, complemented
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic, complemented
28C22×Dic11⋊C4C2212yescomplemented
29C2×C4⋊C4×D11—28no—
30C2×C4⋊C4×D11C2218yescomplemented
31C2×C22⋊C4×D11—216no—
32C2×C22⋊C4×D11—28no—
33C2×C22⋊C4×D11C22116yes—
34C2×C22⋊C4×D11C2218yes—
35C11×#397C2218yescomplemented
36C2×C11×#95C2211yescharacteristic, complemented
37C2×C11×#95C2212yescomplemented
38C2×C11⋊#95C2211yescharacteristic, complemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41C2×C11⋊#95C2212yescomplemented
42C2×C11⋊#95C2212yescomplemented
43#10622606C2218yescomplemented
44#10622566C2218yescomplemented
45#10622565C22116yescomplemented
46#10622288C22116yescomplemented
47#10622287C2218yescomplemented
48D11×#95C22116yescomplemented
49D11×#95C2218yescomplemented
50C25×C11C2311yescharacteristic
51C24×D11—24no—
52C24×D11—24no—
53C24×D11—28no—
54C24×D11—28no—
55C24×D11D418yes—
56C24×D11C2314yes—
57C24×D11C2311yescharacteristic
58C24×D11C2311yescharacteristic
59C23×C4×C11C2312yes—
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C22×C4×D11—28no—
68C22×C4×D11—28no—
69C22×C4×D11—28no—
70C22×C4×D11—24no—
71C22×C4×D11—28no—
72C22×C4×D11—28no—
73C22×C4×D11—28no—
74C22×C4×D11—28no—
75C22×C4×D11—28no—
76C22×C4×D11D418yes—
77C22×C4×D11C2318yes—
78C22×C4×D11C2318yes—
79C22×C4×D11C2314yes—
80C22×C4×D11C2314yes—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4C2314yescomplemented
83C2×C11×C22⋊C4—28no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4C2318yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C22⋊Dic11—28no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2318yes—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—28no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11C2314yescomplemented
101C2×Dic11⋊C4—28no—
102C2×Dic11⋊C4C2318yescomplemented
103C4⋊C4×D11—232no—
104C22⋊C4×D11—264no—
105C22⋊C4×D11—232no—
106C11×#95C2314yescomplemented
107C11×#95C2318yescomplemented
108C11⋊#95C2318yescomplemented
109C11⋊#95C2318yescomplemented
110C11⋊#95C2318yescomplemented
111C11⋊#95C2318yescomplemented
112C11⋊#95C2314yescomplemented
113C22×#397—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11C2×D414yes—
119C24×C11C2412yes—
120C24×C11C2411yescharacteristic
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—232no—
126C23×D11—264no—
127C23×D11—28no—
128C23×D11—28no—
129C23×D11—216no—
130C23×D11—216no—
131C23×D11—416no—
132C23×D11—416no—
133C23×D11—432no—
134C23×D11C2×D4116yes—
135C23×D11C2×D414yes—
136C23×D11C2×D414yes—
137C23×D11C2×D414yes—
138C23×D11#4114yes—
139C23×D11#4118yes—
140C23×D11#4118yes—
141C23×D11C2412yes—
142C23×D11C2412yes—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2414yes—
156C22×C4×C11C2412yes—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—22no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11C2×D414yes—
167C22×Dic11C2412yes—
168C22×Dic11C2414yes—
169C22×Dic11C2414yes—
170C22×Dic11C2412yes—
171C2×C4×D11—232no—
172C2×C4×D11—216no—
173C2×C4×D11—216no—
174C2×C4×D11—28no—
175C2×C4×D11—216no—
176C2×C4×D11—216no—
177C2×C4×D11—216no—
178C2×C4×D11—216no—
179C2×C4×D11—216no—
180C2×C4×D11—216no—
181C2×C4×D11—432no—
182C2×C4×D11—432no—
183C2×C4×D11—416no—
184C2×C4×D11C2×D4116yes—
185C11×C4⋊C4—28no—
186C11×C22⋊C4—216no—
187C11×C22⋊C4—28no—
188C22⋊Dic11—28no—
189C22⋊Dic11—216no—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4—216no—
192(C2×D11)⋊C4—216no—
193(C2×D11)⋊C4—28no—
194C4⋊Dic11—28no—
195Dic11⋊C4—216no—
196C23×C4⋊C4—111no—
197C23×C22⋊C4—111no—
198C23×C22⋊C4—112no—
199C2×#397—1116no—
200C2×#397—111no—
201C2×#397—112no—
202C2×#397—111no—
203C2×#397—111no—
204C2×#397—112no—
205C2×#397D1111yescharacteristic, direct product factor
206C22×#95—111no—
207C22×#95—112no—
208C23×C11—28no—
209C23×C11—216no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11—48no—
217C23×C11C22×D414yes—
218C23×C11C22×D412yes—
219C23×C11C22×D412yes—
220C23×C11C2×#4112yes—
221C23×C11C2×#4114yes—
222C23×C11C2×#4114yes—
223C23×C11C2511yescharacteristic
224C22×D11—28no—
225C22×D11—216no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—232no—
231C22×D11—264no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—48no—
235C22×D11—416no—
236C22×D11—416no—
237C22×D11—432no—
238C22×D11—4128no—
239C22×D11#121116yes—
240C22×D11#123116yes—
241C22×D11#123132yes—
242C22×D11#124116yes—
243C22×D11#126132yes—
244C22×D11C22×D414yes—
245C22×D11C22×D414yes—
246C22×D11C22×D414yes—
247C22×D11C2×#4114yes—
248C22×D11C2×#4118yes—
249C22×D11C2×#4118yes—
250C2×C4×C11—28no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—48no—
261C2×C4×C11—48no—
262C2×C4×C11—44no—
263C2×C4×C11C22×D414yes—
264C2×Dic11—28no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—48no—
275C2×Dic11—48no—
276C2×Dic11—44no—
277C2×Dic11C22×D414yes—
278C4×D11—232no—
279C4×D11—432no—
280C4×D11—432no—
281C4×D11—416no—
282C26—111no—
283C24×C4—111no—
284C24×C4—112no—
285C24×C4—111no—
286C24×C4—112no—
287C22×C4⋊C4—112no—
288C22×C4⋊C4—111no—
289C22×C4⋊C4—118no—
290C22×C4⋊C4—228no—
291C22×C4⋊C4C2×D1111yescharacteristic, complemented
292C22×C22⋊C4—111no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—111no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—111no—
298C22×C22⋊C4—118no—
299C22×C22⋊C4—1116no—
300C22×C22⋊C4—228no—
301C22×C22⋊C4—2216no—
302C22×C22⋊C4C2×D1112yes—
303C22×C22⋊C4C2×D1111yescharacteristic
304#397—118no—
305#397—1116no—
306#397—118no—
307#397—118no—
308#397—1116no—
309#397C2×D1118yesdirect product factor
310C2×#95—112no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95—111no—
315C2×#95—118no—
316C2×#95—1116no—
317C2×#95C2×D1112yescomplemented
318C2×#95C2×D1111yescharacteristic, complemented
319C22×C11—24no—
320C22×C11—28no—
321C22×C11—416no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—44no—
325C22×C11C2×#12114yes—
326C22×C11C2×#12314yes—
327C22×C11C2×#12318yes—
328C22×C11C2×#12414yes—
329C22×C11C2×#12618yes—
330C22×C11C23×D411yescharacteristic
331C22×C11C23×D411yescharacteristic
332C22×C11C22×#4111yescharacteristic
333C22×C11C22×#4112yes—
334C22×C11C22×#4112yes—
335C2×D11—24no—
336C2×D11—28no—
337C2×D11—416no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—44no—
341C2×D11—464no—
342C2×D11#397164yesdirect product factor
343C2×D11C2×#12118yes—
344C2×D11C2×#123116yes—
345C2×D11C2×#12318yes—
346C2×D11C2×#12418yes—
347C2×D11C2×#126116yes—
348C4×C11—24no—
349C4×C11—44no—
350C4×C11—44no—
351C4×C11—42no—
352Dic11—24no—
353Dic11—44no—
354Dic11—44no—
355Dic11—42no—
356C25—111no—
357C25—118no—
358C25—114no—
359C25—111no—
360C25—224no—
361C25—224no—
362C25—228no—
363C25—228no—
364C25C22×D1111yescharacteristic
365C23×C4—111no—
366C23×C4—118no—
367C23×C4—114no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—111no—
371C23×C4—118no—
372C23×C4—114no—
373C23×C4—118no—
374C23×C4—228no—
375C23×C4—224no—
376C23×C4—228no—
377C23×C4—228no—
378C23×C4—228no—
379C23×C4—228no—
380C23×C4—228no—
381C23×C4—228no—
382C23×C4—228no—
383C23×C4C22×D1112yes—
384C23×C4C22×D1112yes—
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387C2×C4⋊C4—24no—
388C2×C4⋊C4—118no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—2232no—
391C2×C4⋊C4—228no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4C22×D1114yescomplemented
394C2×C22⋊C4—28no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—114no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—114no—
402C2×C22⋊C4—2232no—
403C2×C22⋊C4—2264no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—228no—
406C2×C22⋊C4—228no—
407C2×C22⋊C4—224no—
408C2×C22⋊C4—228no—
409C2×C22⋊C4—224no—
410C2×C22⋊C4C22×D1118yes—
411C2×C22⋊C4C22×D1114yes—
412#95—118no—
413#95—118no—
414#95—114no—
415#95—118no—
416#95—118no—
417#95C22×D1118yescomplemented
418#95C22×D1114yescomplemented
419C2×C11—44no—
420C2×C11C2×#39718yescomplemented
421C2×C11C22×#12111yescharacteristic
422C2×C11C22×#12311yescharacteristic
423C2×C11C22×#12312yes—
424C2×C11C22×#12411yescharacteristic
425C2×C11C22×#12612yes—
426D11—44no—
427D11C2×#397116yesdirect product factor
428C24—22no—
429C24—22no—
430C24—24no—
431C24—24no—
432C24—114no—
433C24—114no—
434C24—114no—
435C24—118no—
436C24—118no—
437C24—112no—
438C24—1116no—
439C24—114no—
440C24—112no—
441C24—228no—
442C24—2232no—
443C24—2264no—
444C24—228no—
445C24—2216no—
446C24—2216no—
447C24—222no—
448C24—222no—
449C24—224no—
450C24—224no—
451C24—4432no—
452C24—4416no—
453C24—4416no—
454C24D4×D1114yes—
455C24C23×D1112yes—
456C24C23×D1111yescharacteristic
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—114no—
467C22×C4—112no—
468C22×C4—1116no—
469C22×C4—112no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—2232no—
473C22×C4—2216no—
474C22×C4—228no—
475C22×C4—2216no—
476C22×C4—2216no—
477C22×C4—2216no—
478C22×C4—2216no—
479C22×C4—2216no—
480C22×C4—2216no—
481C22×C4—2216no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—222no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—224no—
491C22×C4—4432no—
492C22×C4—4432no—
493C22×C4—4416no—
494C22×C4D4×D1114yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1114yes—
497C22×C4C23×D1114yes—
498C22×C4C23×D1112yes—
499C4⋊C4—28no—
500C4⋊C4—2216no—
501C4⋊C4—228no—
502C22⋊C4—216no—
503C22⋊C4—28no—
504C22⋊C4—228no—
505C22⋊C4—2216no—
506C22⋊C4—2216no—
507C22⋊C4—228no—
508C22⋊C4—2216no—
509C22⋊C4—228no—
510C11C22×#39711yescharacteristic, complemented, Sylow
511C23—28no—
512C23—216no—
513C23—22no—
514C23—22no—
515C23—24no—
516C23—24no—
517C23—48no—
518C23—44no—
519C23—44no—
520C23—1132no—
521C23—1116no—
522C23—1116no—
523C23—1132no—
524C23—114no—
525C23—114no—
526C23—118no—
527C23—114no—
528C23—118no—
529C23—1116no—
530C23—114no—
531C23—2232no—
532C23—2264no—
533C23—228no—
534C23—2216no—
535C23—222no—
536C23—222no—
537C23—224no—
538C23—224no—
539C23—4416no—
540C23—4432no—
541C23—44128no—
542C23—4416no—
543C23—448no—
544C23—444no—
545C23—444no—
546C23C2×D4×D1114yes—
547C23C2×D4×D1112yes—
548C23C2×D4×D1112yes—
549C23#41×D1112yes—
550C23#41×D1114yes—
551C23#41×D1114yes—
552C23C24×D1111yescharacteristic
553C2×C4—28no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—48no—
564C2×C4—48no—
565C2×C4—44no—
566C2×C4—114no—
567C2×C4—2232no—
568C2×C4—228no—
569C2×C4—224no—
570C2×C4—222no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—4416no—
579C2×C4—4432no—
580C2×C4—4432no—
581C2×C4—448no—
582C2×C4—448no—
583C2×C4—444no—
584C2×C4C2×D4×D1114yes—
585C22—24no—
586C22—28no—
587C22—42no—
588C22—44no—
589C22—416no—
590C22—42no—
591C22—118no—
592C22—1116no—
593C22—1164no—
594C22—118no—
595C22—118no—
596C22—1116no—
597C22—224no—
598C22—228no—
599C22—4464no—
600C22—442no—
601C22—444no—
602C22—4416no—
603C22—442no—
604C22D11×#12114yes—
605C22D11×#12314yes—
606C22D11×#12318yes—
607C22D11×#12414yes—
608C22D11×#12618yes—
609C22C22×D4×D1111yescharacteristic
610C22C22×D4×D1111yescharacteristic
611C22C2×#41×D1112yes—
612C22C2×#41×D1111yescharacteristic
613C22C2×#41×D1112yes—
614C4—24no—
615C4—42no—
616C4—44no—
617C4—44no—
618C4—224no—
619C4—442no—
620C4—444no—
621C4—444no—
622C2—44no—
623C2—1116no—
624C2—444no—
625C2D11×#39718yesdirect product factor
626C2C2×D11×#12111yescharacteristic
627C2C2×D11×#12311yescharacteristic
628C2C2×D11×#12312yes—
629C2C2×D11×#12411yescharacteristic
630C2C2×D11×#12612yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#397D11
hypocenterC11C22×#397
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊C4×D11C2semidirect
4. C2×#10622288C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622287C2semidirect
7. C2×#10622606C2semidirect
8. C2×#10622566C2semidirect
9. D11×#397C2direct (N × H)
10. C2×D11×#95C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#397C2semidirect
18. C22×C11×C4⋊C4C22semidirect
27. C22×C4⋊Dic11C22semidirect
28. C22×Dic11⋊C4C22semidirect
30. C2×C4⋊C4×D11C22semidirect
35. C11×#397C22semidirect
36. C2×C11×#95C22semidirect
37. C2×C11×#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
42. C2×C11⋊#95C22semidirect
43. #10622606C22semidirect
44. #10622566C22semidirect
45. #10622565C22semidirect
46. #10622288C22semidirect
47. #10622287C22semidirect
48. D11×#95C22semidirect
49. D11×#95C22semidirect
82. C2×C11×C4⋊C4C23semidirect
100. C2×C4⋊Dic11C23semidirect
102. C2×Dic11⋊C4C23semidirect
106. C11×#95C23semidirect
107. C11×#95C23semidirect
108. C11⋊#95C23semidirect
109. C11⋊#95C23semidirect
110. C11⋊#95C23semidirect
111. C11⋊#95C23semidirect
112. C11⋊#95C23semidirect
205. C2×#397D11direct (N × H)
291. C22×C4⋊C4C2×D11semidirect
309. #397C2×D11direct (N × H)
317. C2×#95C2×D11semidirect
318. C2×#95C2×D11semidirect
342. C2×D11#397direct (N × H)
393. C2×C4⋊C4C22×D11semidirect
417. #95C22×D11semidirect
418. #95C22×D11semidirect
420. C2×C11C2×#397semidirect
427. D11C2×#397direct (N × H)
510. C11C22×#397semidirect
625. C2D11×#397direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
C22×C22⋊C4×D112
C2×#106222882
C2×#106225652
C2×#106222872
C2×#106226062
C2×#106225662
D11×#3972
C2×D11×#952
C2×C11×#3972
C22×#39711