Finite Group Databasebeta

← #14675601

Subgroups — #14675601

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622605C211yesmaximal, characteristic
2C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622262C212yesmaximal, complemented
4C2×#10622279C211yesmaximal, characteristic
5C2×#10622279C212yesmaximal
6#13066882C212yesmaximal, complemented
7#13066880C211yesmaximal, characteristic, complemented
8#13066862C211yesmaximal, characteristic
9#13066860C212yesmaximal
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×#1445C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35#10622605C418yescomplemented
36C4⋊C4×Dic11—24no—
37#10622279—28no—
38#10622279—24no—
39#10622262—28no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—24no—
52C22×C4×D11—22no—
53C22×C4×D11—22no—
54C22×C4×D11—24no—
55C22×C4×D11Q814yes—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4C2×C414yescomplemented
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4C2×C418yes—
70C2×(C2×D11)⋊C4C2×C414yes—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—24no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4C2×C418yescomplemented
79C2×C4×Dic11—24no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—24no—
86C2×C4×Dic11—24no—
87C2×C4×Dic11D418yes—
88C2×C4×Dic11D414yes—
89C11×#95—24no—
90C11×#95—24no—
91C11×#95—22no—
92C11×#95—22no—
93C11⋊#95—24no—
94C11⋊#95—22no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95C2×C414yescomplemented
99C4×#399—111nomaximal, Sylow
100C24×C11C2411yescharacteristic
101C23×D11—21no—
102C23×D11—22no—
103C23×D11—21no—
104C23×D11—22no—
105C23×D11—21no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—21no—
109C23×D11C22×C412yes—
110C23×D11C2×Q812yes—
111C23×D11#4112yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×Q812yes—
139C22×C4×C11#4112yes—
140C22×C4×C11#4112yes—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11C22×C412yes—
160C22×Dic11C22×C414yes—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×D414yes—
163C22×Dic11C2×D414yes—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×Q812yes—
166C22×Dic11#4114yes—
167C22×Dic11#4114yes—
168C22×Dic11#4112yes—
169C22×Dic11#4114yes—
170C2×C4×D11—28no—
171C2×C4×D11—216no—
172C2×C4×D11—48no—
173C2×C4×D11—44no—
174C2×C4×D11—44no—
175C11×C4⋊C4—28no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—28no—
180C4⋊Dic11—28no—
181Dic11⋊C4—216no—
182Dic11⋊C4—216no—
183C4×Dic11—28no—
184C4×Dic11—216no—
185C4×Dic11—44no—
186C4×Dic11—48no—
187C2×#399—111no—
188C2×C4×C4⋊C4—112no—
189C2×C4×C4⋊C4—111no—
190C2×C4×C22⋊C4—112no—
191C2×C4×C22⋊C4—111no—
192#1445—112no—
193#1445D1111yescharacteristic, complemented
194#1444—111no—
195#1439—112no—
196#1439—111no—
197C4×#95—111no—
198C23×C11C23×C411yescharacteristic
199C23×C11C22×D411yescharacteristic
200C23×C11C22×D412yes—
201C23×C11C22×Q811yescharacteristic
202C23×C11C2×#4111yescharacteristic
203C23×C11C2×#4111yescharacteristic
204C23×C11C2×#4112yes—
205C23×C11C2×#4111yescharacteristic
206C23×C11C2×#4111yescharacteristic
207C23×C11C2×#4112yes—
208C23×C11C2×#4112yes—
209C22×D11—22no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—22no—
213C22×D11—24no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—42no—
222C22×D11—41no—
223C22×D11—42no—
224C22×D11—41no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—41no—
229C22×D11—42no—
230C22×D11—41no—
231C22×D11C4×Q814yes—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11C4×D414yes—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—22no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—41no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—41no—
284C2×Dic11C4×D418yes—
285C2×Dic11C22⋊Q814yes—
286C2×Dic11C22⋊Q818yes—
287C2×Dic11#12318yes—
288C2×Dic11#12314yes—
289C2×Dic11#12714yes—
290C4×D11—416no—
291C24×C4—111no—
292C22×C4⋊C4—112no—
293C22×C4⋊C4—112no—
294C22×C4⋊C4—111no—
295C22×C4⋊C4C2×D1111yescharacteristic
296C22×C22⋊C4—112no—
297C22×C22⋊C4—111no—
298C22×C22⋊C4—111no—
299C22×C22⋊C4—112no—
300C22×C42—112no—
301C22×C42—111no—
302C22×C42—112no—
303C22×C42—111no—
304#399—118no—
305C4×C4⋊C4—228no—
306C4×C4⋊C4—224no—
307C4×C22⋊C4—228no—
308C4×C22⋊C4—224no—
309C2×#95—111no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95—111no—
315C2×#95C2×D1111yescharacteristic
316C2×#95C2×D1112yes—
317C2×#95C2×D1111yescharacteristic
318C2×#95C2×D1112yes—
319C22×C11C2×C4×D411yescharacteristic
320C22×C11C2×C4×D412yes—
321C22×C11C2×C4×Q811yescharacteristic
322C22×C11C4×#4112yes—
323C22×C11C4×#4111yescharacteristic
324C22×C11C2×C22⋊Q811yescharacteristic
325C22×C11C2×C22⋊Q812yes—
326C22×C11C2×#12312yes—
327C22×C11C2×#12311yescharacteristic
328C22×C11#52511yescharacteristic
329C22×C11#52512yes—
330C22×C11#52512yes—
331C22×C11#52511yescharacteristic
332C22×C11#52912yes—
333C22×C11#52912yes—
334C22×C11#52912yes—
335C22×C11#52911yescharacteristic
336C22×C11#52912yes—
337C22×C11C2×#12711yescharacteristic
338C22×C11#53212yes—
339C22×C11#53211yescharacteristic
340C22×C11#53311yescharacteristic
341C22×C11#53312yes—
342C2×D11—28no—
343C2×D11—24no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—44no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—44no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—44no—
353C4×C11—24no—
354C4×C11—44no—
355C4×C11—42no—
356C4×C11—44no—
357C4×C11—42no—
358Dic11—28no—
359Dic11—42no—
360Dic11—42no—
361Dic11—44no—
362Dic11#39918yescomplemented
363C25—111no—
364C23×C4—111no—
365C23×C4—112no—
366C23×C4—111no—
367C23×C4—112no—
368C23×C4—111no—
369C23×C4—114no—
370C23×C4—222no—
371C23×C4—224no—
372C23×C4—222no—
373C23×C4—224no—
374C23×C4C22×D1112yes—
375C23×C4C22×D1112yes—
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1111yescharacteristic
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—118no—
382C2×C4⋊C4—224no—
383C2×C4⋊C4—224no—
384C2×C4⋊C4—224no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—224no—
389C2×C4⋊C4C4×D1114yescomplemented
390C2×C22⋊C4—118no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—224no—
396C2×C22⋊C4—222no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—222no—
402C2×C42—118no—
403C2×C42—114no—
404C2×C42—224no—
405C2×C42—224no—
406C2×C42—224no—
407C2×C42—224no—
408C2×C42—222no—
409C2×C42—224no—
410C2×C42—224no—
411C2×C42—224no—
412#95—24no—
413#95—22no—
414#95—24no—
415#95—22no—
416#95—114no—
417#95—224no—
418#95—224no—
419#95—222no—
420#95—224no—
421#95—224no—
422C2×C11C4×#12311yescharacteristic
423C2×C11C4×#12312yes—
424C2×C11C4×C22⋊Q812yes—
425C2×C11C4×C22⋊Q811yescharacteristic
426C2×C11C4×#12711yescharacteristic
427C2×C11C2×#39911yescharacteristic
428C2×C11#239512yes—
429C2×C11#239511yescharacteristic
430C2×C11#239611yescharacteristic
431C2×C11#239612yes—
432C2×C11#239711yescharacteristic
433D11—44no—
434C24—112no—
435C24—112no—
436C24—112no—
437C24—221no—
438C24—222no—
439C24—221no—
440C24—221no—
441C24—222no—
442C24—222no—
443C24—222no—
444C24—221no—
445C24C23×D1111yescharacteristic
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—112no—
469C22×C4—114no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—114no—
476C22×C4—112no—
477C22×C4—112no—
478C22×C4—114no—
479C22×C4—228no—
480C22×C4—2216no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—221no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—444no—
500C22×C4—448no—
501C22×C4—444no—
502C22×C4C2×C4×D1114yes—
503C22×C4C2×C4×D1112yes—
504C22×C4D4×D1114yes—
505C22×C4D4×D1112yes—
506C22×C4#434112yes—
507C22×C4Q8×D1112yes—
508C22×C4#434312yes—
509C4⋊C4—28no—
510C4⋊C4—2216no—
511C4⋊C4—2216no—
512C4⋊C4—228no—
513C22⋊C4—2216no—
514C22⋊C4—228no—
515C22⋊C4—2216no—
516C22⋊C4—228no—
517C42—228no—
518C42—2216no—
519C42—444no—
520C42—448no—
521C11C4×#39911yescharacteristic, complemented, Sylow
522C23—114no—
523C23—224no—
524C23—222no—
525C23—222no—
526C23—224no—
527C23—224no—
528C23—222no—
529C23—224no—
530C23—222no—
531C23—222no—
532C23—224no—
533C23—222no—
534C23—224no—
535C23—442no—
536C23—441no—
537C23—442no—
538C23—442no—
539C23—442no—
540C23—442no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—442no—
545C23C22×C4×D1111yescharacteristic
546C23C2×D4×D1111yescharacteristic
547C23C2×D4×D1112yes—
548C23C2×#434111yescharacteristic
549C23C2×Q8×D1111yescharacteristic
550C23C2×#434311yescharacteristic
551C23#41×D1112yes—
552C23#41×D1111yescharacteristic
553C23#41×D1111yescharacteristic
554C23#41×D1112yes—
555C23#41×D1112yes—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—114no—
585C2×C4—114no—
586C2×C4—118no—
587C2×C4—118no—
588C2×C4—114no—
589C2×C4—118no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—222no—
597C2×C4—224no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—222no—
604C2×C4—4416no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4—441no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—442no—
612C2×C4—441no—
613C2×C4—442no—
614C2×C4(C22⋊D11)⋊C414yes—
615C22—228no—
616C22—224no—
617C22—444no—
618C22—442no—
619C22—442no—
620C22—444no—
621C22—442no—
622C22—442no—
623C22—444no—
624C22—442no—
625C22—442no—
626C22C2×(C22⋊D11)⋊C411yescharacteristic
627C22#1062305312yes—
628C22C4×D4×D1112yes—
629C22C4×Q8×D1111yescharacteristic
630C22C4×#434311yescharacteristic
631C22#1062312712yes—
632C22D11×C22⋊Q811yescharacteristic
633C22D11×C22⋊Q812yes—
634C22#1062315811yescharacteristic
635C22#1062315812yes—
636C22#1062318012yes—
637C22D11×#12312yes—
638C22D11×#12311yescharacteristic
639C22#1062318712yes—
640C22#1062318711yescharacteristic
641C22#1062319911yescharacteristic
642C22#1062321111yescharacteristic
643C22#1062321912yes—
644C22#1062322212yes—
645C22#1062323712yes—
646C22#1062323712yes—
647C22D11×#12711yescharacteristic
648C22#1062325911yescharacteristic
649C4—24no—
650C4—44no—
651C4—42no—
652C4—44no—
653C4—42no—
654C4—118no—
655C4—228no—
656C4—442no—
657C4—444no—
658C4—442no—
659C2—444no—
660C2#1307113311yescharacteristic
661C2#1307113712yes—
662C2#1307115012yes—
663C2#1307115411yescharacteristic
664C2#1307118011yescharacteristic
665C2D11×#39911yescharacteristic
666C2#1307187412yes—
667C2#1307188211yescharacteristic
668C2#1307188911yescharacteristic
669C2#1307189312yes—
670C2#1307189611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1445D11
hypocenterC11C4×#399
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic11C2semidirect
3. C2×#10622262C2semidirect
6. #13066882C2semidirect
7. #13066880C2semidirect
10. #95×Dic11C2semidirect
11. C11×#1445C2semidirect
35. #10622605C4semidirect
58. C2×C11×C4⋊C4C2×C4semidirect
78. C2×Dic11⋊C4C2×C4semidirect
98. C11⋊#95C2×C4semidirect
193. #1445D11semidirect
362. Dic11#399semidirect
389. C2×C4⋊C4C4×D11semidirect
521. C11C4×#399semidirect

Maximal subgroups

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

subgroupindex
C2×#106226052
C2×C4⋊C4×Dic112
C2×#106222622
C2×#106222792
#130668822
#130668802
#130668622
#130668602
#95×Dic112
C11×#14452
C4×#39911