Finite Group Databasebeta

← #14676017

Subgroups — #14676017

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622589C211yesmaximal, characteristic, complemented
5C2×#10622280C214yesmaximal, complemented
6C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
7#13066860C214yesmaximal, complemented
8#13066845C211yesmaximal, characteristic, complemented
9C11×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2214yes—
16C22×(C2×D11)⋊C4C2214yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C2×#66946—24no—
25C2×#66946—24no—
26C2×#66946C418yescomplemented
27C2×C11×#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30#10622601—24no—
31#10622589—24no—
32#10622552—24no—
33C4×Dic11⋊C4—24no—
34#10622280—216no—
35C24×D11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C22×D44—22no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44C2×C414yes—
49C22×D44D414yes—
50C22×D44Q814yes—
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—28no—
54C22×C4×D11—28no—
55C22×C4×D11C2×C418yes—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4C2×C414yes—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11—22no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—28no—
68C2×(C2×D11)⋊C4—28no—
69C2×(C2×D11)⋊C4—28no—
70C2×(C2×D11)⋊C4—28no—
71C2×(C2×D11)⋊C4—44no—
72C2×(C2×D11)⋊C4—44no—
73C2×(C2×D11)⋊C4C2×C418yes—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—28no—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—24no—
82C2×Dic11⋊C4—44no—
83C2×Dic11⋊C4D418yescomplemented
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11C2×C414yes—
88C2×C4×Dic11D414yes—
89C2×C4×Dic11D414yes—
90#66946—232no—
91C11×#95—28no—
92C11⋊#95—28no—
93C11⋊#95—24no—
94#13906—111nomaximal, Sylow
95C24×C11C2411yescharacteristic
96C23×D11—24no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11—24no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—24no—
103C23×D11—24no—
104C23×D11C22×C414yes—
105C23×D11C2×D414yes—
106C23×D11C2×Q814yes—
107C22×C4×C11—24no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11C22×C414yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C2×D414yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×Q812yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11C22×C412yes—
145C22×Dic11C22×C412yes—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×D412yes—
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150C22×Dic11C2×D412yes—
151C22×Dic11C2×D414yes—
152C22×Dic11#4114yes—
153C2×D44—28no—
154C2×D44—28no—
155C2×D44—28no—
156C2×D44—28no—
157C2×D44—28no—
158C2×D44—28no—
159C2×D44C4⋊C4116yescomplemented
160C2×C4×D11—216no—
161C2×C4×D11—232no—
162C2×C4×D11—416no—
163C2×C4×D11—48no—
164C2×C4×D11—48no—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—44no—
167C42×C11—44no—
168(C2×D11)⋊C4—216no—
169(C2×D11)⋊C4—416no—
170(C2×D11)⋊C4—416no—
171C4⋊Dic11—44no—
172Dic11⋊C4—216no—
173Dic11⋊C4—48no—
174Dic11⋊C4—48no—
175C4×Dic11—44no—
176C4×Dic11C22⋊C4116yescomplemented
177C22×C4×D4—111no—
178C2×#390—111no—
179C2×#390—111no—
180C2×#384—111no—
181C2×#380—114no—
182C2×C4×C4⋊C4—111no—
183#1439—114no—
184C4⋊#95—111no—
185C4⋊#95D1111yescharacteristic, complemented
186C23×C11C23×C411yescharacteristic
187C23×C11C22×D411yescharacteristic
188C23×C11C22×D411yescharacteristic
189C23×C11C22×D411yescharacteristic
190C23×C11C22×D412yes—
191C23×C11C22×Q811yescharacteristic
192C23×C11C2×#4111yescharacteristic
193C23×C11C2×#4111yescharacteristic
194C23×C11C2×#4112yes—
195C23×C11H(5,𝔽2)12yes—
196C23×C112−1+412yes—
197C22×D11—24no—
198C22×D11—24no—
199C22×D11—28no—
200C22×D11—28no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—28no—
206C22×D11—28no—
207C22×D11—28no—
208C22×D11—28no—
209C22×D11—44no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11—44no—
217C22×D11—44no—
218C22×D11—44no—
219C22×D11C2×C4⋊C418yes—
220C2×C4×C11—24no—
221C2×C4×C11—28no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11—44no—
237C2×C4×C11C2×C22⋊C414yes—
238C2×C4×C11C2×C4⋊C414yes—
239C2×C4×C11#11714yes—
240C2×C4×C11#12114yes—
241C2×C4×C11#12114yes—
242C2×C4×C11C22⋊Q814yes—
243C2×C4×C11C22⋊Q814yes—
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—44no—
259C2×Dic11—44no—
260C2×Dic11C2×C22⋊C414yes—
261C2×Dic11C2×C22⋊C414yes—
262C2×Dic11C4×D418yes—
263C2×Dic11#12118yes—
264C2×Dic11#12414yes—
265C2×Dic11#12714yes—
266D44—232no—
267C4×D11—432no—
268C23×D4—111no—
269C24×C4—112no—
270C2×C4×D4—118no—
271C2×C4×D4—224no—
272C2×C4×D4—224no—
273C22×C4⋊C4—112no—
274C22×C4⋊C4—112no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—112no—
277C22×C4⋊C4C2×D1111yescharacteristic
278C22×C4⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4—112no—
280C22×C22⋊C4—114no—
281C22×C22⋊C4—114no—
282C22×C42—111no—
283C22×C42—111no—
284C22×C42C2×D1111yescharacteristic
285#390—224no—
286#390—224no—
287#384—224no—
288#380—2216no—
289C4×C4⋊C4—224no—
290C2×#95—114no—
291C2×#95—112no—
292C2×#95C2×D1114yes—
293C22×C11C22×C22⋊C411yescharacteristic
294C22×C11C22×C4⋊C411yescharacteristic
295C22×C11C2×#11711yescharacteristic
296C22×C11C2×C4×D412yes—
297C22×C11#52012yes—
298C22×C11C2×#12111yescharacteristic
299C22×C11C2×#12111yescharacteristic
300C22×C11C2×#12112yes—
301C22×C11C2×C22⋊Q811yescharacteristic
302C22×C11C2×C22⋊Q811yescharacteristic
303C22×C11C2×#12411yescharacteristic
304C22×C11C2×#12711yescharacteristic
305C22×C11#53511yescharacteristic
306C22×C11#53611yescharacteristic
307C22×C11#53712yes—
308C22×C11D4212yes—
309C22×C11#54712yes—
310C22×C11#54712yes—
311C22×C11D4×Q812yes—
312C22×C11#55012yes—
313C22×C11#55412yes—
314C22×C11#55512yes—
315C22×C11#55612yes—
316C2×D11—216no—
317C2×D11—28no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—48no—
321C2×D11—48no—
322C2×D11—48no—
323C2×D11—44no—
324C2×D11—44no—
325C2×D11—44no—
326C2×D11—44no—
327C4×C11—44no—
328C4×C11—44no—
329C4×C11—82no—
330C4×C11#38018yescomplemented
331Dic11—24no—
332Dic11—44no—
333Dic11—82no—
334Dic11#39018yescomplemented
335C25—112no—
336C22×D4—114no—
337C22×D4—114no—
338C22×D4—114no—
339C22×D4—222no—
340C22×D4—222no—
341C22×D4—222no—
342C22×D4—222no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—112no—
346C23×C4—118no—
347C23×C4—112no—
348C23×C4—224no—
349C23×C4—224no—
350C23×C4—228no—
351C23×C4—228no—
352C23×C4C22×D1112yes—
353C23×C4C22×D1112yes—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356C4×D4—2232no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—118no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—228no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—444no—
372C2×C4⋊C4C4×D1114yes—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—228no—
377C2×C22⋊C4—228no—
378C2×C22⋊C4—228no—
379C2×C22⋊C4—228no—
380C2×C22⋊C4—444no—
381C2×C22⋊C4—444no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—114no—
386C2×C42—114no—
387C2×C42—114no—
388C2×C42—222no—
389C2×C42—222no—
390C2×C42—222no—
391#95—28no—
392#95—224no—
393#95—228no—
394C2×C11C2×#38011yescharacteristic
395C2×C11C2×#39011yescharacteristic
396C2×C11#231111yescharacteristic
397C2×C11D4×C4⋊C412yes—
398C2×C11#235412yes—
399C2×C11#253712yes—
400C2×C11#253812yes—
401C2×C11#254111yescharacteristic
402C2×C11#254211yescharacteristic
403C2×C11#254711yescharacteristic
404C2×C11#256311yescharacteristic
405D11—48no—
406C24—114no—
407C24—114no—
408C24—114no—
409C24—222no—
410C24—222no—
411C24—224no—
412C24—222no—
413C24—222no—
414C24—224no—
415C24—224no—
416C24—224no—
417C24C23×D1111yescharacteristic
418C2×D4—1116no—
419C2×D4—228no—
420C2×D4—228no—
421C2×D4—228no—
422C2×D4—228no—
423C2×D4—228no—
424C2×D4—228no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—112no—
441C22×C4—112no—
442C22×C4—112no—
443C22×C4—114no—
444C22×C4—114no—
445C22×C4—112no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—114no—
449C22×C4—2216no—
450C22×C4—2232no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—224no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—224no—
464C22×C4—448no—
465C22×C4—4416no—
466C22×C4—448no—
467C22×C4C2×C4×D1114yes—
468C22×C4C2×C4×D1112yes—
469C22×C4#433912yes—
470C22×C4#433912yes—
471C22×C4D4×D1114yes—
472C22×C4D4×D1112yes—
473C22×C4D4×D1112yes—
474C22×C4D4×D1112yes—
475C22×C4Q8×D1112yes—
476C4⋊C4—28no—
477C4⋊C4—44no—
478C4⋊C4—2216no—
479C4⋊C4—448no—
480C4⋊C4—448no—
481C4⋊C4—444no—
482C22⋊C4—2216no—
483C22⋊C4—4416no—
484C22⋊C4—4416no—
485C42—44no—
486C42—1116no—
487C42—444no—
488C11#1390611yescharacteristic, complemented, Sylow
489C23—118no—
490C23—228no—
491C23—224no—
492C23—224no—
493C23—224no—
494C23—224no—
495C23—224no—
496C23—224no—
497C23—228no—
498C23—228no—
499C23—228no—
500C23—228no—
501C23—228no—
502C23—442no—
503C23—442no—
504C23—444no—
505C23—444no—
506C23—444no—
507C23—444no—
508C23—444no—
509C23—444no—
510C23—442no—
511C23—442no—
512C23C22×C4×D1111yescharacteristic
513C23C2×#433911yescharacteristic
514C23C2×#433911yescharacteristic
515C23C2×D4×D1111yescharacteristic
516C23C2×D4×D1112yes—
517C23C2×D4×D1111yescharacteristic
518C23C2×D4×D1111yescharacteristic
519C23C2×Q8×D1111yescharacteristic
520C23#6704012yes—
521C23#41×D1112yes—
522C23#6704212yes—
523D4—2232no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—28no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—114no—
542C2×C4—114no—
543C2×C4—118no—
544C2×C4—118no—
545C2×C4—114no—
546C2×C4—114no—
547C2×C4—222no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—222no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—4432no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—444no—
562C2×C4—444no—
563C2×C4—442no—
564C2×C4#6692514yes—
565C2×C4C22⋊C4×D1114yes—
566C2×C4#6693714yes—
567C2×C4#6693714yes—
568C2×C4C4⋊C4×D1114yes—
569C2×C4#6694914yes—
570C2×C4#6694914yes—
571C22—228no—
572C22—2216no—
573C22—444no—
574C22—448no—
575C22—444no—
576C22—448no—
577C22—444no—
578C22—444no—
579C22—448no—
580C22—444no—
581C22—444no—
582C22C2×#6692511yescharacteristic
583C22C2×C22⋊C4×D1111yescharacteristic
584C22C2×#6693711yescharacteristic
585C22C2×#6693711yescharacteristic
586C22C2×C4⋊C4×D1111yescharacteristic
587C22#1062303812yes—
588C22C2×#6694911yescharacteristic
589C22C2×#6694911yescharacteristic
590C22#1062306312yes—
591C22C4×D4×D1112yes—
592C22#1062308412yes—
593C22#1062309912yes—
594C22#1062310512yes—
595C22D11×#12112yes—
596C22#1062314012yes—
597C22#1062316012yes—
598C22#1062316212yes—
599C22D11×#12411yescharacteristic
600C22#1062320511yescharacteristic
601C22#1062322112yes—
602C22D11×#12711yescharacteristic
603C22#1062325511yescharacteristic
604C22#1062325812yes—
605C4—44no—
606C4—44no—
607C4—82no—
608C4—118no—
609C4—224no—
610C4—444no—
611C4—882no—
612C4#1062228018yescomplemented
613C2—448no—
614C2C2×#1062228011yescharacteristic
615C2D11×#39011yescharacteristic
616C2#1307120711yescharacteristic
617C2#1307151712yes—
618C2#1307156112yes—
619C2#1307353112yes—
620C2#1307353712yes—
621C2#1307356111yescharacteristic
622C2#1307356811yescharacteristic
623C2#1307361311yescharacteristic
624C2#1307378811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#13906
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#10622589C2semidirect
5. C2×#10622280C2semidirect
6. C2×C4×Dic11⋊C4C2semidirect
7. #13066860C2semidirect
8. #13066845C2semidirect
9. C11×C4⋊#95C2semidirect
26. C2×#66946C4semidirect
83. C2×Dic11⋊C4D4semidirect
159. C2×D44C4⋊C4semidirect
176. C4×Dic11C22⋊C4semidirect
185. C4⋊#95D11semidirect
330. C4×C11#380semidirect
334. Dic11#390semidirect
488. C11#13906semidirect
612. C4#10622280semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×#106225522
C2×#106226012
C2×#106225892
C2×#106222802
C2×C4×Dic11⋊C42
#130668602
#130668452
C11×C4⋊#952
#1390611