Finite Group Databasebeta

← #14675997

Subgroups — #14675997

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D11)⋊C4C211yesmaximal, characteristic
2C2×#10622824C211yesmaximal, characteristic, complemented
3C2×#10622555C211yesmaximal, characteristic, complemented
4C2×#10622568C211yesmaximal, characteristic
5C2×#10622568C211yesmaximal, characteristic
6C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
7#13066860C214yesmaximal, complemented
8#13066852C214yesmaximal, complemented
9C2×C11×#381C211yesmaximal, characteristic, complemented
10C25×D11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C22×(C2×D11)⋊C4—24no—
18C22×(C2×D11)⋊C4—24no—
19C22×(C2×D11)⋊C4C418yescomplemented
20C22×(C2×D11)⋊C4C2214yes—
21C22×(C2×D11)⋊C4C2214yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×Dic11⋊C4C2212yescomplemented
25C22×C4×Dic11C2212yescomplemented
26C11×#381—24no—
27C2×C11×#95C2214yescomplemented
28#10622824—24no—
29C2×C11⋊#95C2212yescomplemented
30C2×C11⋊#95C2214yescomplemented
31C2×C11⋊#95C2212yescomplemented
32#10622568—24no—
33#10622568—24no—
34#10622555—24no—
35C22⋊C4×Dic11—24no—
36C25×C11C2311yescharacteristic
37C24×D11—22no—
38C24×D11—22no—
39C24×D11—28no—
40C24×D11—22no—
41C24×D11—22no—
42C24×D11—22no—
43C24×D11—22no—
44C24×D11—44no—
45C24×D11C2×C414yes—
46C24×D11C2312yes—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11C2×C414yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×Dic11—44no—
58C23×Dic11C2×C414yes—
59C23×Dic11D414yes—
60C23×Dic11D414yes—
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4D414yes—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11D414yes—
77C2×(C2×D11)⋊C4—232no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4C2×C418yes—
89C2×(C2×D11)⋊C4C2×C418yes—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—44no—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—44no—
94C11×#95—28no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—28no—
98#13903—111nomaximal, Sylow
99C24×C11—24no—
100C24×C11—24no—
101C24×C11C22×C412yes—
102C24×C11C2×D412yes—
103C24×C11C2×D412yes—
104C24×C11C2×D412yes—
105C24×C11C2×D412yes—
106C24×C11#4112yes—
107C24×C11#4112yes—
108C24×C11C2411yescharacteristic
109C23×D11—216no—
110C23×D11—216no—
111C23×D11—28no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—24no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—216no—
122C23×D11—28no—
123C23×D11—28no—
124C23×D11—48no—
125C23×D11—416no—
126C23×D11—416no—
127C23×D11—416no—
128C23×D11—416no—
129C23×D11—48no—
130C23×D11—48no—
131C23×D11—44no—
132C23×D11—44no—
133C23×D11—44no—
134C23×D11—44no—
135C23×D11C22×C414yes—
136C23×D11#4118yes—
137C22×C4×C11—28no—
138C22×C4×C11—28no—
139C22×C4×C11—28no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—24no—
154C22×C4×C11—24no—
155C22×C4×C11—44no—
156C22×C4×C11—44no—
157C22×C4×C11—44no—
158C22×C4×C11—44no—
159C22×C4×C11C22×C414yes—
160C22×C4×C11C2×D414yes—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—24no—
166C22×Dic11—22no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—24no—
172C22×Dic11—48no—
173C22×Dic11—48no—
174C22×Dic11—48no—
175C22×Dic11C22⋊C4116yescomplemented
176C22×Dic11C22×C412yes—
177C22×Dic11C22×C412yes—
178C22×Dic11C2×D414yes—
179C22×Dic11C2×D412yes—
180C22×Dic11C2×D412yes—
181C22×Dic11C2×D412yes—
182C22×Dic11C2×D412yes—
183C11×C22⋊C4—28no—
184C11×C22⋊C4—44no—
185C22⋊Dic11—28no—
186C22⋊Dic11—44no—
187(C2×D11)⋊C4—216no—
188(C2×D11)⋊C4—216no—
189(C2×D11)⋊C4—416no—
190(C2×D11)⋊C4—416no—
191Dic11⋊C4—48no—
192C4×Dic11—48no—
193C23×C22⋊C4—111no—
194C2×#381—111no—
195C2×#381D1111yescharacteristic, complemented
196C2×#380—111no—
197C2×#379—111no—
198C2×#379—111no—
199C2×C4×C22⋊C4—111no—
200#1439—114no—
201#1437—114no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—28no—
209C23×C11—28no—
210C23×C11—28no—
211C23×C11—28no—
212C23×C11C2×C22⋊C414yes—
213C23×C11C4×D414yes—
214C23×C11C4×D414yes—
215C23×C11#12114yes—
216C23×C11#12114yes—
217C23×C11#12414yes—
218C23×C11#12714yes—
219C23×C11C23×C411yescharacteristic
220C23×C11C22×D411yescharacteristic
221C23×C11C22×D411yescharacteristic
222C23×C11C22×D411yescharacteristic
223C23×C11C22×D411yescharacteristic
224C23×C11C2×#4111yescharacteristic
225C23×C11C2×#4111yescharacteristic
226C23×C11C2×#4114yes—
227C23×C11H(5,𝔽2)14yes—
228C22×D11—232no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—28no—
236C22×D11—28no—
237C22×D11—28no—
238C22×D11—28no—
239C22×D11—28no—
240C22×D11—28no—
241C22×D11—432no—
242C22×D11—432no—
243C22×D11—432no—
244C22×D11—416no—
245C22×D11—432no—
246C22×D11—432no—
247C22×D11—432no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—44no—
253C22×D11—44no—
254C22×D11—44no—
255C22×D11—44no—
256C22×D11—44no—
257C22×D11—44no—
258C22×D11—416no—
259C22×D11#11718yes—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—28no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—44no—
272C2×C4×C11—416no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—44no—
277C2×C4×C11—44no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—28no—
286C2×Dic11—416no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—44no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—44no—
294C2×Dic11—44no—
295C2×Dic11C2×C22⋊C414yes—
296C2×Dic11C2×C22⋊C414yes—
297C26—111no—
298C24×C4—111no—
299C24×C4C2×D1111yescharacteristic
300C22×C4⋊C4—112no—
301C22×C22⋊C4—111no—
302C22×C22⋊C4—112no—
303C22×C22⋊C4—112no—
304C22×C22⋊C4—118no—
305C22×C22⋊C4—111no—
306C22×C22⋊C4—114no—
307C22×C22⋊C4—114no—
308C22×C22⋊C4—224no—
309C22×C22⋊C4—224no—
310C22×C22⋊C4C2×D1111yescharacteristic
311C22×C22⋊C4C2×D1111yescharacteristic
312C22×C42—112no—
313#381—24no—
314#381—224no—
315#380—224no—
316#379—224no—
317#379—224no—
318C4×C22⋊C4—224no—
319C2×#95—112no—
320C2×#95—114no—
321C2×#95—112no—
322C2×#95C2×D1114yescomplemented
323C22×C11—28no—
324C22×C11—24no—
325C22×C11—28no—
326C22×C11—28no—
327C22×C11—28no—
328C22×C11—28no—
329C22×C11—24no—
330C22×C11—28no—
331C22×C11#39018yes—
332C22×C11C22×C22⋊C411yescharacteristic
333C22×C11C2×#11712yes—
334C22×C11C2×C4×D411yescharacteristic
335C22×C11C2×C4×D411yescharacteristic
336C22×C11#51812yes—
337C22×C11C2×#12111yescharacteristic
338C22×C11C2×#12111yescharacteristic
339C22×C11#52512yes—
340C22×C11#52512yes—
341C22×C11C2×#12411yescharacteristic
342C22×C11C2×#12711yescharacteristic
343C22×C11#53412yes—
344C22×C11#53412yes—
345C22×C11#54614yes—
346C22×C11#54614yes—
347C22×C11#55114yes—
348C22×C11#55114yes—
349C2×D11—28no—
350C2×D11—28no—
351C2×D11—28no—
352C2×D11—464no—
353C2×D11—48no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—48no—
358C2×D11—48no—
359C2×D11—48no—
360C2×D11—44no—
361C4×C11—44no—
362C4×C11—44no—
363C4×C11—82no—
364Dic11—24no—
365Dic11—24no—
366Dic11—44no—
367Dic11—82no—
368C25—112no—
369C25—114no—
370C25—228no—
371C25—222no—
372C25—222no—
373C25—222no—
374C25—222no—
375C25—222no—
376C25—222no—
377C25—444no—
378C25C22×D1111yescharacteristic
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—114no—
388C23×C4—114no—
389C23×C4—114no—
390C23×C4—112no—
391C23×C4—112no—
392C23×C4—444no—
393C23×C4C4×D1114yes—
394C23×C4C22×D1112yes—
395C23×C4C22×D1112yes—
396C23×C4C22×D1112yes—
397C2×C4⋊C4—224no—
398C2×C4⋊C4—444no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—114no—
405C2×C22⋊C4—118no—
406C2×C22⋊C4—118no—
407C2×C22⋊C4—2232no—
408C2×C22⋊C4—224no—
409C2×C22⋊C4—224no—
410C2×C22⋊C4—224no—
411C2×C22⋊C4—224no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—228no—
415C2×C22⋊C4—228no—
416C2×C22⋊C4—228no—
417C2×C22⋊C4—222no—
418C2×C22⋊C4—222no—
419C2×C22⋊C4—222no—
420C2×C22⋊C4—228no—
421C2×C22⋊C4—444no—
422C2×C22⋊C4—444no—
423C2×C22⋊C4C22⋊D1114yes—
424C2×C42—224no—
425C2×C42—444no—
426#95—28no—
427#95—224no—
428#95—224no—
429#95—228no—
430C2×C11—28no—
431C2×C11#228011yescharacteristic
432C2×C11C2×#39011yescharacteristic
433C2×C11#230811yescharacteristic
434C2×C11#234212yes—
435C2×C11#234212yes—
436C2×C11#253412yes—
437C2×C11#253412yes—
438C2×C11#253912yes—
439C2×C11#256112yes—
440D11—48no—
441C24—24no—
442C24—24no—
443C24—114no—
444C24—118no—
445C24—2216no—
446C24—2216no—
447C24—2216no—
448C24—228no—
449C24—222no—
450C24—222no—
451C24—222no—
452C24—222no—
453C24—222no—
454C24—224no—
455C24—224no—
456C24—224no—
457C24—222no—
458C24—228no—
459C24—228no—
460C24—448no—
461C24—4416no—
462C24—4416no—
463C24—4416no—
464C24—4416no—
465C24—448no—
466C24—448no—
467C24—444no—
468C24—444no—
469C24—444no—
470C24—444no—
471C24C2×C4×D1112yes—
472C24#433912yes—
473C24D4×D1112yes—
474C24D4×D1112yes—
475C24D4×D1112yes—
476C24#434112yes—
477C24C2×C22⋊D1112yes—
478C24C23×D1111yescharacteristic
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—112no—
502C22×C4—112no—
503C22×C4—112no—
504C22×C4—112no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—1116no—
508C22×C4—114no—
509C22×C4—224no—
510C22×C4—224no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—224no—
518C22×C4—224no—
519C22×C4—222no—
520C22×C4—448no—
521C22×C4—448no—
522C22×C4—448no—
523C22×C4C2×C4×D1114yes—
524C22×C4C2×C22⋊D1114yes—
525C4⋊C4—448no—
526C22⋊C4—28no—
527C22⋊C4—44no—
528C22⋊C4—2216no—
529C22⋊C4—2216no—
530C22⋊C4—228no—
531C22⋊C4—4416no—
532C22⋊C4—4416no—
533C22⋊C4—444no—
534C42—448no—
535C11#1390311yescharacteristic, complemented, Sylow
536C23—24no—
537C23—24no—
538C23—28no—
539C23—28no—
540C23—24no—
541C23—24no—
542C23—28no—
543C23—24no—
544C23—24no—
545C23—28no—
546C23—118no—
547C23—2232no—
548C23—224no—
549C23—224no—
550C23—224no—
551C23—224no—
552C23—224no—
553C23—228no—
554C23—224no—
555C23—228no—
556C23—228no—
557C23—228no—
558C23—228no—
559C23—228no—
560C23—4432no—
561C23—4432no—
562C23—4416no—
563C23—4432no—
564C23—4432no—
565C23—4432no—
566C23—4432no—
567C23—442no—
568C23—442no—
569C23—444no—
570C23—442no—
571C23—442no—
572C23—4416no—
573C23—444no—
574C23—444no—
575C23—444no—
576C23—444no—
577C23—444no—
578C23C22⋊C4×D1114yes—
579C23(C22⋊D11)⋊C414yes—
580C23#6693714yes—
581C23#6693814yes—
582C23C4×C22⋊D1114yes—
583C23#6699214yes—
584C23#6699314yes—
585C23C22×C4×D1111yescharacteristic
586C23C2×#433911yescharacteristic
587C23C2×D4×D1111yescharacteristic
588C23C2×D4×D1111yescharacteristic
589C23C2×D4×D1111yescharacteristic
590C23C2×#434111yescharacteristic
591C23#41×D1114yes—
592C23#6704214yes—
593C23C22×C22⋊D1111yescharacteristic
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—28no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—416no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—44no—
607C2×C4—42no—
608C2×C4—44no—
609C2×C4—42no—
610C2×C4—44no—
611C2×C4—42no—
612C2×C4—114no—
613C2×C4—114no—
614C2×C4—224no—
615C2×C4—224no—
616C2×C4—224no—
617C2×C4—224no—
618C2×C4—224no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—228no—
622C2×C4—4416no—
623C2×C4—444no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4—442no—
627C2×C4—444no—
628C2×C4—442no—
629C2×C4—444no—
630C2×C4—442no—
631C22—24no—
632C22—28no—
633C22—28no—
634C22—28no—
635C22—28no—
636C22—28no—
637C22—28no—
638C22—24no—
639C22—228no—
640C22—228no—
641C22—228no—
642C22—4464no—
643C22—444no—
644C22—448no—
645C22—444no—
646C22—448no—
647C22—444no—
648C22—448no—
649C22—448no—
650C22—444no—
651C22#1062257018yes—
652C22C2×C22⋊C4×D1111yescharacteristic
653C22C2×(C22⋊D11)⋊C411yescharacteristic
654C22C2×#6693711yescharacteristic
655C22C2×#6693811yescharacteristic
656C22D11×#11712yes—
657C22#1062305212yes—
658C22#1062305814yes—
659C22#1062318412yes—
660C22#1062318412yes—
661C22#1062318514yes—
662C22#1062318712yes—
663C22#1062318712yes—
664C22#1062318914yes—
665C22C2×C4×C22⋊D1111yescharacteristic
666C22C2×#6699211yescharacteristic
667C22C2×#6699311yescharacteristic
668C22#1062336014yes—
669C4—44no—
670C4—44no—
671C4—82no—
672C4—224no—
673C4—224no—
674C4—444no—
675C4—882no—
676C2—28no—
677C2—448no—
678C2#1307099611yescharacteristic
679C2C2×#1062257011yescharacteristic
680C2#1307119311yescharacteristic
681C2#1307145812yes—
682C2#1307146612yes—
683C2#1307350512yes—
684C2#1307351112yes—
685C2#1307354612yes—
686C2#1307377312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#381C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#381D11
hypocenterC11#13903
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. C2×#10622824C2semidirect
3. C2×#10622555C2semidirect
6. C2×C22⋊C4×Dic11C2semidirect
7. #13066860C2semidirect
8. #13066852C2semidirect
9. C2×C11×#381C2semidirect
19. C22×(C2×D11)⋊C4C4semidirect
24. C22×Dic11⋊C4C22semidirect
25. C22×C4×Dic11C22semidirect
27. C2×C11×#95C22semidirect
29. C2×C11⋊#95C22semidirect
30. C2×C11⋊#95C22semidirect
31. C2×C11⋊#95C22semidirect
175. C22×Dic11C22⋊C4semidirect
195. C2×#381D11semidirect
322. C2×#95C2×D11semidirect
535. C11#13903semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D11)⋊C42
C2×#106228242
C2×#106225552
C2×#106225682
C2×C22⋊C4×Dic112
#130668602
#130668522
C2×C11×#3812
#1390311