Finite Group Databasebeta

← #14675698

Subgroups — #14675698

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622824C211yesmaximal, characteristic
2C2×#10622555C211yesmaximal, characteristic
3C2×C22⋊C4×Dic11C211yesmaximal, characteristic
4C22×C11⋊#95C211yesmaximal, characteristic
5#13066877C212yesmaximal, complemented
6#13066871C212yesmaximal, complemented
7#13066847C212yesmaximal, complemented
8#13066840C212yesmaximal, complemented
9#13066838C211yesmaximal, characteristic
10#13066838C211yesmaximal, characteristic
11C2×C11×#381C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2212yes—
21C11×#381—24no—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24#10622824—24no—
25C2×C11⋊#95C418yescomplemented
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38#10622555—24no—
39C22⋊C4×Dic11—24no—
40C25×C11C2311yescharacteristic
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11C2×C414yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×Dic11—22no—
53C23×Dic11—22no—
54C23×Dic11—22no—
55C23×Dic11—22no—
56C23×Dic11—24no—
57C23×Dic11—24no—
58C23×Dic11—42no—
59C23×Dic11—42no—
60C23×Dic11C2×C414yes—
61C23×Dic11C2×C414yes—
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4D414yes—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11D414yes—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—24no—
82C2×Dic11⋊C4—42no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11—42no—
86C11×#95—24no—
87C11×#95—24no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95—24no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—42no—
95C11⋊#95—42no—
96C11⋊#95C2×C414yes—
97C11⋊#95C2×C414yes—
98C11⋊#95C2×C414yes—
99C11⋊#95C2×C414yes—
100#13874—111nomaximal, Sylow
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11C22×C412yes—
106C24×C11C2×D412yes—
107C24×C11C2×D412yes—
108C24×C11#4112yes—
109C24×C11#4112yes—
110C24×C11#4112yes—
111C24×C11#4112yes—
112C24×C11C2411yescharacteristic
113C22×C4×C11—28no—
114C22×C4×C11—28no—
115C22×C4×C11—28no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
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—44no—
142C22×C4×C11—44no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11C22×C412yes—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D414yes—
148C22×Dic11—28no—
149C22×Dic11—28no—
150C22×Dic11—28no—
151C22×Dic11—28no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—21no—
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×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—44no—
180C22×Dic11—44no—
181C22×Dic11—48no—
182C22×Dic11—48no—
183C22×Dic11—48no—
184C22×Dic11—48no—
185C22×Dic11C22×C412yes—
186C22×Dic11C22×C412yes—
187C22×Dic11C22×C412yes—
188C22×Dic11C22×C412yes—
189C22×Dic11C2×D414yes—
190C22×Dic11#4114yes—
191C22×Dic11#4114yes—
192C11×C22⋊C4—28no—
193C11×C22⋊C4—44no—
194C22⋊Dic11—28no—
195C22⋊Dic11—44no—
196Dic11⋊C4—48no—
197C4×Dic11—48no—
198C2×#381—111no—
199C2×#381D1111yescharacteristic
200C2×#380—111no—
201C2×C4×C22⋊C4—111no—
202C22×#95—111no—
203#1443—112no—
204#1442—112no—
205#1436—112no—
206#1434—112no—
207C22⋊#95—111no—
208C22⋊#95—111no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11#11714yes—
226C23×C11C4×D414yes—
227C23×C11C4×D414yes—
228C23×C11#12114yes—
229C23×C11#12314yes—
230C23×C11#12414yes—
231C23×C11#12614yes—
232C23×C11C23×C411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C22×D411yescharacteristic
235C23×C11C2×#4111yescharacteristic
236C23×C11C2×#4111yescharacteristic
237C23×C11C2×#4111yescharacteristic
238C23×C11C2×#4111yescharacteristic
239C23×C11C2×#4112yes—
240C23×C11C2×#4112yes—
241C23×C11H(5,𝔽2)12yes—
242C23×C112−1+412yes—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—416no—
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—42no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—416no—
290C2×Dic11—416no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11—42no—
302C2×Dic11—42no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11#11714yes—
307C2×Dic11#11714yes—
308C24×C4—111no—
309C24×C4—111no—
310C24×C4C2×D1111yescharacteristic
311C22×C4⋊C4—112no—
312C22×C22⋊C4—111no—
313C22×C22⋊C4—111no—
314C22×C22⋊C4C2×D1111yescharacteristic
315C22×C22⋊C4C2×D1111yescharacteristic
316C22×C42—112no—
317#381—24no—
318#381—224no—
319#380—224no—
320C4×C22⋊C4—224no—
321C2×#95—111no—
322C2×#95—111no—
323C2×#95—111no—
324C2×#95—111no—
325C2×#95—118no—
326C2×#95—112no—
327C2×#95—112no—
328C2×#95—112no—
329C2×#95—112no—
330C2×#95—112no—
331C2×#95—112no—
332C2×#95—112no—
333C2×#95—112no—
334C2×#95C2×D1112yes—
335C2×#95C2×D1112yes—
336C22×C11—24no—
337C22×C11—24no—
338C22×C11—24no—
339C22×C11—24no—
340C22×C11—24no—
341C22×C11—28no—
342C22×C11—28no—
343C22×C11—28no—
344C22×C11—28no—
345C22×C11—24no—
346C22×C11#38818yes—
347C22×C11C2×#11711yescharacteristic
348C22×C11C2×#11711yescharacteristic
349C22×C11C2×#11711yescharacteristic
350C22×C11C2×C4×D411yescharacteristic
351C22×C11C2×C4×D411yescharacteristic
352C22×C11#51811yescharacteristic
353C22×C11#51911yescharacteristic
354C22×C11C2×#12111yescharacteristic
355C22×C11C2×#12311yescharacteristic
356C22×C11C2×#12411yescharacteristic
357C22×C11C2×#12611yescharacteristic
358C22×C11#52912yes—
359C22×C11#52912yes—
360C22×C11#53912yes—
361C22×C11#53912yes—
362C22×C11#54612yes—
363C22×C11#54612yes—
364C22×C11#54712yes—
365C22×C11#54712yes—
366C22×C11#55112yes—
367C22×C11#55112yes—
368C22×C11#55212yes—
369C22×C11#55212yes—
370C4×C11—44no—
371C4×C11—42no—
372C4×C11—42no—
373C4×C11—82no—
374Dic11—24no—
375Dic11—24no—
376Dic11—42no—
377Dic11—42no—
378Dic11—44no—
379Dic11—82no—
380C25C22×D1111yescharacteristic
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—112no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—114no—
393C23×C4—114no—
394C23×C4—112no—
395C23×C4—224no—
396C23×C4—224no—
397C23×C4—222no—
398C23×C4—222no—
399C23×C4—222no—
400C23×C4—222no—
401C23×C4—442no—
402C23×C4—442no—
403C23×C4C4×D1114yes—
404C23×C4C22×D1112yes—
405C23×C4C22×D1111yescharacteristic
406C23×C4C22×D1111yescharacteristic
407C23×C4C22×D1112yes—
408C2×C4⋊C4—224no—
409C2×C4⋊C4—224no—
410C2×C4⋊C4—442no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—114no—
417C2×C22⋊C4—222no—
418C2×C22⋊C4—222no—
419C2×C22⋊C4—222no—
420C2×C22⋊C4—222no—
421C2×C22⋊C4—222no—
422C2×C22⋊C4C22⋊D1114yes—
423C2×C42—224no—
424C2×C42—224no—
425C2×C42—442no—
426#95—24no—
427#95—24no—
428#95—114no—
429#95—114no—
430#95—114no—
431#95—114no—
432#95—224no—
433#95—224no—
434#95—224no—
435#95—224no—
436#95—224no—
437#95—224no—
438#95—442no—
439#95—442no—
440C2×C11—28no—
441C2×C11#228311yescharacteristic
442C2×C11C2×#38811yescharacteristic
443C2×C11#231311yescharacteristic
444C2×C11#234211yescharacteristic
445C2×C11#234211yescharacteristic
446C2×C11#234411yescharacteristic
447C2×C11#234411yescharacteristic
448C2×C11#241912yes—
449C2×C11#242512yes—
450C2×C11#248812yes—
451C2×C11#249312yes—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24C2×C4×D1112yes—
457C24#433912yes—
458C24D4×D1112yes—
459C24#434112yes—
460C24#434112yes—
461C24#434112yes—
462C24C2×C22⋊D1112yes—
463C24C23×D1111yescharacteristic
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—114no—
499C22×C4—114no—
500C22×C4—112no—
501C22×C4—112no—
502C22×C4—114no—
503C22×C4—228no—
504C22×C4—228no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—221no—
511C22×C4—228no—
512C22×C4—228no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—222no—
516C22×C4—221no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—221no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—222no—
530C22×C4—222no—
531C22×C4—222no—
532C22×C4—222no—
533C22×C4—222no—
534C22×C4—444no—
535C22×C4—444no—
536C22×C4—448no—
537C22×C4—448no—
538C22×C4—448no—
539C22×C4—448no—
540C22×C4C2×C4×D1112yes—
541C22×C4C2×C4×D1112yes—
542C22×C4C2×C22⋊D1114yes—
543C4⋊C4—448no—
544C22⋊C4—28no—
545C22⋊C4—44no—
546C22⋊C4—228no—
547C22⋊C4—444no—
548C42—448no—
549C11#1387411yescharacteristic, complemented, Sylow
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23#6693014yes—
567C23#6693214yes—
568C23(C22⋊D11)⋊C414yes—
569C23#6693814yes—
570C23C4×C22⋊D1114yes—
571C23#6698814yes—
572C23#6699114yes—
573C23C22×C4×D1111yescharacteristic
574C23C2×#433911yescharacteristic
575C23C2×D4×D1111yescharacteristic
576C23C2×#434111yescharacteristic
577C23C2×#434111yescharacteristic
578C23C2×#434111yescharacteristic
579C23#41×D1112yes—
580C23#41×D1112yes—
581C23#6704212yes—
582C23#6704312yes—
583C23C22×C22⋊D1111yescharacteristic
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—416no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—114no—
614C2×C4—114no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—224no—
619C2×C4—222no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—224no—
630C2×C4—224no—
631C2×C4—224no—
632C2×C4—4416no—
633C2×C4—4416no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4—442no—
639C2×C4—442no—
640C2×C4—442no—
641C2×C4—442no—
642C2×C4—442no—
643C2×C4—442no—
644C2×C4—442no—
645C2×C4—442no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4—442no—
649C22—28no—
650C22—28no—
651C22—24no—
652C22—28no—
653C22—24no—
654C22—24no—
655C22—24no—
656C22—24no—
657C22—24no—
658C22—28no—
659C22#1062255718yes—
660C22C2×#6693011yescharacteristic
661C22C2×#6693211yescharacteristic
662C22C2×(C22⋊D11)⋊C411yescharacteristic
663C22C2×#6693811yescharacteristic
664C22#1062304711yescharacteristic
665C22D11×#11711yescharacteristic
666C22D11×#11711yescharacteristic
667C22#1062305211yescharacteristic
668C22#1062305812yes—
669C22#1062306212yes—
670C22#1062318012yes—
671C22#1062318012yes—
672C22#1062318112yes—
673C22#1062318512yes—
674C22#1062318612yes—
675C22#1062318912yes—
676C22#1062319612yes—
677C22#1062319612yes—
678C22C2×C4×C22⋊D1111yescharacteristic
679C22C2×#6698811yescharacteristic
680C22C2×#6699111yescharacteristic
681C22#1062335512yes—
682C22#1062336012yes—
683C4—42no—
684C4—42no—
685C4—44no—
686C4—82no—
687C4—224no—
688C4—224no—
689C4—444no—
690C4—442no—
691C4—442no—
692C4—882no—
693C2—28no—
694C2#1307100711yescharacteristic
695C2C2×#1062255711yescharacteristic
696C2#1307121711yescharacteristic
697C2#1307145811yescharacteristic
698C2#1307146611yescharacteristic
699C2#1307148011yescharacteristic
700C2#1307148611yescharacteristic
701C2#1307208912yes—
702C2#1307216312yes—
703C2#1307293812yes—
704C2#1307299712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#381C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#381D11
hypocenterC11#13874
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
5. #13066877C2semidirect
6. #13066871C2semidirect
7. #13066847C2semidirect
8. #13066840C2semidirect
25. C2×C11⋊#95C4semidirect
549. C11#13874semidirect

Maximal subgroups

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

subgroupindex
C2×#106228242
C2×#106225552
C2×C22⋊C4×Dic112
C22×C11⋊#952
#130668772
#130668712
#130668472
#130668402
#130668382
C2×C11×#3812
#1387411