Finite Group Databasebeta

← #14680813

Subgroups — #14680813

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622285C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic
3C2×#10622546C211yesmaximal, characteristic, complemented
4#13066873C211yesmaximal, characteristic, complemented
5#13066870C211yesmaximal, characteristic, complemented
6#13066864C212yesmaximal, complemented
7#13066860C212yesmaximal, complemented
8#13066856C211yesmaximal, characteristic
9#13066854C212yesmaximal, complemented
10#13066854C212yesmaximal, complemented
11C4×C11×#95C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C42×C11C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622552—24no—
36#10622546—24no—
37#10622285C418yescomplemented
38C24×D11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C22×D44—22no—
50C22×D44—22no—
51C22×D44—42no—
52C22×D44—42no—
53C22×D44C2×C414yes—
54C2×C42×C11—24no—
55C2×C42×C11—42no—
56C2×C42×C11—42no—
57C2×C42×C11—42no—
58C2×C42×C11D414yes—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4—42no—
73C2×(C2×D11)⋊C4—42no—
74C2×(C2×D11)⋊C4—42no—
75C2×(C2×D11)⋊C4C2×C418yes—
76C2×(C2×D11)⋊C4C2×C418yes—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—42no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—42no—
83C2×Dic11⋊C4C2×C414yes—
84C11×#95—24no—
85C11×#95—22no—
86C11×#95C2×C414yes—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—42no—
92C11⋊#95—42no—
93C11⋊#95—42no—
94C11⋊#95—42no—
95#14325—111nomaximal, Sylow
96C24×C11C2411yescharacteristic
97C23×D11—22no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11C22×C414yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
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—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11#4114yes—
139C22×C4×C11#4112yes—
140C22×C4×C11#4114yes—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11C22×C412yes—
169C22×Dic11C22×C412yes—
170C2×D44—28no—
171C2×D44—48no—
172C2×D44—44no—
173C2×D44—44no—
174C2×D44—48no—
175C42×C11—44no—
176C42×C11—48no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—48no—
182(C2×D11)⋊C4—48no—
183C4⋊Dic11—44no—
184Dic11⋊C4—28no—
185Dic11⋊C4—44no—
186C2×#394—111no—
187C2×#390—111no—
188C2×#387—111no—
189#1442—111no—
190#1441—111no—
191#1440—112no—
192#1439—112no—
193#1438—111no—
194#1437—112no—
195#1437—112no—
196C4×#95D1111yescharacteristic, complemented
197C23×C11C23×C411yescharacteristic
198C23×C11C22×D411yescharacteristic
199C23×C11C2×#4111yescharacteristic
200C23×C11C2×#4112yes—
201C23×C11C2×#4112yes—
202C23×C11H(5,𝔽2)12yes—
203C23×C11H(5,𝔽2)11yescharacteristic
204C23×C11H(5,𝔽2)12yes—
205C23×C11H(5,𝔽2)11yescharacteristic
206C23×C11H(5,𝔽2)11yescharacteristic
207C23×C112−1+411yescharacteristic
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11—42no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11C4×D414yes—
271C2×C4×C11#12414yes—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—42no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—42no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301D44—416no—
302C23×D4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4—111no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C42C2×D1112yes—
313C22×C42C2×D1111yescharacteristic
314#394—118no—
315#390—224no—
316#387—224no—
317C2×#95—111no—
318C2×#95—111no—
319C2×#95—111no—
320C2×#95—111no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95C2×D1111yescharacteristic
326C2×#95C2×D1112yes—
327C2×#95C2×D1111yescharacteristic
328C22×C11C2×C4×D411yescharacteristic
329C22×C11C4×#4112yes—
330C22×C11#51812yes—
331C22×C11#51811yescharacteristic
332C22×C11#52011yescharacteristic
333C22×C11C2×#12411yescharacteristic
334C22×C11#52912yes—
335C22×C11#53211yescharacteristic
336C22×C11#53411yescharacteristic
337C22×C11#53511yescharacteristic
338C22×C11#53511yescharacteristic
339C22×C11#53711yescharacteristic
340C22×C11#53812yes—
341C22×C11#53812yes—
342C22×C11#53812yes—
343C22×C11#53812yes—
344C22×C11#53912yes—
345C22×C11#54012yes—
346C22×C11#54012yes—
347C22×C11#54011yescharacteristic
348C22×C11#54012yes—
349C22×C11#54211yescharacteristic
350C22×C11#54212yes—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—82no—
359C2×D11—82no—
360C2×D11—82no—
361C2×D11—82no—
362C2×D11—82no—
363C2×D11—82no—
364C2×D11—82no—
365C2×D11—82no—
366C4×C11—24no—
367C4×C11—24no—
368C4×C11—44no—
369C4×C11—44no—
370C4×C11—42no—
371Dic11—42no—
372Dic11—42no—
373Dic11—82no—
374Dic11—81no—
375Dic11—81no—
376C25—112no—
377C22×D4—114no—
378C22×D4—222no—
379C22×D4—222no—
380C22×D4—442no—
381C22×D4—442no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—112no—
386C23×C4—111no—
387C23×C4C22×D1112yes—
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1112yes—
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C2×C4⋊C4—114no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—442no—
398C2×C4⋊C4—442no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—442no—
408C2×C22⋊C4—442no—
409C2×C22⋊C4—442no—
410C2×C22⋊C4—442no—
411C2×C22⋊C4—442no—
412C2×C22⋊C4—442no—
413C2×C22⋊C4—442no—
414C2×C22⋊C4—442no—
415C2×C22⋊C4—442no—
416C2×C22⋊C4—442no—
417C2×C42—24no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42D4414yes—
422#95—24no—
423#95—22no—
424#95—222no—
425#95—222no—
426#95—222no—
427#95—222no—
428#95—442no—
429#95—442no—
430#95—442no—
431#95—442no—
432#95C4×D1114yes—
433C2×C11C4×#12411yescharacteristic
434C2×C11#232111yescharacteristic
435C2×C11#232411yescharacteristic
436C2×C11#233312yes—
437C2×C11#233512yes—
438C2×C11#263911yescharacteristic
439C2×C11#264111yescharacteristic
440C2×C11#264812yes—
441C2×C11#265112yes—
442C2×C11#266111yescharacteristic
443C2×C11#266211yescharacteristic
444D11—84no—
445C24—114no—
446C24—222no—
447C24—222no—
448C24—222no—
449C24—222no—
450C24—222no—
451C24—222no—
452C24—222no—
453C24—222no—
454C24—222no—
455C24—222no—
456C24—222no—
457C24—222no—
458C24—222no—
459C24—222no—
460C24C23×D1111yescharacteristic
461C2×D4—228no—
462C2×D4—448no—
463C2×D4—444no—
464C2×D4—444no—
465C2×D4—448no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—222no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—222no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—221no—
516C22×C4C2×C4×D1114yes—
517C22×C4C2×C4×D1112yes—
518C22×C4C2×D4412yes—
519C22×C4C2×D4412yes—
520C22×C4C2×D4412yes—
521C22×C4#433914yes—
522C22×C4#433912yes—
523C22×C4#433914yes—
524C4⋊C4—228no—
525C4⋊C4—444no—
526C4⋊C4—444no—
527C22⋊C4—448no—
528C22⋊C4—448no—
529C22⋊C4—448no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C42—44no—
534C42—48no—
535C11#1432511yescharacteristic, complemented, Sylow
536C23—224no—
537C23—224no—
538C23—224no—
539C23—224no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—442no—
544C23—442no—
545C23—442no—
546C23—442no—
547C23—442no—
548C23—442no—
549C23—442no—
550C23—442no—
551C23—442no—
552C23—442no—
553C23—442no—
554C23—442no—
555C23—442no—
556C23—442no—
557C23—442no—
558C23—442no—
559C23—442no—
560C23—442no—
561C23—442no—
562C23—442no—
563C23—442no—
564C23—442no—
565C23—442no—
566C23—442no—
567C23—442no—
568C23—442no—
569C23—442no—
570C23—442no—
571C23C22×C4×D1111yescharacteristic
572C23C22×D4411yescharacteristic
573C23C2×#433911yescharacteristic
574C23C2×#433912yes—
575C23C2×#433912yes—
576C23#6703712yes—
577C23#6703711yescharacteristic
578C23#6704011yescharacteristic
579C23#6704212yes—
580C23#6704211yescharacteristic
581C23#6704211yescharacteristic
582D4—4416no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—42no—
601C2×C4—42no—
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—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—224no—
614C2×C4—222no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—442no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—442no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4—442no—
639C2×C4C4×D4414yes—
640C2×C4#6692814yes—
641C22—444no—
642C22—444no—
643C22—444no—
644C22—444no—
645C22—444no—
646C22—444no—
647C22—444no—
648C22—882no—
649C22—882no—
650C22—882no—
651C22—882no—
652C22—882no—
653C22—882no—
654C22—882no—
655C22—882no—
656C22C2×C4×D4411yescharacteristic
657C22C4×#433912yes—
658C22C2×#6692811yescharacteristic
659C22#1062300811yescharacteristic
660C22#1062301012yes—
661C22#1062302411yescharacteristic
662C22#1062302512yes—
663C22#1062304111yescharacteristic
664C22#1062304612yes—
665C22#1062305611yescharacteristic
666C22#1062305611yescharacteristic
667C22#1062306612yes—
668C22#1062306612yes—
669C22#1062307611yescharacteristic
670C22#1062307612yes—
671C22#1062309112yes—
672C22#1062309112yes—
673C22#1062309112yes—
674C22#1062309312yes—
675C22#1062309311yescharacteristic
676C22#1062310511yescharacteristic
677C22#1062311312yes—
678C22#1062311311yescharacteristic
679C4—24no—
680C4—24no—
681C4—44no—
682C4—42no—
683C4—44no—
684C4—442no—
685C4—442no—
686C4—881no—
687C4—881no—
688C4—882no—
689C2—884no—
690C2C4×#6692811yescharacteristic
691C2#1307127611yescharacteristic
692C2#1307131011yescharacteristic
693C2#1307137612yes—
694C2#1307140012yes—
695C2#1307454411yescharacteristic
696C2#1307455911yescharacteristic
697C2#1307459812yes—
698C2#1307464312yes—
699C2#1307474211yescharacteristic
700C2#1307475311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC4×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4×#95D11
hypocenterC11#14325
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622546C2semidirect
4. #13066873C2semidirect
5. #13066870C2semidirect
6. #13066864C2semidirect
7. #13066860C2semidirect
9. #13066854C2semidirect
10. #13066854C2semidirect
11. C4×C11×#95C2semidirect
37. #10622285C4semidirect
196. C4×#95D11semidirect
535. C11#14325semidirect

Maximal subgroups

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

subgroupindex
C2×#106222852
C2×#106225522
C2×#106225462
#130668732
#130668702
#130668642
#130668602
#130668562
#130668542
C4×C11×#952
#1432511