Finite Group Databasebeta

← #14684448

Subgroups — #14684448

Order 2816.

1586 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×#10622604C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic
3C2×#10622594C211yesmaximal, characteristic, complemented
4#13066879C211yesmaximal, characteristic, complemented
5#13066864C212yesmaximal, complemented
6#13066862C212yesmaximal, complemented
7#13066860C212yesmaximal, complemented
8#13066860C212yesmaximal, complemented
9#13066856C211yesmaximal, characteristic
10#13066841C211yesmaximal, characteristic, complemented
11C11×#1441C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
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⋊C4C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35#10622604C418yescomplemented
36#10622601—24no—
37#10622594—24no—
38C24×D11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C22×D44—22no—
50C22×D44—22no—
51C22×D44—42no—
52C22×D44—42no—
53C22×D44C2×C414yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4C2×C414yes—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
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—42no—
80C2×Dic11⋊C4—42no—
81C2×Dic11⋊C4—42no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11D414yes—
84C11×#95—22no—
85C11×#95—42no—
86C11×#95—42no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—42no—
92C11⋊#95—42no—
93C11⋊#95—42no—
94C11⋊#95C2×C414yes—
95#14624—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—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
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—22no—
131C22×C4×C11—22no—
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×C11C22×C412yes—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11#4112yes—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11C22×C414yes—
168C22×Dic11C2×D412yes—
169C22×Dic11C2×D412yes—
170C2×D44—28no—
171C2×D44—48no—
172C2×D44—44no—
173C2×D44—44no—
174C2×D44—48no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—44no—
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—48no—
185C4×Dic11—44no—
186C2×#394—111no—
187C2×#390—111no—
188C2×#387—111no—
189#1444—111no—
190#1441D1111yescharacteristic, complemented
191#1440—112no—
192#1439—112no—
193#1439—112no—
194#1439—112no—
195#1438—111no—
196#1434—111no—
197C23×C11C23×C411yescharacteristic
198C23×C11C22×D411yescharacteristic
199C23×C11C2×#4111yescharacteristic
200C23×C11H(5,𝔽2)12yes—
201C23×C11H(5,𝔽2)11yescharacteristic
202C23×C11H(5,𝔽2)12yes—
203C23×C11H(5,𝔽2)11yescharacteristic
204C23×C11H(5,𝔽2)11yescharacteristic
205C23×C11H(5,𝔽2)12yes—
206C23×C112−1+412yes—
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—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
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×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11C4×D414yes—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301D44—416no—
302C23×D4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—112no—
305C22×C4⋊C4C2×D1111yescharacteristic
306C22×C4⋊C4C2×D1111yescharacteristic
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C22⋊C4—112no—
313C22×C42—111no—
314#394—118no—
315#390—224no—
316#387—224no—
317C2×#95—111no—
318C2×#95—111no—
319C2×#95—111no—
320C2×#95—111no—
321C2×#95—111no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95C2×D1111yescharacteristic
326C2×#95C2×D1112yes—
327C2×#95C2×D1112yes—
328C22×C11C2×C4×D411yescharacteristic
329C22×C11#51811yescharacteristic
330C22×C11#51812yes—
331C22×C11#52011yescharacteristic
332C22×C11#52012yes—
333C22×C11#53411yescharacteristic
334C22×C11#53511yescharacteristic
335C22×C11#53511yescharacteristic
336C22×C11#53511yescharacteristic
337C22×C11#53611yescharacteristic
338C22×C11#53711yescharacteristic
339C22×C11#53812yes—
340C22×C11#54011yescharacteristic
341C22×C11#54212yes—
342C22×C11#54211yescharacteristic
343C22×C11#56012yes—
344C22×C11#56012yes—
345C22×C11#56012yes—
346C22×C11#56212yes—
347C22×C11#56212yes—
348C22×C11#56212yes—
349C22×C11#56212yes—
350C22×C11#56312yes—
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—42no—
368C4×C11—42no—
369C4×C11—82no—
370C4×C11—82no—
371Dic11—42no—
372Dic11—44no—
373Dic11—42no—
374Dic11—81no—
375Dic11—81no—
376C25—112no—
377C22×D4—114no—
378C22×D4—222no—
379C22×D4—222no—
380C22×D4—442no—
381C22×D4—442no—
382C23×C4—112no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4C22×D1112yes—
388C23×C4C22×D1112yes—
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—442no—
398C2×C4⋊C4—442no—
399C2×C4⋊C4—442no—
400C2×C4⋊C4—442no—
401C2×C4⋊C4C4×D1114yes—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—118no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—442no—
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×C22⋊C4—442no—
418C2×C22⋊C4—442no—
419C2×C22⋊C4—442no—
420C2×C42—114no—
421C2×C42—442no—
422#95—22no—
423#95—42no—
424#95—42no—
425#95—114no—
426#95—222no—
427#95—222no—
428#95—222no—
429#95—222no—
430#95—442no—
431#95—442no—
432#95—442no—
433C2×C11#232111yescharacteristic
434C2×C11#232411yescharacteristic
435C2×C11#232611yescharacteristic
436C2×C11#237612yes—
437C2×C11#237712yes—
438C2×C11#281311yescharacteristic
439C2×C11#281611yescharacteristic
440C2×C11#281811yescharacteristic
441C2×C11#282011yescharacteristic
442C2×C11#282912yes—
443C2×C11#283012yes—
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—448no—
465C2×D4—444no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
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—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—114no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
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—222no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—222no—
513C22×C4—221no—
514C22×C4—222no—
515C22×C4—221no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—221no—
519C22×C4C2×C4×D1112yes—
520C22×C4C2×C4×D1112yes—
521C22×C4C2×C4×D1112yes—
522C22×C4D4×D1112yes—
523C22×C4#434112yes—
524C4⋊C4—28no—
525C4⋊C4—44no—
526C4⋊C4—444no—
527C4⋊C4—448no—
528C22⋊C4—448no—
529C22⋊C4—448no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C22⋊C4—448no—
534C42—444no—
535C11#1462411yescharacteristic, 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
572C23C2×D4×D1111yescharacteristic
573C23C2×#434111yescharacteristic
574C23#6703712yes—
575C23#6703711yescharacteristic
576C23#6704012yes—
577C23#6704011yescharacteristic
578C23#6704211yescharacteristic
579C23#6704212yes—
580C23#6704212yes—
581C23#6704211yescharacteristic
582D4—4416no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
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—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—222no—
614C2×C4—224no—
615C2×C4—224no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4—442no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—442no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—442no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—442no—
640C2×C4(C22⋊D11)⋊C414yes—
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×(C22⋊D11)⋊C411yescharacteristic
657C22#1062303511yescharacteristic
658C22#1062305211yescharacteristic
659C22#1062307612yes—
660C22#1062310512yes—
661C22#1062312311yescharacteristic
662C22#1062313811yescharacteristic
663C22#1062314812yes—
664C22#1062315011yescharacteristic
665C22#1062315112yes—
666C22#1062316011yescharacteristic
667C22#1062317412yes—
668C22#1062317411yescharacteristic
669C22#1062317812yes—
670C22#1062317812yes—
671C22#1062318411yescharacteristic
672C22#1062319712yes—
673C22#1062320511yescharacteristic
674C22#1062323112yes—
675C22#1062323112yes—
676C22#1062324212yes—
677C22#1062325511yescharacteristic
678C22#1062326612yes—
679C4—24no—
680C4—42no—
681C4—42no—
682C4—82no—
683C4—82no—
684C4—442no—
685C4—444no—
686C4—442no—
687C4—881no—
688C4—881no—
689C2—884no—
690C2#1307127911yescharacteristic
691C2#1307130511yescharacteristic
692C2#1307133011yescharacteristic
693C2#1307176112yes—
694C2#1307177112yes—
695C2#1307662111yescharacteristic
696C2#1307664911yescharacteristic
697C2#1307665811yescharacteristic
698C2#1307667111yescharacteristic
699C2#1307675012yes—
700C2#1307676312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1441D11
hypocenterC11#14624
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C2×#10622594C2semidirect
4. #13066879C2semidirect
5. #13066864C2semidirect
6. #13066862C2semidirect
7. #13066860C2semidirect
8. #13066860C2semidirect
10. #13066841C2semidirect
11. C11×#1441C2semidirect
35. #10622604C4semidirect
190. #1441D11semidirect
535. C11#14624semidirect

Maximal subgroups

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

subgroupindex
C2×#106226042
C2×#106226012
C2×#106225942
#130668792
#130668642
#130668622
#130668602
#130668562
#130668412
C11×#14412
#1462411