Finite Group Databasebeta

← #14684451

Subgroups — #14684451

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×#10622285C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic
3C2×#10622265C211yesmaximal, characteristic, complemented
4#13066866C211yesmaximal, characteristic, complemented
5#13066864C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066858C212yesmaximal, complemented
9#13066856C211yesmaximal, characteristic
10#13066841C211yesmaximal, characteristic, complemented
11C11×#1444C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
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×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
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#10622601—24no—
36#10622285C418yescomplemented
37#10622265—24no—
38C24×D11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
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—42no—
56C2×C11×C4⋊C4—42no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4—42no—
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×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—42no—
81C2×Dic11⋊C4C2×C414yes—
82C2×C4×Dic11—42no—
83C2×C4×Dic11D414yes—
84C11×#95—22no—
85C11×#95—42no—
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#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—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C22×C414yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4112yes—
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—21no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166C22×Dic11C22×C412yes—
167C22×Dic11C22×C412yes—
168C22×Dic11C2×D412yes—
169C22×Dic11C2×D412yes—
170C2×D44—28no—
171C2×D44—48no—
172C2×D44—44no—
173C2×D44—44no—
174C2×D44—48no—
175C11×C4⋊C4—44no—
176C11×C4⋊C4—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—
183Dic11⋊C4—28no—
184Dic11⋊C4—44no—
185C4×Dic11—44no—
186C2×#394—111no—
187C2×#390—111no—
188C2×#387—111no—
189#1444D1111yescharacteristic, complemented
190#1441—111no—
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)12yes—
204C23×C11H(5,𝔽2)11yescharacteristic
205C23×C11H(5,𝔽2)11yescharacteristic
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—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
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×C11C4×D414yes—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—42no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—42no—
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—
301D44—416no—
302C23×D4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4C2×D1111yescharacteristic
306C22×C4⋊C4C2×D1112yes—
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—112no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95C2×D1111yescharacteristic
326C2×#95C2×D1112yes—
327C2×#95C2×D1111yescharacteristic
328C22×C11C2×C4×D411yescharacteristic
329C22×C11#51812yes—
330C22×C11#51811yescharacteristic
331C22×C11#52012yes—
332C22×C11#52011yescharacteristic
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—44no—
368C4×C11—82no—
369C4×C11—81no—
370C4×C11—81no—
371Dic11—42no—
372Dic11—42no—
373Dic11—42no—
374Dic11—42no—
375Dic11—82no—
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—111no—
386C23×C4—112no—
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1112yes—
390C23×C4C22×D1112yes—
391C23×C4C22×D1111yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—442no—
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—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×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—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
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—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—112no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4C2×C4×D1114yes—
521C22×C4C2×C4×D1112yes—
522C22×C4D4×D1112yes—
523C22×C4#434312yes—
524C4⋊C4—44no—
525C4⋊C4—48no—
526C4⋊C4—228no—
527C4⋊C4—444no—
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
573C23#6703712yes—
574C23#6703711yescharacteristic
575C23#6703712yes—
576C23C2×#434311yescharacteristic
577C23#6704012yes—
578C23#6704011yescharacteristic
579C23#6704211yescharacteristic
580C23#6704212yes—
581C23#6704211yescharacteristic
582D4—4416no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—442no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—441no—
630C2×C4—442no—
631C2×C4—441no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4—442no—
639C2×C4—442no—
640C2×C4#6694614yes—
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×#6694611yescharacteristic
657C22#1062303512yes—
658C22#1062307612yes—
659C22#1062307611yescharacteristic
660C22#1062310511yescharacteristic
661C22#1062312311yescharacteristic
662C22#1062312612yes—
663C22#1062313811yescharacteristic
664C22#1062315112yes—
665C22#1062316011yescharacteristic
666C22#1062317512yes—
667C22#1062317812yes—
668C22#1062317812yes—
669C22#1062317812yes—
670C22#1062318411yescharacteristic
671C22#1062319712yes—
672C22#1062322911yescharacteristic
673C22#1062323112yes—
674C22#1062324611yescharacteristic
675C22#1062325511yescharacteristic
676C22#1062326412yes—
677C22#1062326411yescharacteristic
678C22#1062326612yes—
679C4—24no—
680C4—44no—
681C4—81no—
682C4—82no—
683C4—81no—
684C4—442no—
685C4—442no—
686C4—442no—
687C4—442no—
688C4—882no—
689C2—884no—
690C2#1307127311yescharacteristic
691C2#1307130711yescharacteristic
692C2#1307132411yescharacteristic
693C2#1307176112yes—
694C2#1307177212yes—
695C2#1307661911yescharacteristic
696C2#1307664911yescharacteristic
697C2#1307665511yescharacteristic
698C2#1307667111yescharacteristic
699C2#1307675412yes—
700C2#1307676412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1444D11
hypocenterC11#14624
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
3. C2×#10622265C2semidirect
4. #13066866C2semidirect
5. #13066864C2semidirect
6. #13066860C2semidirect
7. #13066858C2semidirect
8. #13066858C2semidirect
10. #13066841C2semidirect
11. C11×#1444C2semidirect
36. #10622285C4semidirect
189. #1444D11semidirect
535. C11#14624semidirect

Maximal subgroups

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

subgroupindex
C2×#106222852
C2×#106226012
C2×#106222652
#130668662
#130668642
#130668602
#130668582
#130668562
#130668412
C11×#14442
#1462411