Finite Group Databasebeta

← #14680679

Subgroups — #14680679

Order 2816.

1766 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622285C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic
3C2×#10622603C212yesmaximal, complemented
4C2×#10622262C211yesmaximal, characteristic, complemented
5#13066866C211yesmaximal, characteristic, complemented
6#13066860C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066856C211yesmaximal, characteristic
9#13066852C212yesmaximal, complemented
10#13066841C211yesmaximal, characteristic, complemented
11C11×#1444C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
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×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622603—28no—
36#10622601—24no—
37#10622285C418yescomplemented
38#10622262—24no—
39C24×D11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C22×D44—22no—
51C22×D44—22no—
52C22×D44—42no—
53C22×D44—42no—
54C22×D44C2×C414yes—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4—42no—
59C2×C11×C4⋊C4—42no—
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—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—24no—
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)⋊C4—42no—
76C2×(C2×D11)⋊C4C2×C418yes—
77C2×(C2×D11)⋊C4C2×C418yes—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4C2×C414yes—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—42no—
88C2×C4×Dic11—42no—
89C2×C4×Dic11D414yes—
90C2×C4×Dic11D414yescomplemented
91C11×#95—22no—
92C11×#95—42no—
93C11×#95C2×C414yes—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100#14312—111nomaximal, Sylow
101C24×C11C2411yescharacteristic
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×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11C22×C414yes—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
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×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11C22×C414yes—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11#4112yes—
145C22×C4×C11#4112yes—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11C22×C412yes—
168C22×Dic11C22×C412yes—
169C22×Dic11C2×D412yes—
170C22×Dic11C2×D412yes—
171C22×Dic11C2×D412yes—
172C22×Dic11C2×D412yes—
173C22×Dic11#4112yes—
174C22×Dic11#4112yes—
175C2×D44—28no—
176C2×D44—48no—
177C2×D44—44no—
178C2×D44—44no—
179C2×D44—48no—
180C11×C4⋊C4—44no—
181C11×C4⋊C4—48no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—48no—
184(C2×D11)⋊C4—48no—
185(C2×D11)⋊C4—48no—
186(C2×D11)⋊C4—48no—
187(C2×D11)⋊C4—48no—
188Dic11⋊C4—28no—
189Dic11⋊C4—28no—
190C4×Dic11—28no—
191C4×Dic11—44no—
192C4×Dic11—44no—
193C2×#394—111no—
194C2×#390—111no—
195C2×#388—112no—
196C2×C4×C4⋊C4—111no—
197#1444D1111yescharacteristic, complemented
198#1441—111no—
199#1439—112no—
200#1439—112no—
201#1438—111no—
202#1437—112no—
203#1434—111no—
204C23×C11C23×C411yescharacteristic
205C23×C11C22×D411yescharacteristic
206C23×C11C22×D411yescharacteristic
207C23×C11C2×#4111yescharacteristic
208C23×C11C2×#4111yescharacteristic
209C23×C11C2×#4111yescharacteristic
210C23×C11C2×#4111yescharacteristic
211C23×C11H(5,𝔽2)12yes—
212C23×C11H(5,𝔽2)12yes—
213C23×C11H(5,𝔽2)12yes—
214C23×C112−1+412yes—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
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—
243C22×D11—42no—
244C22×D11—42no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
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×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11C4×D414yes—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—22no—
290C2×Dic11—24no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—41no—
295C2×Dic11—41no—
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×Dic11C4×D414yes—
307C2×Dic11#12114yes—
308D44—416no—
309C23×D4—111no—
310C22×C4⋊C4—111no—
311C22×C4⋊C4—111no—
312C22×C4⋊C4C2×D1112yes—
313C22×C4⋊C4C2×D1111yescharacteristic
314C22×C22⋊C4—112no—
315C22×C22⋊C4—112no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4—112no—
318C22×C22⋊C4—112no—
319C22×C22⋊C4—112no—
320C22×C42—111no—
321C22×C42—111no—
322C22×C42—111no—
323#394—118no—
324#390—224no—
325#388—228no—
326C4×C4⋊C4—224no—
327C2×#95—112no—
328C2×#95—111no—
329C2×#95—111no—
330C2×#95—112no—
331C2×#95—112no—
332C2×#95—112no—
333C2×#95C2×D1111yescharacteristic
334C2×#95C2×D1112yes—
335C2×#95C2×D1111yescharacteristic
336C22×C11C2×C4×D411yescharacteristic
337C22×C11C2×C4×D411yescharacteristic
338C22×C11C4×#4111yescharacteristic
339C22×C11#51812yes—
340C22×C11#52012yes—
341C22×C11C2×#12111yescharacteristic
342C22×C11#52511yescharacteristic
343C22×C11#52911yescharacteristic
344C22×C11#53211yescharacteristic
345C22×C11#53411yescharacteristic
346C22×C11#53511yescharacteristic
347C22×C11#53511yescharacteristic
348C22×C11#53512yes—
349C22×C11#53611yescharacteristic
350C22×C11#53712yes—
351C22×C11#53812yes—
352C22×C11#53812yes—
353C22×C11#53912yes—
354C22×C11#54012yes—
355C22×C11#54012yes—
356C22×C11#54212yes—
357C22×C11#54212yes—
358C22×C11#54212yes—
359C2×D11—44no—
360C2×D11—44no—
361C2×D11—44no—
362C2×D11—44no—
363C2×D11—44no—
364C2×D11—44no—
365C2×D11—44no—
366C2×D11—82no—
367C2×D11—82no—
368C2×D11—82no—
369C2×D11—82no—
370C2×D11—82no—
371C2×D11—82no—
372C2×D11—82no—
373C2×D11—82no—
374C4×C11—24no—
375C4×C11—44no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11—82no—
379Dic11—24no—
380Dic11—24no—
381Dic11—42no—
382Dic11—42no—
383Dic11—82no—
384C25—112no—
385C22×D4—114no—
386C22×D4—222no—
387C22×D4—222no—
388C22×D4—442no—
389C22×D4—442no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—112no—
395C23×C4C22×D1112yes—
396C23×C4C22×D1112yes—
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—222no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—224no—
414C2×C22⋊C4—224no—
415C2×C22⋊C4—224no—
416C2×C22⋊C4—224no—
417C2×C22⋊C4—224no—
418C2×C22⋊C4—224no—
419C2×C22⋊C4—224no—
420C2×C22⋊C4—224no—
421C2×C22⋊C4—442no—
422C2×C22⋊C4—442no—
423C2×C22⋊C4—442no—
424C2×C22⋊C4—442no—
425C2×C22⋊C4—442no—
426C2×C22⋊C4—442no—
427C2×C22⋊C4—442no—
428C2×C22⋊C4—442no—
429C2×C42—114no—
430C2×C42—114no—
431C2×C42—222no—
432C2×C42—222no—
433C2×C42—222no—
434C2×C42—442no—
435C2×C42—442no—
436#95—22no—
437#95—42no—
438#95—222no—
439#95—224no—
440#95—224no—
441#95—222no—
442#95—442no—
443#95—442no—
444#95C4×D1114yes—
445C2×C11C4×#12111yescharacteristic
446C2×C11#232111yescharacteristic
447C2×C11#232412yes—
448C2×C11#232611yescharacteristic
449C2×C11#233512yes—
450C2×C11#261811yescharacteristic
451C2×C11#261911yescharacteristic
452C2×C11#263211yescharacteristic
453C2×C11#263511yescharacteristic
454C2×C11#265112yes—
455C2×C11#266212yes—
456D11—84no—
457C24—114no—
458C24—222no—
459C24—222no—
460C24—222no—
461C24—222no—
462C24—222no—
463C24—222no—
464C24—222no—
465C24—222no—
466C24—222no—
467C24—222no—
468C24—222no—
469C24—222no—
470C24—222no—
471C24—222no—
472C24C23×D1111yescharacteristic
473C2×D4—228no—
474C2×D4—448no—
475C2×D4—444no—
476C2×D4—448no—
477C2×D4—444no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—112no—
502C22×C4—112no—
503C22×C4—112no—
504C22×C4—112no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—112no—
508C22×C4—112no—
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×C4—221no—
520C22×C4—221no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—222no—
530C22×C4C2×C4×D1114yes—
531C22×C4C2×C4×D1112yes—
532C22×C4D4×D1112yes—
533C22×C4D4×D1112yes—
534C22×C4#434312yes—
535C22×C4#434312yes—
536C4⋊C4—44no—
537C4⋊C4—48no—
538C4⋊C4—228no—
539C4⋊C4—228no—
540C22⋊C4—2216no—
541C22⋊C4—448no—
542C22⋊C4—448no—
543C22⋊C4—448no—
544C22⋊C4—448no—
545C22⋊C4—448no—
546C42—228no—
547C42—444no—
548C42—444no—
549C11#1431211yescharacteristic, complemented, Sylow
550C23—224no—
551C23—224no—
552C23—224no—
553C23—224no—
554C23—224no—
555C23—224no—
556C23—224no—
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—
571C23—442no—
572C23—442no—
573C23—442no—
574C23—442no—
575C23—442no—
576C23—442no—
577C23—442no—
578C23—442no—
579C23—442no—
580C23—442no—
581C23—442no—
582C23—442no—
583C23—442no—
584C23—442no—
585C23C22×C4×D1111yescharacteristic
586C23C2×D4×D1111yescharacteristic
587C23C2×D4×D1111yescharacteristic
588C23#6703712yes—
589C23#6703712yes—
590C23C2×#434311yescharacteristic
591C23C2×#434311yescharacteristic
592C23#6704012yes—
593C23#41×D1111yescharacteristic
594C23#41×D1111yescharacteristic
595C23#6704212yes—
596D4—4416no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—114no—
626C2×C4—114no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—224no—
634C2×C4—222no—
635C2×C4—222no—
636C2×C4—224no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—224no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—441no—
643C2×C4—442no—
644C2×C4—442no—
645C2×C4—441no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4—442no—
649C2×C4—442no—
650C2×C4—442no—
651C2×C4—442no—
652C2×C4—442no—
653C2×C4—442no—
654C2×C4#6694614yes—
655C22—444no—
656C22—444no—
657C22—444no—
658C22—444no—
659C22—444no—
660C22—444no—
661C22—444no—
662C22—882no—
663C22—882no—
664C22—882no—
665C22—882no—
666C22—882no—
667C22—882no—
668C22—882no—
669C22—882no—
670C22C2×#6694611yescharacteristic
671C22#1062303512yes—
672C22C4×D4×D1111yescharacteristic
673C22#1062307612yes—
674C22C4×#434311yescharacteristic
675C22#1062312311yescharacteristic
676C22#1062312312yes—
677C22D11×#12111yescharacteristic
678C22#1062314612yes—
679C22#1062315811yescharacteristic
680C22#1062316012yes—
681C22#1062317112yes—
682C22#1062317512yes—
683C22#1062317512yes—
684C22#1062318411yescharacteristic
685C22#1062319412yes—
686C22#1062322211yescharacteristic
687C22#1062322312yes—
688C22#1062324611yescharacteristic
689C22#1062325511yescharacteristic
690C22#1062325611yescharacteristic
691C22#1062326412yes—
692C22#1062326412yes—
693C4—24no—
694C4—42no—
695C4—42no—
696C4—44no—
697C4—82no—
698C4—224no—
699C4—224no—
700C4—442no—
701C4—442no—
702C4—882no—
703C2—884no—
704C2#1307112411yescharacteristic
705C2#1307127311yescharacteristic
706C2#1307130812yes—
707C2#1307132411yescharacteristic
708C2#1307140912yes—
709C2#1307435911yescharacteristic
710C2#1307436511yescharacteristic
711C2#1307448211yescharacteristic
712C2#1307450611yescharacteristic
713C2#1307464812yes—
714C2#1307476012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1444D11
hypocenterC11#14312
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
3. C2×#10622603C2semidirect
4. C2×#10622262C2semidirect
5. #13066866C2semidirect
6. #13066860C2semidirect
7. #13066858C2semidirect
9. #13066852C2semidirect
10. #13066841C2semidirect
11. C11×#1444C2semidirect
37. #10622285C4semidirect
90. C2×C4×Dic11D4semidirect
197. #1444D11semidirect
549. C11#14312semidirect

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×#106226032
C2×#106222622
#130668662
#130668602
#130668582
#130668562
#130668522
#130668412
C11×#14442
#1431211