Finite Group Databasebeta

← #14680675

Subgroups — #14680675

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×#10622834C211yesmaximal, characteristic
2C2×#10622564C212yesmaximal, complemented
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
4#13066881C211yesmaximal, characteristic, complemented
5#13066869C211yesmaximal, characteristic, complemented
6#13066861C212yesmaximal, complemented
7#13066861C212yesmaximal, complemented
8#13066857C211yesmaximal, characteristic
9#13066853C212yesmaximal, complemented
10#13066841C211yesmaximal, characteristic, complemented
11C2×C11×#394C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C11×#394C418yescomplemented
27C2×C11×#95C2211yescharacteristic
28#10622834—24no—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C4⋊C4×Dic11—24no—
38#10622564—28no—
39C25×C11C2312yes—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—42no—
43C22×D4×C11—42no—
44C22×D4×C11C2×C414yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2×C414yes—
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—42no—
61C2×C11×C22⋊C4—42no—
62C2×C11×C22⋊C4C2×C418yes—
63C2×C11×C22⋊C4C2×C418yes—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—42no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11—42no—
75C2×C22⋊Dic11—42no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—42no—
82C2×C4⋊Dic11—42no—
83C2×C4⋊Dic11—42no—
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×#95C2×C414yes—
92C11⋊#95—24no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—24no—
96C11⋊#95—22no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100#14312—111nomaximal, Sylow
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11C22×C414yes—
116C24×C11C2411yescharacteristic
117C2×D4×C11—28no—
118C2×D4×C11—48no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—48no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
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×C11C22×C414yes—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C412yes—
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—22no—
150C22×Dic11—22no—
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×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11C2×D412yes—
175C22×Dic11C2×D412yes—
176C22×Dic11C2×D412yes—
177C22×Dic11C2×D412yes—
178C22×Dic11#4112yes—
179C22×Dic11#4112yes—
180C11×C4⋊C4—28no—
181C11×C22⋊C4—216no—
182C11×C22⋊C4—48no—
183C22⋊Dic11—48no—
184C22⋊Dic11—48no—
185C22⋊Dic11—48no—
186C22⋊Dic11—48no—
187C4⋊Dic11—28no—
188C4⋊Dic11—44no—
189C4⋊Dic11—48no—
190C4×Dic11—28no—
191C4×Dic11—44no—
192C4×Dic11—44no—
193C2×#394D1111yescharacteristic
194C2×#390—111no—
195C2×#388—112no—
196C2×C4×C4⋊C4—111no—
197#1444—111no—
198#1441—111no—
199#1439—112no—
200#1439—112no—
201#1438—111no—
202#1437—112no—
203#1434—111no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11C23×C411yescharacteristic
240C23×C11C22×D411yescharacteristic
241C23×C11C22×D411yescharacteristic
242C23×C11C2×#4111yescharacteristic
243C23×C11C2×#4111yescharacteristic
244C23×C11C2×#4111yescharacteristic
245C23×C11C2×#4111yescharacteristic
246C23×C11H(5,𝔽2)12yes—
247C23×C11H(5,𝔽2)12yes—
248C23×C11H(5,𝔽2)12yes—
249C23×C112−1+412yes—
250D4×C11—416no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—22no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11—41no—
267C2×C4×C11—42no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11C4×D414yes—
274C2×C4×C11C4×D414yes—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—41no—
287C2×Dic11—41no—
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—
301C2×Dic11—42no—
302C2×Dic11—42no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11#12114yes—
309C23×D4C2×D1111yescharacteristic
310C22×C4⋊C4—111no—
311C22×C4⋊C4—112no—
312C22×C4⋊C4—111no—
313C22×C4⋊C4C2×D1111yescharacteristic
314C22×C22⋊C4—112no—
315C22×C22⋊C4—112no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4—112no—
318C22×C22⋊C4C2×D1112yes—
319C22×C22⋊C4C2×D1112yes—
320C22×C42—111no—
321C22×C42—111no—
322C22×C42—111no—
323#394Dic1118yescomplemented
324#390—224no—
325#388—228no—
326C4×C4⋊C4—224no—
327C2×#95—112no—
328C2×#95—111no—
329C2×#95—111no—
330C2×#95—111no—
331C2×#95—112no—
332C2×#95—112no—
333C2×#95—112no—
334C2×#95—112no—
335C2×#95C2×D1111yescharacteristic
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—44no—
339C22×C11—44no—
340C22×C11—44no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—82no—
344C22×C11—82no—
345C22×C11—82no—
346C22×C11—82no—
347C22×C11—82no—
348C22×C11—82no—
349C22×C11—82no—
350C22×C11—82no—
351C22×C11C2×C4×D411yescharacteristic
352C22×C11C2×C4×D411yescharacteristic
353C22×C11C4×#4111yescharacteristic
354C22×C11#51812yes—
355C22×C11#52012yes—
356C22×C11C2×#12111yescharacteristic
357C22×C11#52511yescharacteristic
358C22×C11#52911yescharacteristic
359C22×C11#53211yescharacteristic
360C22×C11#53411yescharacteristic
361C22×C11#53511yescharacteristic
362C22×C11#53512yes—
363C22×C11#53511yescharacteristic
364C22×C11#53611yescharacteristic
365C22×C11#53712yes—
366C22×C11#53812yes—
367C22×C11#53812yes—
368C22×C11#53912yes—
369C22×C11#54012yes—
370C22×C11#54012yes—
371C22×C11#54212yes—
372C22×C11#54212yes—
373C22×C11#54212yes—
374C4×C11—24no—
375C4×C11—24no—
376C4×C11—42no—
377C4×C11—44no—
378Dic11—24no—
379Dic11—42no—
380Dic11—42no—
381Dic11—42no—
382Dic11—82no—
383Dic11—82no—
384C25C22×D1112yes—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4C2×Dic1114yes—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—112no—
395C23×C4—112no—
396C23×C4C22×D1112yes—
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—224no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—442no—
408C2×C4⋊C4—442no—
409C2×C4⋊C4—442no—
410C2×C4⋊C4C2×Dic1114yes—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
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⋊C4C2×Dic1118yes—
428C2×C22⋊C4C2×Dic1118yes—
429C2×C42—114no—
430C2×C42—114no—
431C2×C42—222no—
432C2×C42—222no—
433C2×C42—222no—
434C2×C42—442no—
435C2×C42—442no—
436#95—222no—
437#95—224no—
438#95—222no—
439#95—224no—
440#95—222no—
441#95—442no—
442#95—442no—
443#95—442no—
444#95C2×Dic1114yes—
445C2×C11—84no—
446C2×C11C4×#12111yescharacteristic
447C2×C11#232111yescharacteristic
448C2×C11#232412yes—
449C2×C11#232611yescharacteristic
450C2×C11#233512yes—
451C2×C11#261811yescharacteristic
452C2×C11#261911yescharacteristic
453C2×C11#263211yescharacteristic
454C2×C11#263511yescharacteristic
455C2×C11#265112yes—
456C2×C11#266212yes—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24C22×Dic1114yes—
472C24C23×D1111yescharacteristic
473C2×D4—28no—
474C2×D4—48no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—48no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—222no—
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×C4—222no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4D4×D1112yes—
529C22×C4D4×D1112yes—
530C22×C4#434112yes—
531C22×C4#434112yes—
532C22×C4C22×Dic1114yes—
533C22×C4C22×Dic1112yes—
534C22×C4C22×Dic1112yes—
535C22×C4C22×Dic1112yes—
536C4⋊C4—28no—
537C4⋊C4—228no—
538C4⋊C4—444no—
539C4⋊C4—448no—
540C22⋊C4—216no—
541C22⋊C4—48no—
542C22⋊C4—448no—
543C22⋊C4—448no—
544C22⋊C4—448no—
545C22⋊C4—448no—
546C42—228no—
547C42—444no—
548C42—444no—
549C11#1431211yescharacteristic, complemented, Sylow
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23C2×D4×D1111yescharacteristic
586C23C2×D4×D1111yescharacteristic
587C23C2×#434111yescharacteristic
588C23C2×#434111yescharacteristic
589C23#6703712yes—
590C23#6703712yes—
591C23#41×D1111yescharacteristic
592C23#41×D1111yescharacteristic
593C23#6704212yes—
594C23#6704312yes—
595C23C23×Dic1111yescharacteristic
596D4—416no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—114no—
620C2×C4—222no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—224no—
629C2×C4—224no—
630C2×C4—222no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—441no—
638C2×C4—441no—
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—
649C2×C4—442no—
650C2×C4—442no—
651C2×C4—442no—
652C2×C4—442no—
653C2×C4D4×Dic1114yes—
654C2×C4D4×Dic1114yes—
655C22—44no—
656C22—44no—
657C22—44no—
658C22—44no—
659C22—44no—
660C22—44no—
661C22—44no—
662C22—82no—
663C22—82no—
664C22—82no—
665C22—82no—
666C22—82no—
667C22—82no—
668C22—82no—
669C22—82no—
670C22#1062312011yescharacteristic
671C22#1062312311yescharacteristic
672C22#1062312412yes—
673C22#1062312711yescharacteristic
674C22#1062313111yescharacteristic
675C22#1062313412yes—
676C22D11×#12111yescharacteristic
677C22#1062313711yescharacteristic
678C22#1062313812yes—
679C22#1062313912yes—
680C22#1062315012yes—
681C22#1062318812yes—
682C22#1062319112yes—
683C22#1062319312yes—
684C22#1062319412yes—
685C22#1062320511yescharacteristic
686C22#1062320611yescharacteristic
687C22#1062321312yes—
688C22C2×D4×Dic1111yescharacteristic
689C22C2×D4×Dic1111yescharacteristic
690C22#1062332912yes—
691C22#41×Dic1111yescharacteristic
692C22#1062335812yes—
693C4—24no—
694C4—24no—
695C4—42no—
696C4—44no—
697C4—224no—
698C4—442no—
699C4—442no—
700C4—442no—
701C4—882no—
702C4—882no—
703C2—84no—
704C2#121×Dic1111yescharacteristic
705C2#1307127711yescharacteristic
706C2#1307131112yes—
707C2#1307132911yescharacteristic
708C2#1307141012yes—
709C2#1307435711yescharacteristic
710C2#1307436811yescharacteristic
711C2#1307448111yescharacteristic
712C2#1307450811yescharacteristic
713C2#1307465012yes—
714C2#1307475212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#394C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11#14312
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C2×#10622564C2semidirect
3. C2×C4⋊C4×Dic11C2semidirect
4. #13066881C2semidirect
5. #13066869C2semidirect
6. #13066861C2semidirect
7. #13066861C2semidirect
9. #13066853C2semidirect
10. #13066841C2semidirect
26. C11×#394C4semidirect
90. C2×C4×Dic11D4semidirect
323. #394Dic11semidirect
549. C11#14312semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225642
C2×C4⋊C4×Dic112
#130668812
#130668692
#130668612
#130668572
#130668532
#130668412
C2×C11×#3942
#1431211