Finite Group Databasebeta

← #14676477

Subgroups — #14676477

Order 2816.

2078 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66930C211yesmaximal, characteristic
2C2×#10622556C211yesmaximal, characteristic
3C22×C11⋊#95C211yesmaximal, characteristic
4#13066882C212yesmaximal, complemented
5#13066882C212yesmaximal, complemented
6#13066842C212yesmaximal, complemented
7#13066841C212yesmaximal, complemented
8#13066839C211yesmaximal, characteristic
9#13066838C211yesmaximal, characteristic
10#13066838C211yesmaximal, characteristic
11C11×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×#66930—24no—
24C2×#66930—24no—
25C2×#66930C418yescomplemented
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11⋊#95—24no—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622556—24no—
40C25×C11C2311yescharacteristic
41C23×C4×C11—22no—
42C23×C4×C11—24no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—42no—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×Dic11—22no—
51C23×Dic11—22no—
52C23×Dic11—22no—
53C23×Dic11—22no—
54C23×Dic11—22no—
55C23×Dic11—24no—
56C23×Dic11—22no—
57C23×Dic11—22no—
58C23×Dic11—42no—
59C23×Dic11C2×C414yes—
60C23×Dic11D414yes—
61C23×Dic11D414yes—
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4C2×C414yes—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11C2×C414yes—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4C2×C414yescomplemented
85C2×Dic11⋊C4C2×C414yescomplemented
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11C2×C414yescomplemented
91C2×C4×Dic11C2×C414yescomplemented
92#66930—232no—
93C11×#95—24no—
94C11×#95—42no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#13958—111nomaximal, Sylow
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11C22×C412yes—
111C24×C11C2×D412yes—
112C24×C11C2×D412yes—
113C24×C11#4112yes—
114C24×C11#4112yes—
115C24×C11#4112yes—
116C24×C11#4112yes—
117C24×C11C2411yescharacteristic
118C22×C4×C11—28no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
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×C11—48no—
141C22×C4×C11—48no—
142C22×C4×C11—44no—
143C22×C4×C11—44no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C22×C412yes—
146C22×C4×C11#4114yes—
147C22×Dic11—28no—
148C22×Dic11—28no—
149C22×Dic11—28no—
150C22×Dic11—28no—
151C22×Dic11—28no—
152C22×Dic11—28no—
153C22×Dic11—28no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—48no—
184C22×Dic11—48no—
185C22×Dic11—44no—
186C22×Dic11—44no—
187C22×Dic11C22⋊C4116yes—
188C22×Dic11C22×C412yes—
189C22×Dic11C22×C412yes—
190C22×Dic11C22×C412yes—
191C22×Dic11C22×C412yes—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×D412yes—
194C22×Dic11C2×D412yes—
195C22×Dic11C2×D412yes—
196C22×Dic11#4114yes—
197C11×C22⋊C4—28no—
198C11×C22⋊C4—44no—
199C22⋊Dic11—28no—
200C22⋊Dic11—44no—
201Dic11⋊C4—28no—
202Dic11⋊C4—28no—
203C4×Dic11—28no—
204C4×Dic11—28no—
205C22×#117—111no—
206C2×#381—111no—
207C22×#95—111no—
208#1445—112no—
209#1445—112no—
210#1434—112no—
211#1434—112no—
212C22⋊#95—111no—
213C22⋊#95—111no—
214C22⋊#95—111no—
215C22⋊#95D1111yescharacteristic
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—24no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11C2×C22⋊C414yes—
233C23×C11#11714yes—
234C23×C11#11714yes—
235C23×C11#12314yes—
236C23×C11#12314yes—
237C23×C11#12314yes—
238C23×C11#12314yes—
239C23×C11C23×C411yescharacteristic
240C23×C11C22×D411yescharacteristic
241C23×C11C22×D411yescharacteristic
242C23×C11C2×#4111yescharacteristic
243C23×C11C2×#4111yescharacteristic
244C23×C11C2×#4111yescharacteristic
245C23×C11C2×#4112yes—
246C23×C11C2×#4111yescharacteristic
247C23×C11C2×#4112yes—
248C23×C11H(5,𝔽2)12yes—
249C23×C112−1+412yes—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—416no—
258C2×C4×C11—42no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
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×C11—42no—
274C2×C4×C11—42no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
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—232no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—24no—
294C2×Dic11—24no—
295C2×Dic11—416no—
296C2×Dic11—42no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—42no—
300C2×Dic11—41no—
301C2×Dic11—42no—
302C2×Dic11—41no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—42no—
311C2×Dic11—42no—
312C2×Dic11—42no—
313C2×Dic11C2×C22⋊C414yes—
314C2×Dic11C2×C22⋊C414yes—
315C24×C4—111no—
316C24×C4—111no—
317C24×C4C2×D1111yescharacteristic
318C2×#117—118no—
319C2×#117—224no—
320C2×#117—224no—
321C22×C4⋊C4—111no—
322C22×C4⋊C4—111no—
323C22×C22⋊C4—111no—
324C22×C22⋊C4—111no—
325C22×C22⋊C4C2×D1111yescharacteristic
326C22×C22⋊C4C2×D1111yescharacteristic
327C22×C42—111no—
328C22×C42—111no—
329#381—224no—
330C2×#95—112no—
331C2×#95—112no—
332C2×#95—112no—
333C2×#95—112no—
334C2×#95—112no—
335C2×#95—112no—
336C2×#95—112no—
337C2×#95—112no—
338C2×#95—112no—
339C2×#95—112no—
340C2×#95—224no—
341C2×#95C2×D1112yes—
342C2×#95C2×D1112yes—
343C22×C11—24no—
344C22×C11—28no—
345C22×C11—28no—
346C22×C11—24no—
347C22×C11—24no—
348C22×C11—24no—
349C22×C11—24no—
350C22×C11—28no—
351C22×C11—28no—
352C22×C11—24no—
353C22×C11#38118yes—
354C22×C11C22×C22⋊C411yescharacteristic
355C22×C11C2×#11711yescharacteristic
356C22×C11C2×#11711yescharacteristic
357C22×C11C4×#4112yes—
358C22×C11#52012yes—
359C22×C11C2×#12311yescharacteristic
360C22×C11C2×#12311yescharacteristic
361C22×C11C2×#12311yescharacteristic
362C22×C11C2×#12311yescharacteristic
363C22×C11#52511yescharacteristic
364C22×C11#52511yescharacteristic
365C22×C11#53212yes—
366C22×C11#53511yescharacteristic
367C22×C11#53611yescharacteristic
368C22×C11#53712yes—
369C22×C11#55112yes—
370C22×C11#55112yes—
371C22×C11#55112yes—
372C22×C11#55112yes—
373C22×C11#55212yes—
374C22×C11#55212yes—
375C22×C11#55212yes—
376C22×C11#55212yes—
377C4×C11—42no—
378C4×C11—44no—
379C4×C11—42no—
380C4×C11—82no—
381Dic11—24no—
382Dic11—24no—
383Dic11—42no—
384Dic11—44no—
385Dic11—42no—
386Dic11—82no—
387C25C22×D1111yescharacteristic
388C23×C4—22no—
389C23×C4—24no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—42no—
393C23×C4—114no—
394C23×C4—114no—
395C23×C4—114no—
396C23×C4—111no—
397C23×C4—111no—
398C23×C4—111no—
399C23×C4—111no—
400C23×C4—112no—
401C23×C4—112no—
402C23×C4—224no—
403C23×C4—222no—
404C23×C4—222no—
405C23×C4—222no—
406C23×C4—222no—
407C23×C4—222no—
408C23×C4—222no—
409C23×C4—222no—
410C23×C4—442no—
411C23×C4C22×D1112yes—
412C23×C4C22×D1111yescharacteristic
413C23×C4C22×D1111yescharacteristic
414C23×C4C22×D1112yes—
415#117—2232no—
416C2×C4⋊C4—114no—
417C2×C4⋊C4—114no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—222no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—222no—
429C2×C22⋊C4—222no—
430C2×C22⋊C4—222no—
431C2×C22⋊C4—222no—
432C2×C22⋊C4—222no—
433C2×C22⋊C4C4×D1114yes—
434C2×C42—114no—
435C2×C42—114no—
436C2×C42—222no—
437C2×C42—222no—
438C2×C42—222no—
439C2×C42—222no—
440#95—24no—
441#95—42no—
442#95—224no—
443#95—224no—
444#95—224no—
445#95—224no—
446#95—224no—
447#95—224no—
448#95—224no—
449#95—442no—
450#95—442no—
451#95—442no—
452C2×C11—28no—
453C2×C11C2×#38111yescharacteristic
454C2×C11#229711yescharacteristic
455C2×C11#231111yescharacteristic
456C2×C11#234312yes—
457C2×C11#234312yes—
458C2×C11#248211yescharacteristic
459C2×C11#248211yescharacteristic
460C2×C11#248411yescharacteristic
461C2×C11#248411yescharacteristic
462C2×C11#249812yes—
463C2×C11#249812yes—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24C2×C4×D1112yes—
469C24#433912yes—
470C24#433912yes—
471C24D4×D1112yes—
472C24D4×D1112yes—
473C24#434112yes—
474C24#434312yes—
475C24C23×D1111yescharacteristic
476C22×C4—28no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
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—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—1116no—
503C22×C4—112no—
504C22×C4—112no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—112no—
508C22×C4—112no—
509C22×C4—112no—
510C22×C4—112no—
511C22×C4—114no—
512C22×C4—228no—
513C22×C4—228no—
514C22×C4—228no—
515C22×C4—228no—
516C22×C4—228no—
517C22×C4—228no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—228no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—221no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—222no—
540C22×C4—222no—
541C22×C4—222no—
542C22×C4—222no—
543C22×C4—222no—
544C22×C4—222no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—448no—
549C22×C4—448no—
550C22×C4—444no—
551C22×C4—444no—
552C22×C4C2×C4×D1112yes—
553C22×C4C2×C4×D1112yes—
554C22×C4#434114yes—
555C4⋊C4—228no—
556C4⋊C4—228no—
557C22⋊C4—28no—
558C22⋊C4—44no—
559C22⋊C4—228no—
560C22⋊C4—444no—
561C42—228no—
562C42—228no—
563C11#1395811yescharacteristic, complemented, Sylow
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—22no—
571C23—24no—
572C23—22no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—22no—
578C23—24no—
579C23—22no—
580C23#6692514yes—
581C23C22⋊C4×D1114yes—
582C23#6693614yes—
583C23#6693614yes—
584C23#6694514yes—
585C23#6694714yes—
586C23#6694714yes—
587C23C22×C4×D1111yescharacteristic
588C23C2×#433911yescharacteristic
589C23C2×#433911yescharacteristic
590C23C2×D4×D1111yescharacteristic
591C23C2×D4×D1111yescharacteristic
592C23C2×#434111yescharacteristic
593C23C2×#434112yes—
594C23#6703712yes—
595C23C2×#434311yescharacteristic
596C23#41×D1112yes—
597C23#6704312yes—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—416no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
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—114no—
624C2×C4—114no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—222no—
634C2×C4—222no—
635C2×C4—222no—
636C2×C4—222no—
637C2×C4—2232no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—224no—
641C2×C4—224no—
642C2×C4—224no—
643C2×C4—224no—
644C2×C4—224no—
645C2×C4—4416no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4—441no—
649C2×C4—442no—
650C2×C4—441no—
651C2×C4—442no—
652C2×C4—442no—
653C2×C4—442no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—442no—
657C2×C4—442no—
658C2×C4—442no—
659C2×C4—442no—
660C2×C4—442no—
661C2×C4—442no—
662C2×C4—442no—
663C22—24no—
664C22—24no—
665C22—24no—
666C22—28no—
667C22—28no—
668C22—28no—
669C22—28no—
670C22—24no—
671C22—24no—
672C22—24no—
673C22#1062227718yes—
674C22C2×#6692511yescharacteristic
675C22C2×C22⋊C4×D1111yescharacteristic
676C22C2×#6693611yescharacteristic
677C22C2×#6693611yescharacteristic
678C22#1062302612yes—
679C22C2×#6694511yescharacteristic
680C22C2×#6694711yescharacteristic
681C22C2×#6694711yescharacteristic
682C22#1062306212yes—
683C22C4×#434112yes—
684C22#1062307212yes—
685C22#1062307712yes—
686C22#1062308712yes—
687C22#1062311711yescharacteristic
688C22#1062311812yes—
689C22#1062312311yescharacteristic
690C22#1062312712yes—
691C22#1062312812yes—
692C22#1062316812yes—
693C22#1062317312yes—
694C22#1062317911yescharacteristic
695C22#1062318112yes—
696C22#1062318711yescharacteristic
697C4—42no—
698C4—44no—
699C4—42no—
700C4—82no—
701C4—224no—
702C4—224no—
703C4—442no—
704C4—444no—
705C4—442no—
706C4—882no—
707C2—28no—
708C2C2×#1062227711yescharacteristic
709C2#1307110111yescharacteristic
710C2#1307120311yescharacteristic
711C2#1307147012yes—
712C2#1307147412yes—
713C2#1307288711yescharacteristic
714C2#1307288911yescharacteristic
715C2#1307290011yescharacteristic
716C2#1307290211yescharacteristic
717C2#1307305612yes—
718C2#1307305812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#13958
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. #13066882C2semidirect
5. #13066882C2semidirect
6. #13066842C2semidirect
7. #13066841C2semidirect
25. C2×#66930C4semidirect
84. C2×Dic11⋊C4C2×C4semidirect
85. C2×Dic11⋊C4C2×C4semidirect
90. C2×C4×Dic11C2×C4semidirect
91. C2×C4×Dic11C2×C4semidirect
563. C11#13958semidirect

Maximal subgroups

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

subgroupindex
C22×#669302
C2×#106225562
C22×C11⋊#952
#130668822
#130668422
#130668412
#130668392
#130668382
C11×C22⋊#952
#1395811