Finite Group Databasebeta

← #14684535

Subgroups — #14684535

Order 2816.

1586 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622604C211yesmaximal, characteristic
2C2×#10622282C212yesmaximal, complemented
3#13066874C212yesmaximal, complemented
4#13066862C212yesmaximal, complemented
5#13066860C212yesmaximal, complemented
6#13066858C212yesmaximal, complemented
7#13066856C212yesmaximal
8#13066845C211yesmaximal, characteristic, complemented
9C11×#1441C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622604C418yescomplemented
32#10622282—28no—
33C24×D11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C22×D44—42no—
43C22×D44—42no—
44C22×D44—41no—
45C22×D44—41no—
46C22×D44C2×C414yes—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4—41no—
49C2×C11×C4⋊C4—42no—
50C2×C11×C4⋊C4—41no—
51C2×C11×C4⋊C4C2×C414yes—
52C2×(C2×D11)⋊C4—24no—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—24no—
55C2×(C2×D11)⋊C4—24no—
56C2×(C2×D11)⋊C4—42no—
57C2×(C2×D11)⋊C4—42no—
58C2×(C2×D11)⋊C4—42no—
59C2×(C2×D11)⋊C4—42no—
60C2×(C2×D11)⋊C4—42no—
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)⋊C4C2×C418yes—
69C2×(C2×D11)⋊C4C2×C418yes—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—41no—
72C2×C4⋊Dic11—41no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—42no—
75C2×Dic11⋊C4—42no—
76C2×C4×Dic11—41no—
77C2×C4×Dic11—41no—
78C2×C4×Dic11D414yescomplemented
79C11×#95—24no—
80C11×#95—41no—
81C11×#95—42no—
82C11⋊#95—24no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95C2×C414yes—
88#14632—111nomaximal, Sylow
89C24×C11C2411yescharacteristic
90C23×D11—22no—
91C23×D11—22no—
92C23×D11—22no—
93C23×D11—22no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11C22×C414yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
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—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11#4112yes—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11C22×C414yes—
156C22×Dic11C2×D414yes—
157C2×D44—44no—
158C2×D44—48no—
159C2×D44—48no—
160C2×D44—44no—
161C2×D44—44no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—44no—
164(C2×D11)⋊C4—216no—
165(C2×D11)⋊C4—48no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168(C2×D11)⋊C4—48no—
169(C2×D11)⋊C4—48no—
170C4⋊Dic11—44no—
171Dic11⋊C4—48no—
172C4×Dic11—44no—
173C2×#394—111no—
174C2×#388—112no—
175#1442—112no—
176#1441D1111yescharacteristic, complemented
177#1439—112no—
178#1439—112no—
179#1439—112no—
180#1438—112no—
181C4⋊#95—111no—
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C2×#4111yescharacteristic
185C23×C11H(5,𝔽2)11yescharacteristic
186C23×C11H(5,𝔽2)12yes—
187C23×C11H(5,𝔽2)11yescharacteristic
188C23×C11H(5,𝔽2)12yes—
189C23×C11H(5,𝔽2)11yescharacteristic
190C23×C11H(5,𝔽2)12yes—
191C23×C112−1+412yes—
192C23×C112−1+411yescharacteristic
193C22×D11—24no—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
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—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11C4×D414yes—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280D44—416no—
281C23×D4—111no—
282C22×C4⋊C4—112no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4C2×D1111yescharacteristic
285C22×C4⋊C4C2×D1111yescharacteristic
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C42—111no—
293#394—118no—
294#388—228no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95C2×D1112yes—
302C2×#95C2×D1112yes—
303C2×#95C2×D1111yescharacteristic
304C22×C11C2×C4×D411yescharacteristic
305C22×C11#51811yescharacteristic
306C22×C11#51812yes—
307C22×C11#52011yescharacteristic
308C22×C11#52012yes—
309C22×C11#53411yescharacteristic
310C22×C11#53512yes—
311C22×C11#53711yescharacteristic
312C22×C11#53712yes—
313C22×C11#53811yescharacteristic
314C22×C11#53911yescharacteristic
315C22×C11#54012yes—
316C22×C11#54212yes—
317C22×C11#56012yes—
318C22×C11#56012yes—
319C22×C11#56011yescharacteristic
320C22×C11H(3,𝔽4)11yescharacteristic
321C22×C11H(3,𝔽4)11yescharacteristic
322C22×C11#56212yes—
323C22×C11#56212yes—
324C22×C11#56212yes—
325C22×C11#56311yescharacteristic
326C22×C11#56312yes—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—82no—
335C2×D11—82no—
336C2×D11—82no—
337C2×D11—82no—
338C2×D11—82no—
339C2×D11—82no—
340C2×D11—82no—
341C2×D11—82no—
342C4×C11—24no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—82no—
346C4×C11—82no—
347Dic11—44no—
348Dic11—44no—
349Dic11—82no—
350C25—112no—
351C22×D4—114no—
352C22×D4—442no—
353C22×D4—441no—
354C22×D4—441no—
355C22×D4—442no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4C22×D1112yes—
360C23×C4C22×D1112yes—
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—41no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—442no—
371C2×C4⋊C4—442no—
372C2×C4⋊C4—441no—
373C2×C4⋊C4—441no—
374C2×C4⋊C4C4×D1114yes—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—224no—
381C2×C22⋊C4—442no—
382C2×C22⋊C4—442no—
383C2×C22⋊C4—442no—
384C2×C22⋊C4—442no—
385C2×C22⋊C4—442no—
386C2×C22⋊C4—442no—
387C2×C22⋊C4—442no—
388C2×C22⋊C4—442no—
389C2×C22⋊C4—442no—
390C2×C22⋊C4—442no—
391C2×C22⋊C4—442no—
392C2×C22⋊C4—442no—
393C2×C42—114no—
394C2×C42—441no—
395C2×C42—441no—
396#95—24no—
397#95—41no—
398#95—42no—
399#95—114no—
400#95—224no—
401#95—442no—
402#95—442no—
403#95—442no—
404#95—442no—
405C2×C11#232412yes—
406C2×C11#232511yescharacteristic
407C2×C11#237511yescharacteristic
408C2×C11#237612yes—
409C2×C11#237911yescharacteristic
410C2×C11#281312yes—
411C2×C11#281911yescharacteristic
412C2×C11#282311yescharacteristic
413C2×C11#282811yescharacteristic
414C2×C11#283211yescharacteristic
415C2×C11#283712yes—
416D11—84no—
417C24—114no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24—222no—
422C24—222no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24—222no—
430C24—222no—
431C24—222no—
432C24C23×D1111yescharacteristic
433C2×D4—444no—
434C2×D4—448no—
435C2×D4—444no—
436C2×D4—448no—
437C2×D4—444no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4C2×C4×D1112yes—
486C22×C4C2×C4×D1112yes—
487C22×C4C2×C4×D1112yes—
488C22×C4D4×D1112yes—
489C22×C4#434312yes—
490C4⋊C4—44no—
491C4⋊C4—44no—
492C4⋊C4—444no—
493C4⋊C4—448no—
494C22⋊C4—2216no—
495C22⋊C4—448no—
496C22⋊C4—448no—
497C22⋊C4—448no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C42—444no—
501C11#1463211yescharacteristic, complemented, Sylow
502C23—224no—
503C23—224no—
504C23—224no—
505C23—224no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23—442no—
530C23—442no—
531C23—442no—
532C23—442no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23—442no—
537C23C22×C4×D1111yescharacteristic
538C23C2×D4×D1111yescharacteristic
539C23#6703712yes—
540C23#6703711yescharacteristic
541C23#6703711yescharacteristic
542C23C2×#434311yescharacteristic
543C23#6704012yes—
544C23#6704211yescharacteristic
545C23#6704212yes—
546C23#6704212yes—
547C23#6704311yescharacteristic
548D4—4416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4#6694614yes—
601C22—444no—
602C22—444no—
603C22—444no—
604C22—444no—
605C22—444no—
606C22—444no—
607C22—444no—
608C22—882no—
609C22—882no—
610C22—882no—
611C22—882no—
612C22—882no—
613C22—882no—
614C22—882no—
615C22—882no—
616C22#1062301711yescharacteristic
617C22C2×#6694611yescharacteristic
618C22#1062305411yescharacteristic
619C22#1062307612yes—
620C22#1062310512yes—
621C22#1062312511yescharacteristic
622C22#1062312811yescharacteristic
623C22#1062313611yescharacteristic
624C22#1062313812yes—
625C22#1062315112yes—
626C22#1062316012yes—
627C22#1062317511yescharacteristic
628C22#1062317611yescharacteristic
629C22#1062317812yes—
630C22#1062317812yes—
631C22#1062319711yescharacteristic
632C22#1062319812yes—
633C22#1062321411yescharacteristic
634C22#1062322912yes—
635C22#1062323012yes—
636C22#1062324212yes—
637C22#1062326412yes—
638C22#1062326611yescharacteristic
639C4—24no—
640C4—42no—
641C4—42no—
642C4—82no—
643C4—82no—
644C4—444no—
645C4—444no—
646C4—882no—
647C2—884no—
648C2#1307130712yes—
649C2#1307131611yescharacteristic
650C2#1307175411yescharacteristic
651C2#1307176312yes—
652C2#1307178811yescharacteristic
653C2#1307662512yes—
654C2#1307666011yescharacteristic
655C2#1307669111yescharacteristic
656C2#1307674011yescharacteristic
657C2#1307678811yescharacteristic
658C2#1307683612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1441D11
hypocenterC11#14632
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#10622282C2semidirect
3. #13066874C2semidirect
4. #13066862C2semidirect
5. #13066860C2semidirect
6. #13066858C2semidirect
8. #13066845C2semidirect
9. C11×#1441C2semidirect
31. #10622604C4semidirect
78. C2×C4×Dic11D4semidirect
176. #1441D11semidirect
501. C11#14632semidirect

Maximal subgroups

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

subgroupindex
C2×#106226042
C2×#106222822
#130668742
#130668622
#130668602
#130668582
#130668562
#130668452
C11×#14412
#1463211