Finite Group Databasebeta

← #14676153

Subgroups — #14676153

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622264C212yesmaximal
2C2×C4⋊C4×Dic11C211yesmaximal, characteristic
3#13066877C212yesmaximal
4#13066876C212yesmaximal
5#13066846C211yesmaximal, characteristic
6#13066845C211yesmaximal, characteristic
7#13066845C211yesmaximal, characteristic
8#13066845C211yesmaximal, characteristic
9#13066842C212yesmaximal
10C4×C11⋊#95C211yesmaximal, characteristic
11C11×C4⋊#95C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C22×C4×Dic11C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11⋊#95C2211yescharacteristic
23C2×C11⋊#95C2211yescharacteristic
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C4⋊C4×Dic11C418yescomplemented
36#10622264—28no—
37C23×C4×C11C2312yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11C2×C414yes—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11—24no—
66C2×C4×Dic11—24no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11C2×C418yes—
71C2×C4×Dic11C2×C414yes—
72C11×#95—24no—
73C11×#95—42no—
74C11⋊#95—24no—
75C11⋊#95—22no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—24no—
80C11⋊#95—22no—
81C11⋊#95—24no—
82C11⋊#95—22no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95C2×C418yes—
86C11⋊#95D414yes—
87#13921—111nomaximal, Sylow
88C24×C11C2411yescharacteristic
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11C22×C414yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11#4112yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C22×C4×C11#4112yes—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—22no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11C22×C412yes—
160C22×Dic11C22×C414yes—
161C22×Dic11C22×C412yes—
162C22×Dic11C2×D412yes—
163C22×Dic11C2×D412yes—
164C22×Dic11#4112yes—
165C22×Dic11#4112yes—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—44no—
168C42×C11—44no—
169C4⋊Dic11—28no—
170C4⋊Dic11—44no—
171C4×Dic11—216no—
172C4×Dic11—28no—
173C4×Dic11—44no—
174C2×#383—112no—
175C2×C4×C4⋊C4—111no—
176#1443—112no—
177#1443—112no—
178C4⋊#95—111no—
179C4⋊#95—111no—
180C4⋊#95—111no—
181C4⋊#95—111no—
182C4⋊#95D1111yescharacteristic
183#1434—112no—
184C4×#95—111no—
185C23×C11C23×C411yescharacteristic
186C23×C11C22×D411yescharacteristic
187C23×C11C2×#4111yescharacteristic
188C23×C11C2×#4111yescharacteristic
189C23×C11C2×#4111yescharacteristic
190C23×C11C2×#4111yescharacteristic
191C23×C11C2×#4111yescharacteristic
192C23×C11C2×#4111yescharacteristic
193C23×C11C2×#4111yescharacteristic
194C23×C11C2×#4111yescharacteristic
195C23×C11C2×#4111yescharacteristic
196C23×C11H(5,𝔽2)11yescharacteristic
197C23×C112−1+411yescharacteristic
198C23×C112−1+411yescharacteristic
199C23×C112−1+411yescharacteristic
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11#11714yes—
229C2×C4×C11#11714yes—
230C2×C4×C11#11714yes—
231C2×C4×C11#12614yes—
232C2×C4×C11#12614yes—
233C2×C4×C11#12614yes—
234C2×C4×C11#12614yes—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11C4×D414yes—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—111no—
279C22×C4⋊C4C2×D1111yescharacteristic
280C22×C4⋊C4C2×D1111yescharacteristic
281C22×C42—111no—
282C22×C42—112no—
283C22×C42—111no—
284C22×C42C2×D1111yescharacteristic
285#383—228no—
286C4×C4⋊C4—118no—
287C2×#95—111no—
288C2×#95—112no—
289C2×#95—111no—
290C2×#95—111no—
291C2×#95—111no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95C2×D1112yes—
301C2×#95C2×D1112yes—
302C22×C11C2×#11711yescharacteristic
303C22×C11C2×#11711yescharacteristic
304C22×C11C2×#11711yescharacteristic
305C22×C11C2×C4×D411yescharacteristic
306C22×C11C4×#4111yescharacteristic
307C22×C11#51911yescharacteristic
308C22×C11#52011yescharacteristic
309C22×C11C2×#12611yescharacteristic
310C22×C11C2×#12611yescharacteristic
311C22×C11C2×#12611yescharacteristic
312C22×C11C2×#12611yescharacteristic
313C22×C11#52911yescharacteristic
314C22×C11#52911yescharacteristic
315C22×C11#53211yescharacteristic
316C22×C11#53211yescharacteristic
317C22×C11#54111yescharacteristic
318C22×C11#54111yescharacteristic
319C22×C11#54211yescharacteristic
320C22×C11#54211yescharacteristic
321C22×C11#54711yescharacteristic
322C22×C11#54711yescharacteristic
323C22×C11#54711yescharacteristic
324C22×C11#55011yescharacteristic
325C22×C11#55211yescharacteristic
326C22×C11#55211yescharacteristic
327C22×C11#55211yescharacteristic
328C22×C11#55211yescharacteristic
329C22×C11#55311yescharacteristic
330C22×C11#55311yescharacteristic
331C22×C11#55511yescharacteristic
332C22×C11#55611yescharacteristic
333C22×C11#55611yescharacteristic
334C22×C11#55611yescharacteristic
335C22×C11#55611yescharacteristic
336C22×C11#55611yescharacteristic
337C4×C11—44no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—82no—
341C4×C11#38318yescomplemented
342Dic11—24no—
343Dic11—42no—
344Dic11—42no—
345Dic11—42no—
346Dic11—44no—
347Dic11—82no—
348C23×C4—111no—
349C23×C4—112no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—111no—
353C23×C4—112no—
354C23×C4C22×D1112yes—
355C23×C4C22×D1112yes—
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1111yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4C4×D1114yes—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—118no—
375C2×C42—114no—
376C2×C42—224no—
377C2×C42—224no—
378C2×C42—222no—
379C2×C42—222no—
380C2×C42—222no—
381C2×C42—222no—
382C2×C42—222no—
383#95—24no—
384#95—42no—
385#95—118no—
386#95—114no—
387#95—222no—
388#95—222no—
389#95—224no—
390#95—224no—
391#95—224no—
392#95—224no—
393#95—224no—
394#95—222no—
395#95—224no—
396#95—442no—
397#95—442no—
398C2×C11C2×#38311yescharacteristic
399C2×C11#229311yescharacteristic
400C2×C11#232011yescharacteristic
401C2×C11#234411yescharacteristic
402C2×C11#234711yescharacteristic
403C2×C11#235411yescharacteristic
404C2×C11#235611yescharacteristic
405C2×C11#249511yescharacteristic
406C2×C11#249511yescharacteristic
407C2×C11#249611yescharacteristic
408C2×C11#249611yescharacteristic
409C2×C11#251211yescharacteristic
410C2×C11#251211yescharacteristic
411C2×C11#251411yescharacteristic
412C2×C11#251411yescharacteristic
413C24C23×D1111yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—112no—
440C22×C4—112no—
441C22×C4—112no—
442C22×C4—112no—
443C22×C4—114no—
444C22×C4—112no—
445C22×C4—112no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—222no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—222no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—222no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—222no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—222no—
469C22×C4—221no—
470C22×C4—222no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4C2×C4×D1114yes—
482C22×C4C2×C4×D1112yes—
483C22×C4#433912yes—
484C22×C4#433912yes—
485C22×C4D4×D1112yes—
486C22×C4#434112yes—
487C22×C4#434112yes—
488C22×C4#434112yes—
489C22×C4#434312yes—
490C22×C4#434312yes—
491C4⋊C4—28no—
492C4⋊C4—44no—
493C4⋊C4—228no—
494C4⋊C4—444no—
495C42—44no—
496C42—2216no—
497C42—228no—
498C42—444no—
499C11#1392111yescharacteristic, complemented, Sylow
500C23C22×C4×D1111yescharacteristic
501C23C2×#433911yescharacteristic
502C23C2×#433911yescharacteristic
503C23C2×D4×D1111yescharacteristic
504C23C2×#434111yescharacteristic
505C23C2×#434111yescharacteristic
506C23C2×#434111yescharacteristic
507C23#6703711yescharacteristic
508C23C2×#434311yescharacteristic
509C23C2×#434311yescharacteristic
510C23#6704011yescharacteristic
511C23#41×D1111yescharacteristic
512C23#41×D1111yescharacteristic
513C23#6704311yescharacteristic
514C23#6704311yescharacteristic
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—114no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—224no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—442no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—442no—
573C2×C4—441no—
574C2×C4—442no—
575C2×C4—441no—
576C2×C4—442no—
577C2×C4—441no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4#6692514yes—
586C2×C4#6693014yes—
587C2×C4#6693214yes—
588C2×C4#6693214yes—
589C2×C4#6694514yes—
590C2×C4#6695114yes—
591C2×C4#6695114yes—
592C22C2×#6692511yescharacteristic
593C22C2×#6693011yescharacteristic
594C22C2×#6693211yescharacteristic
595C22C2×#6693211yescharacteristic
596C22C2×#6694511yescharacteristic
597C22#1062303811yescharacteristic
598C22C2×#6695111yescharacteristic
599C22C2×#6695111yescharacteristic
600C22#1062304511yescharacteristic
601C22#1062306011yescharacteristic
602C22#1062306411yescharacteristic
603C22C4×D4×D1111yescharacteristic
604C22#1062307711yescharacteristic
605C22#1062308211yescharacteristic
606C22#1062308911yescharacteristic
607C22#1062310311yescharacteristic
608C22C4×#434311yescharacteristic
609C22#1062311211yescharacteristic
610C22#1062311511yescharacteristic
611C22#1062312711yescharacteristic
612C22#1062313411yescharacteristic
613C22#1062314211yescharacteristic
614C22#1062314711yescharacteristic
615C22#1062315511yescharacteristic
616C22#1062315611yescharacteristic
617C22#1062317011yescharacteristic
618C22#1062317311yescharacteristic
619C22#1062320211yescharacteristic
620C22#1062320211yescharacteristic
621C22#1062322211yescharacteristic
622C22#1062322811yescharacteristic
623C22#1062324911yescharacteristic
624C22#1062325611yescharacteristic
625C22#1062326311yescharacteristic
626C22#1062326411yescharacteristic
627C4—42no—
628C4—42no—
629C4—44no—
630C4—82no—
631C4—224no—
632C4—442no—
633C4—442no—
634C4—442no—
635C4—444no—
636C4—882no—
637C4#1062226418yescomplemented
638C2C2×#1062226411yescharacteristic
639C2#1307107411yescharacteristic
640C2#1307126311yescharacteristic
641C2#1307148111yescharacteristic
642C2#1307150511yescharacteristic
643C2#1307156411yescharacteristic
644C2#1307158011yescharacteristic
645C2#1307302311yescharacteristic
646C2#1307302511yescharacteristic
647C2#1307303411yescharacteristic
648C2#1307303611yescharacteristic
649C2#1307319811yescharacteristic
650C2#1307320011yescharacteristic
651C2#1307322011yescharacteristic
652C2#1307322211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4⋊#95D11
hypocenterC11#13921
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
35. C4⋊C4×Dic11C4semidirect
341. C4×C11#383semidirect
499. C11#13921semidirect
637. C4#10622264semidirect

Maximal subgroups

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

subgroupindex
C2×#106222642
C2×C4⋊C4×Dic112
#130668772
#130668762
#130668462
#130668452
#130668422
C4×C11⋊#952
C11×C4⋊#952
#1392111