Finite Group Databasebeta

← #14675138

Subgroups — #14675138

Order 2816.

2194 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3C2×#10622279C212yesmaximal, complemented
4#13066852C212yesmaximal, complemented
5#13066852C212yesmaximal, complemented
6#13066850C212yesmaximal, complemented
7(C2×D11)⋊#95C212yesmaximal, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C11×#1434C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C42×C11C2211yescharacteristic
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622552C418yescomplemented
32#10622279—28no—
33#10622278C4116yescomplemented
34C24×D11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C22×D44—42no—
44C22×D44—41no—
45C22×D44—41no—
46C22×D44C2×C418yes—
47C22×D44C2×C414yes—
48C22×C4×D11—24no—
49C22×C4×D11—24no—
50C22×C4×D11—42no—
51C22×C4×D11—42no—
52C22×C4×D11—42no—
53C22×C4×D11—42no—
54C22×C4×D11C2×C418yescomplemented
55C2×C42×C11—41no—
56C2×C42×C11—41no—
57C2×C42×C11C2×C414yescomplemented
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
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×(C2×D11)⋊C4C2×C418yescomplemented
71C2×(C2×D11)⋊C4C2×C418yescomplemented
72C2×(C2×D11)⋊C4C2×C418yescomplemented
73C2×C4⋊Dic11—42no—
74C2×C4⋊Dic11C2×C414yescomplemented
75C2×C4×Dic11—22no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—41no—
78C2×C4×Dic11—41no—
79C2×C4×Dic11—41no—
80C2×C4×Dic11—41no—
81C2×C4×Dic11—42no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11D414yescomplemented
84C11×#95—24no—
85C11×#95—41no—
86C11×#95—41no—
87C11×#95C2×C418yescomplemented
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C11⋊#95C2×C418yescomplemented
93#13791—111nomaximal, Sylow
94C24×C11C2411yescharacteristic
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×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11C22×C414yes—
108C23×D11C22×C414yes—
109C23×D11C22×C414yes—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
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—21no—
126C22×C4×C11—21no—
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×C11C22×C414yes—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C414yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4112yes—
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×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11C22×C414yes—
158C22×Dic11C22×C414yes—
159C22×Dic11C22×C414yes—
160C22×Dic11C2×D414yes—
161C22×Dic11#4114yes—
162C2×D44—44no—
163C2×D44—44no—
164C2×D44—48no—
165C2×D44—48no—
166C2×D44C42116yescomplemented
167C2×C4×D11—216no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11—48no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C2×C4×D11—48no—
174C42×C11—44no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180C4⋊Dic11—44no—
181C4×Dic11—44no—
182C4×Dic11—44no—
183C4×Dic11—48no—
184C2×#390—111no—
185C2×#386—112no—
186C2×C4×C22⋊C4—112no—
187#1437—112no—
188#1437—112no—
189#1436—112no—
190#1434D1111yescharacteristic, complemented
191C22⋊#95—112no—
192C4×#95—111no—
193C23×C11C23×C411yescharacteristic
194C23×C11C23×C412yes—
195C23×C11C22×D411yescharacteristic
196C23×C11C2×#4111yescharacteristic
197C23×C11C2×#4112yes—
198C23×C11H(5,𝔽2)11yescharacteristic
199C23×C11H(5,𝔽2)11yescharacteristic
200C23×C11H(5,𝔽2)12yes—
201C23×C11H(5,𝔽2)11yescharacteristic
202C23×C11H(5,𝔽2)12yes—
203C23×C112−1+411yescharacteristic
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
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×D11C2×C4218yes—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11C2×C4214yes—
269C2×C4×C11C4×D414yes—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11C4×D418yes—
291D44—416no—
292C4×D11—432no—
293C23×D4—111no—
294C24×C4—112no—
295C22×C4⋊C4—111no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C42—111no—
302C22×C42—111no—
303C22×C42—112no—
304C22×C42C2×D1111yescharacteristic
305#390—118no—
306#386—1116no—
307C4×C22⋊C4—228no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95C2×D1112yes—
314C2×#95C2×D1111yescharacteristic
315C2×#95C2×D1111yescharacteristic
316C2×#95C2×D1112yes—
317C22×C11C22×C4211yescharacteristic
318C22×C11C2×C4×D411yescharacteristic
319C22×C11C2×C4×D412yes—
320C22×C11C4×#4111yescharacteristic
321C22×C11C4×#4112yes—
322C22×C11#51811yescharacteristic
323C22×C11#51812yes—
324C22×C11#51811yescharacteristic
325C22×C11#51811yescharacteristic
326C22×C11#51812yes—
327C22×C11#51812yes—
328C22×C11#52012yes—
329C22×C11#52011yescharacteristic
330C22×C11#53411yescharacteristic
331C22×C11#53512yes—
332C22×C11#53711yescharacteristic
333C22×C11#53812yes—
334C22×C11#53811yescharacteristic
335C22×C11#53812yes—
336C22×C11#53911yescharacteristic
337C22×C11#54012yes—
338C22×C11#54012yes—
339C22×C11#54212yes—
340C2×D11—28no—
341C2×D11—28no—
342C2×D11—28no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—44no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C4×C11—24no—
356C4×C11—24no—
357C4×C11—44no—
358C4×C11—44no—
359C4×C11—42no—
360Dic11—28no—
361Dic11—44no—
362Dic11—44no—
363C25—112no—
364C22×D4—118no—
365C22×D4—114no—
366C22×D4—441no—
367C22×D4—441no—
368C22×D4—442no—
369C23×C4—112no—
370C23×C4—112no—
371C23×C4—112no—
372C23×C4—118no—
373C23×C4—224no—
374C23×C4—224no—
375C23×C4—442no—
376C23×C4—442no—
377C23×C4—442no—
378C23×C4—442no—
379C23×C4C22×D1111yescharacteristic
380C23×C4C22×D1112yes—
381C23×C4C22×D1112yes—
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C2×C4⋊C4—114no—
385C2×C4⋊C4—442no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—118no—
388C2×C22⋊C4—118no—
389C2×C22⋊C4—118no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—442no—
396C2×C22⋊C4—442no—
397C2×C22⋊C4—442no—
398C2×C22⋊C4—442no—
399C2×C22⋊C4—442no—
400C2×C22⋊C4—442no—
401C2×C42—41no—
402C2×C42—41no—
403C2×C42—114no—
404C2×C42—224no—
405C2×C42—222no—
406C2×C42—441no—
407C2×C42—441no—
408C2×C42—441no—
409C2×C42—441no—
410C2×C42—442no—
411C2×C42—442no—
412C2×C42C4×D1114yescomplemented
413#95—24no—
414#95—41no—
415#95—41no—
416#95—118no—
417#95—224no—
418#95—224no—
419#95—442no—
420#95—442no—
421#95C4×D1118yescomplemented
422C2×C11C42×D411yescharacteristic
423C2×C11#227311yescharacteristic
424C2×C11#227511yescharacteristic
425C2×C11#232112yes—
426C2×C11#232412yes—
427C2×C11#232511yescharacteristic
428C2×C11#232811yescharacteristic
429C2×C11#233311yescharacteristic
430C2×C11#233312yes—
431C2×C11#233512yes—
432C2×C11#233711yescharacteristic
433D11—48no—
434C24—114no—
435C24—114no—
436C24—114no—
437C24—222no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24—222no—
442C24—222no—
443C24—222no—
444C24—222no—
445C24—222no—
446C24—222no—
447C24—222no—
448C24—222no—
449C24C23×D1111yescharacteristic
450C2×D4—1116no—
451C2×D4—444no—
452C2×D4—444no—
453C2×D4—448no—
454C2×D4—448no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—114no—
479C22×C4—114no—
480C22×C4—114no—
481C22×C4—114no—
482C22×C4—114no—
483C22×C4—2216no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—448no—
501C22×C4—448no—
502C22×C4—448no—
503C22×C4—448no—
504C22×C4—448no—
505C22×C4—448no—
506C22×C4C2×C4×D1114yes—
507C22×C4C2×C4×D1114yes—
508C22×C4C2×C4×D1112yes—
509C22×C4C2×C4×D1114yes—
510C22×C4C2×C4×D1112yes—
511C22×C4C2×C4×D1112yes—
512C22×C4D4×D1112yes—
513C22×C4#434312yes—
514C4⋊C4—444no—
515C22⋊C4—2216no—
516C22⋊C4—2216no—
517C22⋊C4—448no—
518C22⋊C4—448no—
519C22⋊C4—448no—
520C42—44no—
521C42—444no—
522C42—444no—
523C42—448no—
524C11#1379111yescharacteristic, complemented, Sylow
525C23—118no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—224no—
530C23—224no—
531C23—224no—
532C23—224no—
533C23—224no—
534C23—224no—
535C23—224no—
536C23—224no—
537C23—224no—
538C23—224no—
539C23—224no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—224no—
544C23—442no—
545C23—442no—
546C23—442no—
547C23—442no—
548C23—442no—
549C23—442no—
550C23—442no—
551C23—442no—
552C23—442no—
553C23—442no—
554C23—442no—
555C23—442no—
556C23—442no—
557C23—442no—
558C23—442no—
559C23—442no—
560C23C22×C4×D1111yescharacteristic
561C23C22×C4×D1112yes—
562C23C2×D4×D1111yescharacteristic
563C23#6703711yescharacteristic
564C23#6703711yescharacteristic
565C23C2×#434311yescharacteristic
566C23#41×D1112yes—
567C23#6704211yescharacteristic
568C23#6704212yes—
569C23#6704212yes—
570C23#6704311yescharacteristic
571D4—4416no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—118no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—224no—
614C2×C4—4432no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4C42×D1114yes—
624C2×C4#6694614yes—
625C22—228no—
626C22—228no—
627C22—228no—
628C22—444no—
629C22—444no—
630C22—444no—
631C22—444no—
632C22—444no—
633C22—444no—
634C22—444no—
635C22—444no—
636C22—444no—
637C22—444no—
638C22—444no—
639C22—444no—
640C22C2×C42×D1111yescharacteristic
641C22#1062301711yescharacteristic
642C22C2×#6694611yescharacteristic
643C22#1062305211yescharacteristic
644C22#1062305212yes—
645C22#1062305211yescharacteristic
646C22#1062305311yescharacteristic
647C22#1062305412yes—
648C22#1062305411yescharacteristic
649C22C4×D4×D1112yes—
650C22#1062307612yes—
651C22#1062307612yes—
652C22C4×#434312yes—
653C22#1062312811yescharacteristic
654C22#1062313611yescharacteristic
655C22#1062317511yescharacteristic
656C22#1062317611yescharacteristic
657C22#1062318812yes—
658C22#1062319412yes—
659C22#1062320512yes—
660C22#1062322912yes—
661C22#1062323512yes—
662C22#1062324112yes—
663C4—24no—
664C4—24no—
665C4—42no—
666C4—44no—
667C4—44no—
668C4—228no—
669C4—444no—
670C4—444no—
671C2—448no—
672C2C4×#6694611yescharacteristic
673C2#1307096811yescharacteristic
674C2#1307097811yescharacteristic
675C2#1307126912yes—
676C2#1307130412yes—
677C2#1307131611yescharacteristic
678C2#1307133911yescharacteristic
679C2#1307137811yescharacteristic
680C2#1307138012yes—
681C2#1307140512yes—
682C2#1307142611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#13791
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#10622279C2semidirect
4. #13066852C2semidirect
5. #13066852C2semidirect
6. #13066850C2semidirect
7. (C2×D11)⋊#95C2semidirect
8. C4×C11⋊#95C2semidirect
9. C11×#1434C2semidirect
31. #10622552C4semidirect
33. #10622278C4semidirect
54. C22×C4×D11C2×C4semidirect
57. C2×C42×C11C2×C4semidirect
70. C2×(C2×D11)⋊C4C2×C4semidirect
71. C2×(C2×D11)⋊C4C2×C4semidirect
72. C2×(C2×D11)⋊C4C2×C4semidirect
74. C2×C4⋊Dic11C2×C4semidirect
83. C2×C4×Dic11D4semidirect
87. C11×#95C2×C4semidirect
92. C11⋊#95C2×C4semidirect
166. C2×D44C42semidirect
190. #1434D11semidirect
412. C2×C42C4×D11semidirect
421. #95C4×D11semidirect
524. C11#13791semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106222782
C2×#106222792
#130668522
#130668502
(C2×D11)⋊#952
C4×C11⋊#952
C11×#14342
#1379111