Finite Group Databasebeta

← #14675143

Subgroups — #14675143

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×C4×(C2×D11)⋊C4C212yesmaximal, complemented
4#13066854C212yesmaximal, complemented
5#13066852C212yesmaximal, complemented
6#13066850C212yesmaximal, complemented
7#13066843C211yesmaximal, characteristic, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9C4×C11×#95C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C42×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622552C418yescomplemented
32C4×(C2×D11)⋊C4—28no—
33#10622278C4116yescomplemented
34C24×D11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2312yes—
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—22no—
56C2×C42×C11—41no—
57C2×C42×C11—41no—
58C2×C42×C11—41no—
59C2×C42×C11—41no—
60C2×C42×C11—41no—
61C2×C42×C11—41no—
62C2×C42×C11C2×C414yescomplemented
63C2×C42×C11D414yescomplemented
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4—42no—
73C2×(C2×D11)⋊C4—42no—
74C2×(C2×D11)⋊C4C2×C418yes—
75C2×(C2×D11)⋊C4C2×C418yes—
76C2×(C2×D11)⋊C4C2×C418yescomplemented
77C2×(C2×D11)⋊C4C2×C418yescomplemented
78C2×(C2×D11)⋊C4C2×C418yescomplemented
79C2×C4⋊Dic11—42no—
80C2×C4⋊Dic11C2×C414yescomplemented
81C2×C4×Dic11—24no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11—42no—
84C11×#95—24no—
85C11×#95C2×C418yescomplemented
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—42no—
89C11⋊#95—42no—
90C11⋊#95—41no—
91C11⋊#95—41no—
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—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11C22×C414yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D414yes—
139C22×C4×C11#4114yes—
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×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11C22×C414yes—
160C22×Dic11C22×C414yes—
161C22×Dic11C22×C414yes—
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—
175C42×C11—44no—
176C42×C11—44no—
177(C2×D11)⋊C4—216no—
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—48no—
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#1434—111no—
191C22⋊#95—112no—
192C4×#95D1111yescharacteristic, complemented
193C23×C11C23×C411yescharacteristic
194C23×C11C23×C412yes—
195C23×C11C22×D411yescharacteristic
196C23×C11C2×#4112yes—
197C23×C11C2×#4111yescharacteristic
198C23×C11H(5,𝔽2)11yescharacteristic
199C23×C11H(5,𝔽2)11yescharacteristic
200C23×C11H(5,𝔽2)11yescharacteristic
201C23×C11H(5,𝔽2)12yes—
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—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
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×C11C2×C4214yes—
268C2×C4×C11C4×D414yes—
269C2×C4×C11C4×D418yes—
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—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
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×Dic11—42no—
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—112no—
302C22×C42C2×D1111yescharacteristic
303C22×C42C2×D1111yescharacteristic
304C22×C42C2×D1111yescharacteristic
305#390—118no—
306#386—1116no—
307C4×C22⋊C4—228no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—111no—
312C2×#95—112no—
313C2×#95—111no—
314C2×#95—112no—
315C2×#95C2×D1112yes—
316C2×#95C2×D1112yes—
317C22×C11C22×C4211yescharacteristic
318C22×C11C2×C4×D412yes—
319C22×C11C2×C4×D411yescharacteristic
320C22×C11C4×#4112yes—
321C22×C11C4×#4111yescharacteristic
322C22×C11#51811yescharacteristic
323C22×C11#51811yescharacteristic
324C22×C11#51811yescharacteristic
325C22×C11#51812yes—
326C22×C11#51812yes—
327C22×C11#51812yes—
328C22×C11#52011yescharacteristic
329C22×C11#52012yes—
330C22×C11#53411yescharacteristic
331C22×C11#53512yes—
332C22×C11#53711yescharacteristic
333C22×C11#53811yescharacteristic
334C22×C11#53812yes—
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—28no—
356C4×C11—24no—
357C4×C11—24no—
358C4×C11—44no—
359C4×C11—42no—
360Dic11—44no—
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×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1112yes—
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—22no—
402C2×C42—41no—
403C2×C42—41no—
404C2×C42—41no—
405C2×C42—41no—
406C2×C42—41no—
407C2×C42—41no—
408C2×C42—224no—
409C2×C42—442no—
410C2×C42—442no—
411C2×C42C4×D1114yescomplemented
412C2×C42D4414yescomplemented
413#95—24no—
414#95—118no—
415#95—224no—
416#95—224no—
417#95—441no—
418#95—441no—
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#233312yes—
430C2×C11#233311yescharacteristic
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—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—114no—
477C22×C4—114no—
478C22×C4—114no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
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—2216no—
498C22×C4—448no—
499C22×C4—448no—
500C22×C4—448no—
501C22×C4—448no—
502C22×C4—448no—
503C22×C4—448no—
504C22×C4C2×C4×D1114yes—
505C22×C4C2×C4×D1112yes—
506C22×C4C2×C4×D1114yes—
507C22×C4C2×C4×D1112yes—
508C22×C4C2×C4×D1114yes—
509C22×C4C2×C4×D1112yes—
510C22×C4C2×D4412yes—
511C22×C4C2×D4414yes—
512C22×C4#433914yes—
513C22×C4#433912yes—
514C4⋊C4—444no—
515C22⋊C4—2216no—
516C22⋊C4—2216no—
517C22⋊C4—448no—
518C22⋊C4—448no—
519C22⋊C4—448no—
520C42—44no—
521C42—44no—
522C42—44no—
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—
562C23C22×D4411yescharacteristic
563C23C2×#433911yescharacteristic
564C23C2×#433912yes—
565C23#6703711yescharacteristic
566C23#6703711yescharacteristic
567C23#6703711yescharacteristic
568C23#6704011yescharacteristic
569C23#6704212yes—
570C23#6704212yes—
571D4—4416no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—4432no—
610C2×C4—442no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4C42×D1114yes—
623C2×C4C4×D4414yes—
624C2×C4C4×D4418yes—
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
641C22C2×C4×D4412yes—
642C22C2×C4×D4411yescharacteristic
643C22C4×#433912yes—
644C22C4×#433911yescharacteristic
645C22#1062301711yescharacteristic
646C22#1062302411yescharacteristic
647C22#1062302511yescharacteristic
648C22#1062303511yescharacteristic
649C22#1062304111yescharacteristic
650C22#1062304611yescharacteristic
651C22#1062305211yescharacteristic
652C22#1062305211yescharacteristic
653C22#1062305612yes—
654C22#1062306612yes—
655C22#1062307612yes—
656C22#1062307612yes—
657C22#1062307612yes—
658C22#1062309112yes—
659C22#1062309112yes—
660C22#1062309312yes—
661C22#1062310512yes—
662C22#1062311312yes—
663C4—24no—
664C4—28no—
665C4—24no—
666C4—44no—
667C4—42no—
668C4—444no—
669C4—444no—
670C4—444no—
671C2—448no—
672C2C42×D4411yescharacteristic
673C2#1307096811yescharacteristic
674C2#1307097611yescharacteristic
675C2#1307127612yes—
676C2#1307131012yes—
677C2#1307131911yescharacteristic
678C2#1307134111yescharacteristic
679C2#1307137612yes—
680C2#1307138111yescharacteristic
681C2#1307140012yes—
682C2#1307142911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC4×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4×#95D11
hypocenterC11#13791
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D11)⋊C4C2semidirect
4. #13066854C2semidirect
5. #13066852C2semidirect
6. #13066850C2semidirect
7. #13066843C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C4×C11×#95C2semidirect
31. #10622552C4semidirect
33. #10622278C4semidirect
54. C22×C4×D11C2×C4semidirect
62. C2×C42×C11C2×C4semidirect
63. C2×C42×C11D4semidirect
76. C2×(C2×D11)⋊C4C2×C4semidirect
77. C2×(C2×D11)⋊C4C2×C4semidirect
78. C2×(C2×D11)⋊C4C2×C4semidirect
80. C2×C4⋊Dic11C2×C4semidirect
85. C11×#95C2×C4semidirect
92. C11⋊#95C2×C4semidirect
166. C2×D44C42semidirect
192. C4×#95D11semidirect
411. C2×C42C4×D11semidirect
412. C2×C42D44semidirect
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×C4×(C2×D11)⋊C42
#130668542
#130668522
#130668502
#130668432
(C2×D11)⋊#952
C4×C11×#952
#1379111