Finite Group Databasebeta

← #14676396

Subgroups — #14676396

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C212yesmaximal
2#13066873C212yesmaximal, complemented
3#13066861C212yesmaximal
4#13066850C212yesmaximal, complemented
5#13066846C211yesmaximal, characteristic, complemented
6#13066846C211yesmaximal, characteristic, complemented
7#13066843C211yesmaximal, characteristic, complemented
8#13066839C211yesmaximal, characteristic
9#13066839C211yesmaximal, characteristic
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4⋊Dic11C2212yes—
20C22×C4⋊Dic11C2212yes—
21C22×C4×Dic11C2212yes—
22C4×C11×C22⋊C4C418yescomplemented
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36#10622564—28no—
37C25×C11C2311yescharacteristic
38C23×C4×C11—22no—
39C23×C4×C11—22no—
40C23×C4×C11—42no—
41C23×C4×C11—42no—
42C23×C4×C11C2×C414yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4C2×C414yes—
56C2×C11×C22⋊C4C2×C414yes—
57C2×C11×C22⋊C4D414yes—
58C2×C11×C22⋊C4Q814yes—
59C2×C42×C11—42no—
60C2×C42×C11—42no—
61C2×C42×C11C2×C414yes—
62C2×C42×C11C2×C414yes—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—42no—
68C2×C22⋊Dic11—42no—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11—24no—
71C2×C4⋊Dic11—24no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11—42no—
74C2×C4⋊Dic11—42no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—42no—
78C11×#95C2×C414yes—
79C11×#95C2×C414yes—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—24no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—24no—
88C11⋊#95—42no—
89C11⋊#95—42no—
90C11⋊#95—42no—
91#13948—111nomaximal, Sylow
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—21no—
97C24×C11—21no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11C22×C412yes—
101C24×C11C2×D412yes—
102C24×C11C2×Q812yes—
103C24×C11C2411yescharacteristic
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
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—21no—
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—28no—
121C22×C4×C11—44no—
122C22×C4×C11—44no—
123C22×C4×C11—48no—
124C22×C4×C11—48no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×Q812yes—
134C22×C4×C11C2×Q812yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
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×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11#4114yes—
166C22×Dic11#4114yes—
167C11×C22⋊C4—28no—
168C11×C22⋊C4C4⋊C4116yescomplemented
169C42×C11—44no—
170C42×C11—44no—
171C22⋊Dic11—48no—
172C22⋊Dic11—48no—
173C4⋊Dic11—48no—
174C4⋊Dic11—48no—
175C4×Dic11—48no—
176C2×#388—112no—
177C2×C4×C22⋊C4D1111yescharacteristic
178#1442—112no—
179#1439—112no—
180#1436—112no—
181C4⋊#95—111no—
182C4⋊#95—111no—
183#1434—111no—
184C22⋊#95—111no—
185C22⋊#95—111no—
186C4×#95—111no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11C2×C4⋊C414yes—
210C23×C11C23×C411yescharacteristic
211C23×C11C22×D411yescharacteristic
212C23×C11C22×Q811yescharacteristic
213C23×C11C2×#4111yescharacteristic
214C23×C11C2×#4111yescharacteristic
215C23×C11C2×#4111yescharacteristic
216C23×C11C2×#4111yescharacteristic
217C23×C11C2×#4112yes—
218C23×C11C2×#4112yes—
219C23×C11H(5,𝔽2)12yes—
220C23×C11H(5,𝔽2)12yes—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—416no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11C2×C4⋊C414yes—
249C2×C4×C11C2×C4⋊C414yes—
250C2×C4×C11#11714yes—
251C2×C4×C11#11714yes—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
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—
280C24×C4C2×D1111yescharacteristic
281C22×C4⋊C4—112no—
282C22×C4⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C22⋊C4—112no—
285C22×C22⋊C4C2×D1111yescharacteristic
286C22×C22⋊C4C2×D1111yescharacteristic
287C22×C42—112no—
288C22×C42C2×D1111yescharacteristic
289C22×C42C2×D1111yescharacteristic
290#388—228no—
291C4×C22⋊C4Dic1118yescomplemented
292C2×#95—111no—
293C2×#95—111no—
294C2×#95—112no—
295C2×#95—111no—
296C2×#95—111no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95C2×D1111yescharacteristic
304C2×#95C2×D1111yescharacteristic
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11C22×C4⋊C411yescharacteristic
317C22×C11C2×#11711yescharacteristic
318C22×C11C2×#11711yescharacteristic
319C22×C11C4×#4111yescharacteristic
320C22×C11C4×#4111yescharacteristic
321C22×C11#51811yescharacteristic
322C22×C11#51811yescharacteristic
323C22×C11#52912yes—
324C22×C11#52912yes—
325C22×C11#53211yescharacteristic
326C22×C11#53211yescharacteristic
327C22×C11#53311yescharacteristic
328C22×C11#53311yescharacteristic
329C22×C11#53812yes—
330C22×C11#53812yes—
331C22×C11#54612yes—
332C22×C11#54612yes—
333C22×C11#55112yes—
334C22×C11#55312yes—
335C22×C11#55312yes—
336C22×C11#55412yes—
337C22×C11#55412yes—
338C22×C11#55912yes—
339C4×C11—24no—
340C4×C11—24no—
341C4×C11—24no—
342C4×C11—24no—
343C4×C11—42no—
344C4×C11—42no—
345Dic11—44no—
346Dic11—44no—
347Dic11—82no—
348Dic11—82no—
349C25C22×D1111yescharacteristic
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—42no—
353C23×C4—42no—
354C23×C4—112no—
355C23×C4—112no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4C2×Dic1114yes—
359C23×C4C22×D1111yescharacteristic
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C23×C4C22×D1111yescharacteristic
365C2×C4⋊C4—224no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—442no—
370C2×C4⋊C4—442no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—442no—
378C2×C22⋊C4—442no—
379C2×C22⋊C4Dic2214yes—
380C2×C22⋊C4D4414yes—
381C2×C22⋊C4C2×Dic1114yes—
382C2×C22⋊C4C2×Dic1114yes—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—224no—
386C2×C42—224no—
387C2×C42—442no—
388C2×C42C2×Dic1114yes—
389C2×C42C2×Dic1114yes—
390#95—224no—
391#95—224no—
392#95—224no—
393#95—222no—
394#95—222no—
395#95—224no—
396#95—222no—
397#95—222no—
398#95—442no—
399#95—442no—
400#95—442no—
401#95C2×Dic1114yes—
402#95C2×Dic1114yes—
403C2×C11—44no—
404C2×C11#228511yescharacteristic
405C2×C11#229811yescharacteristic
406C2×C11#231211yescharacteristic
407C2×C11#234911yescharacteristic
408C2×C11#234911yescharacteristic
409C2×C11#235311yescharacteristic
410C2×C11#235711yescharacteristic
411C2×C11#255712yes—
412C2×C11#255912yes—
413C2×C11#258712yes—
414C2×C11#258912yes—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24C2×Dic2212yes—
424C24C2×D4412yes—
425C24C22×Dic1112yes—
426C24C23×D1111yescharacteristic
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—28no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—48no—
447C22×C4—48no—
448C22×C4—114no—
449C22×C4—114no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
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×C4C2×Dic2212yes—
477C22×C4C2×Dic2212yes—
478C22×C4C2×D4412yes—
479C22×C4C2×D4412yes—
480C22×C4#433912yes—
481C22×C4#433912yes—
482C22×C4#433912yes—
483C22×C4#433912yes—
484C22×C4C22×Dic1112yes—
485C22×C4C22×Dic1112yes—
486C22×C4C22×Dic1112yes—
487C22×C4C22×Dic1112yes—
488C22×C4C22×Dic1112yes—
489C22×C4C22×Dic1112yes—
490C4⋊C4—448no—
491C4⋊C4—448no—
492C22⋊C4—28no—
493C22⋊C4—448no—
494C22⋊C4—448no—
495C22⋊C4C4⋊Dic11116yescomplemented
496C42—44no—
497C42—44no—
498C42—448no—
499C11#1394811yescharacteristic, complemented, Sylow
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—22no—
513C23—22no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23C2×C4⋊Dic1114yes—
523C23C22×Dic2211yescharacteristic
524C23C22×D4411yescharacteristic
525C23C2×#433911yescharacteristic
526C23C2×#433911yescharacteristic
527C23C2×#433911yescharacteristic
528C23C2×#433911yescharacteristic
529C23#6703712yes—
530C23#6703712yes—
531C23#41×D1112yes—
532C23#41×D1112yes—
533C23C23×Dic1111yescharacteristic
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—416no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4C2×C4⋊Dic1114yes—
590C2×C4C2×C4⋊Dic1114yes—
591C2×C4#6697914yes—
592C2×C4#6697914yes—
593C22—24no—
594C22—24no—
595C22—24no—
596C22—42no—
597C22—44no—
598C22—44no—
599C22—42no—
600C22—44no—
601C22—44no—
602C22—42no—
603C22—42no—
604C22#1062300111yescharacteristic
605C22#1062300111yescharacteristic
606C22#1062300811yescharacteristic
607C22#1062300811yescharacteristic
608C22#1062302512yes—
609C22#1062302512yes—
610C22#1062305912yes—
611C22#1062305912yes—
612C22#1062307012yes—
613C22#1062307012yes—
614C22#1062307112yes—
615C22#1062308512yes—
616C22#1062308512yes—
617C22#1062308712yes—
618C22#1062308912yes—
619C22#1062309012yes—
620C22C22×C4⋊Dic1111yescharacteristic
621C22C2×#6697911yescharacteristic
622C22C2×#6697911yescharacteristic
623C22#1062332911yescharacteristic
624C22#1062332911yescharacteristic
625C22#41×Dic1111yescharacteristic
626C22#41×Dic1111yescharacteristic
627C4—24no—
628C4—24no—
629C4—24no—
630C4—24no—
631C4—42no—
632C4—42no—
633C4—444no—
634C4—444no—
635C4—882no—
636C4—882no—
637C2—44no—
638C2#1307102311yescharacteristic
639C2#1307111411yescharacteristic
640C2#1307121411yescharacteristic
641C2#1307152611yescharacteristic
642C2#1307152611yescharacteristic
643C2#1307155611yescharacteristic
644C2#1307158911yescharacteristic
645C2#1307370912yes—
646C2#1307373912yes—
647C2#1307403112yes—
648C2#1307406112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13948
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13066873C2semidirect
4. #13066850C2semidirect
5. #13066846C2semidirect
6. #13066846C2semidirect
7. #13066843C2semidirect
10. C4×C11⋊#95C2semidirect
22. C4×C11×C22⋊C4C4semidirect
168. C11×C22⋊C4C4⋊C4semidirect
291. C4×C22⋊C4Dic11semidirect
495. C22⋊C4C4⋊Dic11semidirect
499. C11#13948semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
#130668732
#130668612
#130668502
#130668462
#130668432
#130668392
C4×C11⋊#952
C2×C4×C11×C22⋊C42
#1394811