Finite Group Databasebeta

← #14679193

Subgroups — #14679193

Order 2816.

2062 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622604C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3C2×C4×(C2×D11)⋊C4C212yesmaximal, complemented
4#13066884C211yesmaximal, characteristic, complemented
5#13066864C212yesmaximal, complemented
6#13066852C212yesmaximal, complemented
7#13066842C212yesmaximal, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9C11×#1436C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4×Dic11C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31#10622604C418yescomplemented
32C4×(C2×D11)⋊C4—28no—
33#10622278—28no—
34C24×D11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C22×D44—24no—
44C22×D44—24no—
45C22×D44—41no—
46C22×D44—41no—
47C22×D44C2×C414yes—
48C22×C4×D11—24no—
49C22×C4×D11—24no—
50C22×C4×D11—24no—
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—42no—
54C22×C4×D11—42no—
55C2×C11×C4⋊C4—41no—
56C2×C11×C4⋊C4—41no—
57C2×C11×C4⋊C4C2×C414yescomplemented
58C2×C42×C11—24no—
59C2×C42×C11—41no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
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)⋊C4C2×C418yescomplemented
73C2×(C2×D11)⋊C4C2×C418yescomplemented
74C2×(C2×D11)⋊C4D418yes—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—42no—
78C11×#95—24no—
79C11×#95—24no—
80C11×#95—41no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—42no—
86C11⋊#95—41no—
87C11⋊#95—41no—
88C11⋊#95C2×C414yescomplemented
89#14181—111nomaximal, Sylow
90C24×C11C2411yescharacteristic
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×D11C22×C414yes—
104C23×D11C2×D414yes—
105C23×D11#4114yes—
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—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
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×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D414yes—
133C22×C4×C11#4114yes—
134C22×C4×C11#4114yes—
135C22×Dic11—22no—
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×Dic11C22×C414yes—
154C22×Dic11C2×D414yes—
155C22×Dic11#4114yes—
156C2×D44—216no—
157C2×D44—44no—
158C2×D44—44no—
159C2×D44—48no—
160C2×D44—44no—
161C2×C4×D11—216no—
162C2×C4×D11—48no—
163C2×C4×D11—48no—
164C2×C4×D11—48no—
165C2×C4×D11—48no—
166C2×C4×D11—48no—
167C2×C4×D11—48no—
168C11×C4⋊C4—44no—
169C42×C11—44no—
170(C2×D11)⋊C4—216no—
171(C2×D11)⋊C4—216no—
172(C2×D11)⋊C4—48no—
173(C2×D11)⋊C4—48no—
174(C2×D11)⋊C4—48no—
175C4×Dic11—48no—
176C2×#394—111no—
177C2×#386—112no—
178C2×C4×C22⋊C4—112no—
179#1445—111no—
180#1440—112no—
181#1437—112no—
182#1436D1111yescharacteristic, complemented
183#1434—112no—
184C22⋊#95—112no—
185C23×C11C23×C411yescharacteristic
186C23×C11C22×D412yes—
187C23×C11C2×#4112yes—
188C23×C11C2×#4112yes—
189C23×C11C2×#4112yes—
190C23×C11C2×#4112yes—
191C23×C11H(5,𝔽2)11yescharacteristic
192C23×C11H(5,𝔽2)11yescharacteristic
193C23×C11H(5,𝔽2)12yes—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—24no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—24no—
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—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—
228C22×D11C4×D418yes—
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—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
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#12318yes—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
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—
279D44—416no—
280C4×D11—432no—
281C23×D4—111no—
282C24×C4—112no—
283C22×C4⋊C4C2×D1111yescharacteristic
284C22×C22⋊C4—112no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C42—112no—
290C22×C42C2×D1111yescharacteristic
291#394—118no—
292#386—228no—
293C4×C22⋊C4—228no—
294C2×#95—111no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—111no—
300C2×#95—112no—
301C2×#95—111no—
302C2×#95C2×D1112yes—
303C2×#95C2×D1112yes—
304C2×#95C2×D1111yescharacteristic
305C22×C11C2×C4×D412yes—
306C22×C11C4×#4111yescharacteristic
307C22×C11C4×#4112yes—
308C22×C11#51811yescharacteristic
309C22×C11#51811yescharacteristic
310C22×C11C2×#12312yes—
311C22×C11#52512yes—
312C22×C11#52912yes—
313C22×C11#52912yes—
314C22×C11#53812yes—
315C22×C11#54012yes—
316C22×C11D4211yescharacteristic
317C22×C11#54612yes—
318C22×C11#54612yes—
319C22×C11#54612yes—
320C22×C11#55112yes—
321C22×C11#55111yescharacteristic
322C22×C11#55312yes—
323C22×C11#55312yes—
324C22×C11#55511yescharacteristic
325C22×C11#55511yescharacteristic
326C2×D11—28no—
327C2×D11—28no—
328C2×D11—28no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C4×C11—28no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—82no—
346Dic11—44no—
347Dic11—44no—
348Dic11—44no—
349C25—112no—
350C22×D4—114no—
351C22×D4—224no—
352C22×D4—224no—
353C22×D4—441no—
354C22×D4—441no—
355C23×C4—112no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—224no—
359C23×C4—224no—
360C23×C4—224no—
361C23×C4—224no—
362C23×C4—224no—
363C23×C4—442no—
364C23×C4—442no—
365C23×C4C22×D1112yes—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1112yes—
370C2×C4⋊C4—41no—
371C2×C4⋊C4—41no—
372C2×C4⋊C4C4×D1114yescomplemented
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—224no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—442no—
385C2×C22⋊C4—442no—
386C2×C22⋊C4—442no—
387C2×C22⋊C4—442no—
388C2×C42—24no—
389C2×C42—41no—
390C2×C42—224no—
391C2×C42—224no—
392C2×C42—442no—
393#95—24no—
394#95—24no—
395#95—41no—
396#95—114no—
397#95—224no—
398#95—224no—
399#95—224no—
400#95—224no—
401#95—441no—
402#95—441no—
403#95—442no—
404C2×C11C4×#12312yes—
405C2×C11#233311yescharacteristic
406C2×C11#235811yescharacteristic
407C2×C11#236412yes—
408C2×C11#237211yescharacteristic
409C2×C11#241812yes—
410C2×C11#242012yes—
411C2×C11#247612yes—
412C2×C11#257812yes—
413D11—48no—
414C24—114no—
415C24—114no—
416C24—114no—
417C24—222no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24—222no—
422C24—222no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24C23×D1111yescharacteristic
430C2×D4—2216no—
431C2×D4—444no—
432C2×D4—444no—
433C2×D4—448no—
434C2×D4—444no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
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—114no—
459C22×C4—114no—
460C22×C4—114no—
461C22×C4—2216no—
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×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—448no—
481C22×C4—448no—
482C22×C4—448no—
483C22×C4—448no—
484C22×C4—448no—
485C22×C4—448no—
486C22×C4C2×C4×D1112yes—
487C22×C4C2×C4×D1112yes—
488C22×C4C2×C4×D1112yes—
489C22×C4#433914yes—
490C22×C4D4×D1114yes—
491C22×C4#434314yes—
492C4⋊C4—44no—
493C22⋊C4—2216no—
494C22⋊C4—2216no—
495C22⋊C4—448no—
496C22⋊C4—448no—
497C22⋊C4—448no—
498C42—44no—
499C42—448no—
500C11#1418111yescharacteristic, complemented, Sylow
501C23—118no—
502C23—224no—
503C23—224no—
504C23—224no—
505C23—224no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—224no—
516C23—224no—
517C23—224no—
518C23—224no—
519C23—224no—
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—
536C23C22×C4×D1111yescharacteristic
537C23C2×#433912yes—
538C23C2×D4×D1112yes—
539C23#6703711yescharacteristic
540C23#6703711yescharacteristic
541C23C2×#434312yes—
542C23#41×D1112yes—
543C23#41×D1112yes—
544C23#6704212yes—
545D4—4416no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—4432no—
584C2×C4—442no—
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#6694718yes—
597C22—228no—
598C22—228no—
599C22—228no—
600C22—444no—
601C22—444no—
602C22—444no—
603C22—444no—
604C22—444no—
605C22—444no—
606C22—444no—
607C22—444no—
608C22—444no—
609C22—444no—
610C22—444no—
611C22—444no—
612C22C4×#433911yescharacteristic
613C22#1062301711yescharacteristic
614C22C2×#6694712yes—
615C22#1062305211yescharacteristic
616C22#1062305912yes—
617C22C4×D4×D1112yes—
618C22#1062307812yes—
619C22#1062309112yes—
620C22#1062309312yes—
621C22C4×#434312yes—
622C22#1062311112yes—
623C22#1062312111yescharacteristic
624C22#1062314312yes—
625C22#1062316112yes—
626C22#1062316812yes—
627C22#1062318512yes—
628C22#1062319011yescharacteristic
629C22#1062320111yescharacteristic
630C22#1062322612yes—
631C22#1062324012yes—
632C22#1062326511yescharacteristic
633C4—28no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—82no—
638C4—444no—
639C4—444no—
640C4—444no—
641C2—448no—
642C2C4×#6694712yes—
643C2#1307138111yescharacteristic
644C2#1307159911yescharacteristic
645C2#1307166212yes—
646C2#1307172711yescharacteristic
647C2#1307208012yes—
648C2#1307210912yes—
649C2#1307280412yes—
650C2#1307395212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14181
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D11)⋊C4C2semidirect
4. #13066884C2semidirect
5. #13066864C2semidirect
6. #13066852C2semidirect
7. #13066842C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C11×#1436C2semidirect
31. #10622604C4semidirect
57. C2×C11×C4⋊C4C2×C4semidirect
72. C2×(C2×D11)⋊C4C2×C4semidirect
73. C2×(C2×D11)⋊C4C2×C4semidirect
88. C11⋊#95C2×C4semidirect
182. #1436D11semidirect
372. C2×C4⋊C4C4×D11semidirect
500. C11#14181semidirect

Maximal subgroups

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

subgroupindex
C2×#106226042
C2×#106222782
C2×C4×(C2×D11)⋊C42
#130668842
#130668642
#130668522
#130668422
(C2×D11)⋊#952
C11×#14362
#1418111