Finite Group Databasebeta

← #14682558

Subgroups — #14682558

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3#13066887C211yesmaximal, characteristic, complemented
4#13066864C212yesmaximal, complemented
5#13066864C212yesmaximal, complemented
6#13066840C212yesmaximal, complemented
7(C2×D11)⋊#95C212yesmaximal, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9C11×#1446C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C23×C4×D11C2212yes—
13C2×#67000—28no—
14C2×#67000C418yescomplemented
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33#10622278—28no—
34C24×D11C2312yes—
35C22×Q8×C11—24no—
36C22×Q8×C11—42no—
37C22×Q8×C11—41no—
38C22×Q8×C11—41no—
39C22×Q8×C11C2×C414yescomplemented
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C22×D44—41no—
49C22×D44—42no—
50C22×D44—41no—
51C22×D44C2×C414yes—
52C22×D44D418yes—
53C22×C4×D11—24no—
54C22×C4×D11—24no—
55C22×C4×D11—24no—
56C22×C4×D11—42no—
57C22×C4×D11—42no—
58C22×C4×D11—42no—
59C22×C4×D11—42no—
60#67000—232no—
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—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4—42no—
73C2×(C2×D11)⋊C4—42no—
74C2×(C2×D11)⋊C4C2×C418yescomplemented
75C2×(C2×D11)⋊C4C2×C418yescomplemented
76C2×C4×Dic11—24no—
77C2×C4×Dic11C2×C414yescomplemented
78C11×#95—24no—
79C11×#95—41no—
80C11×#95—42no—
81C11×#95—41no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—41no—
88C11⋊#95—42no—
89C11⋊#95—41no—
90#14473—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
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×D11—22no—
104C23×D11C22×C414yes—
105C23×D11C2×D414yes—
106C23×D11C2×D414yes—
107C2×Q8×C11—28no—
108C2×Q8×C11—44no—
109C2×Q8×C11—44no—
110C2×Q8×C11—48no—
111C2×Q8×C11—48no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
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×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11#4114yes—
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×Dic11C22×C414yes—
161C22×Dic11#4114yes—
162C2×D44—44no—
163C2×D44—44no—
164C2×D44—48no—
165C2×D44—48no—
166C2×D44C22⋊C4116yes—
167C2×C4×D11—48no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11—48no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C2×C4×D11—48no—
174(C2×D11)⋊C4—216no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179C4×Dic11—28no—
180C22×#124—111no—
181C2×#386—112no—
182#1446—111no—
183#1446D1111yescharacteristic, complemented
184#1440—112no—
185#1440—112no—
186#1434—112no—
187C22⋊#95—112no—
188C22⋊#95—112no—
189C23×C11C23×C411yescharacteristic
190C23×C11C22×D412yes—
191C23×C11C2×#4112yes—
192C23×C11C2×#4112yes—
193C23×C11H(5,𝔽2)12yes—
194C23×C11H(5,𝔽2)11yescharacteristic
195C23×C11H(5,𝔽2)11yescharacteristic
196C23×C11H(5,𝔽2)12yes—
197C23×C112−1+412yes—
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—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
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×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11C2×C22⋊C418yes—
233Q8×C11—416no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
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—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11C2×C22⋊C414yes—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
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—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284D44—416no—
285C4×D11—432no—
286C23×Q8C2×D1111yescharacteristic
287C23×D4—111no—
288C24×C4—112no—
289C2×#124—118no—
290C2×#124—228no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C42—111no—
297#386—228no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—111no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—111no—
306C2×#95C2×D1112yes—
307C2×#95C2×D1111yescharacteristic
308C2×#95C2×D1112yes—
309C2×#95C2×D1111yescharacteristic
310C22×C11C22×C22⋊C411yescharacteristic
311C22×C11C4×#4112yes—
312C22×C11#51811yescharacteristic
313C22×C11#51811yescharacteristic
314C22×C11#52012yes—
315C22×C11#53412yes—
316C22×C11#53412yes—
317C22×C11#53812yes—
318C22×C11#53812yes—
319C22×C11#54212yes—
320C22×C11#54212yes—
321C22×C11#54612yes—
322C22×C11#54612yes—
323C22×C11#54712yes—
324C22×C11#54712yes—
325C22×C11#55112yes—
326C22×C11#55511yescharacteristic
327C22×C11#55511yescharacteristic
328C22×C11H(3,𝔽4)11yescharacteristic
329C22×C11#56212yes—
330C22×C11#56311yescharacteristic
331C2×D11—28no—
332C2×D11—28no—
333C2×D11—28no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C4×C11—24no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—44no—
350C4×C11—82no—
351Dic11—44no—
352Dic11—44no—
353Dic11—82no—
354C25—112no—
355C22×Q8—24no—
356C22×Q8—42no—
357C22×Q8—41no—
358C22×Q8—41no—
359C22×Q8C4×D1114yescomplemented
360C22×D4—114no—
361C22×D4—118no—
362C22×D4—441no—
363C22×D4—442no—
364C22×D4—441no—
365C23×C4—112no—
366C23×C4—112no—
367C23×C4—112no—
368C23×C4—224no—
369C23×C4—224no—
370C23×C4—224no—
371C23×C4—442no—
372C23×C4—442no—
373C23×C4—442no—
374C23×C4—442no—
375C23×C4C22×D1112yes—
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1112yes—
379C23×C4C22×D1111yescharacteristic
380#124—2232no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—442no—
393C2×C22⋊C4—442no—
394C2×C22⋊C4—442no—
395C2×C22⋊C4—442no—
396C2×C42—114no—
397C2×C42—224no—
398#95—24no—
399#95—41no—
400#95—42no—
401#95—41no—
402#95—224no—
403#95—224no—
404#95—224no—
405#95—441no—
406#95—442no—
407#95—441no—
408#95—442no—
409#95—442no—
410C2×C11#230811yescharacteristic
411C2×C11#233712yes—
412C2×C11#233912yes—
413C2×C11#237211yescharacteristic
414C2×C11#237911yescharacteristic
415C2×C11#268412yes—
416C2×C11#268612yes—
417C2×C11#268612yes—
418C2×C11#271712yes—
419D11—48no—
420C24—114no—
421C24—114no—
422C24—114no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24—222no—
430C24—222no—
431C24—222no—
432C24—222no—
433C24—222no—
434C24—222no—
435C24C23×D1111yescharacteristic
436C2×Q8—28no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—48no—
440C2×Q8—48no—
441C2×D4—1116no—
442C2×D4—444no—
443C2×D4—444no—
444C2×D4—448no—
445C2×D4—448no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—114no—
471C22×C4—114no—
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—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—448no—
492C22×C4—448no—
493C22×C4—448no—
494C22×C4—448no—
495C22×C4—448no—
496C22×C4—448no—
497C22×C4—448no—
498C22×C4C2×C4×D1112yes—
499C22×C4C2×C4×D1112yes—
500C22×C4C2×C4×D1112yes—
501C22×C4D4×D1114yes—
502C22×C4#434314yes—
503C22⋊C4—2216no—
504C22⋊C4—2216no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C42—228no—
509C11#1447311yescharacteristic, complemented, Sylow
510C23—118no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—224no—
516C23—224no—
517C23—224no—
518C23—224no—
519C23—224no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—442no—
530C23—442no—
531C23—442no—
532C23—442no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23—442no—
537C23—442no—
538C23—442no—
539C23—442no—
540C23—442no—
541C23—442no—
542C23—442no—
543C23—442no—
544C23—442no—
545C23C22×C4×D1111yescharacteristic
546C23C2×D4×D1112yes—
547C23#6703712yes—
548C23#6703711yescharacteristic
549C23#6703711yescharacteristic
550C23C2×#434312yes—
551C23#6704012yes—
552C23#41×D1112yes—
553C23#6704212yes—
554Q8—416no—
555D4—4416no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—4432no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4C22⋊C4×D1114yes—
607C22—228no—
608C22—228no—
609C22—228no—
610C22—444no—
611C22—444no—
612C22—444no—
613C22—444no—
614C22—444no—
615C22—444no—
616C22—444no—
617C22—444no—
618C22—444no—
619C22—444no—
620C22—444no—
621C22—444no—
622C22C2×C22⋊C4×D1111yescharacteristic
623C22#1062301711yescharacteristic
624C22#1062301711yescharacteristic
625C22C4×#434312yes—
626C22#1062310512yes—
627C22#1062312012yes—
628C22#1062312012yes—
629C22#1062316112yes—
630C22#1062316212yes—
631C22#1062316812yes—
632C22#1062317112yes—
633C22#1062317512yes—
634C22#1062317812yes—
635C22#1062320111yescharacteristic
636C22#1062320712yes—
637C22#1062320912yes—
638C22#1062321411yescharacteristic
639C22#1062325712yes—
640C22#1062326412yes—
641C22#1062326511yescharacteristic
642C22#1062326611yescharacteristic
643C4—24no—
644C4—44no—
645C4—42no—
646C4—42no—
647C4—82no—
648C4—444no—
649C4—444no—
650C4—882no—
651C2—448no—
652C2#1307119211yescharacteristic
653C2#1307142812yes—
654C2#1307144512yes—
655C2#1307172711yescharacteristic
656C2#1307178811yescharacteristic
657C2#1307499912yes—
658C2#1307502712yes—
659C2#1307502912yes—
660C2#1307545812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1446C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1446D11
hypocenterC11#14473
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
3. #13066887C2semidirect
4. #13066864C2semidirect
5. #13066864C2semidirect
6. #13066840C2semidirect
7. (C2×D11)⋊#95C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C11×#1446C2semidirect
14. C2×#67000C4semidirect
39. C22×Q8×C11C2×C4semidirect
74. C2×(C2×D11)⋊C4C2×C4semidirect
75. C2×(C2×D11)⋊C4C2×C4semidirect
77. C2×C4×Dic11C2×C4semidirect
183. #1446D11semidirect
359. C22×Q8C4×D11semidirect
509. C11#14473semidirect

Maximal subgroups

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

subgroupindex
C22×#670002
C2×#106222782
#130668872
#130668642
#130668402
(C2×D11)⋊#952
C11×#14462
#1447311