Finite Group Databasebeta

← #14675576

Subgroups — #14675576

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic, complemented
2C2×#10622286C211yesmaximal, characteristic
3C2×#10622279C212yesmaximal
4C2×#10622279C211yesmaximal, characteristic
5#13066886C211yesmaximal, characteristic, complemented
6#13066874C212yesmaximal, complemented
7#13066860C212yesmaximal
8#13066858C211yesmaximal, characteristic
9#95×Dic11C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×#1442C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C2×#66940—28no—
25C2×#66940—24no—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622286C418yescomplemented
38#10622279—24no—
39#10622279—28no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—22no—
52C22×C4×D11—24no—
53C22×C4×D11—22no—
54C22×C4×D11—24no—
55C22×C4×D11Q814yescomplemented
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22—24no—
59C22×Dic22—24no—
60C22×Dic22C2×C414yescomplemented
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—22no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4C2×C418yes—
74C2×(C2×D11)⋊C4C2×C414yes—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—24no—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11—24no—
86C2×C4×Dic11D414yes—
87C2×C4×Dic11D418yes—
88#66940—232no—
89C11×#95—24no—
90C11×#95—22no—
91C11×#95—24no—
92C11×#95C2×C414yescomplemented
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95C2×C418yescomplemented
100C4×#393—111nomaximal, Sylow
101C24×C11C2411yescharacteristic
102C23×D11—21no—
103C23×D11—22no—
104C23×D11—21no—
105C23×D11—22no—
106C23×D11—21no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—21no—
110C23×D11C22×C412yes—
111C23×D11C2×Q812yes—
112C23×D11#4112yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
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—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×Q812yes—
140C22×C4×C11#4112yes—
141C22×C4×C11#4112yes—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—21no—
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—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11C22×C412yes—
161C22×Dic11C22×C414yes—
162C22×Dic11C2×D412yes—
163C22×Dic11C2×D414yes—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×D414yes—
166C22×Dic11C2×Q812yes—
167C22×Dic11#4114yes—
168C22×Dic11#4114yes—
169C22×Dic11#4112yes—
170C22×Dic11#4114yes—
171C2×C4×D11—28no—
172C2×C4×D11—216no—
173C2×C4×D11—44no—
174C2×C4×D11—44no—
175C2×C4×D11—48no—
176C2×Dic22—28no—
177C2×Dic22—28no—
178C2×Dic22—216no—
179C2×Dic22—216no—
180C2×Dic22—28no—
181C11×C4⋊C4—28no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—216no—
185(C2×D11)⋊C4—28no—
186Dic11⋊C4—216no—
187C4×Dic11—28no—
188C4×Dic11—216no—
189C4×Dic11—44no—
190C4×Dic11—48no—
191C22×C4×Q8—111no—
192C2×#393—111no—
193C2×C4×C22⋊C4—111no—
194C2×C4×C22⋊C4—112no—
195#1446—111no—
196#1442—112no—
197#1442D1111yescharacteristic, complemented
198#1439—112no—
199#1439—111no—
200C4×#95—112no—
201C4×#95—111no—
202C23×C11C23×C411yescharacteristic
203C23×C11C22×D411yescharacteristic
204C23×C11C22×D412yes—
205C23×C11C22×Q811yescharacteristic
206C23×C11C2×#4111yescharacteristic
207C23×C11C2×#4111yescharacteristic
208C23×C11C2×#4112yes—
209C23×C11C2×#4111yescharacteristic
210C23×C11C2×#4111yescharacteristic
211C23×C11C2×#4112yes—
212C23×C11C2×#4112yes—
213C22×D11—22no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—24no—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—24no—
225C22×D11—41no—
226C22×D11—42no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—41no—
235C22×D11C4×Q814yescomplemented
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—42no—
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×C11C4×D414yes—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—22no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—41no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—41no—
288C2×Dic11C4×D418yes—
289C2×Dic11#12014yes—
290C2×Dic11C22⋊Q814yes—
291C2×Dic11C22⋊Q818yes—
292C2×Dic11#12414yes—
293C2×Dic11#12418yes—
294C4×D11—416no—
295Dic22—232no—
296C23×Q8—111no—
297C24×C4—111no—
298C2×C4×Q8—224no—
299C2×C4×Q8—228no—
300C22×C4⋊C4—112no—
301C22×C4⋊C4C2×D1111yescharacteristic
302C22×C22⋊C4—112no—
303C22×C22⋊C4—111no—
304C22×C22⋊C4—111no—
305C22×C22⋊C4—112no—
306C22×C42—112no—
307C22×C42—111no—
308C22×C42—112no—
309C22×C42—111no—
310#393—118no—
311C4×C22⋊C4—228no—
312C4×C22⋊C4—224no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95—111no—
318C2×#95—111no—
319C2×#95—112no—
320C2×#95C2×D1112yes—
321C2×#95C2×D1112yes—
322C2×#95C2×D1111yescharacteristic
323C2×#95C2×D1111yescharacteristic
324C22×C11C2×C4×D411yescharacteristic
325C22×C11C2×C4×D412yes—
326C22×C11C2×C4×Q811yescharacteristic
327C22×C11C4×#4112yes—
328C22×C11C4×#4111yescharacteristic
329C22×C11C2×#12011yescharacteristic
330C22×C11C2×C22⋊Q811yescharacteristic
331C22×C11C2×C22⋊Q812yes—
332C22×C11#52511yescharacteristic
333C22×C11#52512yes—
334C22×C11#52512yes—
335C22×C11#52511yescharacteristic
336C22×C11C2×#12411yescharacteristic
337C22×C11C2×#12412yes—
338C22×C11#52912yes—
339C22×C11#52912yes—
340C22×C11#52912yes—
341C22×C11#52912yes—
342C22×C11#52911yescharacteristic
343C22×C11#53212yes—
344C22×C11#53211yescharacteristic
345C22×C11#53311yescharacteristic
346C22×C11#53312yes—
347C2×D11—24no—
348C2×D11—28no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—44no—
353C2×D11—42no—
354C2×D11—44no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—44no—
358C4×C11—24no—
359C4×C11—42no—
360C4×C11—44no—
361C4×C11—42no—
362C4×C11—44no—
363Dic11—28no—
364Dic11—42no—
365Dic11—44no—
366Dic11—42no—
367Dic11#39318yescomplemented
368C25—111no—
369C22×Q8—114no—
370C22×Q8—224no—
371C22×Q8—224no—
372C22×Q8—222no—
373C22×Q8—222no—
374C23×C4—111no—
375C23×C4—112no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—112no—
379C23×C4—114no—
380C23×C4—222no—
381C23×C4—224no—
382C23×C4—222no—
383C23×C4—224no—
384C23×C4C22×D1112yes—
385C23×C4C22×D1112yes—
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C4×Q8—2232no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4—224no—
394C2×C4⋊C4—224no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—222no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4—222no—
406C2×C22⋊C4—222no—
407C2×C42—118no—
408C2×C42—114no—
409C2×C42—224no—
410C2×C42—224no—
411C2×C42—224no—
412C2×C42—224no—
413C2×C42—222no—
414C2×C42—224no—
415C2×C42—224no—
416C2×C42—224no—
417#95—24no—
418#95—22no—
419#95—24no—
420#95—118no—
421#95—224no—
422#95—224no—
423#95—224no—
424#95—224no—
425#95—222no—
426#95—222no—
427#95C4×D1114yescomplemented
428C2×C11C4×#12011yescharacteristic
429C2×C11C4×C22⋊Q811yescharacteristic
430C2×C11C4×C22⋊Q812yes—
431C2×C11C4×#12411yescharacteristic
432C2×C11C4×#12412yes—
433C2×C11C2×#39311yescharacteristic
434C2×C11#238811yescharacteristic
435C2×C11#239611yescharacteristic
436C2×C11#239612yes—
437C2×C11#239811yescharacteristic
438C2×C11#239812yes—
439D11—44no—
440C24—112no—
441C24—112no—
442C24—112no—
443C24—221no—
444C24—222no—
445C24—221no—
446C24—221no—
447C24—222no—
448C24—222no—
449C24—222no—
450C24—221no—
451C24C23×D1111yescharacteristic
452C2×Q8—2216no—
453C2×Q8—228no—
454C2×Q8—2216no—
455C2×Q8—228no—
456C2×Q8—228no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
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—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—112no—
480C22×C4—114no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—114no—
484C22×C4—114no—
485C22×C4—114no—
486C22×C4—114no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—114no—
490C22×C4—228no—
491C22×C4—2216no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—221no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—221no—
500C22×C4—222no—
501C22×C4—221no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—221no—
509C22×C4—222no—
510C22×C4—444no—
511C22×C4—444no—
512C22×C4—448no—
513C22×C4C2×C4×D1114yes—
514C22×C4C2×C4×D1112yes—
515C22×C4D4×D1114yes—
516C22×C4D4×D1112yes—
517C22×C4#434112yes—
518C22×C4Q8×D1112yes—
519C22×C4#434312yes—
520C4⋊C4—28no—
521C4⋊C4—2216no—
522C22⋊C4—2216no—
523C22⋊C4—228no—
524C22⋊C4—2216no—
525C22⋊C4—228no—
526C42—228no—
527C42—2216no—
528C42—444no—
529C42—448no—
530C11C4×#39311yescharacteristic, complemented, Sylow
531C23—114no—
532C23—224no—
533C23—222no—
534C23—222no—
535C23—224no—
536C23—222no—
537C23—224no—
538C23—222no—
539C23—222no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—222no—
544C23—442no—
545C23—441no—
546C23—442no—
547C23—442no—
548C23—442no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23—442no—
553C23—442no—
554C23C22×C4×D1111yescharacteristic
555C23C2×D4×D1111yescharacteristic
556C23C2×D4×D1112yes—
557C23C2×#434111yescharacteristic
558C23C2×Q8×D1111yescharacteristic
559C23C2×#434311yescharacteristic
560C23#41×D1111yescharacteristic
561C23#41×D1112yes—
562C23#41×D1111yescharacteristic
563C23#41×D1112yes—
564C23#41×D1112yes—
565Q8—2232no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—114no—
595C2×C4—114no—
596C2×C4—118no—
597C2×C4—114no—
598C2×C4—118no—
599C2×C4—118no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—222no—
608C2×C4—224no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—224no—
612C2×C4—222no—
613C2×C4—224no—
614C2×C4—4416no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—441no—
620C2×C4—442no—
621C2×C4—441no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4#6694614yes—
625C22—224no—
626C22—228no—
627C22—442no—
628C22—442no—
629C22—444no—
630C22—442no—
631C22—444no—
632C22—442no—
633C22—444no—
634C22—442no—
635C22—442no—
636C22C2×#6694611yescharacteristic
637C22#1062305312yes—
638C22C4×#434111yescharacteristic
639C22C4×D4×D1112yes—
640C22C4×Q8×D1111yescharacteristic
641C22D11×#12011yescharacteristic
642C22#1062312712yes—
643C22#1062313711yescharacteristic
644C22D11×C22⋊Q811yescharacteristic
645C22D11×C22⋊Q812yes—
646C22#1062315812yes—
647C22#1062318012yes—
648C22#1062318711yescharacteristic
649C22#1062318712yes—
650C22#1062319911yescharacteristic
651C22D11×#12411yescharacteristic
652C22D11×#12412yes—
653C22#1062321912yes—
654C22#1062322212yes—
655C22#1062322211yescharacteristic
656C22#1062323712yes—
657C22#1062323712yes—
658C22#1062325911yescharacteristic
659C4—24no—
660C4—42no—
661C4—44no—
662C4—42no—
663C4—44no—
664C4—118no—
665C4—228no—
666C4—444no—
667C4—442no—
668C4—442no—
669C2—444no—
670C2#1307111711yescharacteristic
671C2#1307114611yescharacteristic
672C2#1307115012yes—
673C2#1307115511yescharacteristic
674C2#1307115712yes—
675C2D11×#39311yescharacteristic
676C2#1307183011yescharacteristic
677C2#1307188911yescharacteristic
678C2#1307189312yes—
679C2#1307190111yescharacteristic
680C2#1307190512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1442D11
hypocenterC11C4×#393
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C22×#66940C2semidirect
5. #13066886C2semidirect
6. #13066874C2semidirect
9. #95×Dic11C2semidirect
10. #95×Dic11C2semidirect
11. C11×#1442C2semidirect
37. #10622286C4semidirect
55. C22×C4×D11Q8semidirect
60. C22×Dic22C2×C4semidirect
92. C11×#95C2×C4semidirect
99. C11⋊#95C2×C4semidirect
197. #1442D11semidirect
235. C22×D11C4×Q8semidirect
367. Dic11#393semidirect
427. #95C4×D11semidirect
530. C11C4×#393semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106222862
C2×#106222792
#130668862
#130668742
#130668602
#130668582
#95×Dic112
C11×#14422
C4×#39311