Finite Group Databasebeta

← #14680820

Subgroups — #14680820

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622285C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic
3C2×#10622265C211yesmaximal, characteristic, complemented
4#13066866C211yesmaximal, characteristic, complemented
5#13066864C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7#13066856C211yesmaximal, characteristic
8#13066852C212yesmaximal, complemented
9#13066852C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×#1442C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622601—24no—
36#10622285C418yescomplemented
37#10622265—24no—
38C24×D11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C22×D44—22no—
50C22×D44—22no—
51C22×D44—42no—
52C22×D44—42no—
53C22×D44C2×C414yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—42no—
56C2×(C2×D11)⋊C4—24no—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4C2×C418yes—
73C2×(C2×D11)⋊C4C2×C418yes—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—42no—
78C2×Dic11⋊C4C2×C414yes—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—42no—
81C2×C4×Dic11—42no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11D414yes—
84C11×#95—22no—
85C11×#95—42no—
86C11×#95—42no—
87C11×#95C2×C414yes—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—24no—
93C11⋊#95—42no—
94C11⋊#95—42no—
95#14325—111nomaximal, Sylow
96C24×C11C2411yescharacteristic
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×D11—22no—
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11C22×C414yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
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×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C22×C414yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4112yes—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11C22×C412yes—
165C22×Dic11C22×C412yes—
166C22×Dic11C2×D412yes—
167C22×Dic11C2×D412yes—
168C22×Dic11#4114yes—
169C22×Dic11#4114yes—
170C2×D44—28no—
171C2×D44—48no—
172C2×D44—44no—
173C2×D44—44no—
174C2×D44—48no—
175C11×C4⋊C4—44no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—48no—
182Dic11⋊C4—28no—
183Dic11⋊C4—44no—
184C4×Dic11—44no—
185C4×Dic11—48no—
186C2×#394—111no—
187C2×#390—111no—
188C2×#387—111no—
189#1442D1111yescharacteristic, complemented
190#1441—111no—
191#1440—112no—
192#1439—112no—
193#1438—111no—
194#1437—112no—
195#1437—112no—
196C4×#95—111no—
197C23×C11C23×C411yescharacteristic
198C23×C11C22×D411yescharacteristic
199C23×C11C2×#4111yescharacteristic
200C23×C11C2×#4112yes—
201C23×C11C2×#4112yes—
202C23×C11H(5,𝔽2)12yes—
203C23×C11H(5,𝔽2)11yescharacteristic
204C23×C11H(5,𝔽2)12yes—
205C23×C11H(5,𝔽2)11yescharacteristic
206C23×C11H(5,𝔽2)11yescharacteristic
207C23×C112−1+411yescharacteristic
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
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×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×D11—42no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11—42no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11C4×D414yes—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—41no—
298C2×Dic11—42no—
299C2×Dic11—41no—
300C2×Dic11#12414yes—
301D44—416no—
302C23×D4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4C2×D1111yescharacteristic
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C42—111no—
313C22×C42—112no—
314#394—118no—
315#390—224no—
316#387—224no—
317C2×#95—111no—
318C2×#95—112no—
319C2×#95—111no—
320C2×#95—111no—
321C2×#95—111no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95C2×D1111yescharacteristic
325C2×#95C2×D1112yes—
326C2×#95C2×D1112yes—
327C2×#95C2×D1111yescharacteristic
328C22×C11C2×C4×D411yescharacteristic
329C22×C11C4×#4112yes—
330C22×C11#51812yes—
331C22×C11#51811yescharacteristic
332C22×C11#52011yescharacteristic
333C22×C11C2×#12411yescharacteristic
334C22×C11#52912yes—
335C22×C11#53211yescharacteristic
336C22×C11#53411yescharacteristic
337C22×C11#53511yescharacteristic
338C22×C11#53511yescharacteristic
339C22×C11#53711yescharacteristic
340C22×C11#53812yes—
341C22×C11#53812yes—
342C22×C11#53812yes—
343C22×C11#53812yes—
344C22×C11#53912yes—
345C22×C11#54012yes—
346C22×C11#54012yes—
347C22×C11#54012yes—
348C22×C11#54011yescharacteristic
349C22×C11#54211yescharacteristic
350C22×C11#54212yes—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—82no—
359C2×D11—82no—
360C2×D11—82no—
361C2×D11—82no—
362C2×D11—82no—
363C2×D11—82no—
364C2×D11—82no—
365C2×D11—82no—
366C4×C11—24no—
367C4×C11—44no—
368C4×C11—82no—
369C4×C11—81no—
370C4×C11—81no—
371Dic11—24no—
372Dic11—42no—
373Dic11—42no—
374Dic11—44no—
375Dic11—42no—
376C25—112no—
377C22×D4—114no—
378C22×D4—222no—
379C22×D4—222no—
380C22×D4—442no—
381C22×D4—442no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—112no—
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1112yes—
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1112yes—
391C23×C4C22×D1111yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—114no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—442no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—442no—
408C2×C22⋊C4—442no—
409C2×C22⋊C4—442no—
410C2×C22⋊C4—442no—
411C2×C22⋊C4—442no—
412C2×C22⋊C4—442no—
413C2×C22⋊C4—442no—
414C2×C22⋊C4—442no—
415C2×C22⋊C4—442no—
416C2×C22⋊C4—442no—
417C2×C42—114no—
418C2×C42—224no—
419C2×C42—442no—
420C2×C42—442no—
421C2×C42—442no—
422#95—22no—
423#95—42no—
424#95—42no—
425#95—224no—
426#95—222no—
427#95—222no—
428#95—222no—
429#95—222no—
430#95—442no—
431#95—442no—
432#95C4×D1114yes—
433C2×C11C4×#12411yescharacteristic
434C2×C11#232111yescharacteristic
435C2×C11#232411yescharacteristic
436C2×C11#233312yes—
437C2×C11#233512yes—
438C2×C11#263911yescharacteristic
439C2×C11#264111yescharacteristic
440C2×C11#264812yes—
441C2×C11#265112yes—
442C2×C11#266111yescharacteristic
443C2×C11#266211yescharacteristic
444D11—84no—
445C24—114no—
446C24—222no—
447C24—222no—
448C24—222no—
449C24—222no—
450C24—222no—
451C24—222no—
452C24—222no—
453C24—222no—
454C24—222no—
455C24—222no—
456C24—222no—
457C24—222no—
458C24—222no—
459C24—222no—
460C24C23×D1111yescharacteristic
461C2×D4—228no—
462C2×D4—448no—
463C2×D4—444no—
464C2×D4—448no—
465C2×D4—444no—
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—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—112no—
492C22×C4—114no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—114no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—222no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—221no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—222no—
520C22×C4C2×C4×D1114yes—
521C22×C4C2×C4×D1112yes—
522C22×C4D4×D1112yes—
523C22×C4#434312yes—
524C4⋊C4—44no—
525C4⋊C4—228no—
526C4⋊C4—444no—
527C22⋊C4—448no—
528C22⋊C4—448no—
529C22⋊C4—448no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C42—444no—
534C42—448no—
535C11#1432511yescharacteristic, complemented, Sylow
536C23—224no—
537C23—224no—
538C23—224no—
539C23—224no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—442no—
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—
560C23—442no—
561C23—442no—
562C23—442no—
563C23—442no—
564C23—442no—
565C23—442no—
566C23—442no—
567C23—442no—
568C23—442no—
569C23—442no—
570C23—442no—
571C23C22×C4×D1111yescharacteristic
572C23C2×D4×D1111yescharacteristic
573C23#6703711yescharacteristic
574C23#6703712yes—
575C23C2×#434311yescharacteristic
576C23#6704011yescharacteristic
577C23#41×D1112yes—
578C23#41×D1112yes—
579C23#6704211yescharacteristic
580C23#6704212yes—
581C23#6704211yescharacteristic
582D4—4416no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—114no—
612C2×C4—224no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—224no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—224no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—224no—
626C2×C4—224no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—441no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4—442no—
639C2×C4—441no—
640C2×C4#6694614yes—
641C22—444no—
642C22—444no—
643C22—444no—
644C22—444no—
645C22—444no—
646C22—444no—
647C22—444no—
648C22—882no—
649C22—882no—
650C22—882no—
651C22—882no—
652C22—882no—
653C22—882no—
654C22—882no—
655C22—882no—
656C22C2×#6694611yescharacteristic
657C22#1062305312yes—
658C22#1062307611yescharacteristic
659C22#1062307612yes—
660C22#1062310511yescharacteristic
661C22#1062312311yescharacteristic
662C22#1062313811yescharacteristic
663C22#1062314612yes—
664C22#1062316011yescharacteristic
665C22#1062317112yes—
666C22#1062317512yes—
667C22#1062318411yescharacteristic
668C22#1062319412yes—
669C22#1062319412yes—
670C22#1062319911yescharacteristic
671C22D11×#12411yescharacteristic
672C22#1062320912yes—
673C22#1062322212yes—
674C22#1062322312yes—
675C22#1062322911yescharacteristic
676C22#1062323512yes—
677C22#1062323512yes—
678C22#1062326411yescharacteristic
679C4—24no—
680C4—44no—
681C4—81no—
682C4—81no—
683C4—82no—
684C4—224no—
685C4—442no—
686C4—442no—
687C4—444no—
688C4—442no—
689C2—884no—
690C2#1307115511yescharacteristic
691C2#1307127311yescharacteristic
692C2#1307130711yescharacteristic
693C2#1307137912yes—
694C2#1307141212yes—
695C2#1307454811yescharacteristic
696C2#1307455811yescharacteristic
697C2#1307460312yes—
698C2#1307464812yes—
699C2#1307475011yescharacteristic
700C2#1307476211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1442D11
hypocenterC11#14325
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
3. C2×#10622265C2semidirect
4. #13066866C2semidirect
5. #13066864C2semidirect
6. #13066860C2semidirect
8. #13066852C2semidirect
9. #13066852C2semidirect
10. #95×Dic11C2semidirect
11. C11×#1442C2semidirect
36. #10622285C4semidirect
189. #1442D11semidirect
535. C11#14325semidirect

Maximal subgroups

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

subgroupindex
C2×#106222852
C2×#106226012
C2×#106222652
#130668662
#130668642
#130668602
#130668562
#130668522
#95×Dic112
C11×#14422
#1432511