Finite Group Databasebeta

← #14684445

Subgroups — #14684445

Order 2816.

1586 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×#10622552C211yesmaximal, characteristic
3C2×#10622546C211yesmaximal, characteristic, complemented
4#13066881C211yesmaximal, characteristic, complemented
5#13066870C211yesmaximal, characteristic, complemented
6#13066864C212yesmaximal, complemented
7#13066862C212yesmaximal, complemented
8#13066862C212yesmaximal, complemented
9#13066860C212yesmaximal, complemented
10#13066856C211yesmaximal, characteristic
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2212yes—
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622552—24no—
36#10622546—24no—
37#10622285C418yescomplemented
38C24×D11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C22×D44—22no—
50C22×D44—22no—
51C22×D44—42no—
52C22×D44—42no—
53C22×D44C2×C414yes—
54C2×C42×C11—42no—
55C2×C42×C11D414yes—
56C2×(C2×D11)⋊C4—24no—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—42no—
59C2×(C2×D11)⋊C4—42no—
60C2×(C2×D11)⋊C4—42no—
61C2×(C2×D11)⋊C4—42no—
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×C4⋊Dic11—22no—
75C2×C4⋊Dic11—42no—
76C2×C4⋊Dic11—42no—
77C2×C4⋊Dic11—42no—
78C2×C4⋊Dic11—42no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—42no—
83C2×Dic11⋊C4C2×C414yes—
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—42no—
93C11⋊#95—42no—
94C11⋊#95—42no—
95#14624—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—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
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×C11C22×C414yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4112yes—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11C22×C412yes—
169C22×Dic11C22×C412yes—
170C2×D44—28no—
171C2×D44—48no—
172C2×D44—44no—
173C2×D44—44no—
174C2×D44—48no—
175C42×C11—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—
182C4⋊Dic11—44no—
183C4⋊Dic11—48no—
184Dic11⋊C4—28no—
185Dic11⋊C4—44no—
186C2×#394—111no—
187C2×#390—111no—
188C2×#387—111no—
189#1444—111no—
190#1441—111no—
191#1440—112no—
192#1439—112no—
193#1439—112no—
194#1439—112no—
195#1438—111no—
196#1434D1111yescharacteristic, complemented
197C23×C11C23×C411yescharacteristic
198C23×C11C22×D411yescharacteristic
199C23×C11C2×#4111yescharacteristic
200C23×C11H(5,𝔽2)12yes—
201C23×C11H(5,𝔽2)11yescharacteristic
202C23×C11H(5,𝔽2)12yes—
203C23×C11H(5,𝔽2)11yescharacteristic
204C23×C11H(5,𝔽2)11yescharacteristic
205C23×C11H(5,𝔽2)12yes—
206C23×C112−1+411yescharacteristic
207C23×C112−1+412yes—
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—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
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×C11—42no—
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—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—42no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301D44—416no—
302C23×D4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4—111no—
306C22×C4⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C22⋊C4—112no—
313C22×C42C2×D1111yescharacteristic
314#394—118no—
315#390—224no—
316#387—224no—
317C2×#95—111no—
318C2×#95—111no—
319C2×#95—111no—
320C2×#95—111no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95C2×D1111yescharacteristic
325C2×#95C2×D1112yes—
326C2×#95C2×D1112yes—
327C2×#95C2×D1111yescharacteristic
328C22×C11C2×C4×D411yescharacteristic
329C22×C11#51812yes—
330C22×C11#51811yescharacteristic
331C22×C11#52012yes—
332C22×C11#52011yescharacteristic
333C22×C11#53411yescharacteristic
334C22×C11#53511yescharacteristic
335C22×C11#53511yescharacteristic
336C22×C11#53511yescharacteristic
337C22×C11#53611yescharacteristic
338C22×C11#53711yescharacteristic
339C22×C11#53812yes—
340C22×C11#54011yescharacteristic
341C22×C11#54212yes—
342C22×C11#54211yescharacteristic
343C22×C11#56012yes—
344C22×C11#56012yes—
345C22×C11#56012yes—
346C22×C11#56212yes—
347C22×C11#56212yes—
348C22×C11#56212yes—
349C22×C11#56212yes—
350C22×C11#56312yes—
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—42no—
368C4×C11—44no—
369C4×C11—42no—
370C4×C11—82no—
371Dic11—42no—
372Dic11—42no—
373Dic11—82no—
374Dic11—81no—
375Dic11—81no—
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—112no—
386C23×C4—111no—
387C23×C4C22×D1112yes—
388C23×C4C22×D1112yes—
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C2×C4⋊C4—114no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—442no—
398C2×C4⋊C4—442no—
399C2×C4⋊C4—442no—
400C2×C4⋊C4—442no—
401C2×C4⋊C4—442no—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—118no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—442no—
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×C22⋊C4—442no—
418C2×C22⋊C4—442no—
419C2×C22⋊C4—442no—
420C2×C42—42no—
421C2×C42D4414yes—
422#95—22no—
423#95—42no—
424#95—42no—
425#95—222no—
426#95—222no—
427#95—222no—
428#95—222no—
429#95—442no—
430#95—442no—
431#95—442no—
432#95C4×D1114yes—
433C2×C11#232111yescharacteristic
434C2×C11#232411yescharacteristic
435C2×C11#232611yescharacteristic
436C2×C11#237612yes—
437C2×C11#237712yes—
438C2×C11#281311yescharacteristic
439C2×C11#281611yescharacteristic
440C2×C11#281811yescharacteristic
441C2×C11#282011yescharacteristic
442C2×C11#282912yes—
443C2×C11#283012yes—
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—444no—
465C2×D4—448no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—112no—
490C22×C4—112no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—221no—
505C22×C4—222no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—221no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—221no—
517C22×C4—222no—
518C22×C4C2×C4×D1114yes—
519C22×C4C2×C4×D1112yes—
520C22×C4C2×D4412yes—
521C22×C4C2×D4412yes—
522C22×C4C2×D4412yes—
523C22×C4#433912yes—
524C4⋊C4—228no—
525C4⋊C4—444no—
526C4⋊C4—444no—
527C4⋊C4—448no—
528C22⋊C4—448no—
529C22⋊C4—448no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C22⋊C4—448no—
534C42—44no—
535C11#1462411yescharacteristic, 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
572C23C22×D4411yescharacteristic
573C23C2×#433911yescharacteristic
574C23#6703712yes—
575C23#6703711yescharacteristic
576C23#6704011yescharacteristic
577C23#6704212yes—
578C23#6704212yes—
579C23#6704211yescharacteristic
580C23#6704211yescharacteristic
581C23#6704312yes—
582D4—4416no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—224no—
615C2×C4—222no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—442no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—442no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4—442no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—442no—
639C2×C4—442no—
640C2×C4C4×D4414yes—
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×C4×D4411yescharacteristic
657C22#1062302411yescharacteristic
658C22#1062304111yescharacteristic
659C22#1062305412yes—
660C22#1062305611yescharacteristic
661C22#1062305611yescharacteristic
662C22#1062305611yescharacteristic
663C22#1062305711yescharacteristic
664C22#1062306512yes—
665C22#1062307612yes—
666C22#1062307611yescharacteristic
667C22#1062309112yes—
668C22#1062309311yescharacteristic
669C22#1062310511yescharacteristic
670C22#1062311311yescharacteristic
671C22#1062315112yes—
672C22#1062317812yes—
673C22#1062319812yes—
674C22#1062319812yes—
675C22#1062321512yes—
676C22#1062323012yes—
677C22#1062324212yes—
678C22#1062324212yes—
679C4—24no—
680C4—42no—
681C4—44no—
682C4—42no—
683C4—82no—
684C4—442no—
685C4—442no—
686C4—881no—
687C4—881no—
688C4—882no—
689C2—884no—
690C2#1307127611yescharacteristic
691C2#1307131011yescharacteristic
692C2#1307132711yescharacteristic
693C2#1307176312yes—
694C2#1307176912yes—
695C2#1307662011yescharacteristic
696C2#1307664611yescharacteristic
697C2#1307665911yescharacteristic
698C2#1307666811yescharacteristic
699C2#1307674212yes—
700C2#1307675712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#14624
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#10622546C2semidirect
4. #13066881C2semidirect
5. #13066870C2semidirect
6. #13066864C2semidirect
7. #13066862C2semidirect
8. #13066862C2semidirect
9. #13066860C2semidirect
11. C11×#1434C2semidirect
37. #10622285C4semidirect
196. #1434D11semidirect
535. C11#14624semidirect

Maximal subgroups

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

subgroupindex
C2×#106222852
C2×#106225522
C2×#106225462
#130668812
#130668702
#130668642
#130668622
#130668602
#130668562
C11×#14342
#1462411