Finite Group Databasebeta

← #14685185

Subgroups — #14685185

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic
2C2×#10622604C212yesmaximal, complemented
3C2×#10622826C212yesmaximal, complemented
4C2×#10622826C212yesmaximal, complemented
5#13066869C212yesmaximal, complemented
6#13066858C214yesmaximal, complemented
7#13066839C211yesmaximal, characteristic, complemented
8C23×C11×C4⋊C4C211yesmaximal, characteristic, complemented
9C24×C4×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C23×C22⋊D11C2212yes—
13C23×D44C2211yescharacteristic
14C22×C11×C4⋊C4—24no—
15C22×C11×C4⋊C4—28no—
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2212yes—
18C22×C22⋊Dic11C2212yes—
19C2×#66983—24no—
20C2×#66983—28no—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2214yes—
23C22×(C2×D11)⋊C4C2214yes—
24C22×C4⋊Dic11C2211yescharacteristic
25#10622826—28no—
26#10622826—28no—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2212yes—
31#10622604—28no—
32C25×C11C2311yescharacteristic
33C24×D11C2312yes—
34C23×C4×C11—22no—
35C23×C4×C11—22no—
36C23×C4×C11—24no—
37C23×C4×C11—24no—
38C23×C4×C11—24no—
39C23×C4×C11—22no—
40C23×C4×C11—24no—
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11—42no—
44C23×C4×C11—42no—
45C23×C4×C11D414yes—
46C23×C4×C11D414yescomplemented
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C22×C22⋊D11—24no—
52C22×C22⋊D11—24no—
53C22×C22⋊D11—24no—
54C22×C22⋊D11—24no—
55C22×C22⋊D11—24no—
56C22×C22⋊D11—24no—
57C22×C22⋊D11D418yes—
58C23×Dic11C2314yes—
59C23×Dic11C2312yes—
60C22×D44—24no—
61C22×D44—22no—
62C22×D44—24no—
63C22×D44—42no—
64C2×C11×C4⋊C4—232no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4D418yescomplemented
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74#66983—232no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4—28no—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—44no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—24no—
86C11⋊#95—28no—
87C11⋊#95—24no—
88C11⋊#95—28no—
89C11⋊#95—42no—
90#14719—111nomaximal, Sylow
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11C2×D414yes—
96C24×C11C2×D412yes—
97C24×C11C2×D412yes—
98C24×C11#4112yes—
99C24×C11#4114yes—
100C24×C11C2411yescharacteristic
101C23×D11—24no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—24no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—24no—
110C23×D11—24no—
111C23×D11C2×D414yes—
112C22×C4×C11—28no—
113C22×C4×C11—216no—
114C22×C4×C11—28no—
115C22×C4×C11—28no—
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—216no—
123C22×C4×C11—28no—
124C22×C4×C11—28no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—28no—
133C22×C4×C11—44no—
134C22×C4×C11—416no—
135C22×C4×C11—416no—
136C22×C4×C11—44no—
137C22×C4×C11—44no—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2×D414yes—
144C22×C4×C11#4114yes—
145C2×C22⋊D11—216no—
146C2×C22⋊D11—216no—
147C2×C22⋊D11—216no—
148C2×C22⋊D11—48no—
149C2×C22⋊D11—48no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—48no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11C2×D414yes—
166C2×D44—28no—
167C2×D44—416no—
168C2×D44—44no—
169C2×D44—44no—
170C11×C4⋊C4—216no—
171C11×C4⋊C4—216no—
172C22⋊Dic11—48no—
173(C2×D11)⋊C4—216no—
174(C2×D11)⋊C4—416no—
175(C2×D11)⋊C4—416no—
176C4⋊Dic11—28no—
177C22×#121—111no—
178C23×C4⋊C4D1111yescharacteristic, complemented
179C2×#394—112no—
180C2×#386—112no—
181C2×#386—112no—
182#1441—112no—
183#1439—114no—
184C22⋊#95—111no—
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—24no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—28no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—28no—
197C23×C11#12014yes—
198C23×C11#12118yes—
199C23×C11#12114yes—
200C23×C11#12318yes—
201C23×C11#12414yes—
202C23×C11C22×D411yescharacteristic
203C23×C11C22×D412yes—
204C23×C11C22×D411yescharacteristic
205C23×C11C22×D412yes—
206C23×C11C2×#4111yescharacteristic
207C23×C11C2×#4112yes—
208C23×C11C2×#4112yes—
209C23×C11H(5,𝔽2)12yes—
210C23×C112−1+412yes—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—28no—
215C22×D11—28no—
216C22×D11—42no—
217C22×D11—44no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—44no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11—44no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11—44no—
234C2×C4×C11—232no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—28no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—28no—
249C2×C4×C11—416no—
250C2×C4×C11—416no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—44no—
254C2×C4×C11—44no—
255C2×C4×C11#12014yes—
256C2×C4×C11#12118yescomplemented
257C22⋊D11—432no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—44no—
266C2×Dic11—44no—
267C2×Dic11—44no—
268C2×Dic11—44no—
269C2×Dic11—44no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272D44—416no—
273C23×D4—112no—
274C23×D4—111no—
275C24×C4C2×D1111yescharacteristic
276C24×C4C2×D1111yescharacteristic
277C24×C4C2×D1111yescharacteristic
278C2×#121—228no—
279C2×#121—224no—
280C22×C4⋊C4—24no—
281C22×C4⋊C4—28no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4C2×D1112yes—
284C22×C4⋊C4C2×D1112yes—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—114no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—114no—
289#394—228no—
290#386—228no—
291#386—228no—
292C2×#95—112no—
293C2×#95—114no—
294C2×#95—114no—
295C2×#95—112no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—216no—
302C22×C11—24no—
303C22×C11—216no—
304C22×C11#39418yescomplemented
305C22×C11C2×#12011yescharacteristic
306C22×C11C2×#12011yescharacteristic
307C22×C11C2×#12112yes—
308C22×C11C2×#12111yescharacteristic
309C22×C11C2×#12112yes—
310C22×C11C2×#12312yes—
311C22×C11#52511yescharacteristic
312C22×C11#52512yes—
313C22×C11C2×#12411yescharacteristic
314C22×C11#53411yescharacteristic
315C22×C11#53611yescharacteristic
316C22×C11#53712yes—
317C22×C11#53912yes—
318C22×C11D4214yes—
319C22×C11#54714yes—
320C22×C11#54814yes—
321C22×C11#55314yes—
322C2×D11—44no—
323C2×D11—44no—
324C2×D11—44no—
325C2×D11—48no—
326C2×D11—48no—
327C2×D11—82no—
328C2×D11—82no—
329C2×D11—82no—
330C2×D11—84no—
331C2×D11—82no—
332C2×D11—84no—
333C4×C11—28no—
334C4×C11—24no—
335C4×C11—42no—
336C4×C11—44no—
337Dic11—44no—
338Dic11—84no—
339C25—112no—
340C25C22×D1111yescharacteristic
341C22×D4—118no—
342C22×D4—224no—
343C22×D4—224no—
344C22×D4—224no—
345C22×D4—224no—
346C22×D4—224no—
347C22×D4—224no—
348C22×D4—224no—
349C22×D4—222no—
350C22×D4—224no—
351C22×D4—442no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—22no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—42no—
362C23×C4—42no—
363C23×C4—112no—
364C23×C4—114no—
365C23×C4D4414yescomplemented
366C23×C4C22⋊D1114yes—
367C23×C4C22×D1112yes—
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1112yes—
370C23×C4C22×D1111yescharacteristic
371#121—2232no—
372C2×C4⋊C4—232no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4C22⋊D1118yescomplemented
381C2×C22⋊C4—224no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—228no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—228no—
389C2×C22⋊C4—228no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4—228no—
392C2×C22⋊C4—444no—
393#95—228no—
394#95—228no—
395#95—224no—
396#95—442no—
397C2×C11—28no—
398C2×C11C2×#39411yescharacteristic
399C2×C11#240311yescharacteristic
400C2×C11#240611yescharacteristic
401C2×C11#241614yes—
402C2×C11#243611yescharacteristic
403C2×C11#244314yes—
404C2×C11#259111yescharacteristic
405C2×C11#261811yescharacteristic
406C2×C11#284711yescharacteristic
407D11—84no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—114no—
413C24—222no—
414C24—224no—
415C24—222no—
416C24—222no—
417C24—224no—
418C24—222no—
419C24—222no—
420C24—224no—
421C24—224no—
422C24—222no—
423C24C2×D4412yes—
424C24#433912yes—
425C24D4×D1114yes—
426C24#434314yes—
427C24C2×C22⋊D1112yes—
428C24C23×D1111yescharacteristic
429C2×D4—228no—
430C2×D4—2216no—
431C2×D4—2216no—
432C2×D4—2216no—
433C2×D4—4416no—
434C2×D4—444no—
435C2×D4—448no—
436C2×D4—448no—
437C2×D4—448no—
438C2×D4—448no—
439C2×D4—444no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—216no—
443C22×C4—28no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—216no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—28no—
461C22×C4—44no—
462C22×C4—416no—
463C22×C4—416no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—114no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4C2×D4414yes—
481C22×C4#433914yes—
482C22×C4C2×C22⋊D1112yes—
483C22×C4C2×C22⋊D1114yes—
484C22×C4C2×C22⋊D1114yes—
485C22×C4C2×C22⋊D1114yes—
486C22×C4C2×C22⋊D1112yes—
487C4⋊C4—216no—
488C4⋊C4—216no—
489C4⋊C4—228no—
490C22⋊C4—2216no—
491C22⋊C4—4416no—
492C22⋊C4—448no—
493C22⋊C4—4416no—
494C11#1471911yescharacteristic, complemented, Sylow
495C23—28no—
496C23—24no—
497C23—28no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—22no—
502C23—28no—
503C23—22no—
504C23—22no—
505C23—28no—
506C23—22no—
507C23—224no—
508C23—224no—
509C23—228no—
510C23—224no—
511C23—228no—
512C23—442no—
513C23—442no—
514C23—444no—
515C23—444no—
516C23—444no—
517C23—444no—
518C23—444no—
519C23—444no—
520C23—442no—
521C23—442no—
522C23—444no—
523C23—444no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—444no—
528C23—444no—
529C23—442no—
530C23#6694718yes—
531C23#6694818yes—
532C23#6698314yes—
533C23#6699014yes—
534C23#6700014yes—
535C23C22×D4411yescharacteristic
536C23C2×#433911yescharacteristic
537C23C2×#433912yes—
538C23C2×D4×D1112yes—
539C23#6703712yes—
540C23C2×#434312yes—
541C23#6704012yes—
542C23C22×C22⋊D1111yescharacteristic
543C23C22×C22⋊D1112yes—
544D4—4416no—
545D4—4432no—
546C2×C4—232no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—28no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—28no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—416no—
562C2×C4—416no—
563C2×C4—42no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—42no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—444no—
575C2×C4—444no—
576C2×C4—444no—
577C2×C4—444no—
578C2×C4—444no—
579C2×C4—444no—
580C2×C4—444no—
581C2×C4#6698318yescomplemented
582C2×C4#6700614yes—
583C22—24no—
584C22—24no—
585C22—24no—
586C22—24no—
587C22—24no—
588C22—216no—
589C22—24no—
590C22—216no—
591C22—444no—
592C22—444no—
593C22—448no—
594C22—444no—
595C22—448no—
596C22—882no—
597C22—882no—
598C22—882no—
599C22—884no—
600C22—882no—
601C22—884no—
602C22#1062260418yescomplemented
603C22C2×#6694712yes—
604C22C2×#6694812yes—
605C22#1062303814yes—
606C22#1062304112yes—
607C22#1062304514yes—
608C22#1062304612yes—
609C22C2×#6698312yes—
610C22C2×#6698311yescharacteristic
611C22#1062332211yescharacteristic
612C22#1062332212yes—
613C22C2×#6699011yescharacteristic
614C22D4×C22⋊D1114yes—
615C22#1062333511yescharacteristic
616C22C2×#6700011yescharacteristic
617C22#1062334711yescharacteristic
618C22#1062334814yes—
619C22C2×#6700611yescharacteristic
620C4—24no—
621C4—28no—
622C4—42no—
623C4—44no—
624C4—444no—
625C4—884no—
626C2—28no—
627C2—884no—
628C2C2×#1062260411yescharacteristic
629C2#1307192611yescharacteristic
630C2#1307195111yescharacteristic
631C2#1307205014yes—
632C2#1307227011yescharacteristic
633C2#1307235114yes—
634C2#1307409611yescharacteristic
635C2#1307435811yescharacteristic
636C2#1307689811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC23×C11×C4⋊C4C2
prime radicalC22×#66983C2
hypercenterC23×C4⋊C4D11
hypocenterC11#14719
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622604C2semidirect
3. C2×#10622826C2semidirect
4. C2×#10622826C2semidirect
5. #13066869C2semidirect
6. #13066858C2semidirect
7. #13066839C2semidirect
8. C23×C11×C4⋊C4C2semidirect
46. C23×C4×C11D4semidirect
70. C2×C11×C4⋊C4D4semidirect
178. C23×C4⋊C4D11semidirect
256. C2×C4×C11#121semidirect
304. C22×C11#394semidirect
365. C23×C4D44semidirect
380. C2×C4⋊C4C22⋊D11semidirect
494. C11#14719semidirect
581. C2×C4#66983semidirect
602. C22#10622604semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C2×#106226042
C2×#106228262
#130668692
#130668582
#130668392
C23×C11×C4⋊C42
#1471911