Finite Group Databasebeta

← #14685187

Subgroups — #14685187

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
2C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
3C2×#10622285C212yesmaximal, complemented
4C2×#10622571C212yesmaximal, complemented
5C2×#10622571C212yesmaximal, complemented
6#13066870C212yesmaximal, complemented
7#13066860C214yesmaximal, complemented
8C11×C22⋊#95C211yesmaximal, characteristic, complemented
9C24×C4×C11C2211yescharacteristic
10C23×C22⋊D11C2212yes—
11C24×Dic11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C23×D44C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C2×#66983—24no—
16C2×#66983—28no—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2214yes—
19C22×(C2×D11)⋊C4C2214yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4—24no—
22C22×Dic11⋊C4—28no—
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29#10622571—28no—
30#10622571—28no—
31#10622285—28no—
32C25×C11C2311yescharacteristic
33C24×D11C2312yes—
34C23×C4×C11—24no—
35C23×C4×C11—24no—
36C23×C4×C11—42no—
37C23×C4×C11D414yes—
38C23×C4×C11C2314yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—24no—
42C22×C22⋊D11—24no—
43C22×C22⋊D11—24no—
44C22×C22⋊D11—24no—
45C22×C22⋊D11—24no—
46C22×C22⋊D11—24no—
47C22×C22⋊D11D418yes—
48C23×Dic11—22no—
49C23×Dic11—22no—
50C23×Dic11—24no—
51C23×Dic11—24no—
52C23×Dic11—22no—
53C23×Dic11—24no—
54C23×Dic11—24no—
55C23×Dic11—42no—
56C23×Dic11D414yescomplemented
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C22×D44—24no—
61C22×D44—22no—
62C22×D44—24no—
63C22×D44—42no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67#66983—232no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—28no—
72C2×(C2×D11)⋊C4—28no—
73C2×(C2×D11)⋊C4—28no—
74C2×(C2×D11)⋊C4—28no—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—44no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—24no—
79C2×Dic11⋊C4—232no—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—24no—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—24no—
84C2×Dic11⋊C4—24no—
85C2×Dic11⋊C4D418yescomplemented
86C11×#95—24no—
87C11×#95—42no—
88C11⋊#95—28no—
89C11⋊#95—28no—
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—22no—
113C22×C4×C11—22no—
114C22×C4×C11—28no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—28no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—44no—
127C22×C4×C11—416no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D414yes—
131C2×C22⋊D11—216no—
132C2×C22⋊D11—216no—
133C2×C22⋊D11—216no—
134C2×C22⋊D11—48no—
135C2×C22⋊D11—48no—
136C2×C22⋊D11—48no—
137C2×C22⋊D11—48no—
138C22×Dic11—28no—
139C22×Dic11—28no—
140C22×Dic11—216no—
141C22×Dic11—216no—
142C22×Dic11—28no—
143C22×Dic11—28no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—24no—
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—24no—
158C22×Dic11—416no—
159C22×Dic11—44no—
160C22×Dic11—44no—
161C22×Dic11C2×D414yes—
162C22×Dic11C2×D414yes—
163C22×Dic11C2×D414yes—
164C22×Dic11C2×D414yes—
165C22×Dic11#4114yes—
166C2×D44—28no—
167C2×D44—416no—
168C2×D44—44no—
169C2×D44—44no—
170C11×C22⋊C4—48no—
171(C2×D11)⋊C4—216no—
172(C2×D11)⋊C4—416no—
173(C2×D11)⋊C4—416no—
174C4⋊Dic11—28no—
175Dic11⋊C4—216no—
176Dic11⋊C4—216no—
177C22×#121—111no—
178C23×C4⋊C4—111no—
179C2×#394—112no—
180C2×#386—112no—
181C2×#386—112no—
182#1441—112no—
183#1439—114no—
184C22⋊#95D1111yescharacteristic, complemented
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×D412yes—
205C23×C11C22×D411yescharacteristic
206C23×C11C2×#4112yes—
207C23×C11C2×#4111yescharacteristic
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—22no—
235C2×C4×C11—22no—
236C2×C4×C11—28no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—416no—
241C2×C4×C11—44no—
242C2×C4×C11—44no—
243C2×C4×C11—44no—
244C2×C4×C11—44no—
245C2×C4×C11—44no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11#12014yes—
250C22⋊D11—432no—
251C2×Dic11—232no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—28no—
263C2×Dic11—416no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—44no—
271C2×Dic11#12118yescomplemented
272D44—416no—
273C23×D4—112no—
274C23×D4—111no—
275C24×C4—111no—
276C24×C4—111no—
277C24×C4C2×D1111yescharacteristic
278C2×#121—228no—
279C2×#121—224no—
280C22×C4⋊C4—112no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—228no—
284C22×C4⋊C4—224no—
285C22×C22⋊C4—114no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—114no—
288C22×C22⋊C4C2×D1112yes—
289#394—228no—
290#386—228no—
291#386—228no—
292C2×#95—114no—
293C2×#95—114no—
294C2×#95C2×D1112yes—
295C2×#95C2×D1112yes—
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—24no—
334C4×C11—42no—
335C4×C11—84no—
336Dic11—28no—
337Dic11—44no—
338Dic11—44no—
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—24no—
353C23×C4—24no—
354C23×C4—42no—
355C23×C4—112no—
356C23×C4—114no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—224no—
360C23×C4—224no—
361C23×C4—224no—
362C23×C4—222no—
363C23×C4—222no—
364C23×C4—222no—
365C23×C4—224no—
366C23×C4—442no—
367C23×C4D4414yes—
368C23×C4C22×D1114yes—
369C23×C4C22×D1111yescharacteristic
370C23×C4C22×D1111yescharacteristic
371#121—2232no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—2232no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—224no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—228no—
388C2×C22⋊C4—228no—
389C2×C22⋊C4—228no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4—228no—
392C2×C22⋊C4—444no—
393#95—24no—
394#95—42no—
395#95—228no—
396#95—228no—
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—222no—
415C24—222no—
416C24—222no—
417C24—224no—
418C24—222no—
419C24—224no—
420C24—222no—
421C24—224no—
422C24—224no—
423C24C2×D4412yes—
424C24#433914yes—
425C24D4×D1114yes—
426C24D4×D1112yes—
427C24#434312yes—
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—22no—
441C22×C4—22no—
442C22×C4—28no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—28no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—44no—
455C22×C4—416no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—114no—
460C22×C4—114no—
461C22×C4—2216no—
462C22×C4—228no—
463C22×C4—228no—
464C22×C4—2216no—
465C22×C4—228no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—228no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—224no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—222no—
481C22×C4—4416no—
482C22×C4—444no—
483C22×C4—444no—
484C22×C4C2×D4412yes—
485C22×C4C2×D4412yes—
486C22×C4D4×D1114yes—
487C4⋊C4—2216no—
488C4⋊C4—228no—
489C4⋊C4—2216no—
490C22⋊C4—48no—
491C22⋊C4—2216no—
492C22⋊C4—4416no—
493C22⋊C4—4416no—
494C11#1471911yescharacteristic, complemented, Sylow
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—28no—
500C23—28no—
501C23—28no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—28no—
507C23—224no—
508C23—224no—
509C23—224no—
510C23—228no—
511C23—228no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—444no—
521C23—444no—
522C23—444no—
523C23—444no—
524C23—444no—
525C23—444no—
526C23—444no—
527C23—444no—
528C23—444no—
529C23—444no—
530C23#6692814yes—
531C23#6693514yes—
532C23#6693718yes—
533C23#6694718yes—
534C23#6694814yes—
535C23C22×D4411yescharacteristic
536C23C2×#433912yes—
537C23C2×D4×D1112yes—
538C23C2×D4×D1112yes—
539C23C2×D4×D1111yescharacteristic
540C23#6703712yes—
541C23C2×#434311yescharacteristic
542C23#41×D1112yes—
543C23#6704312yes—
544D4—4416no—
545D4—4432no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—28no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—416no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—118no—
562C2×C4—2232no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—228no—
574C2×C4—4416no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—444no—
582C2×C4#6693514yes—
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#1062228518yescomplemented
603C22C2×#6692811yescharacteristic
604C22C2×#6693511yescharacteristic
605C22C2×#6693511yescharacteristic
606C22C2×#6693712yes—
607C22#1062302411yescharacteristic
608C22C2×#6694712yes—
609C22C2×#6694811yescharacteristic
610C22#1062305511yescharacteristic
611C22#1062305711yescharacteristic
612C22#1062307114yes—
613C22#1062308314yes—
614C22#1062312114yes—
615C22#1062312812yes—
616C22D11×#12112yes—
617C22#1062315812yes—
618C22#1062317612yes—
619C22#1062318614yes—
620C4—24no—
621C4—42no—
622C4—84no—
623C4—228no—
624C4—444no—
625C4—444no—
626C2—28no—
627C2—884no—
628C2C2×#1062228511yescharacteristic
629C2#1307192911yescharacteristic
630C2#1307195311yescharacteristic
631C2#1307205514yes—
632C2#1307227411yescharacteristic
633C2#1307235514yes—
634C2#1307409111yescharacteristic
635C2#1307436111yescharacteristic
636C2#1307689911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×C22⋊#95C2
prime radicalC22×#66983C2
hypercenterC22⋊#95D11
hypocenterC11#14719
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C23×Dic11⋊C4C2semidirect
3. C2×#10622285C2semidirect
4. C2×#10622571C2semidirect
5. C2×#10622571C2semidirect
6. #13066870C2semidirect
7. #13066860C2semidirect
8. C11×C22⋊#95C2semidirect
56. C23×Dic11D4semidirect
85. C2×Dic11⋊C4D4semidirect
184. C22⋊#95D11semidirect
271. C2×Dic11#121semidirect
304. C22×C11#394semidirect
494. C11#14719semidirect
602. C22#10622285semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C23×Dic11⋊C42
C2×#106222852
C2×#106225712
#130668702
#130668602
C11×C22⋊#952
#1471911