Finite Group Databasebeta

← #14685181

Subgroups — #14685181

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
1C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
2C2×#10622835C212yesmaximal, complemented
3C2×#10622833C212yesmaximal, complemented
4C2×#10622833C212yesmaximal, complemented
5#13066866C212yesmaximal, complemented
6#13066859C214yesmaximal, complemented
7#13066839C211yesmaximal, characteristic, complemented
8C22×C11×#121C211yesmaximal, characteristic
9C23×D4×C11C2212yes—
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C2×C11×#121—28no—
15C2×C11×#121—24no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2214yes—
20C22×C22⋊Dic11C2214yes—
21C22×Dic11⋊C4—24no—
22C22×Dic11⋊C4—28no—
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25#10622835—28no—
26#10622833—28no—
27#10622833—28no—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2212yes—
32C25×C11C2312yes—
33C25×C11C2311yescharacteristic
34C22×D4×C11—24no—
35C22×D4×C11—24no—
36C22×D4×C11—24no—
37C22×D4×C11—24no—
38C22×D4×C11—24no—
39C22×D4×C11—24no—
40C22×D4×C11—24no—
41C22×D4×C11—22no—
42C22×D4×C11—24no—
43C22×D4×C11—42no—
44C22×D4×C11D418yes—
45C23×C4×C11—24no—
46C23×C4×C11—24no—
47C23×C4×C11—42no—
48C23×C4×C11D414yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11—22no—
53C23×Dic11—22no—
54C23×Dic11—24no—
55C23×Dic11—24no—
56C23×Dic11—22no—
57C23×Dic11—24no—
58C23×Dic11—24no—
59C23×Dic11—42no—
60C23×Dic11D414yescomplemented
61C23×Dic11C2314yes—
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C11×#121—232no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—24no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—28no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—28no—
75C2×C22⋊Dic11—28no—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11—44no—
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—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×C11—22no—
96C24×C11—24no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—24no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—24no—
104C24×C11—24no—
105C24×C11C2×D414yes—
106C24×C11C2×D414yes—
107C24×C11C2×D412yes—
108C24×C11C2×D412yes—
109C24×C11#4112yes—
110C24×C11#4114yes—
111C24×C11C2411yescharacteristic
112C2×D4×C11—28no—
113C2×D4×C11—216no—
114C2×D4×C11—216no—
115C2×D4×C11—216no—
116C2×D4×C11—416no—
117C2×D4×C11—44no—
118C2×D4×C11—48no—
119C2×D4×C11—48no—
120C2×D4×C11—48no—
121C2×D4×C11—48no—
122C2×D4×C11—44no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—28no—
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—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—28no—
136C22×C4×C11—44no—
137C22×C4×C11—416no—
138C22×C4×C11C2×D414yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2×D412yes—
142C22×Dic11—28no—
143C22×Dic11—28no—
144C22×Dic11—216no—
145C22×Dic11—216no—
146C22×Dic11—28no—
147C22×Dic11—28no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—416no—
164C22×Dic11—44no—
165C22×Dic11—44no—
166C22×Dic11C2×D414yes—
167C22×Dic11C2×D414yes—
168C22×Dic11C2×D414yes—
169C22×Dic11#4114yes—
170C11×C4⋊C4—28no—
171C11×C22⋊C4—216no—
172C22⋊Dic11—416no—
173C22⋊Dic11—416no—
174C22⋊Dic11—48no—
175Dic11⋊C4—216no—
176Dic11⋊C4—216no—
177C22×#121D1111yescharacteristic
178C23×C4⋊C4—111no—
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—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—28no—
201C23×C11—28no—
202C23×C11—42no—
203C23×C11—44no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—44no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11—44no—
217C23×C11—44no—
218C23×C11—44no—
219C23×C11—44no—
220C23×C11#12014yes—
221C23×C11#12114yes—
222C23×C11#12118yes—
223C23×C11#12318yes—
224C23×C11#12414yes—
225C23×C11C22×D412yes—
226C23×C11C22×D411yescharacteristic
227C23×C11C22×D411yescharacteristic
228C23×C11C22×D412yes—
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4112yes—
231C23×C11C2×#4112yes—
232C23×C11H(5,𝔽2)12yes—
233C23×C112−1+412yes—
234D4×C11—416no—
235D4×C11—432no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—28no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—416no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—44no—
251C2×C4×C11#12014yes—
252C2×Dic11—232no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—28no—
261C2×Dic11—416no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—44no—
265C2×Dic11—44no—
266C2×Dic11—44no—
267C2×Dic11—44no—
268C2×Dic11—44no—
269C2×Dic11—44no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272C2×Dic11#12118yescomplemented
273C23×D4C2×D1112yes—
274C23×D4C2×D1111yescharacteristic
275C24×C4—111no—
276C24×C4—111no—
277C24×C4C2×D1111yescharacteristic
278C2×#121—28no—
279C2×#121—24no—
280C22×C4⋊C4—112no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—228no—
283C22×C4⋊C4—224no—
284C22×C4⋊C4C2×D1111yescharacteristic
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—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—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—48no—
308C22×C11—48no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—84no—
313C22×C11—82no—
314C22×C11—84no—
315C22×C11#39418yescomplemented
316C22×C11C2×#12011yescharacteristic
317C22×C11C2×#12011yescharacteristic
318C22×C11C2×#12111yescharacteristic
319C22×C11C2×#12112yes—
320C22×C11C2×#12112yes—
321C22×C11C2×#12312yes—
322C22×C11#52511yescharacteristic
323C22×C11#52512yes—
324C22×C11C2×#12411yescharacteristic
325C22×C11#53411yescharacteristic
326C22×C11#53611yescharacteristic
327C22×C11#53712yes—
328C22×C11#53912yes—
329C22×C11D4214yes—
330C22×C11#54714yes—
331C22×C11#54814yes—
332C22×C11#55314yes—
333C4×C11—24no—
334C4×C11—44no—
335C4×C11—42no—
336Dic11—28no—
337Dic11—44no—
338Dic11—84no—
339C25C22×D1112yes—
340C25C22×D1111yescharacteristic
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—22no—
350C22×D4—42no—
351C22×D4C22⋊D1118yes—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—42no—
355C23×C4—112no—
356C23×C4—114no—
357C23×C4—112no—
358C23×C4—114no—
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×C4C22⋊D1114yes—
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1112yes—
370C23×C4C22×D1111yescharacteristic
371#121—232no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—118no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—2232no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—224no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—228no—
385C2×C22⋊C4—228no—
386C2×C22⋊C4—228no—
387C2×C22⋊C4—228no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—444no—
393#95—228no—
394#95—224no—
395#95—228no—
396#95—442no—
397C2×C11—28no—
398C2×C11—84no—
399C2×C11C2×#39411yescharacteristic
400C2×C11#240311yescharacteristic
401C2×C11#240611yescharacteristic
402C2×C11#241614yes—
403C2×C11#243611yescharacteristic
404C2×C11#244314yes—
405C2×C11#259111yescharacteristic
406C2×C11#261811yescharacteristic
407C2×C11#284711yescharacteristic
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—22no—
421C24—22no—
422C24D4×D1112yes—
423C24#434112yes—
424C24#434114yes—
425C24C2×C22⋊D1114yes—
426C24C2×C22⋊D1114yes—
427C24C2×C22⋊D1112yes—
428C24C23×D1111yescharacteristic
429C2×D4—28no—
430C2×D4—216no—
431C2×D4—216no—
432C2×D4—216no—
433C2×D4—416no—
434C2×D4—44no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—44no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—28no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—44no—
454C22×C4—416no—
455C22×C4—114no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—2216no—
460C22×C4—228no—
461C22×C4—228no—
462C22×C4—2216no—
463C22×C4—228no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—228no—
469C22×C4—222no—
470C22×C4—224no—
471C22×C4—224no—
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×C4—4416no—
481C22×C4—444no—
482C22×C4—444no—
483C22×C4D4×D1114yes—
484C22×C4C2×C22⋊D1114yes—
485C22×C4C2×C22⋊D1112yes—
486C22×C4C2×C22⋊D1112yes—
487C4⋊C4—28no—
488C4⋊C4—2216no—
489C4⋊C4—2216no—
490C22⋊C4—216no—
491C22⋊C4—4416no—
492C22⋊C4—4416no—
493C22⋊C4—448no—
494C11#1471911yescharacteristic, complemented, Sylow
495C23—22no—
496C23—28no—
497C23—22no—
498C23—28no—
499C23—22no—
500C23—22no—
501C23—24no—
502C23—28no—
503C23—28no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—28no—
509C23—24no—
510C23—28no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—44no—
517C23—42no—
518C23—42no—
519C23—44no—
520C23—42no—
521C23—42no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23#6698818yes—
531C23#6698914yes—
532C23#6699114yes—
533C23#6699218yes—
534C23#6700614yes—
535C23C2×D4×D1112yes—
536C23C2×D4×D1111yescharacteristic
537C23C2×#434111yescharacteristic
538C23C2×#434112yes—
539C23#6703712yes—
540C23#41×D1112yes—
541C23#6704312yes—
542C23C22×C22⋊D1112yes—
543C23C22×C22⋊D1111yescharacteristic
544D4—416no—
545D4—432no—
546C2×C4—28no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—416no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—44no—
560C2×C4—42no—
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—228no—
571C2×C4—4416no—
572C2×C4—444no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—444no—
576C2×C4—444no—
577C2×C4—444no—
578C2×C4—444no—
579C2×C4—444no—
580C2×C4—444no—
581C2×C4—444no—
582C2×C4#6699014yes—
583C22—24no—
584C22—24no—
585C22—24no—
586C22—24no—
587C22—24no—
588C22—216no—
589C22—24no—
590C22—216no—
591C22—44no—
592C22—44no—
593C22—48no—
594C22—44no—
595C22—48no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—84no—
600C22—82no—
601C22—84no—
602C22#1062283518yescomplemented
603C22#1062312812yes—
604C22#1062312914yes—
605C22#1062313214yes—
606C22#1062313312yes—
607C22D11×#12112yes—
608C22#1062313712yes—
609C22C2×#6698812yes—
610C22C2×#6698911yescharacteristic
611C22C2×#6699011yescharacteristic
612C22C2×#6699111yescharacteristic
613C22D4×C22⋊D1114yes—
614C22C2×#6699212yes—
615C22#1062333511yescharacteristic
616C22#1062335514yes—
617C22#1062335611yescharacteristic
618C22#1062335911yescharacteristic
619C22C2×#6700611yescharacteristic
620C4—24no—
621C4—42no—
622C4—44no—
623C4—228no—
624C4—444no—
625C4—884no—
626C2—28no—
627C2—84no—
628C2C2×#1062283511yescharacteristic
629C2#1307192611yescharacteristic
630C2#1307194711yescharacteristic
631C2#1307205314yes—
632C2#1307227511yescharacteristic
633C2#1307234714yes—
634C2#1307409711yescharacteristic
635C2#1307436011yescharacteristic
636C2#1307689511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
Fitting, prime radicalC22×C11×#121C2
hypercenterC22×#121D11
hypocenterC11#14719
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C23×Dic11⋊C4C2semidirect
2. C2×#10622835C2semidirect
3. C2×#10622833C2semidirect
4. C2×#10622833C2semidirect
5. #13066866C2semidirect
6. #13066859C2semidirect
7. #13066839C2semidirect
60. C23×Dic11D4semidirect
85. C2×Dic11⋊C4D4semidirect
272. C2×Dic11#121semidirect
315. C22×C11#394semidirect
494. C11#14719semidirect
602. C22#10622835semidirect

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
C2×#106228352
C2×#106228332
#130668662
#130668592
#130668392
C22×C11×#1212
#1471911