Finite Group Databasebeta

← #14676323

Subgroups — #14676323

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622590C211yesmaximal, characteristic, complemented
4C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#13066859C214yesmaximal, complemented
6#13066846C211yesmaximal, characteristic, complemented
7#13066845C211yesmaximal, characteristic, complemented
8#13066838C214yesmaximal, complemented
9C2×C11×#390C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×Dic11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2214yes—
14C22×C42×C11C2211yescharacteristic
15C22×C22⋊Dic11C2214yes—
16C22×C22⋊Dic11C2212yes—
17C2×D4×Dic11—24no—
18C2×D4×Dic11—24no—
19C2×D4×Dic11C418yescomplemented
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C11×#390—24no—
26#10622834—24no—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32#10622590—24no—
33C4×Dic11⋊C4—24no—
34C25×C11C2312yes—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11C2×C414yes—
40C22×D4×C11D414yes—
41C22×D4×C11Q814yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—24no—
46C23×Dic11—24no—
47C23×Dic11—44no—
48C23×Dic11—44no—
49C23×Dic11C2×C418yes—
50C23×Dic11C2312yes—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C22⋊C4—28no—
59C2×C11×C22⋊C4—28no—
60C2×C11×C22⋊C4—44no—
61C2×C42×C11—22no—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—28no—
67C2×C22⋊Dic11—28no—
68C2×C22⋊Dic11—44no—
69C2×C22⋊Dic11C2×C418yes—
70D4×Dic11—232no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11C2×C414yes—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—24no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11C2×C414yes—
84C2×C4×Dic11D414yes—
85C2×C4×Dic11D414yes—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—44no—
90C11⋊#95—44no—
91#13941—111nomaximal, Sylow
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—24no—
95C24×C11—24no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—24no—
99C24×C11—24no—
100C24×C11C22×C414yes—
101C24×C11C2×D414yes—
102C24×C11C2×Q814yes—
103C24×C11C2411yescharacteristic
104C2×D4×C11—28no—
105C2×D4×C11—28no—
106C2×D4×C11—28no—
107C2×D4×C11—28no—
108C2×D4×C11—28no—
109C2×D4×C11—28no—
110C2×D4×C11C4⋊C4116yescomplemented
111C22×C4×C11—22no—
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—24no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×Q812yes—
127C22×C4×C11#4114yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×Dic11—216no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—22no—
149C22×Dic11—24no—
150C22×Dic11—416no—
151C22×Dic11—48no—
152C22×Dic11—416no—
153C22×Dic11—48no—
154C22×Dic11C22×C414yes—
155C22×Dic11C22×C412yes—
156C22×Dic11C22×C412yes—
157C22×Dic11C2×D412yes—
158C22×Dic11C2×D412yes—
159C22×Dic11C2×D412yes—
160C22×Dic11C2×D412yes—
161C22×Dic11#4114yes—
162C11×C4⋊C4—44no—
163C11×C22⋊C4—416no—
164C42×C11—44no—
165C22⋊Dic11—216no—
166C22⋊Dic11—416no—
167C4⋊Dic11—28no—
168C4⋊Dic11—44no—
169Dic11⋊C4—216no—
170C4×Dic11—44no—
171C4×Dic11C22⋊C4116yescomplemented
172C22×C4×D4—111no—
173C2×#390—111no—
174C2×#390D1111yescharacteristic
175C2×#382—111no—
176C2×C4×C4⋊C4—111no—
177#1439—114no—
178C4⋊#95—111no—
179C4⋊#95—111no—
180C22⋊#95—114no—
181C23×C11—24no—
182C23×C11—24no—
183C23×C11—28no—
184C23×C11—28no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—24no—
189C23×C11—28no—
190C23×C11—28no—
191C23×C11—28no—
192C23×C11—28no—
193C23×C11—44no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—44no—
198C23×C11—42no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11C2×C4⋊C418yes—
204C23×C11C23×C411yescharacteristic
205C23×C11C22×D411yescharacteristic
206C23×C11C22×D411yescharacteristic
207C23×C11C22×D411yescharacteristic
208C23×C11C22×Q811yescharacteristic
209C23×C11C2×#4111yescharacteristic
210C23×C11C2×#4111yescharacteristic
211C23×C11C2×#4112yes—
212C23×C11C2×#4112yes—
213C23×C11H(5,𝔽2)12yes—
214C23×C11H(5,𝔽2)12yes—
215D4×C11—232no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—44no—
228C2×C4×C11C2×C22⋊C414yes—
229C2×C4×C11C2×C4⋊C414yes—
230C2×C4×C11#11714yes—
231C2×C4×C11#12114yes—
232C2×C4×C11#12114yes—
233C2×C4×C11C22⋊Q814yes—
234C2×C4×C11C22⋊Q814yes—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—28no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—432no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—44no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—44no—
260C2×Dic11—44no—
261C2×Dic11C2×C22⋊C414yes—
262C2×Dic11C2×C22⋊C414yes—
263C23×D4C2×D1111yescharacteristic
264C24×C4—112no—
265C2×C4×D4—118no—
266C2×C4×D4—224no—
267C2×C4×D4—224no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4—112no—
270C22×C4⋊C4—111no—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4—112no—
273C22×C22⋊C4—114no—
274C22×C22⋊C4C2×D1114yes—
275C22×C42—111no—
276C22×C42—111no—
277C22×C42C2×D1111yescharacteristic
278#390—24no—
279#390—224no—
280#382—224no—
281C4×C4⋊C4—224no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—114no—
286C2×#95—114no—
287C22×C11—216no—
288C22×C11—28no—
289C22×C11—44no—
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—48no—
293C22×C11—48no—
294C22×C11—48no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11C22×C22⋊C411yescharacteristic
299C22×C11C22×C4⋊C411yescharacteristic
300C22×C11C2×#11711yescharacteristic
301C22×C11C4×#4112yes—
302C22×C11#51812yes—
303C22×C11C2×#12111yescharacteristic
304C22×C11C2×#12111yescharacteristic
305C22×C11C2×C22⋊Q811yescharacteristic
306C22×C11C2×C22⋊Q811yescharacteristic
307C22×C11#52512yes—
308C22×C11#53211yescharacteristic
309C22×C11#53211yescharacteristic
310C22×C11#53511yescharacteristic
311C22×C11#53512yes—
312C22×C11#53511yescharacteristic
313C22×C11#54612yes—
314C22×C11#54612yes—
315C22×C11#55312yes—
316C22×C11#55312yes—
317C22×C11#55412yes—
318C22×C11#55412yes—
319C22×C11#55912yes—
320C22×C11#55912yes—
321C4×C11—44no—
322C4×C11—82no—
323C4×C11#38018yes—
324Dic11—24no—
325Dic11—24no—
326Dic11—44no—
327Dic11—44no—
328Dic11—82no—
329C25C22×D1112yes—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4Dic2214yes—
335C22×D4C4×D1114yes—
336C22×D4C22⋊D1114yes—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—112no—
340C23×C4—112no—
341C23×C4—118no—
342C23×C4—112no—
343C23×C4—224no—
344C23×C4—224no—
345C23×C4—444no—
346C23×C4—444no—
347C23×C4C22×D1112yes—
348C23×C4C22×D1112yes—
349C23×C4C22×D1111yescharacteristic
350C4×D4—2232no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—224no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—118no—
367C2×C22⋊C4—224no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—228no—
370C2×C22⋊C4—228no—
371C2×C22⋊C4—444no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—114no—
376C2×C42—114no—
377C2×C42—114no—
378C2×C42—222no—
379C2×C42—222no—
380C2×C42—222no—
381#95—224no—
382#95—224no—
383#95—224no—
384#95—444no—
385#95—444no—
386C2×C11—48no—
387C2×C11C2×#38011yescharacteristic
388C2×C11#229711yescharacteristic
389C2×C11#230911yescharacteristic
390C2×C11#234912yes—
391C2×C11#235712yes—
392C2×C11#253512yes—
393C2×C11#254411yescharacteristic
394C2×C11#254411yescharacteristic
395C2×C11#256611yescharacteristic
396C2×C11#256611yescharacteristic
397C2×C11#258012yes—
398C24—22no—
399C24—22no—
400C24—24no—
401C24—22no—
402C24—22no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24C2×Dic2214yes—
407C24C2×C4×D1114yes—
408C24C2×C22⋊D1114yes—
409C24C23×D1111yescharacteristic
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—28no—
416C2×D4Dic11⋊C4116yescomplemented
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—112no—
429C22×C4—112no—
430C22×C4—112no—
431C22×C4—112no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—2216no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—4416no—
457C22×C4—448no—
458C22×C4—4416no—
459C22×C4—448no—
460C22×C4C2×Dic2212yes—
461C22×C4C2×C4×D1112yes—
462C22×C4D4×D1112yes—
463C22×C4D4×D1112yes—
464C22×C4#434114yes—
465C22×C4#434112yes—
466C22×C4#434112yes—
467C22×C4C2×C22⋊D1112yes—
468C4⋊C4—44no—
469C4⋊C4—2216no—
470C4⋊C4—228no—
471C4⋊C4—444no—
472C22⋊C4—416no—
473C22⋊C4—2216no—
474C22⋊C4—4416no—
475C42—44no—
476C42—1116no—
477C42—444no—
478C11#1394111yescharacteristic, complemented, Sylow
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—28no—
484C23—28no—
485C23—28no—
486C23—28no—
487C23—24no—
488C23—24no—
489C23—28no—
490C23—28no—
491C23—44no—
492C23—42no—
493C23—42no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23—42no—
499C23—42no—
500C23—44no—
501C23C2×Dic11⋊C418yes—
502C23C22×Dic2211yescharacteristic
503C23C22×C4×D1111yescharacteristic
504C23C2×D4×D1111yescharacteristic
505C23C2×D4×D1111yescharacteristic
506C23C2×#434111yescharacteristic
507C23C2×#434112yes—
508C23C2×#434111yescharacteristic
509C23#6703712yes—
510C23#41×D1112yes—
511C23#6704212yes—
512C23C22×C22⋊D1111yescharacteristic
513D4—232no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—114no—
527C2×C4—114no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—228no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—4432no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—444no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—444no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—444no—
554C2×C4#6693014yes—
555C2×C4#6693114yes—
556C2×C4#6693114yes—
557C2×C4C22⋊C4×D1114yes—
558C2×C4C2×Dic11⋊C414yes—
559C2×C4#6699214yes—
560C2×C4#6699214yes—
561C22—28no—
562C22—216no—
563C22—48no—
564C22—44no—
565C22—48no—
566C22—44no—
567C22—44no—
568C22—44no—
569C22—44no—
570C22—48no—
571C22—44no—
572C22C2×#6693011yescharacteristic
573C22C2×#6693111yescharacteristic
574C22C2×#6693111yescharacteristic
575C22C2×C22⋊C4×D1111yescharacteristic
576C22C4×#434112yes—
577C22#1062307012yes—
578C22#1062307412yes—
579C22#1062307612yes—
580C22#1062313712yes—
581C22#1062313812yes—
582C22#1062314512yes—
583C22#1062314912yes—
584C22#1062319911yescharacteristic
585C22#1062320511yescharacteristic
586C22#1062321212yes—
587C22#1062324412yes—
588C22#1062324611yescharacteristic
589C22#1062324711yescharacteristic
590C22C22×Dic11⋊C411yescharacteristic
591C22C2×#6699211yescharacteristic
592C22C2×#6699211yescharacteristic
593C22#1062333712yes—
594C22#1062336012yes—
595C4—44no—
596C4—82no—
597C4—224no—
598C4—224no—
599C4—444no—
600C4—444no—
601C4—882no—
602C4#1062255518yes—
603C2—48no—
604C2C2×#1062255511yescharacteristic
605C2#1307110311yescharacteristic
606C2#1307119511yescharacteristic
607C2#1307152112yes—
608C2#1307158812yes—
609C2#1307351512yes—
610C2#1307358411yescharacteristic
611C2#1307358611yescharacteristic
612C2#1307381811yescharacteristic
613C2#1307381911yescharacteristic
614C2#1307397212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#13941
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#10622590C2semidirect
4. C2×C4×Dic11⋊C4C2semidirect
5. #13066859C2semidirect
6. #13066846C2semidirect
7. #13066845C2semidirect
8. #13066838C2semidirect
19. C2×D4×Dic11C4semidirect
110. C2×D4×C11C4⋊C4semidirect
171. C4×Dic11C22⋊C4semidirect
416. C2×D4Dic11⋊C4semidirect
478. C11#13941semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106228342
C2×#106225902
C2×C4×Dic11⋊C42
#130668592
#130668462
#130668452
#130668382
C2×C11×#3902
#1394111