Finite Group Databasebeta

← #14690490

Subgroups — #14690490

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C2×#10622560C214yesmaximal, complemented
3C2×#10622834C211yesmaximal, characteristic
4C2×#10622834C211yesmaximal, characteristic
5#13066859C214yesmaximal, complemented
6#13066846C211yesmaximal, characteristic, complemented
7#13066845C211yesmaximal, characteristic, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C2×C11×#390C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C23×Dic22C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2214yes—
14C22×C42×C11C2211yescharacteristic
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2214yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×#66941—24no—
24C2×#66941—24no—
25C2×#66941—24no—
26C11×#390—24no—
27#10622834—24no—
28#10622834—24no—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32C2×C11⋊#95C2212yes—
33#10622560—216no—
34C25×C11C2312yes—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11Q814yescomplemented
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C22×Dic22—24no—
51C22×Dic22—24no—
52C22×Dic22—24no—
53C22×Dic22—28no—
54C22×Dic22—44no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4D414yes—
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—28no—
65C2×C22⋊Dic11—28no—
66C2×C22⋊Dic11—28no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—28no—
70C2×C22⋊Dic11—44no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11D414yes—
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×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11D414yes—
86#66941—232no—
87C11⋊#95—28no—
88C11⋊#95—28no—
89C11⋊#95—24no—
90C11⋊#95D418yescomplemented
91#15144—111nomaximal, Sylow
92C24×C11—24no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—24no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—24no—
101C24×C11—24no—
102C24×C11C2×Q814yes—
103C24×C11C2411yescharacteristic
104C2×D4×C11—28no—
105C2×D4×C11—28no—
106C2×D4×C11—28no—
107C2×D4×C11—44no—
108C2×D4×C11—44no—
109C2×D4×C11—44no—
110C2×D4×C11—44no—
111C22×C4×C11—24no—
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×C11C2×D414yes—
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×Q812yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—24no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11C2×D414yes—
152C22×Dic11C2×D414yes—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D414yes—
155C22×Dic11C2×D412yes—
156C22×Dic11#4114yes—
157C2×Dic22—216no—
158C2×Dic22—416no—
159C2×Dic22—416no—
160C2×Dic22—48no—
161C2×Dic22—48no—
162C11×C4⋊C4—28no—
163C11×C22⋊C4—416no—
164C42×C11—44no—
165C22⋊Dic11—416no—
166C22⋊Dic11—48no—
167C22⋊Dic11—48no—
168C4⋊Dic11—28no—
169C4⋊Dic11—44no—
170Dic11⋊C4—216no—
171C4×Dic11—28no—
172C4×Dic11—44no—
173C22×C4⋊Q8—111no—
174C2×#393—114no—
175C2×#390—111no—
176C2×#390—111no—
177C2×#390D1111yescharacteristic
178#1439—114no—
179C4⋊#95—111no—
180C4⋊#95—111no—
181C4×#95—111no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—28no—
186C23×C11—28no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11C22×D411yescharacteristic
206C23×C11C22×D411yescharacteristic
207C23×C11C22×D412yes—
208C23×C11C22×D411yescharacteristic
209C23×C11C22×Q811yescharacteristic
210C23×C11C2×#4111yescharacteristic
211C23×C11C2×#4111yescharacteristic
212C23×C11C2×#4111yescharacteristic
213C23×C11C2×#4112yes—
214C23×C11H(5,𝔽2)12yes—
215C23×C112−1+412yes—
216D4×C11—416no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—28no—
221C2×C4×C11—24no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11#12014yes—
230C2×C4×C11C22⋊Q814yes—
231C2×C4×C11C22⋊Q814yes—
232C2×C4×C11C22⋊Q814yes—
233C2×C4×C11#12414yes—
234C2×C4×C11#12414yes—
235C2×C4×C11#12414yes—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—28no—
248C2×Dic11—24no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—44no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—44no—
260C2×Dic11—44no—
261C2×Dic11#12414yes—
262C2×Dic11#12714yes—
263Dic22—432no—
264C23×Q8—112no—
265C23×D4C2×D1111yescharacteristic
266C2×C4⋊Q8—224no—
267C2×C4⋊Q8—224no—
268C2×C4⋊Q8—224no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—112no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4C2×D1111yescharacteristic
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—114no—
276C22×C22⋊C4C2×D1114yes—
277C22×C42—111no—
278C22×C42—111no—
279C22×C42C2×D1111yescharacteristic
280#393—2216no—
281#390—24no—
282#390—224no—
283#390—224no—
284C2×#95—112no—
285C2×#95—114no—
286C2×#95—114no—
287C2×#95—112no—
288C22×C11—44no—
289C22×C11—44no—
290C22×C11—48no—
291C22×C11—48no—
292C22×C11—44no—
293C22×C11—82no—
294C22×C11—82no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—84no—
298C22×C11—84no—
299C22×C11C2×#12011yescharacteristic
300C22×C11C2×C22⋊Q811yescharacteristic
301C22×C11C2×C22⋊Q811yescharacteristic
302C22×C11C2×C22⋊Q811yescharacteristic
303C22×C11C2×#12411yescharacteristic
304C22×C11C2×#12411yescharacteristic
305C22×C11C2×#12411yescharacteristic
306C22×C11C2×#12411yescharacteristic
307C22×C11C2×#12711yescharacteristic
308C22×C11#53212yes—
309C22×C11#53212yes—
310C22×C11#53511yescharacteristic
311C22×C11#53611yescharacteristic
312C22×C11#54212yes—
313C22×C11#54212yes—
314C22×C11D4212yes—
315C22×C11D4212yes—
316C22×C11#54712yes—
317C22×C11#54812yes—
318C22×C11#54812yes—
319C22×C11D4×Q812yes—
320C22×C11#55412yes—
321C22×C11#55512yes—
322C4×C11—44no—
323C4×C11—44no—
324C4×C11#39318yescomplemented
325Dic11—24no—
326Dic11—24no—
327Dic11—44no—
328Dic11—44no—
329Dic11—82no—
330C25C22×D1112yes—
331C22×Q8—224no—
332C22×Q8—224no—
333C22×Q8—228no—
334C22×Q8—224no—
335C22×Q8—444no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4Dic2214yescomplemented
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—112no—
346C23×C4—112no—
347C23×C4—112no—
348C23×C4C22×D1112yes—
349C23×C4C22×D1112yes—
350C23×C4C22×D1111yescharacteristic
351C4⋊Q8—2232no—
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—224no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4C22⋊D1114yes—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—224no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—228no—
370C2×C22⋊C4—228no—
371C2×C22⋊C4—228no—
372C2×C22⋊C4—228no—
373C2×C22⋊C4—444no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—114no—
378C2×C42—222no—
379C2×C42—222no—
380C2×C42—222no—
381C2×C42—222no—
382C2×C42—222no—
383#95—118no—
384#95—224no—
385#95—228no—
386#95—228no—
387C2×C11—84no—
388C2×C11C2×#39311yescharacteristic
389C2×C11#243311yescharacteristic
390C2×C11#243611yescharacteristic
391C2×C11#245212yes—
392C2×C11#245212yes—
393C2×C11#249112yes—
394C2×C11#249112yes—
395C2×C11#254211yescharacteristic
396C2×C11#256311yescharacteristic
397C2×C11#264011yescharacteristic
398C2×C11#285811yescharacteristic
399C24—22no—
400C24—24no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—24no—
406C24—24no—
407C24—24no—
408C24—22no—
409C24C2×Dic2214yes—
410C24C23×D1111yescharacteristic
411C2×Q8—2216no—
412C2×Q8—4416no—
413C2×Q8—448no—
414C2×Q8—4416no—
415C2×Q8—448no—
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—44no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—114no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—222no—
446C22×C4—224no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—224no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—224no—
460C22×C4C2×Dic2212yes—
461C22×C4#433912yes—
462C22×C4D4×D1114yes—
463C22×C4D4×D1112yes—
464C22×C4D4×D1112yes—
465C22×C4#434112yes—
466C22×C4#434112yes—
467C22×C4C2×C22⋊D1114yes—
468C22×C4C2×C22⋊D1112yes—
469C4⋊C4—28no—
470C4⋊C4—2216no—
471C4⋊C4—228no—
472C4⋊C4—444no—
473C22⋊C4—416no—
474C22⋊C4—448no—
475C22⋊C4—448no—
476C22⋊C4—4416no—
477C42—44no—
478C42—228no—
479C42—444no—
480C11#1514411yescharacteristic, complemented, Sylow
481C23—24no—
482C23—24no—
483C23—24no—
484C23—28no—
485C23—28no—
486C23—42no—
487C23—42no—
488C23—44no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—44no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—44no—
500C23—44no—
501C23—42no—
502C23—42no—
503C23—44no—
504C23C22×Dic2211yescharacteristic
505C23C2×#433911yescharacteristic
506C23C2×D4×D1111yescharacteristic
507C23C2×D4×D1112yes—
508C23C2×D4×D1111yescharacteristic
509C23C2×#434111yescharacteristic
510C23C2×#434111yescharacteristic
511C23#6703712yes—
512C23#41×D1112yes—
513C23#6704312yes—
514C23C22×C22⋊D1111yescharacteristic
515Q8—4432no—
516D4—416no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—28no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—114no—
530C2×C4—114no—
531C2×C4—222no—
532C2×C4—224no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—228no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—444no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—444no—
554C2×C4—444no—
555C2×C4—442no—
556C2×C4#6693114yes—
557C2×C4#6693114yes—
558C2×C4#6693814yes—
559C2×C4#6693814yes—
560C2×C4#6697714yes—
561C2×C4#6698914yes—
562C2×C4#6699014yes—
563C22—48no—
564C22—48no—
565C22—44no—
566C22—44no—
567C22—44no—
568C22—84no—
569C22—84no—
570C22—82no—
571C22—82no—
572C22—82no—
573C22—82no—
574C22C2×#6693111yescharacteristic
575C22C2×#6693111yescharacteristic
576C22C2×#6693811yescharacteristic
577C22C2×#6693811yescharacteristic
578C22D4×Dic2212yes—
579C22#1062307012yes—
580C22#1062307912yes—
581C22#1062309212yes—
582C22#1062312712yes—
583C22#1062313412yes—
584C22#1062314212yes—
585C22#1062314712yes—
586C22D11×#12411yescharacteristic
587C22#1062320611yescharacteristic
588C22#1062320812yes—
589C22D11×#12711yescharacteristic
590C22#1062324611yescharacteristic
591C22#1062324812yes—
592C22C2×#6697711yescharacteristic
593C22C2×#6698911yescharacteristic
594C22C2×#6699011yescharacteristic
595C22D4×C22⋊D1112yes—
596C22#1062336212yes—
597C4—44no—
598C4—44no—
599C4—224no—
600C4—224no—
601C4—444no—
602C4—444no—
603C4—882no—
604C4#1062256018yescomplemented
605C2—84no—
606C2C2×#1062256011yescharacteristic
607C2#1307225011yescharacteristic
608C2#1307227111yescharacteristic
609C2#1307246012yes—
610C2#1307246912yes—
611C2#1307298012yes—
612C2#1307298112yes—
613C2#1307356711yescharacteristic
614C2#1307378711yescharacteristic
615C2#1307455311yescharacteristic
616C2#1307697011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#390C2
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#15144
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
2. C2×#10622560C2semidirect
5. #13066859C2semidirect
6. #13066846C2semidirect
7. #13066845C2semidirect
8. C4×C11⋊#95C2semidirect
41. C22×D4×C11Q8semidirect
90. C11⋊#95D4semidirect
324. C4×C11#393semidirect
342. C22×D4Dic22semidirect
480. C11#15144semidirect
604. C4#10622560semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106225602
C2×#106228342
#130668592
#130668462
#130668452
C4×C11⋊#952
C2×C11×#3902
#1514411