Finite Group Databasebeta

← #14685045

Subgroups — #14685045

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622834C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622598C211yesmaximal, characteristic, complemented
4C2×#10622564C214yesmaximal, complemented
5C2×C42×Dic11C211yesmaximal, characteristic, complemented
6#13066853C214yesmaximal, complemented
7#13066846C211yesmaximal, characteristic, complemented
8#13066845C211yesmaximal, characteristic, complemented
9C2×C11×#390C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2214yes—
13C22×C42×C11C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2214yes—
16C22×C22⋊Dic11C2212yes—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C11×#390C418yescomplemented
25#10622834—24no—
26#10622834—24no—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30#10622598—24no—
31#10622564—216no—
32C42×Dic11—24no—
33C25×C11C2312yes—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11C2×C414yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2×C414yes—
52C2×C11×C22⋊C4—28no—
53C2×C11×C22⋊C4—28no—
54C2×C11×C22⋊C4C2×C4116yes—
55C2×C42×C11—22no—
56C2×C42×C11—22no—
57C2×C42×C11C2×C414yes—
58C2×C22⋊Dic11—28no—
59C2×C22⋊Dic11—28no—
60C2×C22⋊Dic11—28no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—28no—
64C2×C22⋊Dic11—28no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—28no—
72C2×C4⋊Dic11—24no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11D414yes—
83C2×C4×Dic11D414yes—
84C2×C4×Dic11D418yescomplemented
85C11⋊#95—28no—
86C11⋊#95—28no—
87C11⋊#95—24no—
88#14700—111nomaximal, Sylow
89C24×C11—24no—
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—24no—
93C24×C11—24no—
94C24×C11—24no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11C22×C414yes—
100C24×C11C2411yescharacteristic
101C2×D4×C11—28no—
102C2×D4×C11—28no—
103C2×D4×C11—28no—
104C2×D4×C11—44no—
105C2×D4×C11—44no—
106C2×D4×C11—44no—
107C2×D4×C11—44no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—24no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11C22×C414yes—
117C22×C4×C11C22×C414yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C2×D414yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11#4114yes—
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—24no—
130C22×Dic11—22no—
131C22×Dic11—24no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11C2×D414yes—
148C22×Dic11C2×D414yes—
149C22×Dic11C2×D412yes—
150C22×Dic11C2×D412yes—
151C22×Dic11C2×D414yes—
152C22×Dic11#4114yes—
153C22×Dic11#4114yes—
154C11×C4⋊C4—28no—
155C11×C22⋊C4—232no—
156C42×C11—28no—
157C22⋊Dic11—416no—
158C22⋊Dic11—48no—
159C22⋊Dic11—48no—
160C4⋊Dic11—48no—
161C4⋊Dic11—44no—
162C4⋊Dic11—44no—
163C4×Dic11—216no—
164C4×Dic11—216no—
165C4×Dic11—28no—
166C4×Dic11—28no—
167C2×#390—111no—
168C2×#390—111no—
169C2×#390D1111yescharacteristic
170C2×#389—111no—
171C2×#388—114no—
172C2×C43—111no—
173#1437—114no—
174C4⋊#95—111no—
175C4⋊#95—111no—
176C23×C11—24no—
177C23×C11—28no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—28no—
181C23×C11—44no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—44no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11—44no—
191C23×C11—44no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—44no—
197C23×C11—44no—
198C23×C11—42no—
199C23×C11C23×C411yescharacteristic
200C23×C11C22×D411yescharacteristic
201C23×C11C22×D411yescharacteristic
202C23×C11C22×D412yes—
203C23×C11C2×#4111yescharacteristic
204C23×C11C2×#4111yescharacteristic
205C23×C11C2×#4111yescharacteristic
206C23×C11C2×#4112yes—
207C23×C11C2×#4111yescharacteristic
208C23×C11C2×#4112yes—
209C23×C11C2×#4112yes—
210D4×C11—416no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—28no—
218C2×C4×C11—24no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
222C2×C4×C11#11714yes—
223C2×C4×C11C4×D418yes—
224C2×C4×C11C4×D414yes—
225C2×C4×C11C4×D414yes—
226C2×C4×C11#12114yes—
227C2×C4×C11#12314yes—
228C2×C4×C11#12414yes—
229C2×C4×C11#12614yes—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—42no—
245C2×Dic11—44no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—44no—
251C2×Dic11—44no—
252C2×Dic11—44no—
253C2×Dic11—42no—
254C2×Dic11#12118yes—
255C2×Dic11#12414yes—
256C2×Dic11#12714yes—
257C23×D4C2×D1111yescharacteristic
258C22×C4⋊C4—111no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C22⋊C4—112no—
263C22×C22⋊C4—114no—
264C22×C22⋊C4—112no—
265C22×C22⋊C4C2×D1114yes—
266C22×C42—111no—
267C22×C42—112no—
268C22×C42—111no—
269C22×C42—112no—
270C22×C42C2×D1111yescharacteristic
271#390—224no—
272#390—224no—
273#390Dic1118yescomplemented
274#389—224no—
275#388—2216no—
276C2×#95—114no—
277C2×#95—114no—
278C2×#95—112no—
279C43—224no—
280C22×C11—44no—
281C22×C11—44no—
282C22×C11—48no—
283C22×C11—48no—
284C22×C11—44no—
285C22×C11—82no—
286C22×C11—84no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—84no—
290C22×C11—82no—
291C22×C11C2×#11711yescharacteristic
292C22×C11C2×C4×D411yescharacteristic
293C22×C11C2×C4×D412yes—
294C22×C11C2×C4×D411yescharacteristic
295C22×C11C4×#4112yes—
296C22×C11C2×#12111yescharacteristic
297C22×C11C2×#12112yes—
298C22×C11C2×#12311yescharacteristic
299C22×C11#52512yes—
300C22×C11C2×#12411yescharacteristic
301C22×C11C2×#12411yescharacteristic
302C22×C11C2×#12611yescharacteristic
303C22×C11#52912yes—
304C22×C11#52912yes—
305C22×C11#52912yes—
306C22×C11#52912yes—
307C22×C11C2×#12711yescharacteristic
308C22×C11#53211yescharacteristic
309C22×C11#53212yes—
310C22×C11#53212yes—
311C22×C11#53212yes—
312C22×C11#53212yes—
313C22×C11#53211yescharacteristic
314C4×C11—28no—
315C4×C11—44no—
316C4×C11#38818yescomplemented
317Dic11—24no—
318Dic11—28no—
319Dic11—24no—
320Dic11—82no—
321Dic11—82no—
322C25C22×D1112yes—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4C2×Dic1114yes—
330C23×C4—111no—
331C23×C4—112no—
332C23×C4—111no—
333C23×C4—112no—
334C23×C4—112no—
335C23×C4C22×D1112yes—
336C23×C4C22×D1112yes—
337C23×C4C22×D1111yescharacteristic
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—228no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4C2×Dic1114yes—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—228no—
352C2×C22⋊C4—228no—
353C2×C22⋊C4—224no—
354C2×C22⋊C4—228no—
355C2×C22⋊C4—224no—
356C2×C22⋊C4—228no—
357C2×C22⋊C4—228no—
358C2×C22⋊C4C2×Dic11116yes—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—114no—
362C2×C42—118no—
363C2×C42—114no—
364C2×C42—224no—
365C2×C42—224no—
366C2×C42—224no—
367C2×C42—224no—
368C2×C42—222no—
369C2×C42—222no—
370C2×C42—222no—
371C2×C42—224no—
372C2×C42—222no—
373C2×C42C2×Dic1114yes—
374#95—228no—
375#95—224no—
376#95—228no—
377C2×C11—84no—
378C2×C11C2×#38811yescharacteristic
379C2×C11#229312yes—
380C2×C11C4×#12112yes—
381C2×C11C4×#12411yescharacteristic
382C2×C11C4×#12711yescharacteristic
383C2×C11#285011yescharacteristic
384C2×C11#285412yes—
385C2×C11#285611yescharacteristic
386C2×C11#285811yescharacteristic
387C2×C11#286012yes—
388C2×C11#286111yescharacteristic
389C24—22no—
390C24—22no—
391C24—24no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—22no—
396C24—22no—
397C24—24no—
398C24—24no—
399C24C22×Dic1114yes—
400C24C23×D1111yescharacteristic
401C2×D4—28no—
402C2×D4—28no—
403C2×D4—28no—
404C2×D4—44no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4—44no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—114no—
417C22×C4—112no—
418C22×C4—114no—
419C22×C4—112no—
420C22×C4—114no—
421C22×C4—114no—
422C22×C4—114no—
423C22×C4—222no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4#433912yes—
444C22×C4#433912yes—
445C22×C4D4×D1114yes—
446C22×C4D4×D1112yes—
447C22×C4D4×D1112yes—
448C22×C4#434114yes—
449C22×C4#434112yes—
450C22×C4#434112yes—
451C22×C4C22×Dic1114yes—
452C22×C4C22×Dic1114yes—
453C22×C4C22×Dic1112yes—
454C4⋊C4—28no—
455C4⋊C4—448no—
456C4⋊C4—444no—
457C4⋊C4—444no—
458C22⋊C4—232no—
459C22⋊C4—448no—
460C22⋊C4—4416no—
461C22⋊C4—448no—
462C42—28no—
463C42—2216no—
464C42—2216no—
465C42—228no—
466C42—228no—
467C11#1470011yescharacteristic, complemented, Sylow
468C23—24no—
469C23—28no—
470C23—24no—
471C23—24no—
472C23—28no—
473C23—42no—
474C23—42no—
475C23—44no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—44no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23—44no—
486C23—44no—
487C23—44no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23C2×#433911yescharacteristic
492C23C2×#433911yescharacteristic
493C23C2×D4×D1111yescharacteristic
494C23C2×D4×D1112yes—
495C23C2×D4×D1111yescharacteristic
496C23C2×#434111yescharacteristic
497C23C2×#434112yes—
498C23C2×#434111yescharacteristic
499C23#41×D1112yes—
500C23#41×D1112yes—
501C23C23×Dic1111yescharacteristic
502D4—416no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—28no—
510C2×C4—24no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—44no—
514C2×C4—114no—
515C2×C4—118no—
516C2×C4—114no—
517C2×C4—222no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—224no—
529C2×C4—222no—
530C2×C4—224no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—444no—
536C2×C4—444no—
537C2×C4—444no—
538C2×C4—444no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4#6693214yes—
542C2×C4#6693614yes—
543C2×C4#6693714yes—
544C2×C4#6693814yes—
545C2×C4#6697914yes—
546C2×C4D4×Dic1118yes—
547C2×C4D4×Dic1114yes—
548C2×C4D4×Dic1114yes—
549C22—48no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—48no—
554C22—82no—
555C22—84no—
556C22—82no—
557C22—82no—
558C22—84no—
559C22—82no—
560C22C2×#6693211yescharacteristic
561C22C2×#6693611yescharacteristic
562C22C2×#6693711yescharacteristic
563C22C2×#6693811yescharacteristic
564C22#1062307912yes—
565C22#1062307912yes—
566C22#1062308812yes—
567C22#1062308812yes—
568C22#1062312712yes—
569C22#1062313112yes—
570C22D11×#12112yes—
571C22#1062313712yes—
572C22#1062319911yescharacteristic
573C22D11×#12411yescharacteristic
574C22#1062321112yes—
575C22D11×#12711yescharacteristic
576C22#1062324711yescharacteristic
577C22#1062324712yes—
578C22C2×#6697911yescharacteristic
579C22C2×D4×Dic1111yescharacteristic
580C22C2×D4×Dic1112yes—
581C22C2×D4×Dic1111yescharacteristic
582C22#41×Dic1112yes—
583C4—28no—
584C4—44no—
585C4—224no—
586C4—228no—
587C4—224no—
588C4—882no—
589C4—882no—
590C4#1062256418yescomplemented
591C2—84no—
592C2C2×#1062256411yescharacteristic
593C2#1307108112yes—
594C2#121×Dic1112yes—
595C2#124×Dic1111yescharacteristic
596C2#127×Dic1111yescharacteristic
597C2#1307691611yescharacteristic
598C2#1307694612yes—
599C2#1307696011yescharacteristic
600C2#1307697011yescharacteristic
601C2#1307698012yes—
602C2#1307698711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14700
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#10622598C2semidirect
4. C2×#10622564C2semidirect
5. C2×C42×Dic11C2semidirect
6. #13066853C2semidirect
7. #13066846C2semidirect
8. #13066845C2semidirect
24. C11×#390C4semidirect
84. C2×C4×Dic11D4semidirect
273. #390Dic11semidirect
316. C4×C11#388semidirect
467. C11#14700semidirect
590. C4#10622564semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225982
C2×#106225642
C2×C42×Dic112
#130668532
#130668462
#130668452
C2×C11×#3902
#1470011