Finite Group Databasebeta

← #14676962

Subgroups — #14676962

Order 2816.

1838 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622834C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622549C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
5#13066865C214yesmaximal, complemented
6#13066853C214yesmaximal, complemented
7#13066845C211yesmaximal, characteristic, complemented
8C4×C11⋊#95C211yesmaximal, 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×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C11×#390C418yescomplemented
23#10622834—24no—
24#10622834—24no—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30C4⋊C4×Dic11—24no—
31#10622549—24no—
32C25×C11C2312yes—
33C22×D4×C11—22no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11C2×C414yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4C2×C414yes—
51C2×C11×C22⋊C4—44no—
52C2×C11×C22⋊C4—44no—
53C2×C11×C22⋊C4C2×C4116yes—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11C2×C414yes—
57C2×C22⋊Dic11—28no—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—28no—
61C2×C22⋊Dic11—28no—
62C2×C22⋊Dic11—44no—
63C2×C22⋊Dic11—44no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11D414yes—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—44no—
77C2×C4×Dic11D414yes—
78C11⋊#95—28no—
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—44no—
83#14002—111nomaximal, Sylow
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—24no—
87C24×C11—24no—
88C24×C11—22no—
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—24no—
93C24×C11—24no—
94C24×C11C22×C414yes—
95C24×C11C2411yescharacteristic
96C2×D4×C11—28no—
97C2×D4×C11—28no—
98C2×D4×C11—28no—
99C2×D4×C11—44no—
100C2×D4×C11—44no—
101C2×D4×C11—44no—
102C2×D4×C11—44no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11C22×C414yes—
114C22×C4×C11C22×C414yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—24no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11C2×D412yes—
145C22×Dic11C2×D414yes—
146C22×Dic11C2×D412yes—
147C22×Dic11#4114yes—
148C22×Dic11#4114yes—
149C11×C4⋊C4—28no—
150C11×C22⋊C4—416no—
151C42×C11—28no—
152C22⋊Dic11—416no—
153C22⋊Dic11—48no—
154C22⋊Dic11—48no—
155C4⋊Dic11—28no—
156C4⋊Dic11—44no—
157C4×Dic11—28no—
158C4×Dic11—48no—
159C4×Dic11—44no—
160C2×#390—111no—
161C2×#390—111no—
162C2×#390D1111yescharacteristic
163C2×#382—111no—
164C2×C4×C4⋊C4—111no—
165#1440—114no—
166#1437—114no—
167C4⋊#95—111no—
168C4×#95—111no—
169C23×C11—24no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—28no—
173C23×C11—28no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—44no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—44no—
184C23×C11—44no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11—44no—
191C23×C11—44no—
192C23×C11C23×C411yescharacteristic
193C23×C11C22×D411yescharacteristic
194C23×C11C22×D411yescharacteristic
195C23×C11C2×#4111yescharacteristic
196C23×C11C2×#4111yescharacteristic
197C23×C11C2×#4111yescharacteristic
198C23×C11C2×#4111yescharacteristic
199C23×C11C2×#4112yes—
200C23×C11C2×#4112yes—
201C23×C11H(5,𝔽2)12yes—
202C23×C11H(5,𝔽2)12yes—
203D4×C11—416no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—28no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—44no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11#11714yes—
217C2×C4×C11C4×D414yes—
218C2×C4×C11C4×D414yes—
219C2×C4×C11#12114yes—
220C2×C4×C11#12314yes—
221C2×C4×C11#12414yes—
222C2×C4×C11#12614yes—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—24no—
233C2×Dic11—28no—
234C2×Dic11—24no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—44no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—44no—
248C2×Dic11—44no—
249C2×Dic11#12414yes—
250C23×D4C2×D1111yescharacteristic
251C22×C4⋊C4—111no—
252C22×C4⋊C4—111no—
253C22×C4⋊C4C2×D1111yescharacteristic
254C22×C22⋊C4—112no—
255C22×C22⋊C4—114no—
256C22×C22⋊C4—112no—
257C22×C22⋊C4C2×D1114yes—
258C22×C42—111no—
259C22×C42—111no—
260C22×C42—112no—
261C22×C42C2×D1111yescharacteristic
262#390—224no—
263#390—224no—
264#390Dic1118yescomplemented
265#382—224no—
266C4×C4⋊C4—224no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—114no—
270C2×#95—112no—
271C2×#95—114no—
272C22×C11—44no—
273C22×C11—48no—
274C22×C11—48no—
275C22×C11—44no—
276C22×C11—44no—
277C22×C11—84no—
278C22×C11—82no—
279C22×C11—82no—
280C22×C11—84no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11C2×#11711yescharacteristic
284C22×C11C2×C4×D411yescharacteristic
285C22×C11C2×C4×D411yescharacteristic
286C22×C11C4×#4112yes—
287C22×C11#51812yes—
288C22×C11C2×#12111yescharacteristic
289C22×C11C2×#12311yescharacteristic
290C22×C11C2×#12411yescharacteristic
291C22×C11C2×#12411yescharacteristic
292C22×C11C2×#12611yescharacteristic
293C22×C11#52912yes—
294C22×C11#53211yescharacteristic
295C22×C11#53511yescharacteristic
296C22×C11#53511yescharacteristic
297C22×C11#54012yes—
298C22×C11#54612yes—
299C22×C11#55012yes—
300C22×C11#55312yes—
301C22×C11#55312yes—
302C22×C11#55312yes—
303C22×C11#55512yes—
304C22×C11#55912yes—
305C22×C11#55912yes—
306C4×C11—44no—
307C4×C11—44no—
308C4×C11#38818yes—
309Dic11—24no—
310Dic11—44no—
311Dic11—42no—
312Dic11—44no—
313Dic11—82no—
314C25C22×D1112yes—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4C2×Dic1114yes—
322C23×C4—111no—
323C23×C4—112no—
324C23×C4—111no—
325C23×C4—112no—
326C23×C4—112no—
327C23×C4C22×D1112yes—
328C23×C4C22×D1112yes—
329C23×C4C22×D1111yescharacteristic
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—114no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4C2×Dic1114yes—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—224no—
342C2×C22⋊C4—228no—
343C2×C22⋊C4—224no—
344C2×C22⋊C4—228no—
345C2×C22⋊C4—228no—
346C2×C22⋊C4—444no—
347C2×C22⋊C4—444no—
348C2×C22⋊C4C2×Dic11116yes—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—114no—
352C2×C42—222no—
353C2×C42—222no—
354C2×C42—224no—
355C2×C42—222no—
356C2×C42—222no—
357C2×C42—222no—
358C2×C42—444no—
359C2×C42C2×Dic1114yes—
360#95—224no—
361#95—224no—
362#95—224no—
363#95—228no—
364#95—444no—
365C2×C11—84no—
366C2×C11C2×#38811yescharacteristic
367C2×C11C4×#12411yescharacteristic
368C2×C11#232811yescharacteristic
369C2×C11#235712yes—
370C2×C11#236312yes—
371C2×C11#249012yes—
372C2×C11#250011yescharacteristic
373C2×C11#250411yescharacteristic
374C2×C11#251312yes—
375C2×C11#254411yescharacteristic
376C2×C11#254811yescharacteristic
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—24no—
384C24—24no—
385C24—24no—
386C24—24no—
387C24C22×Dic1114yes—
388C24C23×D1111yescharacteristic
389C2×D4—28no—
390C2×D4—28no—
391C2×D4—28no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—44no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—112no—
407C22×C4—114no—
408C22×C4—112no—
409C22×C4—114no—
410C22×C4—114no—
411C22×C4—221no—
412C22×C4—221no—
413C22×C4—222no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—224no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4#433912yes—
434C22×C4#433912yes—
435C22×C4D4×D1112yes—
436C22×C4D4×D1112yes—
437C22×C4#434112yes—
438C22×C4#434112yes—
439C22×C4C22×Dic1114yes—
440C22×C4C22×Dic1114yes—
441C22×C4C22×Dic1112yes—
442C4⋊C4—28no—
443C4⋊C4—228no—
444C4⋊C4—444no—
445C22⋊C4—416no—
446C22⋊C4—448no—
447C22⋊C4—4416no—
448C22⋊C4—448no—
449C42—28no—
450C42—228no—
451C42—448no—
452C42—444no—
453C11#1400211yescharacteristic, complemented, Sylow
454C23—24no—
455C23—24no—
456C23—24no—
457C23—28no—
458C23—28no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23—44no—
473C23—44no—
474C23—42no—
475C23—42no—
476C23—44no—
477C23C2×#433911yescharacteristic
478C23C2×#433911yescharacteristic
479C23C2×D4×D1111yescharacteristic
480C23C2×D4×D1111yescharacteristic
481C23C2×#434111yescharacteristic
482C23C2×#434111yescharacteristic
483C23#6703712yes—
484C23#6703712yes—
485C23#41×D1112yes—
486C23#41×D1112yes—
487C23C23×Dic1111yescharacteristic
488D4—416no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—28no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—114no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—228no—
512C2×C4—222no—
513C2×C4—224no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—444no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—444no—
526C2×C4—444no—
527C2×C4—442no—
528C2×C4#6693214yes—
529C2×C4#6693614yes—
530C2×C4#6693714yes—
531C2×C4#6693814yes—
532C2×C4#6697914yes—
533C2×C4D4×Dic1114yes—
534C2×C4D4×Dic1114yes—
535C22—48no—
536C22—44no—
537C22—44no—
538C22—48no—
539C22—44no—
540C22—84no—
541C22—84no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22—82no—
546C22C2×#6693211yescharacteristic
547C22C2×#6693611yescharacteristic
548C22C2×#6693711yescharacteristic
549C22C2×#6693811yescharacteristic
550C22#1062308912yes—
551C22#1062308912yes—
552C22#1062309012yes—
553C22#1062309012yes—
554C22#1062313012yes—
555C22#1062314312yes—
556C22#1062314512yes—
557C22#1062314712yes—
558C22#1062319911yescharacteristic
559C22D11×#12411yescharacteristic
560C22#1062321112yes—
561C22#1062324611yescharacteristic
562C22#1062324611yescharacteristic
563C22#1062325012yes—
564C22C2×#6697911yescharacteristic
565C22C2×D4×Dic1111yescharacteristic
566C22C2×D4×Dic1111yescharacteristic
567C22#1062332912yes—
568C22#41×Dic1112yes—
569C4—44no—
570C4—44no—
571C4—224no—
572C4—444no—
573C4—442no—
574C4—444no—
575C4—882no—
576C4#1062256418yes—
577C2—84no—
578C2C2×#1062256411yescharacteristic
579C2#124×Dic1111yescharacteristic
580C2#1307134211yescharacteristic
581C2#1307158912yes—
582C2#1307165812yes—
583C2#1307296612yes—
584C2#1307307711yescharacteristic
585C2#1307310711yescharacteristic
586C2#1307321512yes—
587C2#1307359011yescharacteristic
588C2#1307362011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14002
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#10622549C2semidirect
4. C2×C4⋊C4×Dic11C2semidirect
5. #13066865C2semidirect
6. #13066853C2semidirect
7. #13066845C2semidirect
8. C4×C11⋊#95C2semidirect
22. C11×#390C4semidirect
264. #390Dic11semidirect
453. C11#14002semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225492
C2×C4⋊C4×Dic112
#130668652
#130668532
#130668452
C4×C11⋊#952
C2×C11×#3902
#1400211