Finite Group Databasebeta

← #14680171

Subgroups — #14680171

Order 2816.

1774 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×#10622552C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622586C211yesmaximal, characteristic, complemented
5C2×#10622545C211yesmaximal, characteristic, complemented
6#13066864C214yesmaximal, complemented
7#13066860C214yesmaximal, complemented
8#13066845C211yesmaximal, characteristic, complemented
9C11×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2214yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2214yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95C2214yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2214yes—
27#10622601—24no—
28#10622601—24no—
29#10622586—24no—
30#10622552C418yescomplemented
31#10622545—24no—
32C24×D11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2311yescharacteristic
39C23×Dic11C2311yescharacteristic
40C23×Dic11C2312yes—
41C22×D44—22no—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44—22no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44C2×C414yes—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11C2×C414yes—
57C2×(C2×D11)⋊C4—28no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—44no—
61C2×(C2×D11)⋊C4—44no—
62C2×(C2×D11)⋊C4—44no—
63C2×(C2×D11)⋊C4—44no—
64C2×(C2×D11)⋊C4—44no—
65C2×(C2×D11)⋊C4—44no—
66C2×(C2×D11)⋊C4C2×C4116yes—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11C2×C414yes—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—44no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11D414yes—
77C2×C4×Dic11D414yes—
78C11×#95—44no—
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—44no—
83#14260—111nomaximal, Sylow
84C24×C11C2411yescharacteristic
85C23×D11—22no—
86C23×D11—22no—
87C23×D11—22no—
88C23×D11—22no—
89C23×D11—22no—
90C23×D11—22no—
91C23×D11—24no—
92C23×D11—24no—
93C23×D11—24no—
94C23×D11—24no—
95C23×D11C22×C414yes—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11C22×C414yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11#4112yes—
117C22×C4×C11#4112yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—24no—
130C22×Dic11—22no—
131C22×Dic11—24no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11C22×C414yes—
139C22×Dic11C2×D414yes—
140C22×Dic11C2×D412yes—
141C22×Dic11C2×D412yes—
142C2×D44—28no—
143C2×D44—28no—
144C2×D44—28no—
145C2×D44—44no—
146C2×D44—44no—
147C2×D44—44no—
148C2×D44—44no—
149C11×C4⋊C4—44no—
150C11×C4⋊C4—44no—
151C42×C11—28no—
152(C2×D11)⋊C4—416no—
153(C2×D11)⋊C4—48no—
154(C2×D11)⋊C4—416no—
155(C2×D11)⋊C4—48no—
156C4⋊Dic11—28no—
157Dic11⋊C4—48no—
158C4×Dic11—28no—
159C4×Dic11—28no—
160C2×#390—111no—
161C2×#390—111no—
162C2×#390—111no—
163C2×#389—111no—
164C2×#376—111no—
165#1440—114no—
166#1439—114no—
167C4⋊#95—111no—
168C4⋊#95D1111yescharacteristic, complemented
169C23×C11C23×C411yescharacteristic
170C23×C11C22×D411yescharacteristic
171C23×C11C22×D411yescharacteristic
172C23×C11C2×#4111yescharacteristic
173C23×C11C2×#4111yescharacteristic
174C23×C11C2×#4111yescharacteristic
175C23×C11C2×#4111yescharacteristic
176C23×C11H(5,𝔽2)12yes—
177C23×C11H(5,𝔽2)12yes—
178C23×C11H(5,𝔽2)12yes—
179C23×C112−1+412yes—
180C22×D11—24no—
181C22×D11—24no—
182C22×D11—24no—
183C22×D11—28no—
184C22×D11—28no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—44no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—44no—
195C22×D11—44no—
196C22×D11—44no—
197C22×D11—44no—
198C22×D11—44no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11—44no—
202C22×D11—44no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—44no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—44no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11#11714yes—
221C2×C4×C11C4×D414yes—
222C2×C4×C11C4×D414yes—
223C2×C4×C11#12114yes—
224C2×C4×C11#12314yes—
225C2×C4×C11#12414yes—
226C2×C4×C11#12614yes—
227C2×Dic11—24no—
228C2×Dic11—28no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—44no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249D44—416no—
250C23×D4—111no—
251C22×C4⋊C4—111no—
252C22×C4⋊C4—112no—
253C22×C4⋊C4C2×D1111yescharacteristic
254C22×C4⋊C4C2×D1111yescharacteristic
255C22×C22⋊C4—114no—
256C22×C22⋊C4—112no—
257C22×C22⋊C4—114no—
258C22×C22⋊C4—112no—
259C22×C42—111no—
260C22×C42—111no—
261C22×C42C2×D1111yescharacteristic
262#390—118no—
263#390—224no—
264#390—224no—
265#389—224no—
266#376—224no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—112no—
270C2×#95—114no—
271C2×#95C2×D1114yes—
272C22×C11C2×#11711yescharacteristic
273C22×C11C2×C4×D411yescharacteristic
274C22×C11C2×C4×D411yescharacteristic
275C22×C11#51812yes—
276C22×C11#52012yes—
277C22×C11C2×#12111yescharacteristic
278C22×C11C2×#12311yescharacteristic
279C22×C11C2×#12411yescharacteristic
280C22×C11C2×#12611yescharacteristic
281C22×C11#53511yescharacteristic
282C22×C11#53512yes—
283C22×C11#53511yescharacteristic
284C22×C11#53511yescharacteristic
285C22×C11#53611yescharacteristic
286C22×C11#53712yes—
287C22×C11#54012yes—
288C22×C11#54012yes—
289C22×C11#54012yes—
290C22×C11#54012yes—
291C22×C11#54212yes—
292C22×C11#54212yes—
293C22×C11#54212yes—
294C22×C11#54212yes—
295C2×D11—48no—
296C2×D11—48no—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11—44no—
300C2×D11—82no—
301C2×D11—82no—
302C2×D11—84no—
303C2×D11—82no—
304C2×D11—82no—
305C2×D11—84no—
306C4×C11—44no—
307C4×C11—82no—
308C4×C11—82no—
309C4×C11#38818yes—
310Dic11—44no—
311Dic11—42no—
312Dic11—42no—
313Dic11—44no—
314C25—112no—
315C22×D4—114no—
316C22×D4—222no—
317C22×D4—222no—
318C22×D4—222no—
319C22×D4—222no—
320C22×D4—222no—
321C22×D4—222no—
322C23×C4—112no—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—112no—
326C23×C4C22×D1112yes—
327C23×C4C22×D1112yes—
328C23×C4C22×D1112yes—
329C23×C4C22×D1111yescharacteristic
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—114no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—224no—
340C2×C4⋊C4—444no—
341C2×C22⋊C4—1116no—
342C2×C22⋊C4—228no—
343C2×C22⋊C4—224no—
344C2×C22⋊C4—224no—
345C2×C22⋊C4—444no—
346C2×C22⋊C4—444no—
347C2×C22⋊C4—444no—
348C2×C22⋊C4—444no—
349C2×C22⋊C4—444no—
350C2×C22⋊C4—444no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—114no—
354C2×C42—114no—
355C2×C42—222no—
356C2×C42—222no—
357C2×C42—222no—
358C2×C42—222no—
359C2×C42C4×D1114yes—
360#95—44no—
361#95—224no—
362#95—224no—
363#95—224no—
364#95—444no—
365C2×C11C2×#38811yescharacteristic
366C2×C11#231912yes—
367C2×C11#232412yes—
368C2×C11#232611yescharacteristic
369C2×C11#232811yescharacteristic
370C2×C11#261911yescharacteristic
371C2×C11#262011yescharacteristic
372C2×C11#262412yes—
373C2×C11#264011yescharacteristic
374C2×C11#264111yescharacteristic
375C2×C11#264412yes—
376D11—84no—
377C24—114no—
378C24—222no—
379C24—222no—
380C24—222no—
381C24—222no—
382C24—222no—
383C24—224no—
384C24—222no—
385C24—224no—
386C24—224no—
387C24—224no—
388C24C23×D1111yescharacteristic
389C2×D4—228no—
390C2×D4—228no—
391C2×D4—228no—
392C2×D4—444no—
393C2×D4—444no—
394C2×D4—444no—
395C2×D4—444no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—114no—
413C22×C4—112no—
414C22×C4—114no—
415C22×C4—112no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—224no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—224no—
433C22×C4—222no—
434C22×C4C2×C4×D1114yes—
435C22×C4C2×C4×D1112yes—
436C22×C4#433912yes—
437C22×C4#433912yes—
438C22×C4D4×D1112yes—
439C22×C4D4×D1112yes—
440C22×C4#434112yes—
441C22×C4#434312yes—
442C4⋊C4—44no—
443C4⋊C4—44no—
444C4⋊C4—228no—
445C4⋊C4—448no—
446C22⋊C4—4416no—
447C22⋊C4—448no—
448C22⋊C4—4416no—
449C22⋊C4—448no—
450C42—28no—
451C42—228no—
452C42—228no—
453C11#1426011yescharacteristic, complemented, Sylow
454C23—224no—
455C23—224no—
456C23—224no—
457C23—228no—
458C23—228no—
459C23—442no—
460C23—442no—
461C23—444no—
462C23—442no—
463C23—442no—
464C23—442no—
465C23—442no—
466C23—444no—
467C23—444no—
468C23—444no—
469C23—444no—
470C23—444no—
471C23—444no—
472C23—444no—
473C23—444no—
474C23—442no—
475C23—442no—
476C23—444no—
477C23C22×C4×D1111yescharacteristic
478C23C2×#433911yescharacteristic
479C23C2×#433911yescharacteristic
480C23C2×D4×D1111yescharacteristic
481C23C2×D4×D1111yescharacteristic
482C23C2×#434111yescharacteristic
483C23#6703712yes—
484C23C2×#434311yescharacteristic
485C23#6704012yes—
486C23#6704212yes—
487C23#6704212yes—
488D4—4416no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—228no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—444no—
528C2×C4#6692514yes—
529C2×C4(C22⋊D11)⋊C414yes—
530C2×C4#6693714yes—
531C2×C4#6693814yes—
532C2×C4#6694614yes—
533C2×C4#6694714yes—
534C2×C4#6695114yes—
535C22—448no—
536C22—444no—
537C22—448no—
538C22—444no—
539C22—444no—
540C22—882no—
541C22—882no—
542C22—884no—
543C22—882no—
544C22—882no—
545C22—884no—
546C22C2×#6692511yescharacteristic
547C22C2×(C22⋊D11)⋊C411yescharacteristic
548C22C2×#6693711yescharacteristic
549C22C2×#6693811yescharacteristic
550C22C2×#6694611yescharacteristic
551C22#1062303512yes—
552C22C2×#6694711yescharacteristic
553C22C2×#6695111yescharacteristic
554C22#1062305212yes—
555C22#1062309312yes—
556C22#1062309312yes—
557C22#1062311312yes—
558C22#1062311312yes—
559C22#1062313812yes—
560C22#1062315012yes—
561C22#1062316012yes—
562C22#1062317412yes—
563C22#1062320511yescharacteristic
564C22#1062320511yescharacteristic
565C22#1062322912yes—
566C22#1062324611yescharacteristic
567C22#1062325511yescharacteristic
568C22#1062326412yes—
569C4—44no—
570C4—82no—
571C4—82no—
572C4—442no—
573C4—442no—
574C4—444no—
575C4—444no—
576C4#1062228218yes—
577C2—884no—
578C2C2×#1062228211yescharacteristic
579C2#1307125412yes—
580C2#1307130512yes—
581C2#1307132411yescharacteristic
582C2#1307133911yescharacteristic
583C2#1307437111yescharacteristic
584C2#1307438011yescharacteristic
585C2#1307441012yes—
586C2#1307455511yescharacteristic
587C2#1307456011yescharacteristic
588C2#1307457912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#14260
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#10622586C2semidirect
5. C2×#10622545C2semidirect
6. #13066864C2semidirect
7. #13066860C2semidirect
8. #13066845C2semidirect
9. C11×C4⋊#95C2semidirect
30. #10622552C4semidirect
168. C4⋊#95D11semidirect
453. C11#14260semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106226012
C2×#106225862
C2×#106225452
#130668642
#130668602
#130668452
C11×C4⋊#952
#1426011