Finite Group Databasebeta

← #14756864

Subgroups — #14756864

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622627C211yesmaximal, characteristic
2#13071260C211yesmaximal, characteristic, complemented
3#13069243C211yesmaximal, characteristic, complemented
4#13069236C211yesmaximal, characteristic, complemented
5#13069201C211yesmaximal, characteristic, complemented
6#13069194C211yesmaximal, characteristic, complemented
7#13068964C211yesmaximal, characteristic
8#13068964C211yesmaximal, characteristic
9#13068877C211yesmaximal, characteristic, complemented
10#13068863C211yesmaximal, characteristic, complemented
11#13068514C211yesmaximal, characteristic, complemented
12C4×#66873C211yesmaximal, characteristic, complemented
13C4×#66896C211yesmaximal, characteristic, complemented
14#13068368C211yesmaximal, characteristic, complemented
15C11×#2275C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C4×C11×C22⋊C4—21no—
25C4×C11×C22⋊C4—21no—
26C4×C11×C22⋊C4—21no—
27C11×#376C2211yescharacteristic
28C2×C11×#95—21no—
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622627C418yescomplemented
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622552C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46#10622282—21no—
47#10622282—21no—
48#10622280—21no—
49#10622277—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11C2×C414yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×#4323—22no—
85C2×#4323—22no—
86C2×#4323C2×C414yes—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C4×D44—22no—
103C4×D44C2×C414yescomplemented
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111#66896—22no—
112#66896—22no—
113#66896C2×C414yes—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66873—22no—
118#66873—22no—
119#66873C2×C414yescomplemented
120#66872—22no—
121#66872C2×C414yescomplemented
122#66871—22no—
123#66867C2×C414yescomplemented
124C4×C11⋊C8—22no—
125#21126—111nomaximal, Sylow
126C24×C11—21no—
127C23×D11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11C22×C412yes—
132C2×D4×C11#4112yes—
133C2×D4×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—81no—
141C22×C4×C11—81no—
142C22×C4×C11—81no—
143C22×C4×C11—81no—
144C22×C4×C11—81no—
145C22×C4×C11—81no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44C22×C412yes—
162C2×C4×D11—24no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C22×C412yes—
169C11×C4⋊C4#4112yes—
170C11×C4⋊C4#4112yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—81no—
179C42×C11—81no—
180C42×C11—81no—
181C42×C11C22×C412yes—
182C42×C11#4112yes—
183#4323—28no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—81no—
186(C2×D11)⋊C4—81no—
187(C2×D11)⋊C4—81no—
188(C2×D11)⋊C4—81no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C22×C412yes—
195Dic11⋊C4—81no—
196Dic11⋊C4—81no—
197C4×Dic11—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C22×C412yes—
209C2×C11⋊C8C22×C412yes—
210C2×#442—111no—
211#2319—111no—
212#2275D1111yescharacteristic, complemented
213#1926—111no—
214#1925—111no—
215#1920—111no—
216#1919—111no—
217#1879—111no—
218#1879—111no—
219#1864—111no—
220#1862—111no—
221#1776—111no—
222C4×#102—111no—
223C4×#102—111no—
224#1746—111no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—22no—
243D4×C11#11714yes—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—84no—
270C2×C4×C11—84no—
271C2×C4×C11—84no—
272C2×C4×C11C4×D412yes—
273C2×C4×C11C4×D412yes—
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×Dic11—22no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289D44—22no—
290D44—22no—
291D44—41no—
292D44—41no—
293C4×D11—84no—
294C11⋊C8—22no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C22×D8—111no—
299C2×C4×D4—111no—
300C2×C4×D4C2×D1111yescharacteristic
301C2×C4×D4C2×D1111yescharacteristic
302C2×C4×D4C2×D1111yescharacteristic
303#442—118no—
304C2×#107—111no—
305C2×#106—111no—
306C2×#106—111no—
307C2×#102—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×#102—111no—
313C2×#97—111no—
314C2×C4×C8—111no—
315#390—111no—
316#390—111no—
317#389—111no—
318#389—111no—
319#388—221no—
320#388—221no—
321#381—221no—
322#380—221no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4C2×D1111yescharacteristic
325C4×C4⋊C4C2×D1111yescharacteristic
326C4×C4⋊C4C2×D1111yescharacteristic
327C4×C22⋊C4—21no—
328C4×C22⋊C4—21no—
329C4×C22⋊C4—21no—
330#376C2×D1111yescharacteristic
331C2×#95—21no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342C22×C11—24no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11C2×C4×D411yescharacteristic
350C22×C11#52511yescharacteristic
351C22×C11#52511yescharacteristic
352C22×C11#57611yescharacteristic
353C22×C11#57611yescharacteristic
354C22×C11#57711yescharacteristic
355C22×C11#57711yescharacteristic
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C4×C11—22no—
364C4×C11—22no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—42no—
370C4×C11—41no—
371C4×C11—42no—
372C4×C11C2×#11711yescharacteristic
373C4×C11C4×#4111yescharacteristic
374C4×C11#52911yescharacteristic
375C4×C11#52911yescharacteristic
376Dic11—42no—
377Dic11—81no—
378Dic11—81no—
379C22×D4—111no—
380C22×D4C22×D1111yescharacteristic
381C23×C4—21no—
382C23×C4—21no—
383C23×C4—21no—
384C23×C4—221no—
385C2×D8—114no—
386C2×D8—222no—
387C2×D8—222no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—114no—
398C4×D4—222no—
399C4×D4C4×D1114yes—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422C2×C42C22×D1111yescharacteristic
423#107—222no—
424#106—114no—
425#106—222no—
426#102—114no—
427#102—114no—
428#102—222no—
429#102—222no—
430#102—222no—
431#102—222no—
432#97—114no—
433C4×C8—222no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95C22⋊D1111yescharacteristic
441#95C22⋊D1111yescharacteristic
442#95C22⋊D1111yescharacteristic
443#95C22⋊D1111yescharacteristic
444C2×C11—44no—
445C2×C11#229011yescharacteristic
446C2×C11#294611yescharacteristic
447C2×C11#294611yescharacteristic
448C2×C11#311811yescharacteristic
449C2×C11#311911yescharacteristic
450C2×C11#312211yescharacteristic
451C2×C11#312511yescharacteristic
452D11—82no—
453C24—21no—
454C24—221no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—112no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4C2×C4×D1112yes—
465C2×D4#433912yes—
466C2×D4#433912yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4—81no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4—221no—
480C22×C4—224no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492D8—228no—
493C2×C8—112no—
494C2×C8—112no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—112no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—881no—
515C4⋊C4—881no—
516C4⋊C4C2×C4×D1112yes—
517C4⋊C4#433912yes—
518C4⋊C4#433912yes—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—224no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C22⋊C4—881no—
526C22⋊C4—881no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—81no—
532C42—81no—
533C42—81no—
534C42—881no—
535C42C2×C4×D1112yes—
536C42#433912yes—
537C11#2112611yescharacteristic, complemented, Sylow
538C23—22no—
539C23—22no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—222no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23C22×C22⋊D1111yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—222no—
557D4—222no—
558D4—441no—
559D4—441no—
560D4#6692514yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—84no—
587C2×C4—84no—
588C2×C4—84no—
589C2×C4—222no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—884no—
599C2×C4C4×C22⋊D1112yes—
600C2×C4C4×C22⋊D1112yes—
601C2×C4C22×C4×D1111yescharacteristic
602C2×C4C2×#433911yescharacteristic
603C2×C4C2×#433911yescharacteristic
604C2×C4C2×#433911yescharacteristic
605C2×C4C2×#433911yescharacteristic
606C2×C4C2×#433911yescharacteristic
607C8—222no—
608C8—222no—
609C8—441no—
610C8—441no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—881no—
622C22—881no—
623C22—881no—
624C22—881no—
625C22C2×C4×C22⋊D1111yescharacteristic
626C22#1062332211yescharacteristic
627C22#1062332211yescharacteristic
628C22#1062336611yescharacteristic
629C22#1062336611yescharacteristic
630C22#1062336711yescharacteristic
631C22#1062336811yescharacteristic
632C4—22no—
633C4—22no—
634C4—41no—
635C4—42no—
636C4—41no—
637C4—41no—
638C4—42no—
639C4—41no—
640C4—42no—
641C4—442no—
642C4—881no—
643C4—881no—
644C4C2×#6692511yescharacteristic
645C4C4×#433911yescharacteristic
646C4#1062301011yescharacteristic
647C4#1062301011yescharacteristic
648C2—44no—
649C2—882no—
650C2#1307105911yescharacteristic
651C2#1307744411yescharacteristic
652C2#1307744811yescharacteristic
653C2#1307880011yescharacteristic
654C2#1307881511yescharacteristic
655C2#1307885911yescharacteristic
656C2#1307889311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2275C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#2275D11
hypocenterC11#21126
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2275

Complements

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

NH ≅ G/Ntype
2. #13071260C2semidirect
3. #13069243C2semidirect
4. #13069236C2semidirect
5. #13069201C2semidirect
6. #13069194C2semidirect
9. #13068877C2semidirect
10. #13068863C2semidirect
11. #13068514C2semidirect
12. C4×#66873C2semidirect
13. C4×#66896C2semidirect
14. #13068368C2semidirect
15. C11×#2275C2semidirect
32. #10622627C4semidirect
103. C4×D44C2×C4semidirect
119. #66873C2×C4semidirect
121. #66872C2×C4semidirect
123. #66867C2×C4semidirect
212. #2275D11semidirect
537. C11#21126semidirect

Maximal subgroups

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

subgroupindex
C2×#106226272
#130712602
#130692432
#130692362
#130692012
#130691942
#130689642
#130688772
#130688632
#130685142
C4×#668732
C4×#668962
#130683682
C11×#22752
#2112611