Finite Group Databasebeta

← #14762003

Subgroups — #14762003

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66951C211yesmaximal, characteristic
2#13069230C211yesmaximal, characteristic
3#13069227C211yesmaximal, characteristic
4#13069221C211yesmaximal, characteristic
5#13069182C211yesmaximal, characteristic, complemented
6#13069177C211yesmaximal, characteristic, complemented
7#13069172C211yesmaximal, characteristic, complemented
8#13068758C211yesmaximal, characteristic, complemented
9#13068490C211yesmaximal, characteristic, complemented
10#13068488C211yesmaximal, characteristic, complemented
11#13068393C211yesmaximal, characteristic
12#13068393C211yesmaximal, characteristic
13C8×(C2×D11)⋊C4C211yesmaximal, characteristic
14#97×Dic11C211yesmaximal, characteristic, complemented
15C11×#1770C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×#66951C411yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#97C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622603C411yescharacteristic
33#10622594C411yescharacteristic
34#10622591C411yescharacteristic
35C4×(C2×D11)⋊C4C2211yescharacteristic
36C4×(C2×D11)⋊C4C2211yescharacteristic
37C4×(C2×D11)⋊C4C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×Dic11⋊C4C2211yescharacteristic
40C42×Dic11C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43#10622283C411yescharacteristic
44#10622282C411yescharacteristic
45#10622267C411yescharacteristic
46#10622264C411yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4C2×C411yescharacteristic
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×(C2×D11)⋊C4C2×C411yescharacteristic
70C2×(C2×D11)⋊C4C2×C411yescharacteristic
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×C4⋊Dic11C2×C411yescharacteristic
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×C4×Dic11C2×C411yescharacteristic
80C2×C4×Dic11C2×C411yescharacteristic
81C2×C4×Dic11C2×C411yescharacteristic
82C2×C4×Dic11C2×C411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C2×C8×D11—22no—
91C2×C8×D11—22no—
92C2×C8×D11—22no—
93#66951—24no—
94C11×C4⋊C8—22no—
95C11×#97—22no—
96C11×#97—22no—
97C4×C8×C11—22no—
98C11×#95C2×C411yescharacteristic
99C11×#95C2×C411yescharacteristic
100C11⋊#95C2×C411yescharacteristic
101C11⋊#95C2×C411yescharacteristic
102C11⋊#95C2×C411yescharacteristic
103C11⋊#95C2×C411yescharacteristic
104C11⋊#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110(C2×D11)⋊C8—22no—
111(C2×D11)⋊C8—22no—
112(C2×D11)⋊C8—22no—
113#66879—22no—
114#66879—22no—
115#66879—22no—
116Dic11⋊C8—22no—
117C8×Dic11—22no—
118C8×Dic11—22no—
119C4⋊(C11⋊C8)—22no—
120#66867—22no—
121#21665—111nomaximal, Sylow
122C23×D11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11C22×C411yescharacteristic
131C22×Dic11C22×C411yescharacteristic
132C22×Dic11C22×C411yescharacteristic
133C22×Dic11C22×C411yescharacteristic
134C22×Dic11C22×C411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11#4112yes—
152C2×C8×C11#4112yes—
153C2×C8×C11#4112yes—
154C2×C8×C11#4112yes—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—41no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163(C2×D11)⋊C4—22no—
164(C2×D11)⋊C4—22no—
165(C2×D11)⋊C4—22no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4M1614yes—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171Dic11⋊C4—22no—
172Dic11⋊C4—41no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—41no—
182C4×Dic11—41no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8#4112yes—
194C2×C11⋊C8#4112yes—
195C8×D11—44no—
196C4×#126—111no—
197#1924—111no—
198#1924—111no—
199#1923—111no—
200#1917—111no—
201#1917—111no—
202#1916—111no—
203#1839—111no—
204#1771—111no—
205#1771—111no—
206#1770D1111yescharacteristic, complemented
207#1752—111no—
208#1752—111no—
209C8×C22⋊C4—111no—
210C4×#97—111no—
211C23×C11C23×C411yescharacteristic
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—21no—
218C22×D11C2×M1612yes—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11C2×M1612yes—
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11C2×M1612yes—
263C2×Dic11#13112yes—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C8×C11—22no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11#12614yescomplemented
272C11⋊C8—22no—
273C11⋊C8—22no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C23×C8—111no—
277C2×#126—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×C22⋊C8—111no—
282C2×C22⋊C8—111no—
283C2×C22⋊C8—111no—
284C2×#97—111no—
285C2×#97—111no—
286C2×#97—111no—
287C2×#97—111no—
288C2×#97C2×D1111yescharacteristic
289C2×#97C2×D1111yescharacteristic
290C2×C4×C8—111no—
291C2×C4×C8—111no—
292C2×C4×C8C2×D1111yescharacteristic
293#388—111no—
294#388—111no—
295#388—111no—
296#387—111no—
297#387—111no—
298#387—111no—
299#383—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4C2×D1111yescharacteristic
303C4×C22⋊C4—111no—
304C4×C22⋊C4—111no—
305C4×C22⋊C4—111no—
306C43—111no—
307#336—111no—
308#336—111no—
309#336—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313#336—111no—
314#336—111no—
315#336—111no—
316#336—111no—
317#336C2×D1111yescharacteristic
318#336C2×D1111yescharacteristic
319C22×C11C4×#4111yescharacteristic
320C22×C11C4×#4111yescharacteristic
321C22×C11C4×#4111yescharacteristic
322C22×C11C22×M1611yescharacteristic
323C22×C11C2×#13111yescharacteristic
324C22×C11#56811yescharacteristic
325C22×C11#56811yescharacteristic
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11—41no—
330C2×D11—41no—
331C2×D11—41no—
332C2×D11—41no—
333C4×C11—22no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11C2×#12611yescharacteristic
340C4×C11#52911yescharacteristic
341C4×C11#52911yescharacteristic
342C4×C11#52911yescharacteristic
343Dic11—22no—
344Dic11—22no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C23×C4—111no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—222no—
356C22×C8—222no—
357C22×C8—222no—
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362#126—224no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4C4×D1111yescharacteristic
368C2×C4⋊C4C4×D1111yescharacteristic
369C2×C22⋊C4—111no—
370C2×C22⋊C4—111no—
371C2×C22⋊C4—111no—
372C2×C22⋊C4—111no—
373C2×C22⋊C4—111no—
374C2×C22⋊C4—111no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42C22×D1111yescharacteristic
383C2×C42C22×D1111yescharacteristic
384C2×C42C22×D1111yescharacteristic
385C4⋊C8—22no—
386C4⋊C8—222no—
387C4⋊C8—222no—
388C22⋊C8—222no—
389C22⋊C8—222no—
390C22⋊C8—222no—
391#97—22no—
392#97—22no—
393#97—222no—
394#97—222no—
395#97—222no—
396#97—222no—
397C4×C8—22no—
398C4×C8—222no—
399C4×C8—222no—
400#95—111no—
401#95—111no—
402#95—111no—
403#95—111no—
404#95—111no—
405#95—111no—
406#95—111no—
407#95—111no—
408#95—111no—
409#95—111no—
410#95C4×D1111yescharacteristic
411#95C4×D1111yescharacteristic
412C2×C11C4×#12611yescharacteristic
413C2×C11#296511yescharacteristic
414C2×C11#296711yescharacteristic
415C2×C11#296811yescharacteristic
416C2×C11#296911yescharacteristic
417C2×C11#297011yescharacteristic
418C2×C11#297011yescharacteristic
419D11—42no—
420C24—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4C2×C4×D1111yescharacteristic
435C22×C4C2×C4×D1111yescharacteristic
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4C2×C4×D1111yescharacteristic
440C22×C4C23×D1111yescharacteristic
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—112no—
450C2×C8—112no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—444no—
462C2×C8#433912yes—
463C2×C8#433912yes—
464C2×C8#434112yes—
465C2×C8#434312yes—
466C4⋊C4—22no—
467C4⋊C4—41no—
468C4⋊C4—222no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—441no—
472C22⋊C4—114no—
473C22⋊C4—222no—
474C22⋊C4—222no—
475C22⋊C4—222no—
476C22⋊C4—441no—
477C22⋊C4—441no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—222no—
485C42—222no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42—221no—
491C42—221no—
492C42—441no—
493C42—441no—
494C11#2166511yescharacteristic, complemented, Sylow
495C23—112no—
496C23—221no—
497C23—221no—
498C23—221no—
499C23—221no—
500C23—221no—
501C23—221no—
502C23C22×C4×D1111yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—112no—
521C2×C4—112no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4M16×D1112yes—
546C2×C4C2×#433911yescharacteristic
547C2×C4C2×#433911yescharacteristic
548C2×C4C2×#434111yescharacteristic
549C2×C4C2×#434311yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C8—22no—
553C8—41no—
554C8—41no—
555C8—222no—
556C8—222no—
557C8—441no—
558C8—441no—
559C8#6695114yescomplemented
560C22—222no—
561C22—222no—
562C22—222no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22—441no—
567C22C4×#433911yescharacteristic
568C22C4×#434111yescharacteristic
569C22C4×#434311yescharacteristic
570C22C2×M16×D1111yescharacteristic
571C22#1062327611yescharacteristic
572C22D11×#13111yescharacteristic
573C22#1062328111yescharacteristic
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—222no—
581C4—222no—
582C4—441no—
583C4—441no—
584C4—441no—
585C4—441no—
586C4—441no—
587C4C2×#6695111yescharacteristic
588C4#1062305911yescharacteristic
589C4#1062306911yescharacteristic
590C4#1062311111yescharacteristic
591C2—442no—
592C2C4×#6695111yescharacteristic
593C2#1307757911yescharacteristic
594C2#1307760211yescharacteristic
595C2#1307760911yescharacteristic
596C2#1307761611yescharacteristic
597C2#1307762711yescharacteristic
598C2#1307762911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1770C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1770D11
hypocenterC11#21665
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1770

Complements

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

NH ≅ G/Ntype
5. #13069182C2semidirect
6. #13069177C2semidirect
7. #13069172C2semidirect
8. #13068758C2semidirect
9. #13068490C2semidirect
10. #13068488C2semidirect
14. #97×Dic11C2semidirect
15. C11×#1770C2semidirect
206. #1770D11semidirect
271. C8×C11#126semidirect
494. C11#21665semidirect
559. C8#66951semidirect

Maximal subgroups

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

subgroupindex
C4×#669512
#130692302
#130692272
#130692212
#130691822
#130691772
#130691722
#130687582
#130684902
#130684882
#130683932
C8×(C2×D11)⋊C42
#97×Dic112
C11×#17702
#2166511