Finite Group Databasebeta

← #14759248

Subgroups — #14759248

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071113C211yesmaximal, characteristic
2#13069230C211yesmaximal, characteristic
3#13069228C211yesmaximal, characteristic
4#13069223C211yesmaximal, characteristic
5#13069221C211yesmaximal, characteristic
6#13069183C211yesmaximal, characteristic, complemented
7#13069177C211yesmaximal, characteristic, complemented
8#13069176C211yesmaximal, characteristic, complemented
9#13069170C211yesmaximal, characteristic, complemented
10C4×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11#13068385C211yesmaximal, characteristic
12#13068385C211yesmaximal, characteristic
13#13068369C211yesmaximal, characteristic, complemented
14#13068304C211yesmaximal, characteristic, complemented
15C11×#1767C211yesmaximal, characteristic, complemented
16C2×#66925C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#97C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C43×C11C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622553C411yescharacteristic
31#10622553C411yescharacteristic
32#10622553C411yescharacteristic
33#10622553C411yescharacteristic
34C4×(C2×D11)⋊C4C2211yescharacteristic
35C4×(C2×D11)⋊C4C2211yescharacteristic
36#10622546C411yescharacteristic
37#10622546C411yescharacteristic
38#10622546C411yescharacteristic
39#10622546C411yescharacteristic
40#10622545C2211yescharacteristic
41C4×Dic11⋊C4C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C42×C11C2×C411yescharacteristic
65C2×C42×C11C2×C411yescharacteristic
66C2×C42×C11C2×C411yescharacteristic
67C2×C42×C11C2×C411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90#66925—22no—
91#66925—22no—
92C11×C4⋊C8—22no—
93C11×C4⋊C8—22no—
94C11×#97—22no—
95C11×#97—22no—
96C11⋊#95C2×C411yescharacteristic
97C11⋊#95C2×C411yescharacteristic
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
108(C2×D11)⋊C8—22no—
109(C2×D11)⋊C8—22no—
110(C2×D11)⋊C8—22no—
111(C2×D11)⋊C8—22no—
112#66879—22no—
113#66879—22no—
114C8×Dic11—22no—
115C8×Dic11—22no—
116C4⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)—22no—
118C4×C11⋊C8—22no—
119C4×C11⋊C8—22no—
120#21436—111nomaximal, Sylow
121C23×D11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11C22×C411yescharacteristic
130C22×Dic11C22×C411yescharacteristic
131C22×Dic11C22×C411yescharacteristic
132C22×Dic11C22×C411yescharacteristic
133C22×Dic11C22×C411yescharacteristic
134C22×Dic11C22×C411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C8×C11—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—21no—
152C2×C8×C11#4112yes—
153C2×C8×C11#4112yes—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—41no—
161C42×C11—41no—
162C42×C11#4112yes—
163C42×C11#4112yes—
164(C2×D11)⋊C4—22no—
165(C2×D11)⋊C4—22no—
166(C2×D11)⋊C4—22no—
167(C2×D11)⋊C4—22no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170Dic11⋊C4—22no—
171Dic11⋊C4—22no—
172Dic11⋊C4—22no—
173Dic11⋊C4—22no—
174Dic11⋊C4—41no—
175Dic11⋊C4—41no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C2×C11⋊C8—21no—
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#4112yes—
193C2×C11⋊C8#4112yes—
194#2298—111no—
195#1924—111no—
196#1924—111no—
197#1923—111no—
198#1923—111no—
199#1917—111no—
200#1917—111no—
201#1916—111no—
202#1916—111no—
203#1767D1111yescharacteristic, complemented
204C4×C4⋊C8—111no—
205#1750—111no—
206#1750—111no—
207#1746—111no—
208#1726—111no—
209C23×C11C23×C411yescharacteristic
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
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#11712yes—
232C2×C4×C11#11712yes—
233C2×C4×C11#13112yes—
234C2×C4×C11#13112yes—
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×Dic11—21no—
242C2×Dic11—21no—
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—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266C8×C11—22no—
267C8×C11—22no—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C2×#117—111no—
275C2×C4⋊C8—111no—
276C2×C4⋊C8—111no—
277C2×C4⋊C8C2×D1111yescharacteristic
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×C22⋊C8—111no—
280C2×C22⋊C8—111no—
281C2×C22⋊C8—111no—
282C2×C22⋊C8—111no—
283C2×#97—111no—
284C2×#97—111no—
285C2×#97C2×D1111yescharacteristic
286C2×#97C2×D1111yescharacteristic
287C2×C4×C8—111no—
288C2×C4×C8—111no—
289C2×C4×C8—111no—
290C2×C4×C8—111no—
291#388—111no—
292#388—111no—
293#388—111no—
294#388—111no—
295#387—111no—
296#387—111no—
297#387—111no—
298#387—111no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4—111no—
301C4×C22⋊C4—111no—
302C4×C22⋊C4—111no—
303#376—111no—
304C43C2×D1111yescharacteristic
305#336—111no—
306#336—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#336C2×D1111yescharacteristic
316#336C2×D1111yescharacteristic
317C22×C11C2×#11711yescharacteristic
318C22×C11C4×#4111yescharacteristic
319C22×C11C4×#4111yescharacteristic
320C22×C11C2×#13111yescharacteristic
321C22×C11C2×#13111yescharacteristic
322C22×C11#56811yescharacteristic
323C22×C11#56811yescharacteristic
324C2×D11—41no—
325C2×D11—41no—
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—41no—
329C2×D11—41no—
330C2×D11—41no—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11#52911yescharacteristic
338C4×C11#52911yescharacteristic
339C4×C11#52911yescharacteristic
340C4×C11#52911yescharacteristic
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348C23×C4—111no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357#117—222no—
358#117—222no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C22⋊C4—111no—
366C2×C22⋊C4—111no—
367C2×C22⋊C4—111no—
368C2×C22⋊C4—111no—
369C2×C22⋊C4—111no—
370C2×C22⋊C4—111no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42C4×D1111yescharacteristic
375C2×C42C4×D1111yescharacteristic
376C2×C42C4×D1111yescharacteristic
377C2×C42C4×D1111yescharacteristic
378C2×C42C22×D1111yescharacteristic
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381C4⋊C8—22no—
382C4⋊C8—22no—
383C4⋊C8—222no—
384C4⋊C8—222no—
385C22⋊C8—222no—
386C22⋊C8—222no—
387C22⋊C8—222no—
388C22⋊C8—222no—
389#97—22no—
390#97—22no—
391#97—222no—
392#97—222no—
393C4×C8—222no—
394C4×C8—222no—
395C4×C8—222no—
396C4×C8—222no—
397#95—111no—
398#95—111no—
399#95—111no—
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—
409C2×C11#229811yescharacteristic
410C2×C11#292511yescharacteristic
411C2×C11#292511yescharacteristic
412C2×C11#296611yescharacteristic
413C2×C11#296711yescharacteristic
414C2×C11#296811yescharacteristic
415C2×C11#296911yescharacteristic
416D11—81no—
417C24—111no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4C2×C4×D1111yescharacteristic
432C22×C4C2×C4×D1111yescharacteristic
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4C2×C4×D1111yescharacteristic
435C22×C4C2×C4×D1111yescharacteristic
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—112no—
449C2×C8—112no—
450C2×C8—221no—
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#433912yes—
461C2×C8#433912yes—
462C4⋊C4—222no—
463C4⋊C4—222no—
464C4⋊C4—222no—
465C4⋊C4—222no—
466C4⋊C4—441no—
467C4⋊C4—441no—
468C22⋊C4—222no—
469C22⋊C4—222no—
470C22⋊C4—222no—
471C22⋊C4—222no—
472C22⋊C4—441no—
473C22⋊C4—441no—
474C42—22no—
475C42—22no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—41no—
481C42—41no—
482C42—221no—
483C42—221no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42—221no—
488C42#434112yes—
489C42#434312yes—
490C11#2143611yescharacteristic, complemented, Sylow
491C23—221no—
492C23—221no—
493C23—221no—
494C23—221no—
495C23—221no—
496C23—221no—
497C23—221no—
498C23C22×C4×D1111yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
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—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
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—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4#6694512yes—
539C2×C4#6694512yes—
540C2×C4#6696012yes—
541C2×C4#6696012yes—
542C2×C4C2×#433911yescharacteristic
543C2×C4C2×#433911yescharacteristic
544C2×C4C2×#434111yescharacteristic
545C2×C4C2×#434311yescharacteristic
546C2×C4#41×D1111yescharacteristic
547C2×C4#41×D1111yescharacteristic
548C8—22no—
549C8—22no—
550C8—41no—
551C8—41no—
552C8—222no—
553C8—222no—
554C8—441no—
555C8—441no—
556C22—441no—
557C22—441no—
558C22—441no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22C4×#433911yescharacteristic
564C22C2×#6694511yescharacteristic
565C22#1062305311yescharacteristic
566C22C2×#6696011yescharacteristic
567C22C2×#6696011yescharacteristic
568C22#1062327611yescharacteristic
569C22#1062327611yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—41no—
575C4—41no—
576C4—441no—
577C4—441no—
578C4—441no—
579C4—441no—
580C4—441no—
581C4—441no—
582C4—441no—
583C4#1062306911yescharacteristic
584C4#1062306911yescharacteristic
585C4#1062311111yescharacteristic
586C4#1062311111yescharacteristic
587C2—881no—
588C2#1307110911yescharacteristic
589C2#1307728411yescharacteristic
590C2#1307728411yescharacteristic
591C2#1307758511yescharacteristic
592C2#1307759611yescharacteristic
593C2#1307761011yescharacteristic
594C2#1307762011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1767C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1767D11
hypocenterC11#21436
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1767

Complements

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

NH ≅ G/Ntype
6. #13069183C2semidirect
7. #13069177C2semidirect
8. #13069176C2semidirect
9. #13069170C2semidirect
10. C4×C4⋊(C11⋊C8)C2semidirect
13. #13068369C2semidirect
14. #13068304C2semidirect
15. C11×#1767C2semidirect
203. #1767D11semidirect
490. C11#21436semidirect

Maximal subgroups

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

subgroupindex
#130711132
#130692302
#130692282
#130692232
#130692212
#130691832
#130691772
#130691762
#130691702
C4×C4⋊(C11⋊C8)2
#130683852
#130683692
#130683042
C11×#17672
#2143611