Finite Group Databasebeta

← #14759263

Subgroups — #14759263

Order 2816.

710 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
1#13071008C211yesmaximal, 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
10#13068473C211yesmaximal, characteristic, complemented
11#13068379C211yesmaximal, characteristic
12C4×(C2×D11)⋊C8C211yesmaximal, characteristic
13#13068367C211yesmaximal, characteristic, complemented
14#13068304C211yesmaximal, characteristic, complemented
15C11×#1768C211yesmaximal, characteristic, complemented
16C2×C42×D11C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#97C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C11×#376C2211yescharacteristic
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
30C4×(C2×D11)⋊C4C2211yescharacteristic
31C4×(C2×D11)⋊C4C2211yescharacteristic
32#10622545C2211yescharacteristic
33C4×Dic11⋊C4C2211yescharacteristic
34C4×Dic11⋊C4C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×#66867C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622280C411yescharacteristic
40#10622280C411yescharacteristic
41#10622277C411yescharacteristic
42#10622277C411yescharacteristic
43#10622264C411yescharacteristic
44#10622264C411yescharacteristic
45#10622263C411yescharacteristic
46#10622263C411yescharacteristic
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×D11C2×C411yescharacteristic
60C22×C4×D11C2×C411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
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×Dic11⋊C4C2×C411yescharacteristic
74C2×Dic11⋊C4C2×C411yescharacteristic
75C2×Dic11⋊C4C2×C411yescharacteristic
76C2×Dic11⋊C4C2×C411yescharacteristic
77C2×C4×Dic11C2×C411yescharacteristic
78C2×C4×Dic11C2×C411yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C42×D11—22no—
87C42×D11—22no—
88C11×C4⋊C8—22no—
89C11×C4⋊C8—22no—
90C11×#97—22no—
91C4×C8×C11—22no—
92C11×#95C2×C411yescharacteristic
93C11×#95C2×C411yescharacteristic
94C11×#95C2×C411yescharacteristic
95C11×#95C2×C411yescharacteristic
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—
118#66867—22no—
119C4×C11⋊C8—22no—
120#21437—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—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—41no—
147C2×C4×D11—41no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11#4112yes—
159C2×C8×C11#4112yes—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11#4112yes—
165C42×C11#4112yes—
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—41no—
173Dic11⋊C4—41no—
174C4×Dic11—22no—
175C4×Dic11—22no—
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#2283—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#1768—111no—
204#1768D1111yescharacteristic, complemented
205#1749—111no—
206C4×C22⋊C8—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#13112yes—
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—21no—
232C2×C4×C11—21no—
233C2×C4×C11#11712yes—
234C2×C4×C11#11712yes—
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#13112yes—
262C4×D11—44no—
263C4×D11—44no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C8×C11—22no—
269C8×C11—22no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C22×C42—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8C2×D1111yescharacteristic
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×C22⋊C8—111no—
282C2×C22⋊C8—111no—
283C2×C22⋊C8—111no—
284C2×C22⋊C8—111no—
285C2×#97—111no—
286C2×#97—111no—
287C2×#97—111no—
288C2×#97C2×D1111yescharacteristic
289C2×C4×C8—111no—
290C2×C4×C8—111no—
291C2×C4×C8—111no—
292C2×C4×C8C2×D1111yescharacteristic
293#383—111no—
294#383—111no—
295#382—111no—
296#382—111no—
297#381—111no—
298#381—111no—
299#380—111no—
300#380—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303C4×C22⋊C4—111no—
304C4×C22⋊C4—111no—
305#376—111no—
306#376C2×D1111yescharacteristic
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×C11C2×#11711yescharacteristic
320C22×C11C4×#4111yescharacteristic
321C22×C11C4×#4111yescharacteristic
322C22×C11C2×#13111yescharacteristic
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—22no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11#52911yescharacteristic
340C4×C11#52911yescharacteristic
341C4×C11#52911yescharacteristic
342C4×C11#52911yescharacteristic
343Dic11—22no—
344Dic11—41no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—111no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8C22×D1111yescharacteristic
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360C22×C8C22×D1111yescharacteristic
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×C42—111no—
370C2×C42—111no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—222no—
375C2×C42—222no—
376C2×C42C22×D1111yescharacteristic
377C2×C42C22×D1111yescharacteristic
378C2×C42C22×D1111yescharacteristic
379C4⋊C8—22no—
380C4⋊C8—22no—
381C4⋊C8—222no—
382C4⋊C8—222no—
383C22⋊C8—222no—
384C22⋊C8—222no—
385C22⋊C8—222no—
386C22⋊C8—222no—
387#97—22no—
388#97—222no—
389#97—222no—
390#97—222no—
391C4×C8—22no—
392C4×C8—222no—
393C4×C8—222no—
394C4×C8—222no—
395#95—111no—
396#95—111no—
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#95C4×D1111yescharacteristic
408#95C4×D1111yescharacteristic
409#95C4×D1111yescharacteristic
410#95C4×D1111yescharacteristic
411C2×C11#229811yescharacteristic
412C2×C11#292411yescharacteristic
413C2×C11#292411yescharacteristic
414C2×C11#296611yescharacteristic
415C2×C11#296711yescharacteristic
416C2×C11#296811yescharacteristic
417C2×C11#296911yescharacteristic
418D11—42no—
419C24—111no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—441no—
438C22×C4—441no—
439C22×C4C2×C4×D1111yescharacteristic
440C22×C4C2×C4×D1111yescharacteristic
441C22×C4C2×C4×D1111yescharacteristic
442C22×C4C2×C4×D1111yescharacteristic
443C22×C4C2×C4×D1111yescharacteristic
444C22×C4C2×C4×D1111yescharacteristic
445C22×C4C23×D1111yescharacteristic
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—112no—
457C2×C8—112no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8#433912yes—
469C2×C8#433912yes—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4—441no—
473C4⋊C4—441no—
474C22⋊C4—222no—
475C22⋊C4—222no—
476C22⋊C4—441no—
477C22⋊C4—441no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—222no—
483C42—222no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42#434112yes—
491C42#434312yes—
492C11#2143711yescharacteristic, complemented, Sylow
493C23—112no—
494C23—221no—
495C23—221no—
496C23—221no—
497C23—221no—
498C23—221no—
499C23—221no—
500C23C22×C4×D1111yescharacteristic
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—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—112no—
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—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—444no—
539C2×C4—444no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4#6694512yes—
545C2×C4#6694512yes—
546C2×C4C2×#433911yescharacteristic
547C2×C4C2×#433911yescharacteristic
548C2×C4C2×#434111yescharacteristic
549C2×C4C2×#434311yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C8—22no—
553C8—22no—
554C8—41no—
555C8—41no—
556C8—222no—
557C8—222no—
558C8—441no—
559C8—441no—
560C22—222no—
561C22—222no—
562C22—222no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22—441no—
567C22C4×#433911yescharacteristic
568C22C2×#6694511yescharacteristic
569C22#1062305311yescharacteristic
570C22D11×#13111yescharacteristic
571C22D11×#13111yescharacteristic
572C22#1062328111yescharacteristic
573C22#1062328111yescharacteristic
574C4—22no—
575C4—22no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—222no—
581C4—441no—
582C4—441no—
583C4—441no—
584C4—441no—
585C4—441no—
586C4—441no—
587C4#1062306911yescharacteristic
588C4#1062306911yescharacteristic
589C4#1062311111yescharacteristic
590C4#1062311111yescharacteristic
591C2—442no—
592C2#1307110911yescharacteristic
593C2#1307727311yescharacteristic
594C2#1307727311yescharacteristic
595C2#1307758911yescharacteristic
596C2#1307759911yescharacteristic
597C2#1307760611yescharacteristic
598C2#1307761611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1768C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1768D11
hypocenterC11#21437
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1768

Complements

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

NH ≅ G/Ntype
6. #13069183C2semidirect
7. #13069177C2semidirect
8. #13069176C2semidirect
9. #13069170C2semidirect
10. #13068473C2semidirect
13. #13068367C2semidirect
14. #13068304C2semidirect
15. C11×#1768C2semidirect
204. #1768D11semidirect
492. C11#21437semidirect

Maximal subgroups

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

subgroupindex
#130710082
#130692302
#130692282
#130692232
#130692212
#130691832
#130691772
#130691762
#130691702
#130684732
#130683792
C4×(C2×D11)⋊C82
#130683672
#130683042
C11×#17682
#2143711