Finite Group Databasebeta

← #14757376

Subgroups — #14757376

Order 2816.

2010 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622731C211yesmaximal, characteristic, complemented
3C2×#10622820C211yesmaximal, characteristic, complemented
4C2×#10622739C211yesmaximal, characteristic, complemented
5C2×#10622739C211yesmaximal, characteristic, complemented
6C2×M16×Dic11C211yesmaximal, characteristic, complemented
7#13069412C214yesmaximal, complemented
8#13069408C214yesmaximal, complemented
9C2×C11×#407C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C23×C22⋊D11C411yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C22×C22⋊Dic11C411yescharacteristic
16C2×C4×C22⋊D11—24no—
17C2×C4×C22⋊D11—24no—
18C2×C4×C22⋊D11C412yes—
19C2×C4×C22⋊D11C412yes—
20C2×C4×C22⋊D11C2212yes—
21C2×C4×C22⋊D11C2212yes—
22C22×(C2×D11)⋊C4C411yescharacteristic
23C22×Dic11⋊C4C411yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C11×#407—24no—
28C2×C11×C22⋊C8C2214yescomplemented
29#10622820—24no—
30C2×C22⋊(C11⋊C8)C2214yescomplemented
31#10622739—24no—
32#10622739—24no—
33#10622731—24no—
34M16×Dic11—24no—
35C2×(C2×D11)⋊C8C2214yescomplemented
36C2×(C2×D11)⋊C8C2214yescomplemented
37C2×#66879C2212yescomplemented
38C2×Dic11⋊C8C2212yescomplemented
39C2×Dic11⋊C8C2212yescomplemented
40C2×C8×Dic11C2212yescomplemented
41C25×C11C2×C411yescharacteristic
42C24×D11C2×C411yescharacteristic
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11C2×C411yescharacteristic
50C23×C4×C11C2×C412yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—28no—
54C22×C22⋊D11—24no—
55C22×C22⋊D11C2×C412yes—
56C22×C22⋊D11C2×C412yes—
57C23×Dic11C2×C411yescharacteristic
58C23×Dic11C2×C411yescharacteristic
59C23×Dic11C2×C411yescharacteristic
60C22×C4×D11—22no—
61C22×C4×D11—22no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11C2×C412yes—
67C22×C4×D11C2312yes—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16D414yescomplemented
74C22×C8×C11C2312yes—
75C22×C8×C11C2312yes—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11C2×C412yes—
78C2×C22⋊Dic11C2×C412yes—
79C4×C22⋊D11—28no—
80C4×C22⋊D11—28no—
81C4×C22⋊D11—24no—
82C4×C22⋊D11—24no—
83C4×C22⋊D11—24no—
84C4×C22⋊D11—24no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4C2×C412yes—
87C2×(C2×D11)⋊C4C2×C412yes—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4C2×C412yes—
90C2×Dic11⋊C4C2×C412yes—
91C2×C4×Dic11C2×C411yescharacteristic
92C2×C4×Dic11C2×C411yescharacteristic
93C2×C4×Dic11D414yes—
94C2×C4×Dic11D414yes—
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C2×#4318—22no—
98C2×#4318—22no—
99C2×#4318—22no—
100C2×#4318—22no—
101C2×#4318—22no—
102C2×#4318D414yescomplemented
103C22×C11⋊C8C2312yes—
104C22×C11⋊C8C2312yes—
105C11×C22⋊C8—28no—
106C22⋊(C11⋊C8)—28no—
107(C2×D11)⋊C8—28no—
108(C2×D11)⋊C8—28no—
109#66879—24no—
110Dic11⋊C8—24no—
111Dic11⋊C8—24no—
112C8×Dic11—24no—
113#21190—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—42no—
119C24×C11C22×C412yes—
120C24×C11C22×C411yescharacteristic
121C23×D11—22no—
122C23×D11—24no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—42no—
126C23×D11C22×C412yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—44no—
140C22×C4×C11—44no—
141C22×C4×C11—44no—
142C22×C4×C11—44no—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11#4112yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—232no—
153C2×C22⋊D11—24no—
154C2×C22⋊D11—24no—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—24no—
157C2×C22⋊D11—24no—
158C2×C22⋊D11M1618yescomplemented
159C22×Dic11—24no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—42no—
164C22×Dic11C22⋊C414yes—
165C22×Dic11C22⋊C414yes—
166C22×Dic11C22×C412yes—
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C2×C4×D11—24no—
172C2×C4×D11—24no—
173C2×C4×D11—24no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—44no—
181C2×C4×D11—44no—
182C2×C4×D11—44no—
183C2×C4×D11—44no—
184C11×M16—28no—
185C11×M16—44no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C2×C8×C11C2×D414yescomplemented
192C22⋊Dic11—24no—
193C22⋊Dic11—24no—
194(C2×D11)⋊C4—24no—
195(C2×D11)⋊C4—24no—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198C4×Dic11C22⋊C414yes—
199C4×Dic11C22⋊C414yes—
200C4×Dic11C2×D412yes—
201C4×Dic11C2×D412yes—
202C4×Dic11C2×D412yes—
203C4×Dic11C2×D412yes—
204#4318—28no—
205#4318—44no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211C2×C11⋊C8C2×D414yescomplemented
212C22×C4×D4—111no—
213C2×#423—111no—
214C2×#407—111no—
215C2×#407—111no—
216C2×#407—111no—
217C2×#407D1111yescharacteristic, complemented
218C2×C4×M16—111no—
219#1955—114no—
220#1954—114no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—28no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—48no—
231C23×C11—48no—
232C23×C11—44no—
233C23×C11—44no—
234C23×C11C2×C22⋊C412yes—
235C23×C11C4×D412yes—
236C23×C11C4×D412yes—
237C23×C11C2×M1614yes—
238C23×C11C23×C411yescharacteristic
239C22×D11—28no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—48no—
247C22×D11—48no—
248C22×D11—44no—
249C22×D11—44no—
250C22×D11C2×M1614yes—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—44no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—48no—
260C2×C4×C11C2×C22⋊C412yes—
261C2×C4×C11C4×D412yes—
262C2×C4×C11C4×D412yes—
263C2×C4×C11#12114yes—
264C2×C4×C11#12114yes—
265C2×C4×C11#12414yes—
266C2×C4×C11#12714yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C22⋊D11—216no—
274C22⋊D11—216no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—28no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—44no—
283C2×Dic11—44no—
284C2×Dic11C2×C22⋊C412yes—
285C2×Dic11C2×C22⋊C412yes—
286C2×Dic11C2×C22⋊C412yes—
287C2×Dic11C2×C22⋊C412yes—
288C2×Dic11C2×M1614yes—
289C4×D11—42no—
290C4×D11—42no—
291C4×D11—42no—
292C4×D11—42no—
293C4×D11—48no—
294C8×C11—24no—
295C8×C11—42no—
296C11⋊C8—24no—
297C11⋊C8—42no—
298C23×D4—111no—
299C24×C4—111no—
300C24×C4C2×D1111yescharacteristic
301C22×M16—111no—
302C22×M16—111no—
303C22×M16C2×D1111yescharacteristic
304C22×M16C2×D1111yescharacteristic
305C2×C4×D4—112no—
306C2×C4×D4—112no—
307C2×C4×D4—112no—
308C2×C4×D4—112no—
309C2×C4×D4—224no—
310C2×C4×D4—224no—
311C22×C4⋊C4—111no—
312C22×C22⋊C4—111no—
313C22×C22⋊C4—111no—
314C22×C42—111no—
315#423—224no—
316C2×C4⋊C8—112no—
317C2×C4⋊C8—112no—
318#407—24no—
319#407—224no—
320#407—224no—
321#407—224no—
322C2×C22⋊C8—114no—
323C2×C22⋊C8—114no—
324C2×C22⋊C8—114no—
325C2×C22⋊C8C2×D1114yescomplemented
326C4×M16—224no—
327C2×#97—112no—
328C2×C4×C8—112no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—24no—
332C22×C11—24no—
333C22×C11—24no—
334C22×C11—24no—
335C22×C11—24no—
336C22×C11—416no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11#39014yes—
342C22×C11C22×C22⋊C411yescharacteristic
343C22×C11C2×C4×D411yescharacteristic
344C22×C11C2×C4×D411yescharacteristic
345C22×C11C22×M1612yes—
346C22×C11#56812yes—
347C2×D11—24no—
348C2×D11—24no—
349C2×D11—24no—
350C2×D11—416no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C4×C11—42no—
356C4×C11#39014yes—
357C4×C11C2×#12111yescharacteristic
358C4×C11C2×#12111yescharacteristic
359C4×C11C2×#12411yescharacteristic
360C4×C11C2×#12711yescharacteristic
361Dic11—22no—
362Dic11—22no—
363Dic11—22no—
364Dic11—42no—
365Dic11#40714yescomplemented
366C25—111no—
367C25C4×D1111yescharacteristic
368C22×D4—112no—
369C22×D4—112no—
370C22×D4—224no—
371C22×D4—228no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—111no—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4—112no—
382C23×C4—112no—
383C23×C4—222no—
384C23×C4—222no—
385C23×C4—222no—
386C23×C4—222no—
387C23×C4—222no—
388C23×C4—222no—
389C23×C4C4×D1111yescharacteristic
390C23×C4C4×D1112yes—
391C23×C4C22×D1112yes—
392C23×C4C22×D1111yescharacteristic
393C2×M16—22no—
394C2×M16—22no—
395C2×M16—22no—
396C2×M16—22no—
397C2×M16—22no—
398C2×M16—114no—
399C2×M16—222no—
400C2×M16—222no—
401C2×M16—222no—
402C2×M16—222no—
403C2×M16—222no—
404C2×M16C22⋊D1114yescomplemented
405C22×C8—112no—
406C22×C8—112no—
407C22×C8C22×D1112yes—
408C22×C8C22×D1112yes—
409C4×D4—228no—
410C4×D4—228no—
411C4×D4—224no—
412C4×D4—224no—
413C4×D4—224no—
414C4×D4—224no—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—224no—
418C2×C22⋊C4—112no—
419C2×C22⋊C4—112no—
420C2×C22⋊C4—112no—
421C2×C22⋊C4—112no—
422C2×C22⋊C4—224no—
423C2×C22⋊C4—224no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—114no—
427C2×C42—114no—
428C2×C42—111no—
429C2×C42—111no—
430C4⋊C8—224no—
431C4⋊C8—224no—
432C22⋊C8—28no—
433C22⋊C8—228no—
434C22⋊C8—228no—
435C22⋊C8—228no—
436#97—224no—
437C4×C8—224no—
438C2×C11—24no—
439C2×C11—44no—
440C2×C11C2×#39011yescharacteristic
441C2×C11C2×#40711yescharacteristic
442C2×C11#287911yescharacteristic
443C2×C11D4×M1612yes—
444C2×C11D4×M1612yes—
445D11—44no—
446C24—22no—
447C24—24no—
448C24—22no—
449C24—22no—
450C24—42no—
451C24—112no—
452C24—224no—
453C24—222no—
454C24—222no—
455C24—222no—
456C24—442no—
457C24C2×C4×D1112yes—
458C24C2×C4×D1111yescharacteristic
459C2×D4—118no—
460C2×D4—224no—
461C2×D4—224no—
462C2×D4—224no—
463C2×D4—224no—
464C2×D4—2232no—
465C2×D4—224no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—111no—
483C22×C4—114no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—114no—
488C22×C4—112no—
489C22×C4—224no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—224no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—442no—
503C22×C4—444no—
504C22×C4—444no—
505C22×C4—444no—
506C22×C4—444no—
507C22×C4C2×C4×D1112yes—
508C22×C4C2×C4×D1111yescharacteristic
509C22×C4#433912yes—
510C22×C4D4×D1112yes—
511C22×C4D4×D1112yes—
512C22×C4D4×D1112yes—
513C22×C4#434112yes—
514C22×C4C2×C22⋊D1112yes—
515C22×C4C23×D1111yescharacteristic
516M16—28no—
517M16—44no—
518M16—228no—
519M16—444no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—114no—
526C2×C8—222no—
527C2×C8—222no—
528C2×C8—222no—
529C2×C8—222no—
530C2×C8—222no—
531C2×C8C2×C22⋊D1114yescomplemented
532C4⋊C4—224no—
533C4⋊C4—224no—
534C22⋊C4—224no—
535C22⋊C4—224no—
536C22⋊C4—224no—
537C22⋊C4—224no—
538C42—114no—
539C42—114no—
540C42—112no—
541C42—112no—
542C42—112no—
543C42—112no—
544C11#2119011yescharacteristic, complemented, Sylow
545C23—22no—
546C23—22no—
547C23—28no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—48no—
555C23—48no—
556C23—44no—
557C23—44no—
558C23—114no—
559C23—228no—
560C23—222no—
561C23—222no—
562C23—222no—
563C23—222no—
564C23—222no—
565C23—222no—
566C23—448no—
567C23—448no—
568C23—444no—
569C23—444no—
570C23C22⋊C4×D1112yes—
571C23(C22⋊D11)⋊C412yes—
572C23M16×D1114yes—
573C23C4×C22⋊D1112yes—
574C23C22×C4×D1111yescharacteristic
575D4—2216no—
576D4—2216no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—48no—
586C2×C4—112no—
587C2×C4—114no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—228no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—444no—
599C2×C4—444no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—448no—
605C2×C4C22⋊C4×D1112yes—
606C2×C4(C22⋊D11)⋊C412yes—
607C2×C4#6693714yes—
608C2×C4#6693814yes—
609C2×C4C4×C22⋊D1112yes—
610C2×C4#6699214yes—
611C2×C4#6699314yes—
612C2×C4C2×#433911yescharacteristic
613C2×C4C2×D4×D1111yescharacteristic
614C2×C4C2×D4×D1111yescharacteristic
615C2×C4C2×D4×D1111yescharacteristic
616C2×C4C2×#434111yescharacteristic
617C2×C4C22×C22⋊D1111yescharacteristic
618C8—24no—
619C8—42no—
620C8—224no—
621C8—442no—
622C22—22no—
623C22—22no—
624C22—24no—
625C22—24no—
626C22—24no—
627C22—24no—
628C22—24no—
629C22—416no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—224no—
635C22—224no—
636C22—224no—
637C22—4416no—
638C22—442no—
639C22—442no—
640C22—442no—
641C22—442no—
642C22#1062257014yes—
643C22C2×C22⋊C4×D1111yescharacteristic
644C22C2×(C22⋊D11)⋊C411yescharacteristic
645C22C2×M16×D1112yes—
646C22#1062327612yes—
647C22C2×C4×C22⋊D1111yescharacteristic
648C4—42no—
649C4—114no—
650C4—222no—
651C4—222no—
652C4—222no—
653C4—442no—
654C4#1062257014yes—
655C4C2×#6693711yescharacteristic
656C4C2×#6693811yescharacteristic
657C4C2×#6699211yescharacteristic
658C4C2×#6699311yescharacteristic
659C2—24no—
660C2—44no—
661C2—444no—
662C2C2×#1062257011yescharacteristic
663C2D11×#40711yescharacteristic
664C2#1307705911yescharacteristic
665C2#1307734812yes—
666C2M16×C22⋊D1112yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#407C2
prime radicalC23×C22⋊D11C4
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11#21190
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#10622731C2semidirect
3. C2×#10622820C2semidirect
4. C2×#10622739C2semidirect
5. C2×#10622739C2semidirect
6. C2×M16×Dic11C2semidirect
7. #13069412C2semidirect
8. #13069408C2semidirect
9. C2×C11×#407C2semidirect
28. C2×C11×C22⋊C8C22semidirect
30. C2×C22⋊(C11⋊C8)C22semidirect
35. C2×(C2×D11)⋊C8C22semidirect
36. C2×(C2×D11)⋊C8C22semidirect
37. C2×#66879C22semidirect
38. C2×Dic11⋊C8C22semidirect
39. C2×Dic11⋊C8C22semidirect
40. C2×C8×Dic11C22semidirect
73. C2×C11×M16D4semidirect
102. C2×#4318D4semidirect
158. C2×C22⋊D11M16semidirect
191. C2×C8×C11C2×D4semidirect
211. C2×C11⋊C8C2×D4semidirect
217. C2×#407D11semidirect
325. C2×C22⋊C8C2×D11semidirect
365. Dic11#407semidirect
404. C2×M16C22⋊D11semidirect
531. C2×C8C2×C22⋊D11semidirect
544. C11#21190semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106227312
C2×#106228202
C2×#106227392
C2×M16×Dic112
#130694122
#130694082
C2×C11×#4072
#2119011