Finite Group Databasebeta

← #14719669

Subgroups — #14719669

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2#13077245C212yesmaximal, complemented
3#13066954C211yesmaximal, characteristic, complemented
4#13066952C212yesmaximal, complemented
5#13066949C212yesmaximal, complemented
6#13066947C212yesmaximal, complemented
7#13066938C212yesmaximal, complemented
8#13066935C212yesmaximal, complemented
9C11×#1465C211yesmaximal, characteristic, complemented
10C22×#4341C411yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×D4×Dic11C411yescharacteristic
13C2×C4×C22⋊D11C411yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C22×C4×Dic11C411yescharacteristic
16C22×C4×Dic11C2211yescharacteristic
17C4×#4341—22no—
18C4×#4341—22no—
19C4×#4341—22no—
20C4×#4341—22no—
21C2×#66945C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×(C22⋊D11)⋊C4C411yescharacteristic
24C2×(C22⋊D11)⋊C4C2211yescharacteristic
25C2×#66930C411yescharacteristic
26C2×#66930C2211yescharacteristic
27C2×C42×D11C411yescharacteristic
28C2×C4×Dic22C411yescharacteristic
29C11×#407C2212yes—
30#10622820C2212yes—
31#10622731—22no—
32M16×Dic11—22no—
33#10622332—22no—
34#10622332C2214yes—
35#10622331—22no—
36#10622331C2214yes—
37C11×#324C2212yes—
38C11×#323C2212yes—
39#10622166C2212yes—
40#10622163C2212yes—
41#10622107C2214yes—
42#10622106C2214yes—
43C22×D4×C11C2×C411yescharacteristic
44C23×C4×C11C2×C411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11C2×C411yescharacteristic
47C22×C22⋊D11C2×C411yescharacteristic
48C23×Dic11C2×C411yescharacteristic
49C23×Dic11C2×C411yescharacteristic
50C23×Dic11C2×C411yescharacteristic
51C23×Dic11C2×C411yescharacteristic
52C2×#4341—24no—
53C2×#4341—22no—
54C2×#4341—22no—
55C2×#4341—24no—
56C22×C4×D11C2×C411yescharacteristic
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11C2×C411yescharacteristic
59C22×Dic22C2×C411yescharacteristic
60C2×C11×M16—22no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4C2×C411yescharacteristic
65C2×C11×C22⋊C4C2311yescharacteristic
66C2×C42×C11C2×C411yescharacteristic
67C2×C22⋊Dic11C2×C411yescharacteristic
68C2×C22⋊Dic11C2×C411yescharacteristic
69D4×Dic11—22no—
70D4×Dic11—22no—
71C4×C22⋊D11—22no—
72C4×C22⋊D11—22no—
73C4×C22⋊D11—22no—
74C4×C22⋊D11—22no—
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2311yescharacteristic
77C2×C4⋊Dic11C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2311yescharacteristic
82C2×C4×Dic11—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2×C411yescharacteristic
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11C2×C411yescharacteristic
92C2×C4×Dic11C2×C411yescharacteristic
93C2×C4×Dic11D412yes—
94C2×C4×Dic11D412yes—
95C2×C4×Dic11D412yes—
96C2×C4×Dic11D412yes—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C2×#4318—22no—
100#66945—22no—
101#66945—22no—
102#66940—22no—
103#66940—22no—
104(C22⋊D11)⋊C4—22no—
105(C22⋊D11)⋊C4—22no—
106(C22⋊D11)⋊C4—22no—
107(C22⋊D11)⋊C4—22no—
108#66930—22no—
109#66930—22no—
110#66930—22no—
111#66930—22no—
112C42×D11—21no—
113C42×D11—21no—
114C42×D11—21no—
115C42×D11—21no—
116C4×Dic22—22no—
117C4×Dic22—22no—
118C11×C22⋊C8—22no—
119C11×C22⋊C8C2314yes—
120C22⋊(C11⋊C8)—22no—
121C22⋊(C11⋊C8)C2314yes—
122#66879—24no—
123Dic11⋊C8—24no—
124Dic11⋊C8—24no—
125C8×Dic11—24no—
126#17366—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C24×C11C22×C411yescharacteristic
129C23×D11C22×C411yescharacteristic
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—22no—
145C2×C22⋊D11—22no—
146C2×C22⋊D11—22no—
147C2×C22⋊D11—22no—
148C2×C22⋊D11—22no—
149C2×C22⋊D11M1614yescomplemented
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11C22⋊C412yes—
161C22×Dic11C22⋊C412yes—
162C22×Dic11C22⋊C412yes—
163C22×Dic11C22⋊C412yes—
164C22×Dic11C22×C411yescharacteristic
165C22×Dic11C22×C411yescharacteristic
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171#4341—216no—
172#4341—216no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—22no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—22no—
181C2×C4×D11—42no—
182C2×C4×D11—42no—
183C2×Dic22—22no—
184C2×Dic22—22no—
185C2×Dic22M1614yescomplemented
186C11×M16—44no—
187C2×C8×C11—24no—
188C11×C4⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C42×C11—21no—
192C42×C11—21no—
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197C4⋊Dic11—22no—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11C22⋊C412yes—
213C4×Dic11C22⋊C412yes—
214C4×Dic11C22⋊C411yescharacteristic
215C4×Dic11C22⋊C411yescharacteristic
216C4×Dic11C22⋊C411yescharacteristic
217C4×Dic11C22⋊C411yescharacteristic
218C4×Dic11C2×D412yes—
219C4×Dic11C2×D412yes—
220C4×Dic11C2×D412yes—
221C4×Dic11C2×D412yes—
222#4318—44no—
223C2×C11⋊C8—24no—
224C2×C4×#41—111no—
225#2920—112no—
226#1465—112no—
227#1465—111no—
228#1465D1111yescharacteristic, complemented
229#1464—112no—
230#1464—112no—
231#1461—112no—
232#1460—112no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11C2×C22⋊C412yes—
242C23×C11C2×M1612yes—
243C23×C11C23×C411yescharacteristic
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11C2×M1612yes—
249D4×C11—28no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×M1612yes—
265C2×C4×C11C22×D412yes—
266C22⋊D11—28no—
267C22⋊D11—28no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—42no—
281C2×Dic11—41no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11C2×C22⋊C411yescharacteristic
287C2×Dic11C2×C22⋊C411yescharacteristic
288C2×Dic11C2×C22⋊C411yescharacteristic
289C2×Dic11C2×C22⋊C412yes—
290C2×Dic11C2×C22⋊C412yes—
291C2×Dic11C2×C22⋊C411yescharacteristic
292C2×Dic11C2×M1612yes—
293C2×Dic11C2×M1612yes—
294C2×Dic11C2×M1612yes—
295C4×D11—24no—
296C4×D11—24no—
297C4×D11—42no—
298C4×D11—42no—
299C4×D11—42no—
300C4×D11—42no—
301Dic22—28no—
302C8×C11—44no—
303C11⋊C8—44no—
304C22×#41—111no—
305C4×#41—222no—
306C4×#41—222no—
307C4×#41—222no—
308C4×#41—222no—
309C2×C4×Q8—111no—
310C2×C4×Q8—111no—
311C2×C4×D4—111no—
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C2×C4×D4—111no—
315C2×C4×D4—111no—
316C2×C4×D4C2×D1111yescharacteristic
317C2×#117—111no—
318C2×#117—111no—
319C2×#117—111no—
320C22×C42—111no—
321C22×C42—111no—
322C22×C42—111no—
323#432—114no—
324#432—222no—
325#431—114no—
326#431—222no—
327#423—222no—
328#407—112no—
329#407C2×D1112yes—
330C4×M16—222no—
331#324—112no—
332#324—114no—
333#324C2×D1112yes—
334#323—112no—
335#323—114no—
336#323C2×D1112yes—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11C22×C22⋊C411yescharacteristic
350C22×C11C22×M1611yescharacteristic
351C22×C11C22×M1611yescharacteristic
352C2×D11—22no—
353C2×D11—42no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—42no—
357C4×C11—22no—
358C4×C11—21no—
359C4×C11—22no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11#41012yes—
363Dic11—22no—
364Dic11—21no—
365Dic11—21no—
366Dic11—21no—
367Dic11—22no—
368Dic11—41no—
369Dic11—41no—
370Dic11#40714yes—
371Dic11#41312yes—
372C2×#41—222no—
373C2×#41—222no—
374C2×#41—224no—
375C2×#41—224no—
376C22×Q8—111no—
377C22×D4—111no—
378C22×D4—111no—
379C22×D4C4×D1111yescharacteristic
380C23×C4—111no—
381C23×C4—111no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4C4×D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C2×M16—22no—
390C2×M16—222no—
391C4×Q8—222no—
392C4×Q8—222no—
393C4×Q8—222no—
394C4×Q8—222no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—222no—
398C4×D4—222no—
399C4×D4—222no—
400C4×D4—222no—
401C4×D4—222no—
402C4×D4—222no—
403C4×D4—222no—
404C4×D4—222no—
405C4×D4—222no—
406C4×D4—222no—
407#117—222no—
408#117—222no—
409#117—222no—
410#117—222no—
411#117—222no—
412#117—222no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C22⋊C4—111no—
420C2×C22⋊C4—111no—
421C2×C22⋊C4—111no—
422C2×C22⋊C4—111no—
423C2×C22⋊C4C4×D1111yescharacteristic
424C2×C22⋊C4C22×D1111yescharacteristic
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—112no—
428C2×C42—112no—
429C2×C42—112no—
430C2×C42—112no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—111no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—221no—
439C2×C42—221no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42C4×D1111yescharacteristic
447C4⋊C8—224no—
448C4⋊C8—224no—
449C22⋊C8—22no—
450C22⋊C8—114no—
451C22⋊C8—222no—
452C22⋊C8C22×D1114yes—
453#97—224no—
454C4×C8—224no—
455C2×C11—21no—
456C2×C11—21no—
457C2×C11—42no—
458C2×C11—42no—
459C2×C11C2×#40711yescharacteristic
460C2×C11C2×#41011yescharacteristic
461C2×C11C2×#41311yescharacteristic
462D11—42no—
463C24—111no—
464C24C2×C4×D1111yescharacteristic
465C24C2×C4×D1111yescharacteristic
466#41—2216no—
467#41—2216no—
468C2×Q8—114no—
469C2×Q8—222no—
470C2×Q8—222no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—114no—
475C2×D4—222no—
476C2×D4—222no—
477C2×D4—222no—
478C2×D4—222no—
479C2×D4—222no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—111no—
485C22×C4—112no—
486C22×C4—112no—
487C22×C4—112no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—112no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—442no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4C2×C4×D1111yescharacteristic
516C22×C4C2×C4×D1111yescharacteristic
517C22×C4C2×C4×D1111yescharacteristic
518C22×C4C2×C4×D1111yescharacteristic
519C22×C4D4×D1112yes—
520C22×C4D4×D1112yes—
521C22×C4C23×D1111yescharacteristic
522M16—44no—
523M16—444no—
524C2×C8—24no—
525C2×C8—224no—
526C4⋊C4—22no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C4⋊C4—222no—
530C4⋊C4—222no—
531C4⋊C4—222no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—222no—
535C22⋊C4—222no—
536C22⋊C4—222no—
537C22⋊C4—222no—
538C42—21no—
539C42—21no—
540C42—111no—
541C42—111no—
542C42—111no—
543C42—111no—
544C42—112no—
545C42—112no—
546C42—112no—
547C42—112no—
548C42—112no—
549C42—112no—
550C42—221no—
551C42—221no—
552C42—221no—
553C42—221no—
554C42—221no—
555C42—221no—
556C42—221no—
557C42—221no—
558C42—221no—
559C42—221no—
560C11#1736611yescharacteristic, complemented, Sylow
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—112no—
570C23—221no—
571C23—221no—
572C23—441no—
573C23—441no—
574C23C22⋊C4×D1112yes—
575C23M16×D1112yes—
576C23C22×C4×D1111yescharacteristic
577Q8—228no—
578D4—28no—
579D4—228no—
580D4—228no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—111no—
594C2×C4—112no—
595C2×C4—112no—
596C2×C4—112no—
597C2×C4—111no—
598C2×C4—111no—
599C2×C4—111no—
600C2×C4—112no—
601C2×C4—112no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—441no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4C22⋊C4×D1111yescharacteristic
627C2×C4C22⋊C4×D1111yescharacteristic
628C2×C4M16×D1112yes—
629C2×C4C2×D4×D1112yes—
630C8—44no—
631C8—444no—
632C22—21no—
633C22—21no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—41no—
643C22—41no—
644C22—222no—
645C22—442no—
646C22—442no—
647C22—441no—
648C22—441no—
649C22C2×C22⋊C4×D1111yescharacteristic
650C22C2×M16×D1111yescharacteristic
651C22C2×M16×D1111yescharacteristic
652C4—22no—
653C4—22no—
654C4—21no—
655C4—41no—
656C4—41no—
657C4—114no—
658C4—112no—
659C4—221no—
660C4—221no—
661C4—222no—
662C4—221no—
663C4—222no—
664C4—441no—
665C4—441no—
666C4#1062235312yes—
667C2—21no—
668C2—21no—
669C2—42no—
670C2—42no—
671C2—442no—
672C2D11×#40711yescharacteristic
673C2C2×#1062235311yescharacteristic
674C2D11×#41311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1465C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4341C4
cosocleC22×C4×C11C24
hypercenter#1465D11
hypocenterC11#17366
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #13077245C2semidirect
3. #13066954C2semidirect
4. #13066952C2semidirect
5. #13066949C2semidirect
6. #13066947C2semidirect
7. #13066938C2semidirect
8. #13066935C2semidirect
9. C11×#1465C2semidirect
149. C2×C22⋊D11M16semidirect
185. C2×Dic22M16semidirect
228. #1465D11semidirect
560. C11#17366semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
#130772452
#130669542
#130669522
#130669492
#130669472
#130669382
#130669352
C11×#14652
#1736611