Finite Group Databasebeta

← #14720507

Subgroups — #14720507

Order 2816.

958 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic
3#13077244C211yesmaximal, characteristic
4#13067087C214yesmaximal, complemented
5#13067046C211yesmaximal, characteristic, complemented
6#13067045C211yesmaximal, characteristic, complemented
7#13067044C211yesmaximal, characteristic, complemented
8#13067035C214yesmaximal, complemented
9C11×#1487C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66999C411yescharacteristic
12C2×#66997C411yescharacteristic
13#10623109—21no—
14#10623109—21no—
15#10623109—21no—
16#10623109—21no—
17#10623109C412yes—
18#10623109C412yes—
19#10623109C2212yes—
20#10623109C2212yes—
21C2×#66950C411yescharacteristic
22C2×#66949—21no—
23C2×#66942—21no—
24C2×#66941C411yescharacteristic
25C2×#66925—21no—
26C2×C42×D11C2211yescharacteristic
27C2×C4×Dic22—21no—
28C2×C4×Dic22C2211yescharacteristic
29C11×#431C2211yescharacteristic
30C11×#423C2211yescharacteristic
31#10622739—21no—
32M16×Dic11—21no—
33#10622538C2211yescharacteristic
34#10622537C2211yescharacteristic
35#10622450—21no—
36#10622448—21no—
37#10622448—21no—
38#10622448C2212yes—
39#10622446—21no—
40#10622446C2212yes—
41#10622339—21no—
42#10622332—21no—
43C4×#4313C2212yes—
44#10622298C2212yes—
45C11×Q8⋊C8C2214yescomplemented
46Q8⋊(C11⋊C8)C2214yescomplemented
47#10622122C2214yescomplemented
48#10622094C2214yescomplemented
49C22×Q8×C11C2×C411yescharacteristic
50C22×C4×D11C2×C411yescharacteristic
51C22×C4×D11D411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×Dic22—21no—
54C22×Dic22C2×C411yescharacteristic
55C2×C11×M16—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11C2×C412yes—
59C4×Q8×C11C2312yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64#66999—21no—
65#66999—21no—
66#66999C2×C412yes—
67#66999C2×C412yes—
68#66997—21no—
69#66997—21no—
70#66997C2×C412yes—
71#66997C2×C412yes—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11C2×C411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×#4318—21no—
86C2×#4313—22no—
87#66950—21no—
88#66950—21no—
89#66950C2×C412yes—
90#66950C2×C412yes—
91#66949—22no—
92#66949—22no—
93#66949—22no—
94#66949—22no—
95#66942—22no—
96#66942—22no—
97#66942—22no—
98#66942—22no—
99#66941—21no—
100#66941—21no—
101#66941C2×C412yes—
102#66941C2×C412yes—
103#66925—22no—
104#66925—22no—
105#66925—22no—
106#66925—22no—
107C42×D11C2×C411yescharacteristic
108C42×D11C2×C411yescharacteristic
109C42×D11D411yescharacteristic
110C42×D11D411yescharacteristic
111C42×D11D411yescharacteristic
112C42×D11D411yescharacteristic
113C42×D11C2311yescharacteristic
114C42×D11C2311yescharacteristic
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22—22no—
118C4×Dic22—22no—
119C4×Dic22—22no—
120C4×Dic22—22no—
121C4×Dic22C2×C412yes—
122C4×Dic22C2312yes—
123C11×C4⋊C8—21no—
124C11×C4⋊C8—21no—
125C11×C4⋊C8C2312yes—
126C11×C22⋊C8—21no—
127C4×C8×C11C2312yes—
128C22⋊(C11⋊C8)—21no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132#66879—22no—
133#66879—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2312yes—
139C4×C11⋊C8C2312yes—
140#17491—111nomaximal, Sylow
141C23×D11C22⋊C411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—42no—
144C2×Q8×C11C22×C412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C22⋊C411yescharacteristic
153C22×Dic11C22⋊C411yescharacteristic
154C22×Dic11C22⋊C411yescharacteristic
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11C22⋊C411yescharacteristic
160C2×C4×D11C22⋊C411yescharacteristic
161C2×C4×D11C22⋊C411yescharacteristic
162C2×C4×D11C22⋊C411yescharacteristic
163C2×C4×D11C22⋊C411yescharacteristic
164C2×C4×D11C22⋊C411yescharacteristic
165C2×C4×D11C22×C411yescharacteristic
166C2×C4×D11C22×C411yescharacteristic
167C2×C4×D11C2×D411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×C4×D11C2×D411yescharacteristic
170C2×C4×D11C2×D411yescharacteristic
171C2×Dic22—22no—
172C2×Dic22—22no—
173C2×Dic22—21no—
174C2×Dic22—42no—
175C2×Dic22—44no—
176C2×Dic22C22×C412yes—
177C11×M16—42no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4C22×C412yes—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11C22×C411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2411yescharacteristic
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11—22no—
196C4⋊Dic11—21no—
197C4⋊Dic11C22×C412yes—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208C4×Dic11—22no—
209C4×Dic11—22no—
210C4×Dic11C22⋊C411yescharacteristic
211C4×Dic11C22⋊C411yescharacteristic
212C4×Dic11C22⋊C411yescharacteristic
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C22⋊C411yescharacteristic
215C4×Dic11C22⋊C411yescharacteristic
216C4×Dic11C22×C411yescharacteristic
217C4×Dic11C22×C411yescharacteristic
218C4×Dic11C2×D411yescharacteristic
219C4×Dic11C2×D411yescharacteristic
220C4×Dic11C2×D411yescharacteristic
221C4×Dic11C2×D411yescharacteristic
222#4318—42no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—22no—
225#4313—44no—
226C2×#533—111no—
227#2920—111no—
228#2920—111no—
229#1497—114no—
230#1487—111no—
231#1487—111no—
232#1487—111no—
233#1487D1111yescharacteristic, complemented
234#1485—114no—
235C23×C11C2×C22⋊C411yescharacteristic
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11C2×C22⋊C411yescharacteristic
240C22×D11C2×C22⋊C411yescharacteristic
241Q8×C11—24no—
242Q8×C11—42no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11#13712yes—
253C2×C4×C11#13712yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—41no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11C2×C22⋊C411yescharacteristic
265C2×Dic11C2×C22⋊C411yescharacteristic
266C2×Dic11C2×C22⋊C411yescharacteristic
267C2×Dic11C2×C22⋊C411yescharacteristic
268C2×Dic11C2×C22⋊C411yescharacteristic
269C2×Dic11C2×C22⋊C411yescharacteristic
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—21no—
273C4×D11—21no—
274C4×D11—21no—
275C4×D11—21no—
276C4×D11—22no—
277C4×D11—22no—
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—41no—
283C4×D11—41no—
284Dic22—24no—
285Dic22—44no—
286Dic22—42no—
287Dic22—44no—
288C8×C11—42no—
289C8×C11—42no—
290C11⋊C8—42no—
291C11⋊C8—42no—
292#533—112no—
293#533—112no—
294#533—112no—
295#533—112no—
296#533—221no—
297#533—221no—
298#533—221no—
299#533—221no—
300C2×C4⋊Q8—111no—
301C2×C4⋊Q8—111no—
302C2×#125—221no—
303C2×C22⋊Q8—111no—
304C2×C22⋊Q8—111no—
305C2×C22⋊Q8—221no—
306C2×C4×Q8—111no—
307C2×C4×Q8—221no—
308C2×C4×Q8C2×D1111yescharacteristic
309C2×#117—221no—
310C22×C42—111no—
311#432—112no—
312#432—221no—
313#432—221no—
314#432—221no—
315#431—111no—
316#431—112no—
317#431—112no—
318#431—221no—
319#431C2×D1111yescharacteristic
320#423—111no—
321#423—221no—
322#423C2×D1111yescharacteristic
323#407—221no—
324#407—221no—
325C4×M16—112no—
326C4×M16—221no—
327Q8⋊C8—114no—
328Q8⋊C8—114no—
329Q8⋊C8—114no—
330Q8⋊C8C2×D1114yescomplemented
331C22×C11—21no—
332C22×C11—21no—
333C22×C11#41912yes—
334C22×C11C22×C22⋊C411yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—21no—
341C2×D11—44no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11#41912yes—
348C4×C11#56812yes—
349C4×C11C2×#13711yescharacteristic
350C4×C11C2×#13711yescharacteristic
351Dic11—21no—
352Dic11—21no—
353Dic11—21no—
354Dic11—21no—
355Dic11—21no—
356Dic11—42no—
357Dic11—42no—
358Dic11#42112yes—
359C22×Q8—111no—
360C22×Q8—221no—
361C22×Q8C4×D1111yescharacteristic
362C23×C4—111no—
363C23×C4—111no—
364C23×C4—111no—
365C2×M16—21no—
366C2×M16—222no—
367C2×M16—221no—
368C4⋊Q8—112no—
369C4⋊Q8—112no—
370C4⋊Q8—112no—
371C4⋊Q8—112no—
372C4⋊Q8—221no—
373C4⋊Q8—221no—
374C4⋊Q8—221no—
375C4⋊Q8—221no—
376#125—222no—
377#125—222no—
378#125—222no—
379#125—222no—
380C22⋊Q8—112no—
381C22⋊Q8—112no—
382C22⋊Q8—112no—
383C22⋊Q8—112no—
384C22⋊Q8—221no—
385C22⋊Q8—221no—
386C22⋊Q8—222no—
387C22⋊Q8—222no—
388C22⋊Q8—222no—
389C22⋊Q8—222no—
390C22⋊Q8—221no—
391C22⋊Q8—221no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—112no—
395C4×Q8—112no—
396C4×Q8—222no—
397C4×Q8—222no—
398C4×Q8—222no—
399C4×Q8—222no—
400C4×Q8—221no—
401C4×Q8—221no—
402C4×Q8C4×D1112yes—
403C4×Q8C22×D1112yes—
404#117—222no—
405#117—222no—
406#117—222no—
407#117—222no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4C4×D1111yescharacteristic
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C42—21no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—221no—
432C2×C42C22×D1111yescharacteristic
433C4⋊C8—21no—
434C4⋊C8—21no—
435C4⋊C8—112no—
436C4⋊C8—222no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439C4⋊C8C22×D1112yes—
440C22⋊C8—21no—
441C22⋊C8—222no—
442C22⋊C8—222no—
443C22⋊C8—222no—
444C22⋊C8—221no—
445#97—222no—
446#97—222no—
447C4×C8—112no—
448C4×C8—222no—
449C4×C8C22×D1112yes—
450C2×C11—22no—
451C2×C11#287911yescharacteristic
452C2×C11C2×#41911yescharacteristic
453C2×C11C2×#42111yescharacteristic
454D11—41no—
455D11—41no—
456C24—111no—
457C2×Q8—21no—
458C2×Q8—42no—
459C2×Q8—112no—
460C2×Q8—222no—
461C2×Q8—222no—
462C2×Q8—221no—
463C2×Q8—442no—
464C2×Q8—444no—
465C2×Q8C2×C4×D1112yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4C2×C4×D1111yescharacteristic
490C22×C4D4×D1111yescharacteristic
491C22×C4D4×D1111yescharacteristic
492M16—42no—
493M16—444no—
494M16—442no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—222no—
498C2×C8—222no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—112no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—221no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C4⋊C4C2×C4×D1112yes—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C42—22no—
522C42—22no—
523C42—111no—
524C42—111no—
525C42—111no—
526C42—111no—
527C42—111no—
528C42—111no—
529C42—111no—
530C42—111no—
531C42—111no—
532C42—111no—
533C42—111no—
534C42—111no—
535C42—222no—
536C42—222no—
537C42C2×C4×D1111yescharacteristic
538C42D4×D1111yescharacteristic
539C42D4×D1111yescharacteristic
540C42C23×D1111yescharacteristic
541C11#1749111yescharacteristic, complemented, Sylow
542C23—111no—
543C23—111no—
544C23—222no—
545C23—441no—
546C23—441no—
547C23C22⋊C4×D1111yescharacteristic
548Q8—24no—
549Q8—42no—
550Q8—224no—
551Q8—442no—
552Q8—444no—
553Q8—444no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—111no—
561C2×C4—111no—
562C2×C4—111no—
563C2×C4—111no—
564C2×C4—111no—
565C2×C4—111no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4C22⋊C4×D1111yescharacteristic
588C2×C4C22⋊C4×D1111yescharacteristic
589C2×C4C22⋊C4×D1111yescharacteristic
590C2×C4#6696812yes—
591C2×C4#6697112yes—
592C2×C4C22×C4×D1111yescharacteristic
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4C2×D4×D1111yescharacteristic
595C8—42no—
596C8—42no—
597C8—442no—
598C8—442no—
599C22—21no—
600C22—21no—
601C22—221no—
602C22—221no—
603C22—221no—
604C22—221no—
605C22—221no—
606C22—221no—
607C22—444no—
608C22#1062241512yes—
609C22C2×C22⋊C4×D1111yescharacteristic
610C4—21no—
611C4—21no—
612C4—21no—
613C4—42no—
614C4—42no—
615C4—112no—
616C4—221no—
617C4—221no—
618C4—221no—
619C4—221no—
620C4—221no—
621C4—442no—
622C4—442no—
623C4#1062241512yes—
624C4#1062327612yes—
625C4C2×#6696811yescharacteristic
626C4C2×#6697111yescharacteristic
627C2—22no—
628C2—441no—
629C2—441no—
630C2#1307705911yescharacteristic
631C2C2×#1062241511yescharacteristic
632C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1487C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1487D11
hypocenterC11#17491
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
4. #13067087C2semidirect
5. #13067046C2semidirect
6. #13067045C2semidirect
7. #13067044C2semidirect
8. #13067035C2semidirect
9. C11×#1487C2semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
233. #1487D11semidirect
330. Q8⋊C8C2×D11semidirect
541. C11#17491semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130772482
#130772442
#130670872
#130670462
#130670452
#130670442
#130670352
C11×#14872
#1749111