Finite Group Databasebeta

← #14720419

Subgroups — #14720419

Order 2816.

988 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13077244C211yesmaximal, characteristic
3D11×#431C211yesmaximal, characteristic
4#13067087C214yesmaximal, complemented
5#13067069C214yesmaximal, complemented
6#13067012C211yesmaximal, characteristic, complemented
7#13067011C211yesmaximal, characteristic, complemented
8#13067010C211yesmaximal, characteristic, complemented
9C11×#1479C211yesmaximal, 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×#431C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622450C2212yes—
34#10622448C2212yes—
35#10622446—21no—
36D11×C4⋊C8—21no—
37#10622339—21no—
38D11×C22⋊C8—21no—
39#10622332—21no—
40#10622331—21no—
41C4×#4313—21no—
42#10622298—21no—
43#10622298C2212yes—
44C4×C8×D11C2212yes—
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
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11C2×C412yes—
58C4×Q8×C11C2312yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63#66999—21no—
64#66999—21no—
65#66999C2×C412yes—
66#66999C2×C412yes—
67#66997—21no—
68#66997—21no—
69#66997C2×C412yes—
70#66997C2×C412yes—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2×C411yescharacteristic
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11C2×C411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×#4313—22no—
85C2×C8×D11—22no—
86#66950—21no—
87#66950—21no—
88#66950C2×C412yes—
89#66950C2×C412yes—
90#66949—22no—
91#66949—22no—
92#66949—22no—
93#66949—22no—
94#66942—22no—
95#66942—22no—
96#66942—22no—
97#66942—22no—
98#66941—21no—
99#66941—21no—
100#66941C2×C412yes—
101#66941C2×C412yes—
102#66925—22no—
103#66925—22no—
104#66925—22no—
105#66925—22no—
106C42×D11C2×C411yescharacteristic
107C42×D11C2×C411yescharacteristic
108C42×D11D411yescharacteristic
109C42×D11D411yescharacteristic
110C42×D11D411yescharacteristic
111C42×D11D411yescharacteristic
112C42×D11C2311yescharacteristic
113C42×D11C2311yescharacteristic
114C4×Dic22—21no—
115C4×Dic22—21no—
116C4×Dic22—22no—
117C4×Dic22—22no—
118C4×Dic22—22no—
119C4×Dic22—22no—
120C4×Dic22C2×C412yes—
121C4×Dic22C2312yes—
122C11×C4⋊C8—21no—
123C11×C4⋊C8C2312yes—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—21no—
126C4×C8×C11—21no—
127C4×C8×C11C2312yes—
128C22⋊(C11⋊C8)—21no—
129C22⋊(C11⋊C8)—21no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132#66879—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2312yes—
138C4×C11⋊C8—21no—
139C4×C11⋊C8C2312yes—
140#17479—111nomaximal, Sylow
141C23×D11C22⋊C411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11C22×C412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C22⋊C411yescharacteristic
154C22×Dic11C22⋊C411yescharacteristic
155C22×Dic11C22⋊C411yescharacteristic
156C2×C4×D11—24no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—42no—
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×D11C22×C411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×C4×D11C2×D411yescharacteristic
170C2×C4×D11C2×D411yescharacteristic
171C2×C4×D11C2×D411yescharacteristic
172C2×Dic22—22no—
173C2×Dic22—22no—
174C2×Dic22—21no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—44no—
178C2×Dic22C22×C412yes—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4C22×C412yes—
185C42×C11—22no—
186C42×C11—22no—
187C42×C11C22×C411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2411yescharacteristic
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—22no—
195C4⋊Dic11—22no—
196C4⋊Dic11—22no—
197C4⋊Dic11—21no—
198C4⋊Dic11C22×C412yes—
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—
208Dic11⋊C4—22no—
209C4×Dic11—22no—
210C4×Dic11—22no—
211C4×Dic11C22⋊C411yescharacteristic
212C4×Dic11C22⋊C411yescharacteristic
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C22⋊C411yescharacteristic
215C4×Dic11C22⋊C411yescharacteristic
216C4×Dic11C22⋊C411yescharacteristic
217C4×Dic11C22×C411yescharacteristic
218C4×Dic11C22×C411yescharacteristic
219C4×Dic11C2×D411yescharacteristic
220C4×Dic11C2×D411yescharacteristic
221C4×Dic11C2×D411yescharacteristic
222C4×Dic11C2×D411yescharacteristic
223C2×C11⋊C8—22no—
224C2×C11⋊C8—22no—
225#4313—44no—
226C8×D11—44no—
227C2×#533—111no—
228#2920—111no—
229C2×#431—111no—
230#1497—114no—
231#1493—114no—
232#1479—111no—
233#1479—111no—
234#1479—111no—
235#1479D1111yescharacteristic, complemented
236C23×C11C2×C22⋊C411yescharacteristic
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—41no—
240C22×D11C2×C22⋊C411yescharacteristic
241C22×D11C2×C22⋊C411yescharacteristic
242Q8×C11—22no—
243Q8×C11—22no—
244Q8×C11—42no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C2×C22⋊C411yescharacteristic
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11#13112yes—
255C2×C4×C11#13112yes—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11C2×C22⋊C411yescharacteristic
267C2×Dic11C2×C22⋊C411yescharacteristic
268C2×Dic11C2×C22⋊C411yescharacteristic
269C2×Dic11C2×C22⋊C411yescharacteristic
270C2×Dic11C2×C22⋊C411yescharacteristic
271C2×Dic11C2×C22⋊C411yescharacteristic
272C4×D11—22no—
273C4×D11—21no—
274C4×D11—21no—
275C4×D11—21no—
276C4×D11—21no—
277C4×D11—22no—
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—22no—
281C4×D11—22no—
282C4×D11—22no—
283C4×D11—41no—
284C4×D11—41no—
285C4×D11#13714yes—
286Dic22—22no—
287Dic22—22no—
288Dic22—44no—
289Dic22—42no—
290Dic22—44no—
291C8×C11—42no—
292C8×C11—42no—
293C11⋊C8—42no—
294C11⋊C8—42no—
295#533—112no—
296#533—112no—
297#533—112no—
298#533—112no—
299#533—221no—
300#533—221no—
301#533—221no—
302#533—221no—
303C2×C4⋊Q8—111no—
304C2×C4⋊Q8—111no—
305C2×#125—221no—
306C2×C22⋊Q8—111no—
307C2×C22⋊Q8—111no—
308C2×C22⋊Q8—221no—
309C2×C4×Q8—111no—
310C2×C4×Q8—221no—
311C2×C4×Q8C2×D1111yescharacteristic
312C2×#117—221no—
313C22×C42—111no—
314#432—112no—
315#432—221no—
316#431—111no—
317#431—112no—
318#431—111no—
319#431—221no—
320#431—221no—
321#431—221no—
322#431C2×D1111yescharacteristic
323#431C2×D1111yescharacteristic
324#423—112no—
325C2×C4⋊C8—221no—
326#407—221no—
327C2×C22⋊C8—221no—
328C4×M16—221no—
329C2×C4×C8—112no—
330Q8⋊C8—114no—
331Q8⋊C8—114no—
332Q8⋊C8—114no—
333Q8⋊C8C2×D1114yescomplemented
334C22×C11—21no—
335C22×C11—21no—
336C22×C11#40812yes—
337C22×C11C22×C22⋊C411yescharacteristic
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—21no—
341C2×D11—21no—
342C2×D11—21no—
343C2×D11—44no—
344C2×D11#41912yes—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11#40812yes—
351C4×C11C2×#13111yescharacteristic
352C4×C11C2×#13111yescharacteristic
353C4×C11C2×#13712yes—
354Dic11—21no—
355Dic11—21no—
356Dic11—21no—
357Dic11—21no—
358Dic11—42no—
359Dic11—42no—
360Dic11#41912yes—
361Dic11#42112yes—
362C22×Q8—111no—
363C22×Q8—221no—
364C22×Q8C4×D1111yescharacteristic
365C23×C4—111no—
366C23×C4—111no—
367C23×C4—111no—
368C2×M16—222no—
369C22×C8—222no—
370C4⋊Q8—112no—
371C4⋊Q8—112no—
372C4⋊Q8—112no—
373C4⋊Q8—112no—
374C4⋊Q8—221no—
375C4⋊Q8—221no—
376C4⋊Q8—221no—
377C4⋊Q8—221no—
378#125—222no—
379#125—222no—
380#125—222no—
381#125—222no—
382C22⋊Q8—112no—
383C22⋊Q8—112no—
384C22⋊Q8—112no—
385C22⋊Q8—112no—
386C22⋊Q8—221no—
387C22⋊Q8—221no—
388C22⋊Q8—222no—
389C22⋊Q8—222no—
390C22⋊Q8—222no—
391C22⋊Q8—222no—
392C22⋊Q8—221no—
393C22⋊Q8—221no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—112no—
397C4×Q8—112no—
398C4×Q8—222no—
399C4×Q8—222no—
400C4×Q8—222no—
401C4×Q8—222no—
402C4×Q8—221no—
403C4×Q8—221no—
404C4×Q8C4×D1112yes—
405C4×Q8C22×D1112yes—
406#117—222no—
407#117—222no—
408#117—222no—
409#117—222no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C4×D1111yescharacteristic
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C42—21no—
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—111no—
432C2×C42—111no—
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435C4⋊C8—21no—
436C4⋊C8—112no—
437C4⋊C8—222no—
438C4⋊C8—222no—
439C4⋊C8—221no—
440C4⋊C8C22×D1112yes—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—222no—
444C22⋊C8—222no—
445C22⋊C8—221no—
446C22⋊C8—221no—
447#97—222no—
448C4×C8—21no—
449C4×C8—112no—
450C4×C8—222no—
451C4×C8—221no—
452C4×C8C22×D1112yes—
453C2×C11—22no—
454C2×C11C2×#40811yescharacteristic
455C2×C11C2×#41911yescharacteristic
456C2×C11C2×#42111yescharacteristic
457D11—22no—
458D11—41no—
459C24—111no—
460C2×Q8—21no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—112no—
464C2×Q8—222no—
465C2×Q8—222no—
466C2×Q8—221no—
467C2×Q8—222no—
468C2×Q8—222no—
469C2×Q8—444no—
470C2×Q8C2×C4×D1112yes—
471C22×C4—21no—
472C22×C4—21no—
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—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—224no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—442no—
494C22×C4C2×C4×D1111yescharacteristic
495C22×C4D4×D1111yescharacteristic
496C22×C4D4×D1111yescharacteristic
497M16—444no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—222no—
501C2×C8—222no—
502C2×C8—444no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—112no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C4⋊C4—222no—
517C4⋊C4—221no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4C2×C4×D1112yes—
521C22⋊C4—222no—
522C22⋊C4—222no—
523C22⋊C4—222no—
524C22⋊C4—222no—
525C42—22no—
526C42—22no—
527C42—111no—
528C42—111no—
529C42—111no—
530C42—111no—
531C42—111no—
532C42—111no—
533C42—111no—
534C42—111no—
535C42—111no—
536C42—111no—
537C42—111no—
538C42—111no—
539C42—222no—
540C42—222no—
541C42C2×C4×D1111yescharacteristic
542C42D4×D1111yescharacteristic
543C42D4×D1111yescharacteristic
544C42C23×D1111yescharacteristic
545C11#1747911yescharacteristic, complemented, Sylow
546C23—111no—
547C23—111no—
548C23—222no—
549C23—222no—
550C23—441no—
551C23C22⋊C4×D1111yescharacteristic
552Q8—22no—
553Q8—22no—
554Q8—42no—
555Q8—222no—
556Q8—222no—
557Q8—444no—
558Q8—444no—
559Q8—442no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—111no—
567C2×C4—111no—
568C2×C4—114no—
569C2×C4—111no—
570C2×C4—111no—
571C2×C4—111no—
572C2×C4—111no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4C22⋊C4×D1111yescharacteristic
594C2×C4C22⋊C4×D1111yescharacteristic
595C2×C4C22⋊C4×D1111yescharacteristic
596C2×C4#6695412yes—
597C2×C4#6696012yes—
598C2×C4C22×C4×D1111yescharacteristic
599C2×C4C2×D4×D1111yescharacteristic
600C2×C4C2×D4×D1111yescharacteristic
601C8—42no—
602C8—42no—
603C8—442no—
604C8—442no—
605C22—21no—
606C22—21no—
607C22—112no—
608C22—221no—
609C22—221no—
610C22—221no—
611C22—221no—
612C22—221no—
613C22—444no—
614C22#1062234012yes—
615C22C2×C22⋊C4×D1111yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—42no—
620C4—42no—
621C4—112no—
622C4—112no—
623C4—221no—
624C4—221no—
625C4—221no—
626C4—221no—
627C4—442no—
628C4—442no—
629C4#1062234012yes—
630C4C2×#6695411yescharacteristic
631C4C2×#6696011yescharacteristic
632C4D11×#13712yes—
633C2—22no—
634C2—222no—
635C2—441no—
636C2C2×#1062234011yescharacteristic
637C2D11×#41911yescharacteristic
638C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1479C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1479D11
hypocenterC11#17479
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
4. #13067087C2semidirect
5. #13067069C2semidirect
6. #13067012C2semidirect
7. #13067011C2semidirect
8. #13067010C2semidirect
9. C11×#1479C2semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
235. #1479D11semidirect
333. Q8⋊C8C2×D11semidirect
545. C11#17479semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130772442
D11×#4312
#130670872
#130670692
#130670122
#130670112
#130670102
C11×#14792
#1747911