Finite Group Databasebeta

← #14720092

Subgroups — #14720092

Order 2816.

916 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623064C211yesmaximal, characteristic
2#13077703C212yesmaximal, complemented
3#13066983C212yesmaximal, complemented
4#13066982C212yesmaximal, complemented
5#13066966C212yesmaximal
6#13066958C211yesmaximal, characteristic, complemented
7#13066950C211yesmaximal, characteristic, complemented
8#13066949C211yesmaximal, characteristic, complemented
9#13066938C211yesmaximal, characteristic, complemented
10#13066929C211yesmaximal, characteristic, complemented
11C11×#1458C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×C4×C22⋊D11C411yescharacteristic
14C2×#66977C411yescharacteristic
15#10623064—22no—
16#10623064—22no—
17#10623064—22no—
18#10623064—22no—
19C2×#66950C411yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×#66941C411yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×#66938C411yescharacteristic
24C2×#66938C2211yescharacteristic
25C2×#66932C411yescharacteristic
26C2×#66932C2211yescharacteristic
27C2×#66929C411yescharacteristic
28C2×#66929C2211yescharacteristic
29C2×C4×Dic22C411yescharacteristic
30C2×C4×Dic22C2211yescharacteristic
31C11×#431C2212yes—
32#10622539C2212yes—
33#10622441—22no—
34#10622441—22no—
35#10622332C2212yes—
36#10622332C2212yes—
37#10622331C2212yes—
38#10622331C2212yes—
39#10622292—22no—
40C8×Dic22—22no—
41C11×#324C2211yescharacteristic
42C11×#324C2211yescharacteristic
43C11×#323C2212yes—
44#10622166C2211yescharacteristic
45#10622166C2211yescharacteristic
46#10622163C2212yes—
47#10622107C2212yes—
48#10622107C2212yes—
49#10622106C2212yes—
50#10622106C2212yes—
51C23×C4×C11C2×C411yescharacteristic
52C22×C22⋊D11C2×C411yescharacteristic
53C22×C4×D11C2×C411yescharacteristic
54C22×Dic22C2×C411yescharacteristic
55C22×Dic22C2×C411yescharacteristic
56C22×Dic22C2×C411yescharacteristic
57C11×#117—22no—
58C11×#117—22no—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4C2311yescharacteristic
63C2×C42×C11C2×C411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11C2×C411yescharacteristic
66C2×C22⋊Dic11C2×C411yescharacteristic
67C2×C22⋊Dic11C2×C411yescharacteristic
68C4×C22⋊D11—21no—
69C4×C22⋊D11—21no—
70C4×C22⋊D11—21no—
71C4×C22⋊D11—21no—
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2311yescharacteristic
77C2×C4⋊Dic11C2×C411yescharacteristic
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×C4⋊Dic11C2×C411yescharacteristic
80#66977—22no—
81#66977—22no—
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×Dic11⋊C4C2311yescharacteristic
89C2×C4×Dic11C2×C411yescharacteristic
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11C2×C411yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94#66950—22no—
95#66950—22no—
96#66945—22no—
97#66945—22no—
98#66941—22no—
99#66941—22no—
100#66940—22no—
101#66940—22no—
102#66938—22no—
103#66938—22no—
104#66938—22no—
105#66938—22no—
106#66932—22no—
107#66932—22no—
108#66932—22no—
109#66932—22no—
110#66929—22no—
111#66929—22no—
112#66929—22no—
113#66929—22no—
114C4×Dic22—21no—
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22—21no—
118C4×Dic22D412yes—
119C4×Dic22D412yes—
120C4×Dic22D412yes—
121C4×Dic22D412yes—
122C11×C4⋊C8—22no—
123C11×C22⋊C8C2312yes—
124C11×C22⋊C8C2312yes—
125C4×C8×C11—22no—
126C22⋊(C11⋊C8)C2312yes—
127C22⋊(C11⋊C8)C2312yes—
128#66879—22no—
129#66879—22no—
130Dic11⋊C8—22no—
131Dic11⋊C8—22no—
132Dic11⋊C8—22no—
133Dic11⋊C8—22no—
134C8×Dic11—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—22no—
137#66867—22no—
138#17428—111nomaximal, Sylow
139C24×C11C22×C411yescharacteristic
140C23×D11C22×C411yescharacteristic
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—41no—
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—42no—
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C411yescharacteristic
160C22×Dic11C22×C411yescharacteristic
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—22no—
164C2×C4×D11—41no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—41no—
170C2×Dic22—42no—
171C2×Dic22—42no—
172C2×Dic22C22⋊C412yes—
173C2×Dic22C22⋊C412yes—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11C2×D412yes—
183C42×C11C2×D412yes—
184C22⋊Dic11—21no—
185C22⋊Dic11—21no—
186C22⋊Dic11—22no—
187C22⋊Dic11—22no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—22no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—22no—
197C4⋊Dic11C22⋊C412yes—
198C4⋊Dic11C22⋊C412yes—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—21no—
202Dic11⋊C4—21no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4C22⋊C411yescharacteristic
206Dic11⋊C4C22⋊C411yescharacteristic
207Dic11⋊C4C22⋊C411yescharacteristic
208Dic11⋊C4C22⋊C411yescharacteristic
209Dic11⋊C4C22⋊C412yes—
210Dic11⋊C4C22⋊C412yes—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11C2×D412yes—
218C4×Dic11C2×D412yes—
219C4×Dic11C2×D412yes—
220C4×Dic11C2×D412yes—
221C2×C11⋊C8—22no—
222C2×C11⋊C8—22no—
223C2×#556—111no—
224#2984—112no—
225#1473—112no—
226#1473—112no—
227#1469—112no—
228#1467—111no—
229#1464—111no—
230#1464—111no—
231#1461—111no—
232#1458—111no—
233#1458D1111yescharacteristic, complemented
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11C23×C411yescharacteristic
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—41no—
244C22×D11—41no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11#13112yes—
261C2×C4×C11C22×D412yes—
262C22⋊D11—42no—
263C22⋊D11—42no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—22no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11C2×C22⋊C411yescharacteristic
278C2×Dic11C2×C22⋊C411yescharacteristic
279C2×Dic11C2×C22⋊C411yescharacteristic
280C2×Dic11C2×C22⋊C412yes—
281C2×Dic11C2×C22⋊C412yes—
282C2×Dic11C2×C22⋊C411yescharacteristic
283C4×D11—42no—
284C4×D11—42no—
285Dic22—24no—
286Dic22—42no—
287Dic22—44no—
288Dic22—42no—
289Dic22—42no—
290C8×C11—42no—
291C8×C11—42no—
292C11⋊C8—42no—
293C11⋊C8—42no—
294#556—222no—
295#556—222no—
296#556—222no—
297#556—222no—
298C2×C4⋊Q8—111no—
299C2×#126—111no—
300C2×#126—111no—
301C2×#126—111no—
302C2×#126—111no—
303C2×#124—111no—
304C2×#124—111no—
305C2×C22⋊Q8—111no—
306C2×C22⋊Q8—111no—
307C2×C4×Q8—111no—
308C2×C4×Q8—111no—
309C2×C4×Q8—111no—
310C2×C4×D4—111no—
311C2×#117—111no—
312C2×#117C2×D1111yescharacteristic
313#446—222no—
314#446—222no—
315#446—222no—
316C8×Q8—222no—
317#432—112no—
318#432—112no—
319#432—112no—
320#431—112no—
321#431—112no—
322#431C2×D1112yes—
323#324—111no—
324#324—111no—
325#324—112no—
326#324—112no—
327#324C2×D1111yescharacteristic
328#324C2×D1111yescharacteristic
329#323—112no—
330#323—112no—
331#323—112no—
332#323C2×D1112yes—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11C22×C22⋊C411yescharacteristic
341C22×C11C2×#13111yescharacteristic
342C22×C11#56811yescharacteristic
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—81no—
347C2×D11—81no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—41no—
355Dic11—22no—
356Dic11—21no—
357Dic11—21no—
358Dic11—22no—
359Dic11—21no—
360Dic11—41no—
361Dic11—41no—
362Dic11—41no—
363Dic11#41312yes—
364C22×Q8—111no—
365C22×Q8—111no—
366C22×Q8—111no—
367C22×D4—111no—
368C23×C4—111no—
369C23×C4C4×D1111yescharacteristic
370C4⋊Q8—222no—
371C4⋊Q8—222no—
372#126—222no—
373#126—222no—
374#126—222no—
375#126—222no—
376#126—222no—
377#126—222no—
378#126—222no—
379#126—222no—
380#124—222no—
381#124—222no—
382#124—222no—
383#124—222no—
384C22⋊Q8—222no—
385C22⋊Q8—222no—
386C22⋊Q8—222no—
387C22⋊Q8—222no—
388C4×Q8—112no—
389C4×Q8—112no—
390C4×Q8—112no—
391C4×Q8—112no—
392C4×Q8—221no—
393C4×Q8—221no—
394C4×Q8—221no—
395C4×Q8—221no—
396C4×Q8—222no—
397C4×Q8—222no—
398C4×D4—221no—
399C4×D4—221no—
400C4×D4—221no—
401C4×D4—221no—
402#117—22no—
403#117—22no—
404#117—222no—
405#117—222no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4C4×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—111no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—111no—
421C2×C22⋊C4—111no—
422C2×C22⋊C4—111no—
423C2×C22⋊C4—111no—
424C2×C22⋊C4—111no—
425C2×C22⋊C4—111no—
426C2×C22⋊C4C4×D1111yescharacteristic
427C2×C22⋊C4C22×D1111yescharacteristic
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42C4×D1111yescharacteristic
434C2×C42C22×D1111yescharacteristic
435C4⋊C8—22no—
436C4⋊C8—222no—
437C4⋊C8—222no—
438C4⋊C8—222no—
439C4⋊C8—222no—
440C4⋊C8—222no—
441C22⋊C8—112no—
442C22⋊C8—112no—
443C22⋊C8C22×D1112yes—
444C22⋊C8C22×D1112yes—
445#97—222no—
446#97—222no—
447#97—222no—
448C4×C8—22no—
449C4×C8—222no—
450C4×C8—222no—
451C2×C11—21no—
452C2×C11—21no—
453C2×C11—81no—
454C2×C11#288011yescharacteristic
455C2×C11#288411yescharacteristic
456C2×C11C2×#41311yescharacteristic
457D11—81no—
458C24—111no—
459C24C2×C4×D1111yescharacteristic
460C2×Q8—112no—
461C2×Q8—112no—
462C2×Q8—222no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—222no—
466C2×Q8—441no—
467C2×Q8—442no—
468C2×Q8—442no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—442no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—41no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—222no—
486C22×C4—441no—
487C22×C4C2×C4×D1111yescharacteristic
488C22×C4C2×C4×D1111yescharacteristic
489C22×C4C2×C4×D1111yescharacteristic
490C22×C4C2×C4×D1111yescharacteristic
491C22×C4C2×C4×D1111yescharacteristic
492C22×C4C23×D1111yescharacteristic
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—222no—
496C2×C8—222no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—111no—
500C4⋊C4—111no—
501C4⋊C4—111no—
502C4⋊C4—111no—
503C4⋊C4—112no—
504C4⋊C4—112no—
505C4⋊C4—112no—
506C4⋊C4—112no—
507C4⋊C4—222no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—221no—
521C22⋊C4—221no—
522C22⋊C4—222no—
523C22⋊C4—222no—
524C22⋊C4—221no—
525C22⋊C4—221no—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C42—21no—
529C42—21no—
530C42—112no—
531C42—112no—
532C42—112no—
533C42—112no—
534C42—221no—
535C42—221no—
536C42—221no—
537C42—221no—
538C42—221no—
539C42—221no—
540C42D4×D1112yes—
541C42D4×D1112yes—
542C11#1742811yescharacteristic, complemented, Sylow
543C23—21no—
544C23—21no—
545C23—21no—
546C23—41no—
547C23—41no—
548C23—221no—
549C23—221no—
550C23—221no—
551C23—441no—
552C23—441no—
553C23C22×C4×D1111yescharacteristic
554Q8—224no—
555Q8—442no—
556Q8—444no—
557Q8—442no—
558Q8—442no—
559D4—442no—
560D4—442no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—111no—
574C2×C4—111no—
575C2×C4—111no—
576C2×C4—111no—
577C2×C4—112no—
578C2×C4—112no—
579C2×C4—222no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4C22⋊C4×D1111yescharacteristic
595C2×C4C22⋊C4×D1111yescharacteristic
596C2×C4C22⋊C4×D1112yes—
597C2×C4#6695412yes—
598C2×C4C2×D4×D1112yes—
599C8—42no—
600C8—42no—
601C8—442no—
602C8—442no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—81no—
609C22—81no—
610C22—441no—
611C22—441no—
612C22—441no—
613C22—881no—
614C22—881no—
615C22C2×C22⋊C4×D1111yescharacteristic
616C22C2×#6695411yescharacteristic
617C22#1062327611yescharacteristic
618C4—22no—
619C4—21no—
620C4—21no—
621C4—22no—
622C4—22no—
623C4—41no—
624C4—41no—
625C4—112no—
626C4—221no—
627C4—221no—
628C4—222no—
629C4—221no—
630C4—222no—
631C4—441no—
632C4—441no—
633C4—441no—
634C2—21no—
635C2—21no—
636C2—81no—
637C2—881no—
638C2#1307706211yescharacteristic
639C2#1307707811yescharacteristic
640C2D11×#41311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1458C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1458D11
hypocenterC11#17428
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #13077703C2semidirect
3. #13066983C2semidirect
4. #13066982C2semidirect
6. #13066958C2semidirect
7. #13066950C2semidirect
8. #13066949C2semidirect
9. #13066938C2semidirect
10. #13066929C2semidirect
11. C11×#1458C2semidirect
233. #1458D11semidirect
542. C11#17428semidirect

Maximal subgroups

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

subgroupindex
C2×#106230642
#130777032
#130669832
#130669822
#130669662
#130669582
#130669502
#130669492
#130669382
#130669292
C11×#14582
#1742811