Finite Group Databasebeta

← #14913205

Subgroups — #14913205

Order 2816.

2510 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623053C211yesmaximal, characteristic
2#13071586C214yesmaximal, complemented
3#13071585C212yesmaximal, complemented
4#13071535C212yesmaximal, complemented
5#13071510C212yesmaximal, complemented
6#13071509C211yesmaximal, characteristic, complemented
7#13071504C212yesmaximal, complemented
8#13071456C211yesmaximal, characteristic
9#13071453C211yesmaximal, characteristic
10#13071076C214yesmaximal, complemented
11#13071074C212yesmaximal, complemented
12#13071013C212yesmaximal, complemented
13#13071011C211yesmaximal, characteristic, complemented
14C4×#66940C212yesmaximal, complemented
15C4×#66945C212yesmaximal, complemented
16C4×#66930C211yesmaximal, characteristic, complemented
17C11×#2347C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21#10623053C4116yescomplemented
22C2×#66946C2211yescharacteristic
23C2×#66946C2211yescharacteristic
24C2×#66945C2214yes—
25C2×#66940C2212yes—
26C2×#66940C2211yescharacteristic
27C2×#66940C2211yescharacteristic
28C2×(C22⋊D11)⋊C4C2212yes—
29C2×(C22⋊D11)⋊C4C2212yes—
30C2×#66930C2212yes—
31C2×#66925C2212yes—
32C2×C42×D11C2212yes—
33C2×C4×Dic22C2212yes—
34C11×#389C2212yes—
35C11×#388C2214yes—
36C11×#383C2212yes—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C22⋊C4C2211yescharacteristic
41#10622825C2211yescharacteristic
42C4×C22⋊Dic11C2211yescharacteristic
43#10622603C2214yes—
44#10622601C2212yes—
45#10622598C2212yes—
46#10622590C2212yes—
47C4⋊C4×Dic11C2214yes—
48C4⋊C4×Dic11C2212yes—
49C4⋊C4×Dic11C2212yes—
50#10622585C2214yes—
51#10622570C2214yes—
52#10622570C2214yes—
53#10622564C2214yes—
54#10622556C2212yes—
55C22⋊C4×Dic11C2212yes—
56C22⋊C4×Dic11C2212yes—
57#10622553C2214yes—
58#10622552C2212yes—
59C4×(C2×D11)⋊C4C2214yes—
60#10622550C2212yes—
61C4×C4⋊Dic11C2212yes—
62C4×Dic11⋊C4C2212yes—
63C4×Dic11⋊C4C2214yes—
64C42×Dic11C2212yes—
65C42×Dic11C2214yes—
66#10622283C2214yes—
67#10622282C2214yes—
68#10622280C2212yes—
69#10622280C2212yes—
70#10622279C2212yes—
71#10622279C2212yes—
72#10622279C2214yes—
73#10622277C2214yes—
74#10622264C2212yes—
75#10622263C2214yes—
76#10622262C2211yescharacteristic
77#10622262C2211yescharacteristic
78#10622262C2214yes—
79#10622262C2214yes—
80#10622261C2211yescharacteristic
81#10622261C2211yescharacteristic
82#10622261C2212yes—
83#10622260C2214yes—
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11C2312yes—
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C2×#4339—28no—
89C2×#4339C2×C418yes—
90C22×D44C2311yescharacteristic
91C22×C4×D11C2312yes—
92C22×C4×D11C2312yes—
93C22×C4×D11C2312yes—
94C22×Dic22C2311yescharacteristic
95C11×#117C2×C418yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4C2312yes—
101C2×C11×C22⋊C4C2312yes—
102C2×C11×C22⋊C4C2312yes—
103C2×C42×C11C2312yes—
104C2×C42×C11C2314yes—
105C2×C42×C11C2312yes—
106C2×C22⋊Dic11C2312yes—
107C2×C22⋊Dic11C2312yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2312yes—
113C2×(C2×D11)⋊C4C2312yes—
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2312yes—
122C2×C4×Dic11C2×C418yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2311yescharacteristic
135C2×C4×Dic11C2311yescharacteristic
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2312yes—
138#66946C2×C418yes—
139#66946C2×C418yes—
140#66945—216no—
141#66940—28no—
142#66940C2×C418yes—
143#66940C2×C418yes—
144(C22⋊D11)⋊C4C2×C4116yes—
145(C22⋊D11)⋊C4C2×C4116yes—
146#66930—28no—
147#66925C2×C4116yes—
148C42×D11C2×C4116yes—
149C4×Dic22—28no—
150C11×#95C2314yes—
151C11×#95C2311yescharacteristic
152C11×#95C2311yescharacteristic
153C11×#95C2312yes—
154C11×#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2311yescharacteristic
157C11⋊#95C2311yescharacteristic
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161C11⋊#95C2312yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165#34125—111nomaximal, Sylow
166C24×C11C2411yescharacteristic
167C23×D11C2412yes—
168C22×C4×C11—24no—
169C22×C4×C11C22×C414yes—
170C22×C4×C11C2414yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2412yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2411yescharacteristic
177C2×C22⋊D11—28no—
178C2×C22⋊D11C22×C418yes—
179C22×Dic11—24no—
180C22×Dic11—41no—
181C22×Dic11—41no—
182C22×Dic11C22×C414yes—
183C22×Dic11C22×C414yes—
184C22×Dic11C2412yes—
185C22×Dic11C2414yes—
186C22×Dic11C2411yescharacteristic
187C22×Dic11C2411yescharacteristic
188C22×Dic11C2411yescharacteristic
189C22×Dic11C2412yes—
190C22×Dic11C2411yescharacteristic
191C22×Dic11C2412yes—
192#4339—232no—
193C2×D44—24no—
194C2×D44C22×C414yes—
195C2×C4×D11—28no—
196C2×C4×D11—28no—
197C2×C4×D11—42no—
198C2×C4×D11—42no—
199C2×C4×D11C22×C418yes—
200C2×C4×D11C22×C418yes—
201C2×C4×D11C22×C418yes—
202C2×Dic22C22×C414yes—
203C2×Dic22#4118yes—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—28no—
206C11×C4⋊C4C22×C414yes—
207C11×C4⋊C4C22×C414yes—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4C22×C418yes—
211C42×C11—24no—
212C42×C11—44no—
213C42×C11C22×C418yes—
214C22⋊Dic11—24no—
215C22⋊Dic11—42no—
216(C2×D11)⋊C4—28no—
217(C2×D11)⋊C4—28no—
218(C2×D11)⋊C4—44no—
219(C2×D11)⋊C4—44no—
220(C2×D11)⋊C4C22×C418yes—
221(C2×D11)⋊C4C22×C418yes—
222C4⋊Dic11—28no—
223C4⋊Dic11—24no—
224Dic11⋊C4—28no—
225Dic11⋊C4—24no—
226Dic11⋊C4—28no—
227Dic11⋊C4—24no—
228Dic11⋊C4C22×C418yes—
229Dic11⋊C4C22×C418yes—
230C4×Dic11—28no—
231C4×Dic11—24no—
232C4×Dic11—28no—
233C4×Dic11—28no—
234C4×Dic11—24no—
235C4×Dic11—44no—
236C4×Dic11—42no—
237C4×Dic11—42no—
238C4×Dic11C22×C414yes—
239C4×Dic11C22×C418yes—
240C4×Dic11C22×C418yes—
241C4×Dic11C22×C414yes—
242C4×Dic11C22×C414yes—
243C4×Dic11C22×C414yes—
244C4×Dic11#4118yescomplemented
245C2×C4×#41—111no—
246#2357—114no—
247#2357—112no—
248#2351—112no—
249#2347—112no—
250#2347—112no—
251#2347—111no—
252#2347D1111yescharacteristic, complemented
253#2341—111no—
254#2341—111no—
255#2293—112no—
256#2293—114no—
257#2283—112no—
258#2283—111no—
259C42×Q8—112no—
260C4×#117—112no—
261C4×#117—111no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11C23×C412yes—
267C23×C11C2511yescharacteristic
268C22×D11—24no—
269C22×D11—24no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11C23×C414yes—
273C2×C4×C11—22no—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—28no—
280C2×C4×C11—22no—
281C2×C4×C11—24no—
282C2×C4×C11—24no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11C23×C412yes—
287C2×C4×C11C23×C414yes—
288C2×C4×C11C23×C414yes—
289C2×C4×C11C23×C412yes—
290C2×C4×C11C2×#4114yes—
291C2×C4×C11C2×#4114yes—
292C22⋊D11—216no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—28no—
301C2×Dic11—22no—
302C2×Dic11—24no—
303C2×Dic11—22no—
304C2×Dic11—24no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—44no—
308C2×Dic11C23×C412yes—
309C2×Dic11C23×C412yes—
310C2×Dic11C23×C412yes—
311C2×Dic11C23×C414yes—
312C2×Dic11C23×C412yes—
313C2×Dic11C2×#4114yes—
314C2×Dic11C2×#4118yes—
315C2×Dic11C2×#4114yes—
316D44—28no—
317C4×D11—216no—
318C4×D11—216no—
319C4×D11—48no—
320Dic22#117116yescomplemented
321C22×#41—111no—
322C4×#41—1116no—
323C2×C4×Q8—111no—
324C2×C4×Q8—111no—
325C2×C4×Q8—112no—
326C2×C4×Q8—112no—
327C2×C4×D4—111no—
328C2×C4×D4—111no—
329C2×C4×D4—112no—
330C2×C4×D4—112no—
331C2×#117—114no—
332C2×#117—112no—
333C2×#117—112no—
334C2×#117C2×D1111yescharacteristic
335C22×C42—111no—
336C22×C42—112no—
337#390—112no—
338#390—114no—
339#390—114no—
340#390—112no—
341#389—114no—
342#389—112no—
343#389—114no—
344#389C2×D1112yes—
345#388—114no—
346#388—114no—
347#388—114no—
348#388—114no—
349#388—114no—
350#388C2×D1114yes—
351#383—112no—
352#383—112no—
353#383C2×D1112yes—
354#382—112no—
355#382—114no—
356#381—112no—
357#381—114no—
358#380—111no—
359#380—112no—
360#380—112no—
361#380C2×D1111yescharacteristic
362C4×C4⋊C4—112no—
363C4×C4⋊C4—114no—
364C4×C4⋊C4—112no—
365C4×C4⋊C4—112no—
366C4×C4⋊C4—114no—
367C4×C4⋊C4—112no—
368C4×C4⋊C4—111no—
369C4×C4⋊C4—111no—
370C4×C4⋊C4—114no—
371C4×C4⋊C4—114no—
372C4×C4⋊C4C2×D1112yes—
373C4×C4⋊C4C2×D1112yes—
374C4×C22⋊C4—111no—
375C4×C22⋊C4—112no—
376C4×C22⋊C4—112no—
377C4×C22⋊C4—114no—
378C4×C22⋊C4—112no—
379C4×C22⋊C4—112no—
380C4×C22⋊C4—114no—
381C4×C22⋊C4C2×D1111yescharacteristic
382#376—111no—
383#376—112no—
384#376—111no—
385C43—114no—
386C43—112no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11C24×C411yescharacteristic
393C22×C11C22×#4112yes—
394C22×C11C22×#4112yes—
395C22×C11#58511yescharacteristic
396C22×C11#58511yescharacteristic
397C2×D11—24no—
398C2×D11—24no—
399C2×D11—24no—
400C2×D11—44no—
401C2×D11—44no—
402C4×C11—22no—
403C4×C11—24no—
404C4×C11—24no—
405C4×C11—24no—
406C4×C11—42no—
407C4×C11—44no—
408C4×C11C2×#11714yes—
409Dic11—22no—
410Dic11—22no—
411Dic11—22no—
412Dic11—24no—
413Dic11—44no—
414Dic11—42no—
415Dic11C2×#11718yes—
416Dic11C4×#4114yes—
417C2×#41—118no—
418C2×#41—228no—
419C22×Q8—111no—
420C22×D4—112no—
421C22×D4—111no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—112no—
425C23×C4—112no—
426C23×C4—112no—
427C23×C4C22×D1111yescharacteristic
428C4×Q8—118no—
429C4×Q8—118no—
430C4×Q8—228no—
431C4×Q8—228no—
432C4×D4—118no—
433C4×D4—118no—
434C4×D4—1116no—
435C4×D4—1116no—
436#117—1116no—
437#117—228no—
438#117—2216no—
439#117C4×D1118yes—
440C2×C4⋊C4—112no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—112no—
443C2×C4⋊C4—112no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—112no—
448C2×C4⋊C4C22×D1114yes—
449C2×C4⋊C4C22×D1112yes—
450C2×C4⋊C4C22×D1111yescharacteristic
451C2×C4⋊C4C22×D1111yescharacteristic
452C2×C22⋊C4—112no—
453C2×C22⋊C4—112no—
454C2×C22⋊C4—112no—
455C2×C22⋊C4—114no—
456C2×C22⋊C4—114no—
457C2×C22⋊C4—112no—
458C2×C22⋊C4—114no—
459C2×C22⋊C4—114no—
460C2×C22⋊C4C22×D1112yes—
461C2×C22⋊C4C22×D1112yes—
462C2×C22⋊C4C22×D1112yes—
463C2×C42—118no—
464C2×C42—112no—
465C2×C42—111no—
466C2×C42—112no—
467C2×C42—111no—
468C2×C42—112no—
469C2×C42—111no—
470C2×C42—111no—
471C2×C42—1116no—
472C2×C42—114no—
473C2×C42—112no—
474C2×C42—114no—
475C2×C42—114no—
476C2×C42—112no—
477C2×C42—112no—
478C2×C42—112no—
479C2×C42—114no—
480C2×C42C22×D1112yes—
481C2×C42C22×D1114yes—
482C2×C42C22×D1112yes—
483#95—112no—
484#95—111no—
485#95—111no—
486#95—112no—
487#95—114no—
488#95—112no—
489#95—114no—
490#95—114no—
491#95—114no—
492#95—114no—
493#95C22×D1111yescharacteristic
494#95C22×D1112yes—
495#95C22×D1111yescharacteristic
496#95C22×D1114yes—
497#95C22×D1114yes—
498C2×C11—42no—
499C2×C11C22×#11711yescharacteristic
500C2×C11C2×C4×#4111yescharacteristic
501C2×C11#342811yescharacteristic
502C2×C11#348012yes—
503C2×C11#348012yes—
504D11—44no—
505C24—112no—
506C24C23×D1111yescharacteristic
507#41—2232no—
508C2×Q8—114no—
509C2×Q8—118no—
510C2×D4—118no—
511C2×D4—114no—
512C2×D4—228no—
513C2×D4—224no—
514C22×C4—24no—
515C22×C4—111no—
516C22×C4—112no—
517C22×C4—114no—
518C22×C4—111no—
519C22×C4—111no—
520C22×C4—111no—
521C22×C4—112no—
522C22×C4—114no—
523C22×C4—118no—
524C22×C4—118no—
525C22×C4—118no—
526C22×C4—112no—
527C22×C4—114no—
528C22×C4—228no—
529C22×C4—228no—
530C22×C4—224no—
531C22×C4—442no—
532C22×C4—442no—
533C22×C4—441no—
534C22×C4—441no—
535C22×C4C2×C4×D1114yes—
536C22×C4C23×D1114yes—
537C22×C4C23×D1112yes—
538C22×C4C23×D1111yescharacteristic
539C22×C4C23×D1112yes—
540C22×C4C23×D1112yes—
541C22×C4C23×D1112yes—
542C22×C4C23×D1111yescharacteristic
543C4⋊C4—28no—
544C4⋊C4—24no—
545C4⋊C4—118no—
546C4⋊C4—118no—
547C4⋊C4—224no—
548C4⋊C4—228no—
549C4⋊C4—228no—
550C4⋊C4—228no—
551C4⋊C4—224no—
552C4⋊C4—224no—
553C4⋊C4C2×C4×D1114yes—
554C4⋊C4C2×C4×D1114yes—
555C22⋊C4—24no—
556C22⋊C4—42no—
557C22⋊C4—118no—
558C22⋊C4—118no—
559C22⋊C4—228no—
560C22⋊C4—224no—
561C22⋊C4—228no—
562C22⋊C4—444no—
563C22⋊C4—444no—
564C22⋊C4—442no—
565C22⋊C4C2×C4×D1118yes—
566C42—24no—
567C42—44no—
568C42—114no—
569C42—114no—
570C42—118no—
571C42—114no—
572C42—118no—
573C42—114no—
574C42—118no—
575C42—224no—
576C42—228no—
577C42—228no—
578C42—228no—
579C42—224no—
580C42—442no—
581C42—444no—
582C42—442no—
583C42C2×C4×D1118yes—
584C11#3412511yescharacteristic, complemented, Sylow
585C23—22no—
586C23—22no—
587C23—21no—
588C23—21no—
589C23—114no—
590C23—224no—
591C23—224no—
592C23—222no—
593C23—222no—
594C23C22×C4×D1112yes—
595C23C24×D1111yescharacteristic
596Q8—1116no—
597D4—2216no—
598D4—228no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—28no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—112no—
613C2×C4—114no—
614C2×C4—114no—
615C2×C4—118no—
616C2×C4—112no—
617C2×C4—112no—
618C2×C4—112no—
619C2×C4—114no—
620C2×C4—2216no—
621C2×C4—2216no—
622C2×C4—228no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—222no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—224no—
631C2×C4—222no—
632C2×C4—224no—
633C2×C4—222no—
634C2×C4—222no—
635C2×C4—224no—
636C2×C4—448no—
637C2×C4—444no—
638C2×C4C22×C4×D1112yes—
639C2×C4C22×C4×D1114yes—
640C2×C4C22×C4×D1114yes—
641C2×C4C22×C4×D1112yes—
642C2×C4#41×D1114yes—
643C2×C4#41×D1114yes—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—42no—
648C22—42no—
649C22—224no—
650C22—224no—
651C22—224no—
652C22—444no—
653C22—444no—
654C22C23×C4×D1111yescharacteristic
655C22C2×#41×D1112yes—
656C22C2×#41×D1112yes—
657C22#1062345511yescharacteristic
658C22#1062345711yescharacteristic
659C4—24no—
660C4—22no—
661C4—24no—
662C4—24no—
663C4—42no—
664C4—44no—
665C4—118no—
666C4—114no—
667C4—224no—
668C4—222no—
669C4—222no—
670C4—222no—
671C4—444no—
672C4—442no—
673C4D11×#11714yes—
674C2—42no—
675C2—444no—
676C2C2×D11×#11711yescharacteristic
677C2C4×#41×D1111yescharacteristic
678C2#1308181611yescharacteristic
679C2#1308220812yes—
680C2#1308221012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2347C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2347D11
hypocenterC11#34125
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #13071586C2semidirect
3. #13071585C2semidirect
4. #13071535C2semidirect
5. #13071510C2semidirect
6. #13071509C2semidirect
7. #13071504C2semidirect
10. #13071076C2semidirect
11. #13071074C2semidirect
12. #13071013C2semidirect
13. #13071011C2semidirect
14. C4×#66940C2semidirect
15. C4×#66945C2semidirect
16. C4×#66930C2semidirect
17. C11×#2347C2semidirect
21. #10623053C4semidirect
244. C4×Dic11#41semidirect
252. #2347D11semidirect
320. Dic22#117semidirect
584. C11#34125semidirect

Maximal subgroups

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

subgroupindex
C2×#106230532
#130715862
#130715852
#130715352
#130715102
#130715092
#130715042
#130714562
#130714532
#130710762
#130710742
#130710132
#130710112
C4×#669402
C4×#669452
C4×#669302
C11×#23472
#3412511