Finite Group Databasebeta

← #14912871

Subgroups — #14912871

Order 2816.

2518 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623066C211yesmaximal, characteristic
2#13071412C214yesmaximal, complemented
3#13071379C214yesmaximal, complemented
4#13071355C211yesmaximal, characteristic, complemented
5#13071339C211yesmaximal, characteristic, complemented
6#13071305C212yesmaximal, complemented
7#13071254C212yesmaximal, complemented
8#13071178C211yesmaximal, characteristic, complemented
9#13071171C211yesmaximal, characteristic, complemented
10#13071137C214yesmaximal, complemented
11#13071128C214yesmaximal, complemented
12#13071122C212yesmaximal, complemented
13C4×#66946C212yesmaximal, complemented
14#117×Dic11C211yesmaximal, characteristic, complemented
15C11×#2314C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×#66983C2212yes—
18C2×#66979C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20#10623066C4116yescomplemented
21C2×#66947C2214yes—
22C2×#66946C2212yes—
23C2×#66946C2212yes—
24C2×#66946C2214yes—
25C2×#66937C2214yes—
26C2×(C22⋊D11)⋊C4C2214yes—
27C2×#66927C2211yescharacteristic
28C2×C4×D44C2212yes—
29C2×C42×D11C2214yes—
30C2×#66923C2211yescharacteristic
31C11×#388C2214yes—
32C11×#387C2214yes—
33C11×#384C2211yescharacteristic
34C11×#382C2211yescharacteristic
35C11×#380C2212yes—
36C4×C11×C4⋊C4C2212yes—
37#10622601C2212yes—
38#10622601C2214yes—
39#10622601C2212yes—
40#10622591C2214yes—
41C4⋊C4×Dic11C2212yes—
42C4⋊C4×Dic11C2212yes—
43C4⋊C4×Dic11C2212yes—
44C4⋊C4×Dic11C2212yes—
45#10622586C2212yes—
46#10622586C2212yes—
47#10622585C2214yes—
48#10622571C2214yes—
49#10622570C2214yes—
50#10622569C2214yes—
51C22⋊C4×Dic11C2212yes—
52C22⋊C4×Dic11C2212yes—
53#10622553C2214yes—
54#10622553C2214yes—
55C4×(C2×D11)⋊C4C2214yes—
56#10622545C2211yescharacteristic
57#10622545C2211yescharacteristic
58C42×Dic11C2211yescharacteristic
59C42×Dic11C2211yescharacteristic
60#10622283C2214yes—
61#10622282C2214yes—
62#10622281C2214yes—
63#10622280C2214yes—
64#10622279C2214yes—
65#10622279C2214yes—
66#10622279C2214yes—
67#10622278C2214yes—
68#10622278C2214yes—
69#10622277C2214yes—
70#10622265C2214yes—
71#10622262C2214yes—
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11C2314yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C22×D44C2312yes—
77C22×D44C2314yes—
78C22×C4×D11C2314yes—
79C22×C4×D11C2314yes—
80C22×C4×D11C2314yes—
81C11×#117C2×C418yescomplemented
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2312yes—
88C2×C42×C11C2314yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11C2312yes—
92#66983C2×C4116yescomplemented
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101#66979—24no—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2312yes—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×C4×Dic11—24no—
108C2×C4×Dic11C2312yes—
109C2×C4×Dic11C2314yes—
110C2×C4×Dic11C2312yes—
111C2×C4×Dic11C2311yescharacteristic
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2312yes—
117C2×C4×Dic11C2312yes—
118C2×C4×Dic11C2311yescharacteristic
119C2×C4×Dic11C2311yescharacteristic
120#66947C2×C4132yescomplemented
121#66946—28no—
122#66946—28no—
123#66946—48no—
124#66937C2×C4132yescomplemented
125(C22⋊D11)⋊C4—48no—
126#66927C2×C418yescomplemented
127C4×D44C2×C4116yescomplemented
128C42×D11—48no—
129#66923C2×C418yescomplemented
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11×#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2312yes—
136C11⋊#95C2314yes—
137C11⋊#95C2312yes—
138C11⋊#95C2312yes—
139C11⋊#95C2314yes—
140C11⋊#95C2312yes—
141C4×#540—111nomaximal, Sylow
142C24×C11C2411yescharacteristic
143C23×D11C2414yes—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11C22×C414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—44no—
154C2×C22⋊D11—44no—
155C2×C22⋊D11C22×C4116yes—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—24no—
159C22×Dic11—42no—
160C22×Dic11C2411yescharacteristic
161C22×Dic11C2412yes—
162C22×Dic11C2411yescharacteristic
163C22×Dic11C2414yes—
164C22×Dic11C2411yescharacteristic
165C22×Dic11C2412yes—
166C22×Dic11C2411yescharacteristic
167C2×D44—24no—
168C2×D44—24no—
169C2×D44—44no—
170C2×D44—44no—
171C2×D44C22×C418yes—
172C2×D44C22×C4116yes—
173C2×C4×D11—28no—
174C2×C4×D11—28no—
175C2×C4×D11—28no—
176C2×C4×D11—28no—
177C2×C4×D11—44no—
178C2×C4×D11—44no—
179C2×C4×D11—44no—
180C2×C4×D11—44no—
181C2×C4×D11C22×C4116yes—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—44no—
185C11×C4⋊C4C22×C418yes—
186C11×C22⋊C4—44no—
187C11×C22⋊C4C22×C418yes—
188C42×C11—44no—
189C42×C11C22×C414yes—
190C42×C11C22×C414yes—
191C22⋊Dic11—24no—
192(C2×D11)⋊C4—28no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—44no—
195(C2×D11)⋊C4—44no—
196(C2×D11)⋊C4—44no—
197(C2×D11)⋊C4—44no—
198(C2×D11)⋊C4C22×C4116yes—
199(C2×D11)⋊C4C22×C4116yes—
200C4⋊Dic11—24no—
201C4⋊Dic11C22×C418yes—
202Dic11⋊C4—44no—
203Dic11⋊C4—44no—
204Dic11⋊C4C22×C4116yes—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—24no—
208C4×Dic11—28no—
209C4×Dic11—24no—
210C4×Dic11—22no—
211C4×Dic11—22no—
212C4×Dic11—44no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215C4×Dic11#4114yes—
216C4×Dic11#4114yes—
217C2×#540—111no—
218#2335—114no—
219#2333—114no—
220#2330—111no—
221#2328—111no—
222#2324—112no—
223#2319—112no—
224#2314D1111yescharacteristic, complemented
225C4×#127—111no—
226C4×#125—111no—
227C4×#123—114no—
228C4×#121—114no—
229C4×#121—112no—
230C42×D4—112no—
231C4×#117—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11C23×C412yes—
237C23×C11C2511yescharacteristic
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11C23×C418yes—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—28no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11C23×C414yes—
259C2×C4×C11C23×C412yes—
260C2×C4×C11C23×C414yes—
261C2×C4×C11C23×C412yes—
262C2×C4×C11C2×#4112yes—
263C2×C4×C11C2×#4112yes—
264C22⋊D11—416no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—44no—
278C2×Dic11—44no—
279C2×Dic11C23×C418yes—
280C2×Dic11C2×#4112yes—
281C2×Dic11C2×#4114yes—
282C2×Dic11C2×#4112yes—
283C2×Dic11H(5,𝔽2)14yes—
284D44—216no—
285D44—416no—
286C4×D11—416no—
287C4×D11—416no—
288C4×D11—416no—
289#540—1116no—
290C2×#127—111no—
291C2×#125—111no—
292C2×#123—114no—
293C2×#121—112no—
294C2×#121—114no—
295C2×C4×D4—112no—
296C2×C4×D4—112no—
297C2×C4×D4—114no—
298C2×C4×D4—114no—
299C2×C4×D4—112no—
300C2×#117—111no—
301C2×#117C2×D1111yescharacteristic
302C22×C42—111no—
303C22×C42—114no—
304#390—112no—
305#390—114no—
306#390—112no—
307#390—114no—
308#389—112no—
309#389—112no—
310#389—114no—
311#388—114no—
312#388—114no—
313#388—114no—
314#388—114no—
315#388C2×D1114yes—
316#387—114no—
317#387—114no—
318#387C2×D1114yes—
319#386—114no—
320#386—114no—
321#386—114no—
322#386—114no—
323#385—114no—
324#384C2×D1111yescharacteristic
325#382C2×D1111yescharacteristic
326#381—114no—
327#380—114no—
328#380C2×D1112yes—
329C4×C4⋊C4—112no—
330C4×C4⋊C4—112no—
331C4×C4⋊C4—112no—
332C4×C4⋊C4—112no—
333C4×C4⋊C4—114no—
334C4×C4⋊C4C2×D1112yes—
335C4×C22⋊C4—112no—
336C4×C22⋊C4—112no—
337C4×C22⋊C4—114no—
338C4×C22⋊C4—114no—
339C4×C22⋊C4—114no—
340C4×C22⋊C4—114no—
341#376—111no—
342#376—111no—
343C43—111no—
344C43—111no—
345C22×C11—22no—
346C22×C11—24no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—42no—
350C22×C11C24×C411yescharacteristic
351C22×C11C22×#4111yescharacteristic
352C22×C11C22×#4111yescharacteristic
353C22×C11C2×H(5,𝔽2)12yes—
354C22×C11#58512yes—
355C2×D11—28no—
356C2×D11—28no—
357C2×D11—28no—
358C2×D11—44no—
359C2×D11—44no—
360C2×D11—44no—
361C2×D11—44no—
362C4×C11—22no—
363C4×C11—24no—
364C4×C11—24no—
365C4×C11—44no—
366C4×C11—44no—
367C4×C11C4×#4114yes—
368Dic11—28no—
369Dic11—22no—
370Dic11—24no—
371Dic11—41no—
372Dic11—41no—
373Dic11—42no—
374Dic11#54014yescomplemented
375C22×D4—114no—
376C22×D4—112no—
377C22×D4—114no—
378C23×C4—114no—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4—114no—
382C23×C4—114no—
383C23×C4C22×D1111yescharacteristic
384#127—118no—
385#125—118no—
386#123—1132no—
387#121—1116no—
388#121—1132no—
389C4×D4—1116no—
390C4×D4—228no—
391C4×D4—228no—
392C4×D4—448no—
393C4×D4—448no—
394#117—224no—
395#117C4×D1118yescomplemented
396C2×C4⋊C4—112no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—112no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4C22×D1112yes—
402C2×C4⋊C4C22×D1112yes—
403C2×C4⋊C4C22×D1114yes—
404C2×C4⋊C4C22×D1112yes—
405C2×C22⋊C4—114no—
406C2×C22⋊C4—114no—
407C2×C22⋊C4—112no—
408C2×C22⋊C4—114no—
409C2×C22⋊C4—114no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—114no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4C22×D1114yes—
415C2×C22⋊C4C22×D1112yes—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—112no—
420C2×C42—114no—
421C2×C42—112no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—112no—
426C2×C42—112no—
427C2×C42—114no—
428C2×C42—224no—
429C2×C42—448no—
430C2×C42C22×D1114yes—
431C2×C42C22×D1111yescharacteristic
432C2×C42C22×D1111yescharacteristic
433#95—112no—
434#95—112no—
435#95—112no—
436#95—112no—
437#95—114no—
438#95—114no—
439#95—114no—
440#95—114no—
441#95C22×D1114yes—
442#95C22×D1114yes—
443#95C22×D1114yes—
444C2×C11—42no—
445C2×C11C2×C4×#4111yescharacteristic
446C2×C11C4×H(5,𝔽2)12yes—
447C2×C11C2×#54011yescharacteristic
448C2×C11#345511yescharacteristic
449C2×C11#346012yes—
450D11—48no—
451C24—114no—
452C24C23×D1111yescharacteristic
453C2×D4—1116no—
454C2×D4—118no—
455C2×D4—1116no—
456C2×D4—224no—
457C2×D4—224no—
458C2×D4—444no—
459C2×D4—444no—
460C2×D4—444no—
461C2×D4—444no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—112no—
467C22×C4—114no—
468C22×C4—1116no—
469C22×C4—111no—
470C22×C4—112no—
471C22×C4—111no—
472C22×C4—228no—
473C22×C4—228no—
474C22×C4—228no—
475C22×C4—228no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—224no—
479C22×C4—444no—
480C22×C4—444no—
481C22×C4—444no—
482C22×C4—444no—
483C22×C4—442no—
484C22×C4C2×C4×D1114yes—
485C22×C4C23×D1114yes—
486C22×C4C23×D1114yes—
487C22×C4C23×D1112yes—
488C22×C4C23×D1112yes—
489C22×C4C23×D1111yescharacteristic
490C22×C4C23×D1111yescharacteristic
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—44no—
494C4⋊C4—118no—
495C4⋊C4—1116no—
496C4⋊C4—224no—
497C4⋊C4—444no—
498C4⋊C4—444no—
499C4⋊C4C2×C4×D1118yes—
500C22⋊C4—44no—
501C22⋊C4—1116no—
502C22⋊C4—1116no—
503C22⋊C4—228no—
504C22⋊C4—228no—
505C22⋊C4—224no—
506C22⋊C4—444no—
507C22⋊C4—444no—
508C22⋊C4—444no—
509C22⋊C4—444no—
510C22⋊C4C2×C4×D1118yes—
511C42—44no—
512C42—114no—
513C42—114no—
514C42—222no—
515C42—222no—
516C42—224no—
517C42—228no—
518C42—224no—
519C42—222no—
520C42—222no—
521C42—444no—
522C42—442no—
523C42—442no—
524C42C2×C4×D1114yes—
525C42C2×C4×D1114yes—
526C11C4×#54011yescharacteristic, complemented, Sylow
527C23—21no—
528C23—21no—
529C23—22no—
530C23—22no—
531C23—118no—
532C23—224no—
533C23—224no—
534C23—224no—
535C23—224no—
536C23—224no—
537C23—224no—
538C23C22×C4×D1112yes—
539C23C24×D1111yescharacteristic
540D4—2216no—
541D4—4416no—
542D4—4416no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—28no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—112no—
557C2×C4—114no—
558C2×C4—118no—
559C2×C4—112no—
560C2×C4—114no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—224no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—4416no—
574C2×C4—4416no—
575C2×C4—4416no—
576C2×C4—444no—
577C2×C4—444no—
578C2×C4C22×C4×D1114yes—
579C2×C4C22×C4×D1114yes—
580C2×C4C22×C4×D1112yes—
581C2×C4C22×C4×D1112yes—
582C2×C4#41×D1112yes—
583C2×C4#41×D1112yes—
584C22—22no—
585C22—24no—
586C22—41no—
587C22—41no—
588C22—42no—
589C22—228no—
590C22—228no—
591C22—228no—
592C22—444no—
593C22—444no—
594C22—444no—
595C22—444no—
596C22C23×C4×D1111yescharacteristic
597C22C2×#41×D1111yescharacteristic
598C22C2×#41×D1111yescharacteristic
599C22D11×H(5,𝔽2)12yes—
600C22#1062345712yes—
601C4—22no—
602C4—24no—
603C4—24no—
604C4—44no—
605C4—44no—
606C4—114no—
607C4—222no—
608C4—224no—
609C4—228no—
610C4—441no—
611C4—441no—
612C4—442no—
613C4#1062305314yes—
614C2—42no—
615C2—448no—
616C2C2×#1062305311yescharacteristic
617C2#1308182212yes—
618C2D11×#54011yescharacteristic
619C2#1308200711yescharacteristic
620C2#1308203612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2314C2
socle, cosocleC23×C11C25
prime radicalC2×#10623066C2
hypercenter#2314D11
hypocenterC11C4×#540
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #13071412C2semidirect
3. #13071379C2semidirect
4. #13071355C2semidirect
5. #13071339C2semidirect
6. #13071305C2semidirect
7. #13071254C2semidirect
8. #13071178C2semidirect
9. #13071171C2semidirect
10. #13071137C2semidirect
11. #13071128C2semidirect
12. #13071122C2semidirect
13. C4×#66946C2semidirect
14. #117×Dic11C2semidirect
15. C11×#2314C2semidirect
20. #10623066C4semidirect
81. C11×#117C2×C4semidirect
92. #66983C2×C4semidirect
120. #66947C2×C4semidirect
124. #66937C2×C4semidirect
126. #66927C2×C4semidirect
127. C4×D44C2×C4semidirect
129. #66923C2×C4semidirect
224. #2314D11semidirect
374. Dic11#540semidirect
395. #117C4×D11semidirect
526. C11C4×#540semidirect

Maximal subgroups

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

subgroupindex
C2×#106230662
#130714122
#130713792
#130713552
#130713392
#130713052
#130712542
#130711782
#130711712
#130711372
#130711282
#130711222
C4×#669462
#117×Dic112
C11×#23142
C4×#54011