Finite Group Databasebeta

← #14915138

Subgroups — #14915138

Order 2816.

2486 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623250C211yesmaximal, characteristic
2#13071749C214yesmaximal, complemented
3#13071664C214yesmaximal, complemented
4#13071657C214yesmaximal, complemented
5#13071614C214yesmaximal, complemented
6#13071357C211yesmaximal, characteristic, complemented
7#13071312C212yesmaximal, complemented
8#13071226C211yesmaximal, characteristic, complemented
9#127×Dic11C211yesmaximal, characteristic, complemented
10#13071171C211yesmaximal, characteristic, complemented
11C4×#66991C212yesmaximal, complemented
12#13071078C212yesmaximal, complemented
13#13070977C212yesmaximal, complemented
14#13070955C211yesmaximal, characteristic, complemented
15C11×#2328C211yesmaximal, characteristic, complemented
16C2×C11×#127C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C2×#66992C2214yes—
19C2×#66991C2212yes—
20C2×#66988C2214yes—
21C2×D4×Dic11C2212yes—
22C2×D4×Dic11C2214yes—
23C2×D4×Dic11C2212yes—
24C2×C4×C22⋊D11C2214yes—
25#10623250C4116yescomplemented
26C2×#66930C2214yes—
27C2×#66925C2211yescharacteristic
28C2×#66925C2211yescharacteristic
29C2×C42×D11C2211yescharacteristic
30C2×#66923C2211yescharacteristic
31C11×#390C2212yes—
32C11×#386C2214yes—
33C11×#386C2214yes—
34C11×#382C2211yescharacteristic
35C11×#376C2211yescharacteristic
36#10622834C2212yes—
37#10622834C2214yes—
38C4×C22⋊Dic11C2214yes—
39C4×C22⋊Dic11C2214yes—
40C2×C11⋊#95C2214yes—
41#10622600C2212yes—
42C4⋊C4×Dic11C2212yes—
43C4⋊C4×Dic11C2212yes—
44#10622586C2212yes—
45#10622571C2214yes—
46#10622570C2214yes—
47#10622569C2214yes—
48#10622559C2214yes—
49#10622558C2214yes—
50#10622557C2214yes—
51#10622557C2214yes—
52#10622557C2214yes—
53C22⋊C4×Dic11C2214yes—
54C22⋊C4×Dic11C2214yes—
55C22⋊C4×Dic11C2214yes—
56#10622548C2211yescharacteristic
57C4×C4⋊Dic11C2212yes—
58#10622545C2211yescharacteristic
59C42×Dic11C2211yescharacteristic
60C42×Dic11C2211yescharacteristic
61#10622541C2212yes—
62#10622283C2214yes—
63#10622279C2212yes—
64#10622279C2212yes—
65#10622268C2214yes—
66#10622268C2214yes—
67#10622265C2214yes—
68#10622262C2214yes—
69#10622262C2212yes—
70#10622262C2212yes—
71#10622260C2214yes—
72C22×D4×C11C2312yes—
73C22×D4×C11C2314yes—
74C23×C4×C11C2314yes—
75C22×C22⋊D11C2314yes—
76C23×Dic11C2314yes—
77C23×Dic11C2314yes—
78C22×C4×D11C2312yes—
79C22×C4×D11C2311yescharacteristic
80C11×#127C2×C418yescomplemented
81C4×D4×C11—28no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2314yes—
94#66992C2×C4132yescomplemented
95#66991C2×C4116yescomplemented
96#66988C2×C4132yescomplemented
97D4×Dic11—28no—
98D4×Dic11—48no—
99D4×Dic11C2×C4116yescomplemented
100C4×C22⋊D11—48no—
101C2×(C2×D11)⋊C4C2311yescharacteristic
102C2×(C2×D11)⋊C4C2311yescharacteristic
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2314yes—
107C2×C4⋊Dic11C2312yes—
108C2×Dic11⋊C4C2311yescharacteristic
109C2×Dic11⋊C4C2311yescharacteristic
110C2×Dic11⋊C4C2314yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2312yes—
114C2×C4×Dic11C2312yes—
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2312yes—
117C2×C4×Dic11C2312yes—
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2314yes—
120C2×C4×Dic11C2312yes—
121C2×C4×Dic11C2314yes—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2311yescharacteristic
124C2×C4×Dic11C2311yescharacteristic
125#66930—48no—
126#66925—24no—
127#66925C2×C418yescomplemented
128C42×D11—24no—
129#66923C2×C418yescomplemented
130C11×#95C2312yes—
131C11×#95C2314yes—
132C11×#95C2312yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2312yes—
136C11⋊#95C2312yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141#34280—111nomaximal, Sylow
142C24×C11C2414yes—
143C23×D11C2411yescharacteristic
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11C22×C418yes—
149C2×D4×C11C22×C4116yes—
150C22×C4×C11—28no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11C2411yescharacteristic
154C22×C4×C11C2414yes—
155C22×C4×C11C2411yescharacteristic
156C22×C4×C11C2412yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—44no—
160C2×C22⋊D11—44no—
161C2×C22⋊D11C22×C4116yes—
162C22×Dic11—28no—
163C22×Dic11—44no—
164C22×Dic11—44no—
165C22×Dic11—44no—
166C22×Dic11—44no—
167C22×Dic11C22×C4116yes—
168C22×Dic11C2414yes—
169C22×Dic11C2412yes—
170C22×Dic11C2414yes—
171C22×Dic11C2411yescharacteristic
172C22×Dic11C2411yescharacteristic
173C22×Dic11C2411yescharacteristic
174C22×Dic11C2412yes—
175C2×C4×D11—24no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—24no—
179C2×C4×D11—42no—
180C2×C4×D11C22×C414yes—
181C11×C4⋊C4—24no—
182C11×C22⋊C4—28no—
183C11×C22⋊C4—44no—
184C11×C22⋊C4—44no—
185C42×C11—22no—
186C42×C11C22×C414yes—
187C42×C11#4114yes—
188C22⋊Dic11—28no—
189C22⋊Dic11—28no—
190C22⋊Dic11—28no—
191C22⋊Dic11C22×C4116yes—
192C22⋊Dic11C22×C4116yes—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—44no—
196(C2×D11)⋊C4C22×C418yes—
197C4⋊Dic11—24no—
198C4⋊Dic11—44no—
199C4⋊Dic11C22×C418yes—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—28no—
203Dic11⋊C4—44no—
204Dic11⋊C4C22×C4116yes—
205Dic11⋊C4C22×C418yes—
206C4×Dic11—24no—
207C4×Dic11—24no—
208C4×Dic11—24no—
209C4×Dic11—22no—
210C4×Dic11—44no—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C4×Dic11—44no—
214C4×Dic11—44no—
215C4×Dic11C22×C414yes—
216C4×Dic11#4114yes—
217C2×#540—111no—
218#2374—114no—
219#2364—114no—
220#2363—114no—
221#2359—114no—
222#2330—111no—
223#2328D1111yescharacteristic, complemented
224#2324—112no—
225#2314—111no—
226C4×#127—111no—
227C4×#125—111no—
228C4×#121—112no—
229#2293—112no—
230#2275—112no—
231C4×#117—111no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11C23×C418yes—
239C23×C11C2511yescharacteristic
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11C23×C412yes—
245D4×C11—216no—
246D4×C11—416no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—88no—
259C2×C4×C11C23×C414yes—
260C2×C4×C11C23×C412yes—
261C2×C4×C11C2×#4114yes—
262C2×C4×C11C2×#4112yes—
263C2×C4×C11C2×#4112yes—
264C22⋊D11—416no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—416no—
279C2×Dic11—88no—
280C2×Dic11C23×C414yes—
281C2×Dic11C23×C418yes—
282C2×Dic11C23×C412yes—
283C2×Dic11C2×#4112yes—
284C2×Dic11C2×#4112yes—
285C2×Dic11H(5,𝔽2)14yes—
286C4×D11—28no—
287C4×D11—48no—
288#540—1116no—
289C2×#127C2×D1111yescharacteristic
290C2×#125—111no—
291C2×#123—114no—
292C2×#121—112no—
293C2×#121—114no—
294C2×C4×D4—112no—
295C2×C4×D4—112no—
296C2×C4×D4—114no—
297C2×C4×D4—114no—
298C2×C4×D4C2×D1112yes—
299C2×#117—114no—
300C2×#117—111no—
301C2×#117—111no—
302C22×C42—111no—
303#390—114no—
304#390—112no—
305#390—114no—
306#390C2×D1112yes—
307#389—112no—
308#389—112no—
309#389—114no—
310#388—114no—
311#388—114no—
312#388—114no—
313#388—114no—
314#388—114no—
315#387—114no—
316#387—114no—
317#387—114no—
318#386—114no—
319#386—114no—
320#386C2×D1114yes—
321#386C2×D1114yes—
322#385—114no—
323#384—111no—
324#382C2×D1111yescharacteristic
325#380—112no—
326C4×C4⋊C4—112no—
327C4×C4⋊C4—112no—
328C4×C4⋊C4—112no—
329C4×C4⋊C4—114no—
330C4×C4⋊C4—112no—
331C4×C4⋊C4—112no—
332C4×C22⋊C4—114no—
333C4×C22⋊C4—114no—
334C4×C22⋊C4—114no—
335C4×C22⋊C4—114no—
336C4×C22⋊C4—114no—
337C4×C22⋊C4—112no—
338C4×C22⋊C4—112no—
339#376—111no—
340#376C2×D1111yescharacteristic
341C2×#95—114no—
342C43—111no—
343C43—111no—
344C22×C11—28no—
345C22×C11—28no—
346C22×C11—28no—
347C22×C11—44no—
348C22×C11—44no—
349C22×C11—44no—
350C22×C11—44no—
351C22×C11C24×C411yescharacteristic
352C22×C11C22×#4111yescharacteristic
353C22×C11C22×#4111yescharacteristic
354C22×C11C2×H(5,𝔽2)12yes—
355C22×C11#58512yes—
356C2×D11—22no—
357C2×D11—24no—
358C2×D11—42no—
359C2×D11—41no—
360C2×D11—41no—
361C4×C11—24no—
362C4×C11—24no—
363C4×C11—44no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11C4×#4114yes—
367Dic11—22no—
368Dic11—24no—
369Dic11—28no—
370Dic11—24no—
371Dic11—22no—
372Dic11—22no—
373Dic11—44no—
374C22×D4—114no—
375C22×D4C22×D1112yes—
376C22×D4C22×D1114yes—
377C23×C4—114no—
378C23×C4—111no—
379C23×C4—114no—
380C23×C4—112no—
381C23×C4C22×D1114yes—
382#127C4×D1118yescomplemented
383#125—118no—
384#123—1132no—
385#121—1116no—
386#121—1132no—
387C4×D4—28no—
388C4×D4—1116no—
389C4×D4—228no—
390C4×D4—448no—
391C4×D4—448no—
392#117—118no—
393#117—224no—
394#117—448no—
395C2×C4⋊C4—112no—
396C2×C4⋊C4—112no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—112no—
402C2×C4⋊C4—114no—
403C2×C4⋊C4—114no—
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—111no—
412C2×C22⋊C4—111no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4C22×D1114yes—
415C2×C22⋊C4C22×D1114yes—
416C2×C22⋊C4C22×D1114yes—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—112no—
420C2×C42—112no—
421C2×C42—111no—
422C2×C42—112no—
423C2×C42—114no—
424C2×C42—114no—
425C2×C42—112no—
426C2×C42—112no—
427C2×C42—114no—
428C2×C42—224no—
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432#95—112no—
433#95—114no—
434#95—114no—
435#95—114no—
436#95—112no—
437#95—114no—
438#95—114no—
439#95—114no—
440#95C22×D1112yes—
441#95C22×D1112yes—
442#95C22×D1114yes—
443C2×C11—48no—
444C2×C11C2×C4×#4111yescharacteristic
445C2×C11C4×H(5,𝔽2)12yes—
446C2×C11#349412yes—
447C2×C11#350811yescharacteristic
448C2×C11#351211yescharacteristic
449D11—42no—
450C24—111no—
451C24C23×D1114yes—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—1116no—
457C2×D4—444no—
458C2×D4—444no—
459C2×D4C2×C4×D1118yes—
460C2×D4C2×C4×D11116yes—
461C22×C4—28no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—111no—
465C22×C4—112no—
466C22×C4—111no—
467C22×C4—114no—
468C22×C4—111no—
469C22×C4—112no—
470C22×C4—1116no—
471C22×C4—114no—
472C22×C4—114no—
473C22×C4—224no—
474C22×C4—228no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—224no—
478C22×C4—442no—
479C22×C4—444no—
480C22×C4—444no—
481C22×C4—444no—
482C22×C4—444no—
483C22×C4C23×D1111yescharacteristic
484C22×C4C23×D1114yes—
485C22×C4C23×D1111yescharacteristic
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C22×C4C23×D1111yescharacteristic
489C4⋊C4—24no—
490C4⋊C4—118no—
491C4⋊C4—118no—
492C4⋊C4—1116no—
493C4⋊C4—222no—
494C4⋊C4—222no—
495C4⋊C4—228no—
496C4⋊C4—224no—
497C4⋊C4—444no—
498C4⋊C4—444no—
499C22⋊C4—28no—
500C22⋊C4—44no—
501C22⋊C4—44no—
502C22⋊C4—1116no—
503C22⋊C4—1116no—
504C22⋊C4—118no—
505C22⋊C4—222no—
506C22⋊C4—222no—
507C22⋊C4—228no—
508C22⋊C4—228no—
509C22⋊C4—228no—
510C22⋊C4—444no—
511C42—22no—
512C42—114no—
513C42—114no—
514C42—224no—
515C42—224no—
516C42—224no—
517C42—222no—
518C42—444no—
519C42—444no—
520C42—442no—
521C42—442no—
522C42—444no—
523C42C2×C4×D1114yes—
524C42#434114yes—
525C11#3428011yescharacteristic, complemented, Sylow
526C23—24no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—112no—
533C23—221no—
534C23—221no—
535C23—222no—
536C23—222no—
537C23C22×C4×D1118yes—
538C23C24×D1111yescharacteristic
539D4—216no—
540D4—416no—
541D4—4416no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—88no—
554C2×C4—114no—
555C2×C4—112no—
556C2×C4—118no—
557C2×C4—112no—
558C2×C4—112no—
559C2×C4—114no—
560C2×C4—221no—
561C2×C4—222no—
562C2×C4—221no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—228no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—448no—
575C2×C4—4416no—
576C2×C4—888no—
577C2×C4C22×C4×D1114yes—
578C2×C4C22×C4×D1112yes—
579C2×C4C2×#434114yes—
580C2×C4C2×#434112yes—
581C2×C4#41×D1112yes—
582C22—28no—
583C22—28no—
584C22—28no—
585C22—44no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—222no—
590C22—224no—
591C22—441no—
592C22—441no—
593C22—442no—
594C22C23×C4×D1111yescharacteristic
595C22C22×#434111yescharacteristic
596C22C2×#41×D1111yescharacteristic
597C22D11×H(5,𝔽2)12yes—
598C22#1062345512yes—
599C4—24no—
600C4—24no—
601C4—41no—
602C4—41no—
603C4—44no—
604C4—222no—
605C4—222no—
606C4—222no—
607C4—224no—
608C4—228no—
609C4—224no—
610C4—444no—
611C4C4×#434114yes—
612C2—48no—
613C2—442no—
614C2C2×C4×#434111yescharacteristic
615C2#1308182012yes—
616C2#1308234812yes—
617C2#1308248811yescharacteristic
618C2#1308253511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2328C2
socle, cosocleC23×C11C25
prime radicalC2×#10623250C2
hypercenter#2328D11
hypocenterC11#34280
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2328

Complements

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

NH ≅ G/Ntype
2. #13071749C2semidirect
3. #13071664C2semidirect
4. #13071657C2semidirect
5. #13071614C2semidirect
6. #13071357C2semidirect
7. #13071312C2semidirect
8. #13071226C2semidirect
9. #127×Dic11C2semidirect
10. #13071171C2semidirect
11. C4×#66991C2semidirect
12. #13071078C2semidirect
13. #13070977C2semidirect
14. #13070955C2semidirect
15. C11×#2328C2semidirect
25. #10623250C4semidirect
80. C11×#127C2×C4semidirect
94. #66992C2×C4semidirect
95. #66991C2×C4semidirect
96. #66988C2×C4semidirect
99. D4×Dic11C2×C4semidirect
127. #66925C2×C4semidirect
129. #66923C2×C4semidirect
223. #2328D11semidirect
382. #127C4×D11semidirect
525. C11#34280semidirect

Maximal subgroups

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

subgroupindex
C2×#106232502
#130717492
#130716642
#130716572
#130716142
#130713572
#130713122
#130712262
#127×Dic112
#130711712
C4×#669912
#130710782
#130709772
#130709552
C11×#23282
#3428011