Finite Group Databasebeta

← #14914240

Subgroups — #14914240

Order 2816.

2422 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2#13071704C214yesmaximal, complemented
3#13071671C214yesmaximal, complemented
4#13071490C214yesmaximal
5#13071450C214yesmaximal
6#13071365C211yesmaximal, characteristic, complemented
7#13071364C211yesmaximal, characteristic, complemented
8#13071362C211yesmaximal, characteristic, complemented
9#13071231C212yesmaximal
10#13071187C212yesmaximal, complemented
11C4×#66941C212yesmaximal, complemented
12#13071022C211yesmaximal, characteristic
13#13070970C212yesmaximal
14#13070955C211yesmaximal, characteristic
15C11×#2331C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×#66997C2212yes—
19D11×C4⋊Q8C4116yescomplemented
20C2×#66945C2212yes—
21C2×C4⋊C4×D11C2212yes—
22C2×C4⋊C4×D11C2212yes—
23C2×#66941C2212yes—
24C2×#66941C2212yes—
25C2×#66940C2214yes—
26C2×#66925C2211yescharacteristic
27C2×#66925C2211yescharacteristic
28C2×C42×D11C2211yescharacteristic
29C2×#66922C2211yescharacteristic
30C2×C4×Dic22C2214yes—
31C11×#391C2214yes—
32C11×#389C2212yes—
33C11×#387C2214yes—
34C11×#382C2211yescharacteristic
35C4×C11×C4⋊C4C2212yes—
36C11×#376C2211yescharacteristic
37#10622843C2214yes—
38#10622600C2214yes—
39#10622598C2212yes—
40#10622594C2214yes—
41#10622589C2212yes—
42C4⋊C4×Dic11C2212yes—
43C4⋊C4×Dic11C2212yes—
44#10622586C2212yes—
45#10622585C2214yes—
46#10622585C2214yes—
47C4×(C2×D11)⋊C4C2214yes—
48#10622549C2211yescharacteristic
49C4×C4⋊Dic11C2212yes—
50#10622545C2211yescharacteristic
51C4×Dic11⋊C4C2214yes—
52C4×Dic11⋊C4C2214yes—
53C42×Dic11C2211yescharacteristic
54C42×Dic11C2211yescharacteristic
55#10622541C2212yes—
56#10622280C2212yes—
57#10622280C2214yes—
58#10622280C2212yes—
59#10622279C2212yes—
60#10622279C2214yes—
61#10622279C2212yes—
62#10622267C2214yes—
63#10622266C2214yes—
64#10622262C2212yes—
65#10622262C2212yes—
66#10622262C2214yes—
67#10622262C2214yes—
68#10622262C2212yes—
69#10622262C2212yes—
70#10622260C2214yes—
71#10622260C2214yes—
72#10622259C2214yes—
73#10622259C2214yes—
74#10622259C2214yes—
75#10622259C2214yes—
76C22×Q8×C11C2312yes—
77C2×Q8×D11—48no—
78C2×Q8×D11C2×C4116yes—
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×C4×D11C2314yes—
82C22×C4×D11C2311yescharacteristic
83C22×Dic22C2314yes—
84C22×Dic22C2312yes—
85C11×C4⋊Q8C2×C418yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2314yes—
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94#66997C2×C4116yes—
95C2×(C2×D11)⋊C4C2312yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2312yes—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2314yes—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2312yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2312yes—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2312yes—
110C2×C4×Dic11C2312yes—
111C2×C4×Dic11C2311yescharacteristic
112C2×C4×Dic11C2312yes—
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2312yes—
116C2×C4×Dic11C2314yes—
117C2×C4×Dic11C2314yes—
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2311yescharacteristic
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2311yescharacteristic
123#66945—28no—
124C4⋊C4×D11C2×C4116yes—
125C4⋊C4×D11C2×C4116yes—
126#66941C2×C4116yes—
127#66941C2×C4116yes—
128#66940—48no—
129#66925—24no—
130#66925Q818yescomplemented
131C42×D11C2×C418yes—
132#66922C2×C418yes—
133C4×Dic22—48no—
134C11×#95C2312yes—
135C11×#95C2312yes—
136C11×#95C2314yes—
137C11×#95C2314yes—
138C11×#95C2312yes—
139C11×#95C2312yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2312yes—
145C11⋊#95C2312yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2312yes—
149C11⋊#95C2312yes—
150#34216—111nomaximal, Sylow
151C23×D11C2411yescharacteristic
152C2×Q8×C11—44no—
153C2×Q8×C11C22×C418yes—
154C22×C4×C11C2414yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2414yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2411yescharacteristic
161C22×Dic11C2412yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C22×Dic11C2411yescharacteristic
166C22×Dic11C2411yescharacteristic
167C22×Dic11C2411yescharacteristic
168Q8×D11—432no—
169C2×C4×D11—24no—
170C2×C4×D11—24no—
171C2×C4×D11—44no—
172C2×C4×D11—44no—
173C2×C4×D11C22×C414yes—
174C2×C4×D11C22×C414yes—
175C2×C4×D11C22×C4116yes—
176C2×C4×D11C22×C414yes—
177C2×C4×D11C2×Q814yes—
178C2×C4×D11#4114yes—
179C2×Dic22—28no—
180C2×Dic22—28no—
181C2×Dic22—44no—
182C2×Dic22C22×C4116yes—
183C2×Dic22C22×C418yes—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—44no—
186C11×C4⋊C4C22×C418yes—
187C11×C4⋊C4C22×C418yes—
188C42×C11—22no—
189C42×C11—44no—
190C42×C11C22×C414yes—
191C42×C11C2×Q814yescomplemented
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4C2×Q818yes—
195C4⋊Dic11—24no—
196C4⋊Dic11—44no—
197C4⋊Dic11C22×C418yes—
198C4⋊Dic11C22×C418yes—
199Dic11⋊C4—24no—
200Dic11⋊C4—28no—
201Dic11⋊C4—28no—
202Dic11⋊C4—44no—
203Dic11⋊C4—44no—
204Dic11⋊C4C22×C4116yes—
205Dic11⋊C4C22×C4116yes—
206Dic11⋊C4C2×Q818yescomplemented
207C4×Dic11—28no—
208C4×Dic11—24no—
209C4×Dic11—24no—
210C4×Dic11—24no—
211C4×Dic11—24no—
212C4×Dic11—22no—
213C4×Dic11—44no—
214C4×Dic11—44no—
215C4×Dic11—44no—
216C4×Dic11C22×C414yes—
217C4×Dic11C22×C414yes—
218C4×Dic11C22×C414yes—
219C4×Dic11C2×Q814yescomplemented
220C22×C4⋊Q8—111no—
221#2369—114no—
222#2365—114no—
223#2345—114no—
224Q8×C22⋊C4—114no—
225#2331—111no—
226#2331—111no—
227#2331—111no—
228#2331D1111yescharacteristic, complemented
229#2316—112no—
230C4×C4⋊Q8—112no—
231C4×C4⋊Q8—112no—
232#2285—111no—
233#2274—112no—
234C4×#117—111no—
235C23×C11C2511yescharacteristic
236C22×D11—22no—
237C22×D11—22no—
238C22×D11C23×C412yes—
239C22×D11C22×Q812yes—
240C22×D11C2×#4112yes—
241Q8×C11—48no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11C23×C412yes—
255C2×C4×C11C23×C412yes—
256C2×C4×C11C23×C418yes—
257C2×C4×C11C23×C412yes—
258C2×C4×C11C22×Q814yes—
259C2×C4×C11C22×Q812yes—
260C2×C4×C11C2×#4112yes—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11C23×C418yes—
272C2×Dic11C23×C412yes—
273C2×Dic11C23×C412yes—
274C2×Dic11C23×C412yes—
275C2×Dic11C22×Q814yes—
276C2×Dic11C22×Q812yes—
277C2×Dic11C2×#4112yes—
278C2×Dic11H(5,𝔽2)14yes—
279C2×Dic112−1+414yes—
280C4×D11—28no—
281C4×D11—28no—
282C4×D11—416no—
283C4×D11C4×Q8116yescomplemented
284Dic22—232no—
285Dic22—48no—
286C23×Q8—112no—
287C2×C4⋊Q8—112no—
288C2×C4⋊Q8—1116no—
289C2×C4⋊Q8—112no—
290C2×C4⋊Q8—112no—
291C2×C4⋊Q8—111no—
292C2×C4⋊Q8C2×D1111yescharacteristic
293C2×C4×Q8—114no—
294C2×C4×Q8—114no—
295C2×#117—112no—
296C2×#117—111no—
297C2×#117—111no—
298C22×C4⋊C4—112no—
299C22×C4⋊C4—112no—
300C22×C42—111no—
301#391—114no—
302#391—114no—
303#391—114no—
304#391—114no—
305#391—114no—
306#391C2×D1114yes—
307#389—112no—
308#389—112no—
309#389—114no—
310#389—114no—
311#389—112no—
312#389—114no—
313#389—114no—
314#389C2×D1112yes—
315#387—114no—
316#387—114no—
317#387—114no—
318#387C2×D1114yes—
319#384—112no—
320#382—111no—
321#382C2×D1111yescharacteristic
322#380—114no—
323#380—114no—
324#380—112no—
325#380—112no—
326C4×C4⋊C4—112no—
327C4×C4⋊C4—112no—
328C4×C4⋊C4—112no—
329C4×C4⋊C4—114no—
330C4×C4⋊C4—114no—
331C4×C4⋊C4—114no—
332C4×C4⋊C4—112no—
333C4×C4⋊C4—112no—
334C4×C4⋊C4—114no—
335C4×C4⋊C4—112no—
336C4×C4⋊C4—112no—
337C4×C4⋊C4C2×D1112yes—
338C4×C22⋊C4—114no—
339C4×C22⋊C4—112no—
340C4×C22⋊C4—114no—
341C4×C22⋊C4—112no—
342#376—111no—
343#376C2×D1111yescharacteristic
344C43—111no—
345C43—111no—
346C22×C11C24×C411yescharacteristic
347C22×C11C23×Q811yescharacteristic
348C22×C11C22×#4111yescharacteristic
349C22×C11C2×H(5,𝔽2)12yes—
350C22×C11C2×2−1+412yes—
351C2×D11—22no—
352C2×D11—22no—
353C2×D11—24no—
354C2×D11—24no—
355C2×D11C2×C4×Q814yes—
356C4×C11—22no—
357C4×C11—28no—
358C4×C11—22no—
359C4×C11—24no—
360C4×C11—44no—
361C4×C11—42no—
362C4×C11C2×C4×Q814yes—
363Dic11—28no—
364Dic11—24no—
365Dic11—42no—
366Dic11—44no—
367Dic11C2×C4×Q814yes—
368Dic11#51814yes—
369Dic11#51914yes—
370C22×Q8—1116no—
371C22×Q8—114no—
372C22×Q8—112no—
373C22×Q8—448no—
374C22×Q8C22×D1112yes—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—114no—
379C4⋊Q8—1116no—
380C4⋊Q8—1116no—
381C4⋊Q8—1116no—
382C4⋊Q8—118no—
383C4⋊Q8C4×D1118yes—
384C4×Q8—448no—
385C4×Q8—448no—
386#117—118no—
387#117—224no—
388#117—228no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—114no—
391C2×C4⋊C4—112no—
392C2×C4⋊C4—112no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4—1116no—
395C2×C4⋊C4—1116no—
396C2×C4⋊C4—112no—
397C2×C4⋊C4—112no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—114no—
403C2×C4⋊C4C22×D1112yes—
404C2×C4⋊C4C22×D1114yes—
405C2×C4⋊C4C22×D1112yes—
406C2×C4⋊C4C22×D1112yes—
407C2×C22⋊C4—112no—
408C2×C22⋊C4—114no—
409C2×C22⋊C4—112no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—111no—
414C2×C42—118no—
415C2×C42—111no—
416C2×C42—114no—
417C2×C42—112no—
418C2×C42—112no—
419C2×C42—112no—
420C2×C42—112no—
421C2×C42—114no—
422C2×C42—114no—
423C2×C42—114no—
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1114yes—
426C2×C42C22×D1111yescharacteristic
427C2×C42C22×D1111yescharacteristic
428#95—112no—
429#95—112no—
430#95—114no—
431#95—114no—
432#95—114no—
433#95—112no—
434#95—112no—
435#95—114no—
436#95—114no—
437#95—114no—
438#95C22×D1112yes—
439#95C22×D1112yes—
440#95C22×D1114yes—
441#95C22×D1112yes—
442#95C22×D1112yes—
443#95C22×D1114yes—
444C2×C11C22×C4×Q811yescharacteristic
445C2×C11C2×#51811yescharacteristic
446C2×C11C2×#51911yescharacteristic
447C2×C11#350312yes—
448C2×C11#351112yes—
449D11—24no—
450C24—111no—
451C2×Q8—44no—
452C2×Q8—1116no—
453C2×Q8—118no—
454C2×Q8—228no—
455C2×Q8—228no—
456C2×Q8—444no—
457C2×Q8—4432no—
458C2×Q8C2×C4×D1118yes—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—114no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—112no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—114no—
469C22×C4—1116no—
470C22×C4—112no—
471C22×C4—114no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—444no—
475C22×C4—444no—
476C22×C4C23×D1112yes—
477C22×C4C23×D1114yes—
478C22×C4C23×D1111yescharacteristic
479C22×C4C23×D1111yescharacteristic
480C22×C4C23×D1114yes—
481C22×C4C23×D1112yes—
482C22×C4C23×D1111yescharacteristic
483C4⋊C4—24no—
484C4⋊C4—44no—
485C4⋊C4—1116no—
486C4⋊C4—1116no—
487C4⋊C4—118no—
488C4⋊C4—118no—
489C4⋊C4—118no—
490C4⋊C4—224no—
491C4⋊C4—228no—
492C4⋊C4—228no—
493C4⋊C4—224no—
494C4⋊C4—444no—
495C4⋊C4—444no—
496C4⋊C4—444no—
497C4⋊C4C2×C4×D1118yes—
498C4⋊C4C2×C4×D1118yes—
499C22⋊C4—118no—
500C22⋊C4—224no—
501C22⋊C4—228no—
502C42—22no—
503C42—44no—
504C42—114no—
505C42—114no—
506C42—114no—
507C42—114no—
508C42—228no—
509C42—224no—
510C42—224no—
511C42—224no—
512C42—224no—
513C42—222no—
514C42—444no—
515C42—444no—
516C42—444no—
517C42C2×C4×D1114yes—
518C42Q8×D1114yescomplemented
519C11#3421611yescharacteristic, complemented, Sylow
520C23—112no—
521C23—112no—
522C23—112no—
523C23—222no—
524C23—222no—
525C23C24×D1111yescharacteristic
526Q8—48no—
527Q8—2232no—
528Q8—448no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—112no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—114no—
547C2×C4—114no—
548C2×C4—1116no—
549C2×C4—118no—
550C2×C4—114no—
551C2×C4—228no—
552C2×C4—228no—
553C2×C4—222no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—4416no—
564C2×C4C22×C4×D1112yes—
565C2×C4C22×C4×D1112yes—
566C2×C4C22×C4×D1118yes—
567C2×C4C22×C4×D1112yes—
568C2×C4C2×Q8×D1114yes—
569C2×C4C2×Q8×D1112yes—
570C2×C4#41×D1112yes—
571C22—114no—
572C22—224no—
573C22—224no—
574C22—222no—
575C22—222no—
576C22C23×C4×D1111yescharacteristic
577C22C22×Q8×D1111yescharacteristic
578C22C2×#41×D1111yescharacteristic
579C22D11×H(5,𝔽2)12yes—
580C22D11×2−1+412yes—
581C4—24no—
582C4—22no—
583C4—28no—
584C4—22no—
585C4—42no—
586C4—44no—
587C4—114no—
588C4—114no—
589C4—114no—
590C4—224no—
591C4—228no—
592C4—442no—
593C4—444no—
594C4C4×Q8×D1114yes—
595C2—224no—
596C2C2×C4×Q8×D1111yescharacteristic
597C2D11×#51811yescharacteristic
598C2D11×#51911yescharacteristic
599C2#1308243112yes—
600C2#1308252112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2331C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2331D11
hypocenterC11#34216
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2331

Complements

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

NH ≅ G/Ntype
2. #13071704C2semidirect
3. #13071671C2semidirect
6. #13071365C2semidirect
7. #13071364C2semidirect
8. #13071362C2semidirect
10. #13071187C2semidirect
11. C4×#66941C2semidirect
15. C11×#2331C2semidirect
19. D11×C4⋊Q8C4semidirect
130. #66925Q8semidirect
191. C42×C11C2×Q8semidirect
206. Dic11⋊C4C2×Q8semidirect
219. C4×Dic11C2×Q8semidirect
228. #2331D11semidirect
283. C4×D11C4×Q8semidirect
518. C42Q8×D11semidirect
519. C11#34216semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
#130717042
#130716712
#130714902
#130714502
#130713652
#130713642
#130713622
#130712312
#130711872
C4×#669412
#130710222
#130709702
#130709552
C11×#23312
#3421611