Finite Group Databasebeta

← #14759448

Subgroups — #14759448

Order 2816.

1436 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2C2×#10622352C211yesmaximal, characteristic
3C2×#10622466C212yesmaximal, complemented
4#13071144C211yesmaximal, characteristic
5#13068958C212yesmaximal, complemented
6#13068923C211yesmaximal, characteristic
7#13068881C212yesmaximal, complemented
8#13068550C211yesmaximal, characteristic
9#13068445C212yesmaximal, complemented
10#13068380C211yesmaximal, characteristic
11C11×#1853C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66977C2211yescharacteristic
15C22×Dic11⋊C4—21no—
16C22×C4×Dic11—21no—
17C22×C4×Dic11C2211yescharacteristic
18C22×Dic44C2212yes—
19C2×#66940—21no—
20C2×#66940—21no—
21C2×#66940—28no—
22C2×#66940C2211yescharacteristic
23C2×#66940C2212yes—
24C2×#66940C2212yes—
25C2×C11×#106C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66880C2212yes—
30C2×#66879C2212yes—
31C4⋊C4×Dic11C2211yescharacteristic
32#10622587C2211yescharacteristic
33#10622586C2211yescharacteristic
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37#10622559—21no—
38C22⋊C4×Dic11—21no—
39#10622466—28no—
40#10622352C418yescomplemented
41#10622265—21no—
42#10622262—21no—
43C11×#340C2212yes—
44#10622188C2212yes—
45#10622167C2212yes—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11D411yescharacteristic
50C23×Dic11D411yescharacteristic
51C22×Dic22—21no—
52C22×Dic22—22no—
53C22×Dic22—24no—
54C22×Dic22—24no—
55C22×Dic22C2×C414yes—
56C22×Dic22C2311yescharacteristic
57C22×Dic22C2312yes—
58C22×C8×C11C2312yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—21no—
65C2×C22⋊Dic11—21no—
66C2×C4⋊Dic11C2311yescharacteristic
67#66977—22no—
68#66977C2×C414yes—
69C2×Dic11⋊C4—28no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×C4×Dic11—28no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86C2×Dic44—24no—
87C2×Dic44—24no—
88C2×Dic44C2×C418yescomplemented
89#66940—28no—
90#66940—28no—
91#66940—24no—
92#66940—24no—
93#66940—24no—
94#66940—24no—
95#66940D418yes—
96C11×#106—24no—
97C11×C22⋊C8C2×C414yes—
98C11×#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C22⋊(C11⋊C8)—22no—
104#66880C2×C418yescomplemented
105#66879—24no—
106#66874—24no—
107#66874—24no—
108#66874—24no—
109#21455—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4112yes—
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—24no—
124C22×Dic11—24no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—24no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—41no—
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C2×Dic22—24no—
140C2×Dic22—24no—
141C2×Dic22—216no—
142C2×Dic22—216no—
143C2×Dic22—24no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—21no—
150C2×Dic22C22×C412yes—
151C2×Dic22C22×C414yes—
152C2×Dic22C2×D414yes—
153C2×Dic22#4114yes—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11C22×C414yes—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4C2×D414yes—
162C11×C22⋊C4—42no—
163C22⋊Dic11—24no—
164C4⋊Dic11—21no—
165C4⋊Dic11C22×C412yes—
166Dic11⋊C4—28no—
167Dic11⋊C4—28no—
168Dic11⋊C4—24no—
169Dic11⋊C4—42no—
170Dic11⋊C4—42no—
171C4×Dic11—28no—
172C4×Dic11—22no—
173C4×Dic11—22no—
174C4×Dic11—28no—
175C4×Dic11—22no—
176C4×Dic11—42no—
177C4×Dic11—42no—
178C4×Dic11C2×D414yes—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182Dic44—216no—
183C22×C4×Q8—111no—
184C2×#451—111no—
185C2×#441—112no—
186C4×C22⋊Q8—111no—
187#1878—112no—
188#1872—111no—
189#1865—112no—
190#1853D1111yescharacteristic
191#1787—111no—
192#1763—112no—
193#1749—111no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11C4×D412yes—
199C23×C11#13712yes—
200C23×C11#13712yes—
201C23×C11C22×D411yescharacteristic
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—48no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11C4×D412yes—
217C2×C4×C11C23×C411yescharacteristic
218C2×C4×C11C22×D412yes—
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4112yes—
221C2×Dic11—216no—
222C2×Dic11—28no—
223C2×Dic11—24no—
224C2×Dic11—21no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—44no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11#12012yes—
243C2×Dic11#12012yes—
244C2×Dic11#13712yes—
245Dic22—216no—
246Dic22—24no—
247Dic22—24no—
248Dic22—24no—
249Dic22—24no—
250Dic22—42no—
251Dic22C4×D418yes—
252C8×C11—24no—
253C11⋊C8—42no—
254C23×Q8—111no—
255C22×Q16—112no—
256C2×C22⋊Q8—111no—
257C2×C4×Q8—112no—
258C2×C4×Q8—112no—
259C2×C4×Q8—111no—
260C2×C4×Q8—221no—
261C2×C4×Q8—221no—
262C2×C4×Q8—228no—
263C22×C4⋊C4—221no—
264C22×C4⋊C4C2×D1111yescharacteristic
265C22×C42—111no—
266C22×C42—221no—
267#451—118no—
268#441—228no—
269C2×#106C2×D1112yes—
270C2×#103—112no—
271C2×#103—112no—
272C2×#103—112no—
273C2×#103—112no—
274C2×C22⋊C8—111no—
275C2×C22⋊C8C2×D1111yescharacteristic
276C2×#97—112no—
277#391—111no—
278#389—111no—
279#387—221no—
280#385—221no—
281#380C2×D1111yescharacteristic
282C4×C4⋊C4—111no—
283C4×C4⋊C4—221no—
284C4×C22⋊C4—221no—
285#340—112no—
286#340C2×D1112yes—
287#336—112no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11#44114yescomplemented
295C22×C11C2×C4×D411yescharacteristic
296C22×C11C2×#12011yescharacteristic
297C22×C11#52511yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C22×C11C2×#13711yescharacteristic
300C22×C11C2×#13711yescharacteristic
301C22×C11#57511yescharacteristic
302C4×C11—22no—
303C4×C11—44no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11C2×C4×D412yes—
307C4×C11#52512yes—
308Dic11—22no—
309Dic11—22no—
310Dic11—22no—
311Dic11—28no—
312Dic11—42no—
313Dic11—41no—
314Dic11—42no—
315C22×Q8—114no—
316C22×Q8—112no—
317C22×Q8—111no—
318C22×Q8—224no—
319C22×Q8—224no—
320C22×Q8—221no—
321C22×Q8—222no—
322C23×C4—21no—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—221no—
326C23×C4C22×D1111yescharacteristic
327C2×Q16—118no—
328C2×Q16—224no—
329C2×Q16—224no—
330C22×C8—112no—
331C22×C8C22×D1112yes—
332C22⋊Q8—114no—
333C22⋊Q8—222no—
334C4×Q8—118no—
335C4×Q8—224no—
336C4×Q8—224no—
337C4×Q8—224no—
338C4×Q8—228no—
339C4×Q8—228no—
340C4×Q8—224no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—228no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4C22×D1111yescharacteristic
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C4⋊C4C22×D1112yes—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—221no—
355C2×C42—111no—
356C2×C42—111no—
357C2×C42—111no—
358C2×C42—111no—
359C2×C42—224no—
360C2×C42—222no—
361C2×C42—222no—
362C2×C42—228no—
363C2×C42—221no—
364C2×C42—221no—
365#106—24no—
366#103—118no—
367#103—224no—
368#103—224no—
369#103—224no—
370C22⋊C8—222no—
371C22⋊C8C4×D1114yes—
372#97—224no—
373#95—21no—
374#95—221no—
375#95—221no—
376#95—221no—
377#95—221no—
378C2×C11—24no—
379C2×C11C4×#12011yescharacteristic
380C2×C11C2×#44111yescharacteristic
381C2×C11C4×#13711yescharacteristic
382C2×C11#300411yescharacteristic
383C2×C11#300711yescharacteristic
384C2×C11#311311yescharacteristic
385C2×C11#311711yescharacteristic
386C24D4×D1111yescharacteristic
387C2×Q8—114no—
388C2×Q8—112no—
389C2×Q8—114no—
390C2×Q8—114no—
391C2×Q8—2216no—
392C2×Q8—224no—
393C2×Q8—224no—
394C2×Q8—2216no—
395C2×Q8—224no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×Q8—221no—
399C2×Q8—222no—
400C2×Q8—222no—
401C2×Q8—222no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—224no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—441no—
426C22×C4C2×C4×D1112yes—
427C22×C4D4×D1111yescharacteristic
428C22×C4#434312yes—
429C22×C4C23×D1111yescharacteristic
430Q16—2216no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8C2×C4×D1114yes—
437C4⋊C4—24no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—112no—
442C4⋊C4—228no—
443C4⋊C4—228no—
444C4⋊C4—224no—
445C4⋊C4—221no—
446C4⋊C4—442no—
447C4⋊C4—442no—
448C4⋊C4D4×D1114yes—
449C22⋊C4—42no—
450C22⋊C4—224no—
451C42—114no—
452C42—222no—
453C42—222no—
454C42—228no—
455C42—228no—
456C42—222no—
457C42—442no—
458C42—442no—
459C11#2145511yescharacteristic, complemented, Sylow
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23#6694612yes—
465C23#6696812yes—
466C23#6696812yes—
467C23C2×D4×D1111yescharacteristic
468Q8—118no—
469Q8—2216no—
470Q8—224no—
471Q8—224no—
472Q8—224no—
473Q8—224no—
474Q8—442no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—48no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—112no—
490C2×C4—112no—
491C2×C4—112no—
492C2×C4—2216no—
493C2×C4—228no—
494C2×C4—224no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—444no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4#6694612yes—
514C2×C4C22×C4×D1111yescharacteristic
515C2×C4C2×D4×D1112yes—
516C2×C4C2×#434311yescharacteristic
517C2×C4#41×D1112yes—
518C8—24no—
519C8—442no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22#1062246614yescomplemented
527C22C2×#6694611yescharacteristic
528C22D11×#12011yescharacteristic
529C22#1062318711yescharacteristic
530C22C2×#6696811yescharacteristic
531C22C2×#6696811yescharacteristic
532C22#1062330411yescharacteristic
533C22D11×#13711yescharacteristic
534C4—22no—
535C4—44no—
536C4—81no—
537C4—81no—
538C4—228no—
539C4—222no—
540C4—222no—
541C4—222no—
542C4—442no—
543C4—441no—
544C4—442no—
545C4C4×D4×D1112yes—
546C4#1062315812yes—
547C2—24no—
548C2#1307111711yescharacteristic
549C2C2×#1062246611yescharacteristic
550C2#1307743411yescharacteristic
551C2#1307784711yescharacteristic
552C2#1307787111yescharacteristic
553C2#1307874311yescharacteristic
554C2#1307878411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1853C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1853D11
hypocenterC11#21455
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
3. C2×#10622466C2semidirect
5. #13068958C2semidirect
7. #13068881C2semidirect
9. #13068445C2semidirect
40. #10622352C4semidirect
88. C2×Dic44C2×C4semidirect
104. #66880C2×C4semidirect
294. C22×C11#441semidirect
459. C11#21455semidirect
526. C22#10622466semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106223522
C2×#106224662
#130711442
#130689582
#130689232
#130688812
#130685502
#130684452
#130683802
C11×#18532
#2145511