Finite Group Databasebeta

← #14814901

Subgroups — #14814901

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622616C212yesmaximal, complemented
2#13073562C211yesmaximal, characteristic
3#13069805C212yesmaximal, complemented
4#13069798C212yesmaximal, complemented
5#13069543C211yesmaximal, characteristic, complemented
6#13069421C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13069377C211yesmaximal, characteristic, complemented
9#13068938C212yesmaximal, complemented
10C4×#66871C211yesmaximal, characteristic, complemented
11C11×#2354C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×C11×#117C2212yes—
14C2×#66993—21no—
15C2×#66983C2212yes—
16C2×#66983C2212yes—
17C2×#66927C2211yescharacteristic
18C11×#390—21no—
19C11×#388—22no—
20C11×#384C2211yescharacteristic
21C11×#380C2212yes—
22C4×C11×C4⋊C4—21no—
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2212yes—
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622616—28no—
27#10622601—21no—
28C2×#66873C2212yes—
29C2×#66873C2212yes—
30C2×#66873C2212yes—
31C2×#66873C2212yes—
32C2×#66872C2212yes—
33C2×#66871C2211yescharacteristic
34C2×#66871C2211yescharacteristic
35#10622573—22no—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×D4×C11D411yescharacteristic
43C23×C4×C11C2312yes—
44C22×C22⋊D11—22no—
45C22×C22⋊D11—22no—
46C22×D44—21no—
47C22×D44—21no—
48C22×D44C2312yes—
49C4×D4×C11—22no—
50C4×D4×C11—22no—
51C11×#117—24no—
52C11×#117—42no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4D412yes—
62C2×C42×C11—22no—
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65#66993—44no—
66#66983—24no—
67#66983—24no—
68#66983—42no—
69#66983—42no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4×Dic11—21no—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77C22×C11⋊C8C2311yescharacteristic
78#66927—22no—
79#66927—22no—
80C11×#95—22no—
81C11×#95—21no—
82C11⋊#95—21no—
83C22⋊(C11⋊C8)—24no—
84C22⋊(C11⋊C8)—42no—
85#66873—24no—
86#66873—24no—
87#66873—42no—
88#66873—42no—
89#66872—24no—
90#66871—22no—
91#66871D414yescomplemented
92C4⋊(C11⋊C8)—22no—
93C4×C11⋊C8—22no—
94#26237—111nomaximal, Sylow
95C24×C11C2×D412yes—
96C23×D11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—44no—
114C2×C22⋊D11—44no—
115C2×C22⋊D11—44no—
116C2×C22⋊D11—44no—
117C2×C22⋊D11—82no—
118C2×C22⋊D11—82no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—42no—
128C2×D44—42no—
129C2×D44—42no—
130C2×D44—42no—
131C2×D44—81no—
132C2×D44—81no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—81no—
141C11×C4⋊C4C2×D412yes—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—44no—
144C11×C22⋊C4—82no—
145C42×C11—44no—
146C42×C11—42no—
147C42×C11#4112yes—
148C42×C11#4112yes—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—44no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11C2×D412yes—
154C4⋊Dic11#4112yes—
155C4×Dic11—42no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8C2×D412yes—
165C2×#482—112no—
166#2541—111no—
167#2354D1111yescharacteristic, complemented
168#2034—112no—
169#2033—112no—
170#1982—111no—
171#1957—111no—
172#1954—111no—
173#1948—111no—
174#1875—112no—
175C4×#107—111no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11C22×D411yescharacteristic
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191D4×C11—44no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11#12312yes—
211C2×C4×C11#12312yes—
212C2×C4×C11#13512yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C11H(5,𝔽2)11yescharacteristic
220C22⋊D11—88no—
221C22⋊D11—88no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228D44—42no—
229D44—42no—
230D44—42no—
231D44—42no—
232D44—84no—
233D44—84no—
234C11⋊C8—22no—
235C11⋊C8—41no—
236C11⋊C8—42no—
237C2×#127—111no—
238C2×#127—221no—
239C2×#121—112no—
240C2×#121—112no—
241C2×C4×D4C2×D1111yescharacteristic
242C2×#117C2×D1112yes—
243#482—228no—
244C2×#107—111no—
245C2×#107—111no—
246C2×#106—112no—
247C2×C4⋊C8—111no—
248C2×#102—112no—
249C2×#102—112no—
250C2×#102—112no—
251C2×#102—112no—
252C2×C22⋊C8—112no—
253C2×C22⋊C8—112no—
254C2×C4×C8—111no—
255#392—222no—
256#390—21no—
257#390—221no—
258#388—22no—
259#384C2×D1111yescharacteristic
260#380C2×D1112yes—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—111no—
263C4×C4⋊C4C2×D1111yescharacteristic
264#340—111no—
265#340—112no—
266#340—111no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11C2×#12311yescharacteristic
275C22×C11D4211yescharacteristic
276C22×C11#54611yescharacteristic
277C22×C11C2×#13511yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C11#57611yescharacteristic
280C22×C11#57711yescharacteristic
281C2×D11—82no—
282C2×D11—82no—
283C2×D11—82no—
284C2×D11—82no—
285C2×D11—82no—
286C2×D11—82no—
287C2×D11—82no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—82no—
292C4×C11—81no—
293C4×C11#48214yescomplemented
294C4×C11#53211yescharacteristic
295C4×C11#54011yescharacteristic
296C4×C11#55011yescharacteristic
297C4×C11#55911yescharacteristic
298Dic11—42no—
299Dic11—42no—
300C22×D4—112no—
301C22×D4—222no—
302C22×D4—222no—
303C22×D4—221no—
304C22×D4—221no—
305C22×D4C22⋊D1111yescharacteristic
306C23×C4C22×D1112yes—
307C22×C8—111no—
308C22×C8—111no—
309C22×C8—112no—
310#127—222no—
311#127—222no—
312#127—444no—
313#121—224no—
314#121—224no—
315#121—442no—
316#121—442no—
317C4×D4—22no—
318C4×D4—22no—
319#117—24no—
320#117—42no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4C22⋊D1111yescharacteristic
326C2×C4⋊C4C22×D1112yes—
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4C22⋊D1112yes—
334C2×C42—22no—
335C2×C42—21no—
336C2×C42—221no—
337C2×C42C22×D1111yescharacteristic
338#107—114no—
339#107—222no—
340#106—224no—
341C4⋊C8—222no—
342#102—224no—
343#102—224no—
344#102—442no—
345#102—442no—
346C22⋊C8—224no—
347C22⋊C8—442no—
348C4×C8—222no—
349#95—22no—
350#95—21no—
351#95—221no—
352C2×C11—82no—
353C2×C11#244511yescharacteristic
354C2×C11C2×#48211yescharacteristic
355C2×C11#309611yescharacteristic
356C2×C11#327211yescharacteristic
357C2×C11#328711yescharacteristic
358C2×C11#330411yescharacteristic
359C2×C11#332511yescharacteristic
360D11—162no—
361C24—222no—
362C24C2×C22⋊D1112yes—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—222no—
367C2×D4—222no—
368C2×D4—222no—
369C2×D4—222no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—444no—
373C2×D4—444no—
374C2×D4—444no—
375C2×D4—444no—
376C2×D4—442no—
377C2×D4—442no—
378C2×D4—442no—
379C2×D4—442no—
380C2×D4—881no—
381C2×D4—881no—
382C2×D4—882no—
383C2×D4—882no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4C2×C22⋊D1112yes—
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C23×D1111yescharacteristic
399C2×C8—112no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8—221no—
406C2×C8—221no—
407C2×C8—222no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—42no—
415C4⋊C4—81no—
416C4⋊C4—112no—
417C4⋊C4—112no—
418C4⋊C4—221no—
419C4⋊C4—221no—
420C4⋊C4D4×D1112yes—
421C22⋊C4—24no—
422C22⋊C4—44no—
423C22⋊C4—82no—
424C22⋊C4—444no—
425C22⋊C4—444no—
426C42—44no—
427C42—42no—
428C42—442no—
429C42#433912yes—
430C42#433912yes—
431C11#2623711yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—442no—
440C23—442no—
441C23—442no—
442C23—442no—
443C23—442no—
444C23—442no—
445C23—442no—
446C23C22×C22⋊D1111yescharacteristic
447D4—44no—
448D4—442no—
449D4—442no—
450D4—442no—
451D4—442no—
452D4—884no—
453D4—888no—
454D4—888no—
455D4—884no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4#6698212yes—
481C2×C4#6698212yes—
482C2×C4#6700212yes—
483C2×C4#6700312yes—
484C2×C4C2×#433911yescharacteristic
485C2×C4C2×#433911yescharacteristic
486C2×C4C2×D4×D1111yescharacteristic
487C2×C4#6703711yescharacteristic
488C2×C4#41×D1111yescharacteristic
489C2×C4#6704211yescharacteristic
490C8—222no—
491C8—442no—
492C8—441no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—882no—
501C22—882no—
502C22—882no—
503C22—882no—
504C22—882no—
505C22—882no—
506C22—882no—
507C22C2×#6698211yescharacteristic
508C22D4×C22⋊D1111yescharacteristic
509C22C2×#6700211yescharacteristic
510C22C2×#6700311yescharacteristic
511C22#1062336011yescharacteristic
512C22#1062336611yescharacteristic
513C22#1062336811yescharacteristic
514C4—22no—
515C4—42no—
516C4—42no—
517C4—81no—
518C4—82no—
519C4—442no—
520C4—442no—
521C4#1062261614yescomplemented
522C4#1062307911yescharacteristic
523C4#1062308411yescharacteristic
524C4#1062309011yescharacteristic
525C4#1062309311yescharacteristic
526C2—82no—
527C2—1762no—
528C2#1307237511yescharacteristic
529C2C2×#1062261611yescharacteristic
530C2#1307857411yescharacteristic
531C2#1308021611yescharacteristic
532C2#1308037211yescharacteristic
533C2#1308054911yescharacteristic
534C2#1308085211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2354C2
socleC23×C11C22×D4
prime radical#13073562C2
hypercenter#2354D11
hypocenterC11#26237
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
1. C2×#10622616C2semidirect
3. #13069805C2semidirect
4. #13069798C2semidirect
5. #13069543C2semidirect
6. #13069421C2semidirect
7. #13069411C2semidirect
8. #13069377C2semidirect
9. #13068938C2semidirect
10. C4×#66871C2semidirect
11. C11×#2354C2semidirect
91. #66871D4semidirect
167. #2354D11semidirect
293. C4×C11#482semidirect
431. C11#26237semidirect
521. C4#10622616semidirect

Maximal subgroups

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

subgroupindex
C2×#106226162
#130735622
#130698052
#130697982
#130695432
#130694212
#130694112
#130693772
#130689382
C4×#668712
C11×#23542
#2623711