Finite Group Databasebeta

← #14814888

Subgroups — #14814888

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×#10622392C212yesmaximal, complemented
2#13073563C211yesmaximal, characteristic
3#13071567C211yesmaximal, characteristic, complemented
4#13069804C212yesmaximal, complemented
5#13069796C212yesmaximal, complemented
6#13069544C211yesmaximal, characteristic, complemented
7#13069410C211yesmaximal, characteristic, complemented
8#13069372C211yesmaximal, characteristic, complemented
9#13068935C212yesmaximal, complemented
10C4×#66881C211yesmaximal, characteristic, complemented
11C11×#1957C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×#66993—21no—
14C2×#66991C2212yes—
15C2×#66991C2212yes—
16C2×#66945C2212yes—
17C2×C4×D44C2211yescharacteristic
18C2×C11×#102C2212yes—
19C2×C11×#102C2212yes—
20C2×C4×C8×C11C2211yescharacteristic
21C11×#384C2211yescharacteristic
22#10622836—22no—
23#10622834—21no—
24C2×#66896C2212yes—
25C2×#66896C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×#66881C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30#10622603—22no—
31#10622601—21no—
32#10622600C2212yes—
33C4⋊C4×Dic11—21no—
34C2×#66871C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622392—28no—
39#10622189C2211yescharacteristic
40#10622189C2211yescharacteristic
41#10622167C2212yes—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11C2312yes—
45C22×C22⋊D11—22no—
46C22×C22⋊D11—22no—
47C22×D44D411yescharacteristic
48C22×C4×D11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×#127—22no—
52C11×#127—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59#66993—44no—
60#66991—24no—
61#66991—24no—
62#66991—42no—
63#66991—42no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4D412yes—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4×Dic11—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—22no—
75C22×C11⋊C8C2312yes—
76#66945—24no—
77#66945—42no—
78C4×D44—22no—
79C4×D44—22no—
80C11×#102—24no—
81C11×#102—42no—
82C4×C8×C11—22no—
83#66896—24no—
84#66896—42no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88(C2×D11)⋊C8—24no—
89(C2×D11)⋊C8—42no—
90#66881—22no—
91#66881D414yescomplemented
92#66871—24no—
93C4⋊(C11⋊C8)—22no—
94#26235—111nomaximal, Sylow
95C24×C11—22no—
96C23×D11C2×D412yes—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11—81no—
108C2×D4×C11—81no—
109C22×C4×C11—22no—
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—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11C2×D412yes—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11C2×D412yes—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—81no—
143C42×C11#4112yes—
144C42×C11#4112yes—
145C22⋊Dic11—44no—
146C22⋊Dic11—44no—
147(C2×D11)⋊C4—24no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—82no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11C2×D412yes—
157C4⋊Dic11C2×D412yes—
158C4⋊Dic11#4112yes—
159C4×Dic11—44no—
160C4×Dic11—42no—
161C4×Dic11—42no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×#482—112no—
166#2541—111no—
167#2354—111no—
168#2034—112no—
169#2033—112no—
170#1982—111no—
171#1957D1111yescharacteristic, complemented
172#1954—111no—
173#1947—111no—
174#1875—112no—
175C4×#106—111no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11C22×D411yescharacteristic
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—22no—
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—22no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—84no—
196D4×C11—84no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11#12312yes—
203C2×C4×C11#12312yes—
204C2×C4×C11#13512yes—
205C2×C4×C11AGL(1,ℤ/8)12yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C11H(5,𝔽2)11yescharacteristic
212C22⋊D11—88no—
213C22⋊D11—88no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229D44—44no—
230C4×D11—42no—
231C4×D11—42no—
232C4×D11—42no—
233C4×D11—42no—
234C8×C11—22no—
235C8×C11—41no—
236C11⋊C8—42no—
237C2×#127—221no—
238C2×#127C2×D1111yescharacteristic
239C2×#121—112no—
240C2×#121—112no—
241C2×C4×D4—111no—
242C2×#117—112no—
243#482—228no—
244C2×#107—112no—
245C2×#106—111no—
246C2×#106—111no—
247C2×C4⋊C8—111no—
248C2×#102—112no—
249C2×#102—112no—
250C2×#102C2×D1112yes—
251C2×#102C2×D1112yes—
252C2×C22⋊C8—112no—
253C2×C22⋊C8—112no—
254C2×C4×C8C2×D1111yescharacteristic
255#392—222no—
256#390—221no—
257#390—221no—
258#388—222no—
259#384C2×D1111yescharacteristic
260#380—112no—
261C4×C4⋊C4—111no—
262C4×C4⋊C4—111no—
263C4×C4⋊C4—221no—
264#340—111no—
265#340—111no—
266#340—112no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
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—42no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—42no—
287C2×D11—42no—
288C4×C11—22no—
289C4×C11—82no—
290C4×C11#48214yescomplemented
291C4×C11#53211yescharacteristic
292C4×C11#54011yescharacteristic
293C4×C11#55011yescharacteristic
294C4×C11#55911yescharacteristic
295Dic11—42no—
296Dic11—42no—
297Dic11—42no—
298Dic11—42no—
299Dic11—81no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—111no—
303C22×D4—222no—
304C22×D4—222no—
305C22×D4C22×D1112yes—
306C23×C4—112no—
307C22×C8—112no—
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310#127—22no—
311#127—22no—
312#127—444no—
313#121—224no—
314#121—224no—
315#121—442no—
316#121—442no—
317C4×D4—222no—
318C4×D4—222no—
319#117—224no—
320#117—442no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4C22×D1112yes—
329C2×C22⋊C4—112no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C42—222no—
335C2×C42—221no—
336C2×C42—221no—
337C2×C42C22×D1111yescharacteristic
338#107—224no—
339#106—114no—
340#106—222no—
341C4⋊C8—222no—
342#102—24no—
343#102—42no—
344#102—224no—
345#102—442no—
346C22⋊C8—224no—
347C22⋊C8—442no—
348C4×C8—22no—
349#95—222no—
350#95—221no—
351#95—221no—
352C2×C11—162no—
353C2×C11#244511yescharacteristic
354C2×C11C2×#48211yescharacteristic
355C2×C11#309611yescharacteristic
356C2×C11#327411yescharacteristic
357C2×C11#328411yescharacteristic
358C2×C11#330511yescharacteristic
359C2×C11#332411yescharacteristic
360D11—82no—
361C24—22no—
362C24—112no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—81no—
374C2×D4—81no—
375C2×D4—222no—
376C2×D4—222no—
377C2×D4—222no—
378C2×D4—444no—
379C2×D4—444no—
380C2×D4—444no—
381C2×D4—444no—
382C2×D4—882no—
383C2×D4—882no—
384C22×C4—22no—
385C22×C4—112no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—221no—
396C22×C4D4×D1111yescharacteristic
397C22×C4D4×D1111yescharacteristic
398C22×C4C23×D1111yescharacteristic
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—222no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8D4×D1112yes—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—42no—
411C4⋊C4—81no—
412C4⋊C4—112no—
413C4⋊C4—112no—
414C4⋊C4—112no—
415C4⋊C4—222no—
416C4⋊C4—221no—
417C4⋊C4—221no—
418C4⋊C4—221no—
419C4⋊C4—221no—
420C4⋊C4—221no—
421C22⋊C4—224no—
422C22⋊C4—444no—
423C22⋊C4—444no—
424C22⋊C4—444no—
425C22⋊C4—882no—
426C42—444no—
427C42—442no—
428C42—442no—
429C42#433912yes—
430C42#434112yes—
431C11#2623511yescharacteristic, complemented, Sylow
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—222no—
440C23—222no—
441C23—222no—
442C23—222no—
443C23—222no—
444C23—222no—
445C23—222no—
446C23C2×D4×D1111yescharacteristic
447D4—42no—
448D4—42no—
449D4—42no—
450D4—42no—
451D4—84no—
452D4—84no—
453D4—444no—
454D4—888no—
455D4—888no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4#6693612yes—
481C2×C4#6693612yes—
482C2×C4#6696412yes—
483C2×C4#6696912yes—
484C2×C4C2×#433911yescharacteristic
485C2×C4C2×D4×D1111yescharacteristic
486C2×C4C2×#434111yescharacteristic
487C2×C4#6703711yescharacteristic
488C2×C4#41×D1111yescharacteristic
489C2×C4#6704211yescharacteristic
490C8—22no—
491C8—41no—
492C8—442no—
493C22—82no—
494C22—82no—
495C22—82no—
496C22—82no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—442no—
501C22—442no—
502C22—442no—
503C22—442no—
504C22—442no—
505C22—442no—
506C22—442no—
507C22C2×#6693611yescharacteristic
508C22#1062320711yescharacteristic
509C22#1062324811yescharacteristic
510C22C2×#6696411yescharacteristic
511C22#1062328811yescharacteristic
512C22C2×#6696911yescharacteristic
513C22#1062329311yescharacteristic
514C4—22no—
515C4—82no—
516C4—442no—
517C4—442no—
518C4—442no—
519C4—442no—
520C4—881no—
521C4#1062239214yescomplemented
522C4#1062308411yescharacteristic
523C4#1062309011yescharacteristic
524C4#1062312711yescharacteristic
525C4#1062315011yescharacteristic
526C2—162no—
527C2—882no—
528C2#1307238411yescharacteristic
529C2C2×#1062239211yescharacteristic
530C2#1307857011yescharacteristic
531C2#1308023511yescharacteristic
532C2#1308034511yescharacteristic
533C2#1308056511yescharacteristic
534C2#1308084611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1957C2
socleC23×C11C22×D4
prime radical#13073563C2
hypercenter#1957D11
hypocenterC11#26235
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
1. C2×#10622392C2semidirect
3. #13071567C2semidirect
4. #13069804C2semidirect
5. #13069796C2semidirect
6. #13069544C2semidirect
7. #13069410C2semidirect
8. #13069372C2semidirect
9. #13068935C2semidirect
10. C4×#66881C2semidirect
11. C11×#1957C2semidirect
91. #66881D4semidirect
171. #1957D11semidirect
290. C4×C11#482semidirect
431. C11#26235semidirect
521. C4#10622392semidirect

Maximal subgroups

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

subgroupindex
C2×#106223922
#130735632
#130715672
#130698042
#130697962
#130695442
#130694102
#130693722
#130689352
C4×#668812
C11×#19572
#2623511