Finite Group Databasebeta

← #14814881

Subgroups — #14814881

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×#10622648C212yesmaximal, complemented
2#13071565C211yesmaximal, characteristic, complemented
3#13069802C212yesmaximal, complemented
4#13069795C212yesmaximal, complemented
5#13069544C211yesmaximal, characteristic, complemented
6#13069423C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13069374C211yesmaximal, characteristic, complemented
9#13068939C212yesmaximal, complemented
10C4×#66872C211yesmaximal, characteristic, complemented
11C11×#2541C211yesmaximal, characteristic
12C2×C11×#127—21no—
13C2×C11×#127C2211yescharacteristic
14C2×C11×#121C2212yes—
15C2×C11×#121C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66979C2212yes—
18C11×#392—22no—
19C11×#390—21no—
20C4×C11×C4⋊C4C2211yescharacteristic
21#10622834—21no—
22C2×#66896C2212yes—
23C2×#66896C2212yes—
24C2×#66896C2212yes—
25C2×#66896C2212yes—
26#10622825C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622648—28no—
30C4⋊C4×Dic11—21no—
31C2×#66872C2211yescharacteristic
32C2×#66872C2211yescharacteristic
33C2×#66871C2212yes—
34#10622564—22no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2312yes—
48C23×C4×C11C2312yes—
49C11×#127—22no—
50C11×#127—22no—
51C11×#127—44no—
52C11×#121—24no—
53C11×#121—24no—
54C11×#121—42no—
55C11×#121—42no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4D412yes—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68#66979—24no—
69#66979—42no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4×Dic11—21no—
76C2×C4×Dic11—22no—
77C22×C11⋊C8C2311yescharacteristic
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C11×#95—21no—
81#66896—24no—
82#66896—24no—
83#66896—42no—
84#66896—42no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C22⋊(C11⋊C8)—24no—
88C22⋊(C11⋊C8)—42no—
89#66872—22no—
90#66872D414yescomplemented
91#66871—24no—
92C4⋊(C11⋊C8)—22no—
93C4×C11⋊C8—22no—
94#26235—111nomaximal, Sylow
95C24×C11—22no—
96C24×C11C2×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—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—44no—
107C2×D4×C11—44no—
108C2×D4×C11—44no—
109C2×D4×C11—44no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11—81no—
115C2×D4×C11—81no—
116C2×D4×C11—82no—
117C2×D4×C11—82no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4C2×D412yes—
137C11×C4⋊C4#4112yes—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—44no—
141C42×C11—42no—
142C42×C11#4112yes—
143C42×C11#4112yes—
144C22⋊Dic11—44no—
145C22⋊Dic11—82no—
146C4⋊Dic11—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—42no—
152C4⋊Dic11—81no—
153C4⋊Dic11C2×D412yes—
154C4×Dic11—44no—
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#2541D1111yescharacteristic
167#2354—111no—
168#2034—112no—
169#2033—112no—
170#1982—111no—
171#1957—111no—
172#1954—111no—
173#1947—111no—
174#1875—112no—
175C4×#106—111no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11C22×D411yescharacteristic
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—44no—
196D4×C11—84no—
197D4×C11—88no—
198D4×C11—88no—
199D4×C11—84no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11#12312yes—
216C2×C4×C11#12312yes—
217C2×C4×C11#13512yes—
218C2×C4×C11AGL(1,ℤ/8)12yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×Dic11—22no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—41no—
234C11⋊C8—22no—
235C11⋊C8—41no—
236C11⋊C8—42no—
237C2×#127—21no—
238C2×#127C2×D1111yescharacteristic
239C2×#121C2×D1112yes—
240C2×#121C2×D1112yes—
241C2×C4×D4C2×D1111yescharacteristic
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×#102—112no—
251C2×#102—112no—
252C2×C22⋊C8—112no—
253C2×C22⋊C8—112no—
254C2×C4×C8—111no—
255#392—22no—
256#390—21no—
257#390—221no—
258#388—222no—
259#384—111no—
260#380—112no—
261C4×C4⋊C4—111no—
262C4×C4⋊C4—221no—
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×C11—82no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—82no—
278C22×C11—82no—
279C22×C11—82no—
280C22×C11—82no—
281C22×C11C2×#12311yescharacteristic
282C22×C11D4211yescharacteristic
283C22×C11#54611yescharacteristic
284C22×C11C2×#13511yescharacteristic
285C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C11#57611yescharacteristic
287C22×C11#57711yescharacteristic
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11#48214yescomplemented
293C4×C11#53211yescharacteristic
294C4×C11#54011yescharacteristic
295C4×C11#55011yescharacteristic
296C4×C11#55911yescharacteristic
297Dic11—42no—
298Dic11—82no—
299Dic11—81no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4C22⋊D1111yescharacteristic
305C22×D4C22×D1112yes—
306C23×C4C22×D1112yes—
307C22×C8—111no—
308C22×C8—111no—
309C22×C8—112no—
310#127—22no—
311#127—22no—
312#127—44no—
313#121—24no—
314#121—24no—
315#121—42no—
316#121—42no—
317C4×D4—22no—
318C4×D4—22no—
319#117—224no—
320#117—442no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4C22⋊D1111yescharacteristic
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—21no—
335C2×C42—222no—
336C2×C42—221no—
337C2×C42C22×D1111yescharacteristic
338#107—224no—
339#106—114no—
340#106—222no—
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—21no—
350#95—221no—
351#95—222no—
352C2×C11—82no—
353C2×C11—162no—
354C2×C11#244511yescharacteristic
355C2×C11C2×#48211yescharacteristic
356C2×C11#309611yescharacteristic
357C2×C11#327411yescharacteristic
358C2×C11#328411yescharacteristic
359C2×C11#330511yescharacteristic
360C2×C11#332411yescharacteristic
361C24—22no—
362C24C2×C22⋊D1112yes—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—44no—
373C2×D4—44no—
374C2×D4—44no—
375C2×D4—44no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—81no—
381C2×D4—81no—
382C2×D4—82no—
383C2×D4—82no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—221no—
393C22×C4—221no—
394C22×C4—222no—
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—222no—
403C2×C8—221no—
404C2×C8—222no—
405C2×C8—221no—
406C2×C8—222no—
407C2×C8—221no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—112no—
412C4⋊C4—221no—
413C4⋊C4—222no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—222no—
417C4⋊C4—442no—
418C4⋊C4—881no—
419C4⋊C4D4×D1112yes—
420C4⋊C4#434112yes—
421C22⋊C4—24no—
422C22⋊C4—44no—
423C22⋊C4—44no—
424C22⋊C4—444no—
425C22⋊C4—882no—
426C42—42no—
427C42—444no—
428C42—442no—
429C42#434112yes—
430C42#434112yes—
431C11#2623511yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23C22×C22⋊D1111yescharacteristic
447D4—42no—
448D4—42no—
449D4—42no—
450D4—42no—
451D4—44no—
452D4—84no—
453D4—88no—
454D4—88no—
455D4—84no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—222no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—442no—
480C2×C4#6698512yes—
481C2×C4#6698812yes—
482C2×C4#6698812yes—
483C2×C4#6700312yes—
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4C2×#434111yescharacteristic
486C2×C4C2×#434111yescharacteristic
487C2×C4C2×#434111yescharacteristic
488C2×C4#6703711yescharacteristic
489C2×C4#6703711yescharacteristic
490C8—222no—
491C8—442no—
492C8—441no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—82no—
501C22—82no—
502C22—82no—
503C22—82no—
504C22—82no—
505C22—82no—
506C22—82no—
507C22C2×#6698511yescharacteristic
508C22C2×#6698811yescharacteristic
509C22D4×C22⋊D1111yescharacteristic
510C22#1062333711yescharacteristic
511C22C2×#6700311yescharacteristic
512C22#1062336611yescharacteristic
513C22#1062336711yescharacteristic
514C4—22no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—442no—
519C4—882no—
520C4—881no—
521C4#1062264814yescomplemented
522C4#1062324411yescharacteristic
523C4#1062324711yescharacteristic
524C4#1062324911yescharacteristic
525C4#1062325011yescharacteristic
526C2—82no—
527C2—162no—
528C2#1307237711yescharacteristic
529C2C2×#1062264811yescharacteristic
530C2#1307856811yescharacteristic
531C2#1308023211yescharacteristic
532C2#1308034611yescharacteristic
533C2#1308056611yescharacteristic
534C2#1308084711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2541C2
socleC23×C11C22×D4
hypercenter#2541D11
hypocenterC11#26235
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C2×#10622648C2semidirect
2. #13071565C2semidirect
3. #13069802C2semidirect
4. #13069795C2semidirect
5. #13069544C2semidirect
6. #13069423C2semidirect
7. #13069411C2semidirect
8. #13069374C2semidirect
9. #13068939C2semidirect
10. C4×#66872C2semidirect
90. #66872D4semidirect
292. C4×C11#482semidirect
431. C11#26235semidirect
521. C4#10622648semidirect

Maximal subgroups

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

subgroupindex
C2×#106226482
#130715652
#130698022
#130697952
#130695442
#130694232
#130694112
#130693742
#130689392
C4×#668722
C11×#25412
#2623511