Finite Group Databasebeta

← #14739180

Subgroups — #14739180

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079557C211yesmaximal, characteristic, complemented
2#13078404C211yesmaximal, characteristic, complemented
3#13077727C211yesmaximal, characteristic, complemented
4#13068030C212yesmaximal, complemented
5#13068023C212yesmaximal, complemented
6#13067962C212yesmaximal, complemented
7#13067955C212yesmaximal, complemented
8#13067388C211yesmaximal, characteristic, complemented
9#13067307C211yesmaximal, characteristic, complemented
10C2×#10622182C211yesmaximal, characteristic, complemented
11C11×#3038C211yesmaximal, characteristic
12C2×C11×AGL(1,ℤ/8)—21no—
13C2×C11×#127C2211yescharacteristic
14C4×C11×#41C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#460—21no—
17C11×#460C2212yes—
18C11×#459—21no—
19C11×#459C2212yes—
20C11×#423C2211yescharacteristic
21C11×#418—21no—
22#10622846—21no—
23#10622831—22no—
24#10622689C2212yes—
25#10622688—21no—
26#10622688—21no—
27#10622683C2212yes—
28Q8×C11⋊C8C2212yescomplemented
29#10622635—21no—
30#10622634C2211yescharacteristic, complemented
31#10622633C2211yescharacteristic, complemented
32D4×C11⋊C8—22no—
33D4×C11⋊C8C2212yescomplemented
34#10622622—21no—
35#10622621C2211yescharacteristic, complemented
36#10622620C2211yescharacteristic, complemented
37#10622611—21no—
38#10622538—21no—
39#10622538C2211yescharacteristic
40C2×C4⋊(C11⋊C8)—21no—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622182C2212yes—
44#10622182C2212yes—
45#10622124C2212yescomplemented
46#10622119C2212yescomplemented
47#10622118C2212yescomplemented
48#10622118C2212yescomplemented
49C2×C11×#41D411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C11×AGL(1,ℤ/8)—44no—
54C2×C11×SD16—22no—
55C2×C11×D8—22no—
56C2×C11×M16—21no—
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127C2312yes—
61C4×Q8×C11D411yescharacteristic
62C4×Q8×C11C2311yescharacteristic
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11D411yescharacteristic
66C4×D4×C11C2311yescharacteristic
67C11×#117—21no—
68C11×#117D411yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×#4324—22no—
72C2×#4324—22no—
73#66979—21no—
74#66977—21no—
75#66977—21no—
76C22×C11⋊C8—21no—
77C22×C11⋊C8—21no—
78C22×C11⋊C8—22no—
79#66923—21no—
80#66922C2311yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2312yes—
86C11×#102—22no—
87C11×#102—22no—
88#66899—21no—
89#66899—21no—
90#66896—21no—
91#66896—21no—
92#66896—22no—
93#66896—22no—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)D412yes—
96#66872—21no—
97#66872—21no—
98#66871—21no—
99#66871—21no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—22no—
103C4⋊(C11⋊C8)D411yescharacteristic
104C4⋊(C11⋊C8)D411yescharacteristic
105C4⋊(C11⋊C8)C2311yescharacteristic
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8—22no—
109C4×C11⋊C8C2312yes—
110#19409—111nomaximal, Sylow
111C24×C11—41no—
112C11×#41—22no—
113C11×#41SD1614yescomplemented
114C2×Q8×C11C2×D411yescharacteristic
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—81no—
125C2×D4×C11—81no—
126C2×D4×C11—82no—
127C2×D4×C11C2×D411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C2×Dic22—21no—
135C2×Dic22—21no—
136C11×SD16—44no—
137C11×D8—44no—
138C11×M16—42no—
139C2×C8×C11—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4C2×D411yescharacteristic
143C11×C4⋊C4C2×D411yescharacteristic
144C11×C22⋊C4—21no—
145C11×C22⋊C4—21no—
146C11×C22⋊C4—21no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11#4111yescharacteristic
153C42×C11C2411yescharacteristic
154C22⋊Dic11—41no—
155#4324—82no—
156#4324—82no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—42no—
168C2×C11⋊C8—81no—
169C2×C11⋊C8—82no—
170C2×C11⋊C8C2×D412yes—
171C2×C11⋊C8C2×D412yes—
172#3208—111no—
173#3076—111no—
174#3038D1111yescharacteristic
175#2988—111no—
176#1678—112no—
177#1677—112no—
178#1666—112no—
179#1665—112no—
180#1570—111no—
181#1550—111no—
182C2×#331—111no—
183C23×C11—21no—
184C23×C11—42no—
185C23×C11—82no—
186C23×C11—82no—
187C23×C11—82no—
188C23×C11#12111yescharacteristic
189Q8×C11—21no—
190Q8×C11C2×SD1612yes—
191D4×C11—24no—
192D4×C11—21no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—82no—
198D4×C11—82no—
199D4×C11—82no—
200D4×C11—82no—
201D4×C11C2×SD1612yes—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—24no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—81no—
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11C2×SD1612yes—
216C2×C4×C11#13512yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×Dic11—41no—
221C2×Dic11—41no—
222Dic22—41no—
223Dic22—41no—
224Dic22—81no—
225C8×C11—42no—
226C11⋊C8—22no—
227C11⋊C8—22no—
228C11⋊C8—41no—
229C11⋊C8—41no—
230C11⋊C8—42no—
231C2×AGL(1,ℤ/8)—21no—
232#533—111no—
233C2×#127C2×D1111yescharacteristic
234C4×#41C2×D1111yescharacteristic
235#492—112no—
236#486—112no—
237#479—221no—
238#478—221no—
239#477—111no—
240#476—111no—
241#475—111no—
242#474—111no—
243#460—21no—
244#460—221no—
245#460—221no—
246#460C2×D1112yes—
247#459—21no—
248#459C2×D1112yes—
249#450—222no—
250C8×Q8—112no—
251C8×D4—112no—
252C8×D4—222no—
253#431—111no—
254#431—221no—
255#427—221no—
256#423C2×D1111yescharacteristic
257C2×C4⋊C8—111no—
258C2×C4⋊C8—111no—
259C2×C4⋊C8—221no—
260#418—21no—
261#416—221no—
262#334—112no—
263#334—112no—
264#333—112no—
265#332—112no—
266#331—112no—
267#331—112no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—22no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—164no—
277C22×C11#46512yes—
278C22×C11C2×#12111yescharacteristic
279C4×C11—21no—
280C4×C11—22no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—41no—
284C4×C11—41no—
285C4×C11#46512yes—
286C4×C11C22×SD1611yescharacteristic
287C4×C11C2×#13511yescharacteristic
288C4×C11#57611yescharacteristic
289C4×C11#57711yescharacteristic
290Dic11—81no—
291Dic11—81no—
292C2×#41C22⋊D1111yescharacteristic
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296AGL(1,ℤ/8)—44no—
297C2×SD16—22no—
298C2×SD16—222no—
299C2×SD16—222no—
300C2×D8—22no—
301C2×M16—21no—
302C22×C8—222no—
303C22×C8—221no—
304C22×C8—221no—
305C4⋊Q8—111no—
306C4⋊Q8—111no—
307#127—21no—
308#127—21no—
309#127—21no—
310#127C22×D1112yes—
311#125—221no—
312C22⋊Q8—221no—
313C22⋊Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×Q8C22⋊D1111yescharacteristic
317C4×Q8C22×D1111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4C22⋊D1111yescharacteristic
321C4×D4C22×D1111yescharacteristic
322#117—21no—
323#117—221no—
324#117C22⋊D1111yescharacteristic
325C2×C42—21no—
326C2×C42C22×D1111yescharacteristic
327#107—221no—
328#107—221no—
329#106—221no—
330#106—221no—
331C4⋊C8—21no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—112no—
335C4⋊C8—111no—
336C4⋊C8—111no—
337C4⋊C8—222no—
338C4⋊C8—221no—
339C4⋊C8—221no—
340C4⋊C8C22×D1112yes—
341#103—221no—
342#103—221no—
343#102—22no—
344#102—22no—
345#102—222no—
346#102—222no—
347#102—221no—
348#102—221no—
349C22⋊C8—112no—
350C22⋊C8—222no—
351C4×C8—112no—
352C4×C8—222no—
353C2×C11—22no—
354C2×C11—42no—
355C2×C11—162no—
356C2×C11#304511yescharacteristic
357C2×C11C2×#46511yescharacteristic
358C2×C11#306811yescharacteristic
359C24—41no—
360#41—22no—
361#41#432414yescomplemented
362C2×Q8—221no—
363C2×Q8—221no—
364C2×Q8C2×C22⋊D1111yescharacteristic
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—42no—
374C2×D4—81no—
375C2×D4—81no—
376C2×D4—82no—
377C2×D4C2×C22⋊D1111yescharacteristic
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4D4×D1111yescharacteristic
382C22×C4#434111yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384SD16—44no—
385SD16—882no—
386SD16—882no—
387D8—44no—
388M16—42no—
389C2×C8—22no—
390C2×C8—112no—
391C2×C8—112no—
392C2×C8—222no—
393C2×C8—221no—
394C2×C8—221no—
395C2×C8—442no—
396C2×C8—882no—
397C2×C8—881no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—221no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4C2×C22⋊D1111yescharacteristic
407C4⋊C4C2×C22⋊D1111yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—441no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42—441no—
416C42D4×D1111yescharacteristic
417C42#434111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1940911yescharacteristic, complemented, Sylow
421C23—21no—
422C23—42no—
423C23—82no—
424C23—82no—
425C23—82no—
426C23#6699211yescharacteristic
427Q8—21no—
428Q8—441no—
429Q8—441no—
430Q8—881no—
431Q8C2×#432412yes—
432D4—24no—
433D4—21no—
434D4—42no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—82no—
439D4—82no—
440D4—82no—
441D4—82no—
442D4C2×#432412yes—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—24no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4C2×#432412yes—
456C2×C4#6699211yescharacteristic
457C2×C4#6699211yescharacteristic
458C2×C4#6699211yescharacteristic
459C2×C4#6700312yes—
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C2×#434111yescharacteristic
462C2×C4C22×C22⋊D1111yescharacteristic
463C8—42no—
464C8—222no—
465C8—222no—
466C8—442no—
467C8—441no—
468C8—441no—
469C22—21no—
470C22—21no—
471C22—22no—
472C22—41no—
473C22—41no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—164no—
478C22#1062265412yes—
479C22C2×#6699211yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—881no—
487C4—881no—
488C4#1062265412yes—
489C4#1062330511yescharacteristic
490C4#1062330611yescharacteristic
491C4C22×#432411yescharacteristic
492C4C2×#6700311yescharacteristic
493C2—22no—
494C2—42no—
495C2—162no—
496C2#1307815911yescharacteristic
497C2C2×#1062265411yescharacteristic
498C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3038C2
socleC22×C11C2×#121
hypercenter#3038D11
hypocenterC11#19409
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. #13079557C2semidirect
2. #13078404C2semidirect
3. #13077727C2semidirect
4. #13068030C2semidirect
5. #13068023C2semidirect
6. #13067962C2semidirect
7. #13067955C2semidirect
8. #13067388C2semidirect
9. #13067307C2semidirect
10. C2×#10622182C2semidirect
28. Q8×C11⋊C8C22semidirect
30. #10622634C22semidirect
31. #10622633C22semidirect
33. D4×C11⋊C8C22semidirect
35. #10622621C22semidirect
36. #10622620C22semidirect
45. #10622124C22semidirect
46. #10622119C22semidirect
47. #10622118C22semidirect
48. #10622118C22semidirect
113. C11×#41SD16semidirect
361. #41#4324semidirect
420. C11#19409semidirect

Maximal subgroups

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

subgroupindex
#130795572
#130784042
#130777272
#130680302
#130680232
#130679622
#130679552
#130673882
#130673072
C2×#106221822
C11×#30382
#1940911