Finite Group Databasebeta

← #14736355

Subgroups — #14736355

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078939C211yesmaximal, characteristic, complemented
2#13078624C211yesmaximal, characteristic, complemented
3#13078616C211yesmaximal, characteristic
4#13068191C212yesmaximal, complemented
5#13068177C212yesmaximal, complemented
6#13068163C212yesmaximal, complemented
7#13068149C212yesmaximal, complemented
8#13067364C211yesmaximal, characteristic, complemented
9#13067274C211yesmaximal, characteristic, complemented
10#13067266C211yesmaximal, characteristic, complemented
11C2×C11×#436C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C2×C4×D4×C11C2211yescharacteristic
14#10623008C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#436—21no—
17C11×#436—21no—
18C11×#436C2212yes—
19C11×#436C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8—21no—
22C2×C4×C8×C11C2211yescharacteristic
23#10622831—21no—
24#10622830—21no—
25#10622726—21no—
26#10622726—21no—
27#10622632C2212yes—
28C4×#4324—22no—
29#10622628C2212yes—
30C4×#4323—22no—
31#10622621C2212yes—
32#10622620C2212yes—
33#10622584—21no—
34#10622580—21no—
35#10622538C2211yescharacteristic
36#10622538C2211yescharacteristic
37#10622310—21no—
38#10622310—21no—
39#10622307C2211yescharacteristic, complemented
40#10622307C2211yescharacteristic, complemented
41#10622294C2211yescharacteristic, complemented
42#10622294C2211yescharacteristic, complemented
43#10622124C2212yescomplemented
44#10622123C2212yescomplemented
45#10622120C2212yescomplemented
46#10622119C2212yescomplemented
47#10622096C2212yescomplemented
48#10622095C2212yescomplemented
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C2×#4339—21no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16—44no—
55C22×C8×C11—21no—
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D411yescharacteristic
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11D412yes—
61C4×D4×C11C2312yes—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4324—22no—
66C2×#4323—22no—
67#66983—21no—
68#66983—21no—
69#66979—21no—
70#66977—21no—
71#66977—21no—
72#66928—21no—
73#66927C2311yescharacteristic
74C4×D44—21no—
75C4×D44—21no—
76#66923—21no—
77#66922C2311yescharacteristic
78#66922C2311yescharacteristic
79#66922C2311yescharacteristic
80C4×Dic22—21no—
81C4×Dic22—21no—
82C11×C4⋊C8—21no—
83C11×C4⋊C8C2312yes—
84C11×C22⋊C8—22no—
85C11×C22⋊C8—22no—
86C4×C8×C11D411yescharacteristic
87C4×C8×C11D411yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C4×C8×C11C2311yescharacteristic
90#66896—22no—
91#66896—22no—
92C22⋊(C11⋊C8)—21no—
93C22⋊(C11⋊C8)—21no—
94#66885—21no—
95#66885—21no—
96#66885—21no—
97#66885—21no—
98#66880—21no—
99#66880—21no—
100#66880—21no—
101#66880—21no—
102#66874—22no—
103#66873—22no—
104#66872—22no—
105#66871—22no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8—21no—
109C4×C11⋊C8—21no—
110#19142—111nomaximal, Sylow
111C24×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—42no—
114C2×D4×C11C2×D412yes—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C2×C22⋊D11—41no—
124#4339—42no—
125#4339—42no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×C4×D11—41no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C11×M16—44no—
134C11×M16—44no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—42no—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2×D411yescharacteristic
143C11×C4⋊C4—21no—
144C11×C4⋊C4C2×D412yes—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—22no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11#4111yescharacteristic
150C42×C11C2411yescharacteristic
151C22⋊Dic11—41no—
152#4324—44no—
153#4323—44no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164C4×Dic11—41no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167#3131—111no—
168#3101—111no—
169#3100—111no—
170C2×#436D1111yescharacteristic, complemented
171#1703—112no—
172#1701—112no—
173#1699—112no—
174#1697—112no—
175#1564—111no—
176#1542—111no—
177#1540—111no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11#12111yescharacteristic
183C22×D11—41no—
184D4×C11—22no—
185D4×C11—22no—
186D4×C11—42no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—44no—
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#13512yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C22⋊D11—82no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206D44—41no—
207D44—41no—
208D44—42no—
209D44—81no—
210C4×D11—82no—
211Dic22—41no—
212Dic22—41no—
213Dic22—42no—
214Dic22—81no—
215C8×C11—21no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11—42no—
220C11⋊C8—42no—
221C11⋊C8—42no—
222C22×M16—21no—
223#533—111no—
224#532—111no—
225C2×C4×D4C2×D1111yescharacteristic
226#488—221no—
227#488—221no—
228#487—111no—
229#487—111no—
230#486—111no—
231#486—111no—
232#483—221no—
233#480—221no—
234#476—112no—
235#474—112no—
236#461—112no—
237#459—112no—
238#450—221no—
239#447—221no—
240C4×SD16—222no—
241C4×D8—222no—
242#436—21no—
243#436—21no—
244#436C2×D1112yes—
245#436C2×D1112yes—
246#431—111no—
247#431—111no—
248C2×C4⋊C8C2×D1111yescharacteristic
249#416—221no—
250#416—221no—
251C2×C22⋊C8—21no—
252C2×C4×C8C2×D1111yescharacteristic
253#335—112no—
254#334—112no—
255#333—112no—
256#332—112no—
257#332—112no—
258#331—112no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—84no—
265C22×C11#46312yes—
266C22×C11C2×#12111yescharacteristic
267C2×D11—81no—
268C2×D11—81no—
269C2×D11—81no—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—42no—
274C4×C11#46312yes—
275C4×C11C2×#13511yescharacteristic
276C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C4×C11#57512yes—
278Dic11—81no—
279Dic11—81no—
280Dic11—81no—
281C2×#41—221no—
282C22×D4D4411yescharacteristic
283C23×C4—21no—
284C2×SD16—222no—
285C2×D8—222no—
286C2×M16—22no—
287C2×M16—22no—
288C2×M16—44no—
289C22×C8—21no—
290C22×C8C22⋊D1111yescharacteristic
291C22×C8C22⋊D1111yescharacteristic
292C4⋊Q8—111no—
293C4⋊Q8—111no—
294C4⋊Q8—111no—
295#127—111no—
296#125—221no—
297#124—221no—
298C22⋊Q8—221no—
299C22⋊Q8—221no—
300#121—221no—
301#121—221no—
302C4×Q8—221no—
303C4×Q8—221no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—221no—
307C4×D4—221no—
308C4×D4D4412yes—
309C4×D4C22×D1112yes—
310#117—221no—
311C2×C4⋊C4D4411yescharacteristic
312C2×C22⋊C4—21no—
313C2×C42C22×D1111yescharacteristic
314#107—222no—
315#106—222no—
316C4⋊C8—21no—
317C4⋊C8—112no—
318C4⋊C8—112no—
319C4⋊C8C22×D1112yes—
320#103—221no—
321#103—221no—
322#103—221no—
323#103—221no—
324#103—222no—
325#102—222no—
326#102—222no—
327#102—221no—
328#102—221no—
329#102—221no—
330#102—221no—
331#102—222no—
332C22⋊C8—22no—
333C22⋊C8—22no—
334C22⋊C8—221no—
335C22⋊C8—221no—
336C4×C8—221no—
337C4×C8—221no—
338C4×C8C22⋊D1111yescharacteristic
339C4×C8C22⋊D1111yescharacteristic
340C4×C8C22×D1111yescharacteristic
341C4×C8C22×D1111yescharacteristic
342C2×C11—22no—
343C2×C11—82no—
344C2×C11C2×#46311yescharacteristic
345C2×C11#305411yescharacteristic
346C2×C11#306711yescharacteristic
347D11—161no—
348C24—21no—
349#41—442no—
350#41—442no—
351C2×Q8—221no—
352C2×Q8—221no—
353C2×Q8—221no—
354C2×D4—21no—
355C2×D4—42no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—441no—
360C2×D4C2×D4412yes—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—441no—
367C22×C4C2×D4411yescharacteristic
368C22×C4#433911yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370SD16—444no—
371D8—444no—
372M16—44no—
373M16—44no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—42no—
378C2×C8—222no—
379C2×C8—222no—
380C2×C8C2×C22⋊D1111yescharacteristic
381C2×C8C2×C22⋊D1111yescharacteristic
382C2×C8C2×C22⋊D1111yescharacteristic
383C2×C8C2×C22⋊D1111yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4C2×D4412yes—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C42—441no—
400C42C2×D4411yescharacteristic
401C42#433911yescharacteristic
402C42C2×C22⋊D1111yescharacteristic
403C42C23×D1111yescharacteristic
404C11#1914211yescharacteristic, complemented, Sylow
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—441no—
410C23#6698311yescharacteristic
411Q8—442no—
412Q8—441no—
413Q8—441no—
414Q8—881no—
415D4—22no—
416D4—22no—
417D4—42no—
418D4—442no—
419D4—441no—
420D4—441no—
421D4—881no—
422D4—882no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—882no—
434C2×C4#6698311yescharacteristic
435C2×C4#6698311yescharacteristic
436C2×C4#6698311yescharacteristic
437C2×C4#6698512yes—
438C2×C4#6700312yes—
439C2×C4C22×D4411yescharacteristic
440C2×C4C2×#433911yescharacteristic
441C2×C4C22×C22⋊D1111yescharacteristic
442C8—21no—
443C8—21no—
444C8—21no—
445C8—21no—
446C8—42no—
447C8—442no—
448C8—442no—
449C22—21no—
450C22—21no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—881no—
456C22—881no—
457C22—881no—
458C22#1062262912yes—
459C22C2×#6698311yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—881no—
465C4—881no—
466C4—881no—
467C4#1062262912yes—
468C4#1062327912yes—
469C4C2×#6698511yescharacteristic
470C4C2×#6700311yescharacteristic
471C2—22no—
472C2—82no—
473C2—1761no—
474C2C2×#1062262911yescharacteristic
475C2#1307822511yescharacteristic
476C2#1307833611yescharacteristic
subgroupG/H
centerC2×C4#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#436C2
socleC22×C11C2×#121
prime radical#13078616C2
hypercenterC2×#436D11
hypocenterC11#19142
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. #13078939C2semidirect
2. #13078624C2semidirect
4. #13068191C2semidirect
5. #13068177C2semidirect
6. #13068163C2semidirect
7. #13068149C2semidirect
8. #13067364C2semidirect
9. #13067274C2semidirect
10. #13067266C2semidirect
11. C2×C11×#436C2semidirect
39. #10622307C22semidirect
40. #10622307C22semidirect
41. #10622294C22semidirect
42. #10622294C22semidirect
43. #10622124C22semidirect
44. #10622123C22semidirect
45. #10622120C22semidirect
46. #10622119C22semidirect
47. #10622096C22semidirect
48. #10622095C22semidirect
170. C2×#436D11semidirect
404. C11#19142semidirect

Maximal subgroups

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

subgroupindex
#130789392
#130786242
#130786162
#130681912
#130681772
#130681632
#130681492
#130673642
#130672742
#130672662
C2×C11×#4362
#1914211