Finite Group Databasebeta

← #14736352

Subgroups — #14736352

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#13078938C211yesmaximal, characteristic, complemented
2#13078624C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4#13068189C212yesmaximal, complemented
5#13068175C212yesmaximal, complemented
6#13068161C212yesmaximal, complemented
7#13068147C212yesmaximal, complemented
8#13067362C211yesmaximal, characteristic, complemented
9#13067271C211yesmaximal, characteristic, complemented
10#13067265C211yesmaximal, characteristic, complemented
11C11×#3100C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4318—21no—
15#10623001C2211yescharacteristic
16C11×#480—21no—
17C11×#474C2212yes—
18C11×#459C2212yes—
19C11×#447—21no—
20C4×C11×D8—22no—
21C11×#431C2211yescharacteristic
22#10622846—21no—
23#10622846—21no—
24#10622831—21no—
25C2×C22⋊(C11⋊C8)—21no—
26#10622694C2211yescharacteristic, complemented
27#10622694C2211yescharacteristic, complemented
28#10622683C2211yescharacteristic, complemented
29#10622683C2211yescharacteristic, complemented
30#10622669—21no—
31#10622669—21no—
32#10622632C2212yes—
33C4×#4324—22no—
34#10622625—21no—
35#10622625—21no—
36#10622625C2212yes—
37#10622625C2212yes—
38#10622621C2212yes—
39#10622584—21no—
40#10622538C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622182C2212yescomplemented
45#10622120C2212yescomplemented
46#10622119C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C2×C11×#41—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C2×C11×D8—22no—
53C11×C4⋊Q8C2311yescharacteristic
54C11×#127C2311yescharacteristic
55C11×#124—21no—
56C11×#121—21no—
57C11×#121—21no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11D412yes—
63C4×D4×C11C2312yes—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4324—22no—
68#66979—21no—
69#66977—21no—
70#66977—21no—
71C2×#4318—22no—
72C2×#4318—22no—
73C2×#4318—44no—
74C22×C11⋊C8—21no—
75C22×C11⋊C8D411yescharacteristic
76C22×C11⋊C8D411yescharacteristic
77#66923—21no—
78#66922C2311yescharacteristic
79#66922C2311yescharacteristic
80C4×Dic22—21no—
81C4×Dic22—21no—
82C11×#107—22no—
83C11×C4⋊C8C2312yes—
84C11×#102—22no—
85C11×#102—22no—
86C11×C22⋊C8—21no—
87C4×C8×C11—21no—
88#66899—21no—
89#66899—21no—
90#66899—21no—
91#66899—21no—
92#66896—22no—
93#66896—21no—
94#66896—21no—
95#66896—21no—
96#66896—21no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—22no—
99C22⋊(C11⋊C8)—22no—
100#66874—22no—
101#66872—22no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)C2312yes—
104C4⋊(C11⋊C8)C2312yes—
105C4×C11⋊C8—21no—
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110#19142—111nomaximal, Sylow
111C24×C11—21no—
112C11×#41—42no—
113C11×#41—42no—
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—42no—
120C2×D4×C11—41no—
121C2×D4×C11C2×D412yes—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—41no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C2×Dic22—21no—
132C2×Dic22—21no—
133C11×D8—44no—
134C2×C8×C11—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4C2×D412yes—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146C42×C11C2411yescharacteristic
147C22⋊Dic11—41no—
148#4324—44no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155C4×Dic11—41no—
156#4318—44no—
157#4318—44no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—42no—
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167#3131—111no—
168#3101—111no—
169#3100D1111yescharacteristic
170C2×#436—111no—
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—41no—
183C23×C11#12111yescharacteristic
184Q8×C11—41no—
185Q8×C11—41no—
186D4×C11—22no—
187D4×C11—22no—
188D4×C11—42no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—42no—
192D4×C11—81no—
193D4×C11—82no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—44no—
201C2×C4×C11—41no—
202C2×C4×C11—82no—
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#13512yes—
207C2×C4×C11AGL(1,ℤ/8)12yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×Dic11—41no—
212C2×Dic11—41no—
213Dic22—42no—
214Dic22—81no—
215C8×C11—42no—
216C11⋊C8—21no—
217C11⋊C8—21no—
218C11⋊C8—21no—
219C11⋊C8—21no—
220C11⋊C8—42no—
221C11⋊C8—42no—
222C22×M16—221no—
223#533—111no—
224#532C2×D1111yescharacteristic
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—21no—
234#476—112no—
235#474C2×D1112yes—
236#461—112no—
237#459C2×D1112yes—
238#450—221no—
239#447—21no—
240C4×SD16—222no—
241C4×D8—22no—
242#436—112no—
243#436—112no—
244#436—221no—
245#436—221no—
246#431—111no—
247#431C2×D1111yescharacteristic
248C2×C4⋊C8—111no—
249#416—221no—
250#416—221no—
251C2×C22⋊C8—221no—
252C2×C4×C8—111no—
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—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11#46312yes—
269C22×C11C2×#12111yescharacteristic
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—42no—
274C4×C11—81no—
275C4×C11#46312yes—
276C4×C11C2×#13511yescharacteristic
277C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
278C4×C11#57512yes—
279Dic11—81no—
280Dic11—81no—
281C2×#41—21no—
282C22×D4C22⋊D1111yescharacteristic
283C23×C4—21no—
284C2×SD16—222no—
285C2×D8—22no—
286C2×M16—222no—
287C2×M16—222no—
288C2×M16—444no—
289C22×C8—111no—
290C22×C8—111no—
291C22×C8—221no—
292C4⋊Q8—111no—
293C4⋊Q8—111no—
294C4⋊Q8C22×D1111yescharacteristic
295#127C22×D1111yescharacteristic
296#125—221no—
297#124—21no—
298C22⋊Q8—221no—
299C22⋊Q8—221no—
300#121—21no—
301#121—21no—
302C4×Q8—221no—
303C4×Q8—221no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—21no—
307C4×D4—21no—
308C4×D4C22⋊D1112yes—
309C4×D4C22×D1112yes—
310#117—221no—
311C2×C4⋊C4C22⋊D1111yescharacteristic
312C2×C22⋊C4—21no—
313C2×C42C22×D1111yescharacteristic
314#107—22no—
315#106—222no—
316C4⋊C8—112no—
317C4⋊C8—112no—
318C4⋊C8—221no—
319C4⋊C8C22×D1112yes—
320#103—221no—
321#103—221no—
322#103—221no—
323#103—221no—
324#103—222no—
325#102—22no—
326#102—22no—
327#102—221no—
328#102—221no—
329#102—221no—
330#102—221no—
331#102—222no—
332C22⋊C8—21no—
333C22⋊C8—222no—
334C22⋊C8—222no—
335C22⋊C8—221no—
336C4×C8—21no—
337C4×C8—111no—
338C4×C8—111no—
339C4×C8—111no—
340C4×C8—111no—
341C4×C8—221no—
342C2×C11—22no—
343C2×C11—82no—
344C2×C11—161no—
345C2×C11C2×#46311yescharacteristic
346C2×C11#305411yescharacteristic
347C2×C11#306711yescharacteristic
348C24—21no—
349#41—42no—
350#41—42no—
351C2×Q8—21no—
352C2×Q8—221no—
353C2×Q8—221no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—42no—
359C2×D4—41no—
360C2×D4C2×C22⋊D1112yes—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—41no—
367C22×C4D4×D1111yescharacteristic
368C22×C4#434111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370SD16—444no—
371D8—44no—
372M16—444no—
373M16—444no—
374C2×C8—22no—
375C2×C8—111no—
376C2×C8—111no—
377C2×C8—111no—
378C2×C8—111no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—442no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4C2×C22⋊D1112yes—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—441no—
399C42—441no—
400C42D4×D1111yescharacteristic
401C42#434111yescharacteristic
402C42C2×C22⋊D1111yescharacteristic
403C42C23×D1111yescharacteristic
404C11#1914211yescharacteristic, complemented, Sylow
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—41no—
410C23#6699211yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—442no—
414Q8—881no—
415D4—22no—
416D4—22no—
417D4—42no—
418D4—41no—
419D4—41no—
420D4—42no—
421D4—81no—
422D4—82no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—82no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4#6696412yes—
435C2×C4#6696512yes—
436C2×C4#6699211yescharacteristic
437C2×C4#6699211yescharacteristic
438C2×C4#6699211yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C2×C4C2×#434111yescharacteristic
441C2×C4C22×C22⋊D1111yescharacteristic
442C8—42no—
443C8—221no—
444C8—221no—
445C8—221no—
446C8—221no—
447C8—442no—
448C8—442no—
449C22—21no—
450C22—21no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22#1062276612yes—
459C22C2×#6699211yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—81no—
465C4—881no—
466C4—881no—
467C4#1062276612yes—
468C4C2×#6696411yescharacteristic
469C4C2×#6696511yescharacteristic
470C4#1062335312yes—
471C2—22no—
472C2—82no—
473C2—161no—
474C2C2×#1062276611yescharacteristic
475C2#1307822211yescharacteristic
476C2#1307833311yescharacteristic
subgroupG/H
centerC2×C4#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3100C2
socleC22×C11C2×#121
hypercenter#3100D11
hypocenterC11#19142
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #13078938C2semidirect
2. #13078624C2semidirect
3. C2×#10622625C2semidirect
4. #13068189C2semidirect
5. #13068175C2semidirect
6. #13068161C2semidirect
7. #13068147C2semidirect
8. #13067362C2semidirect
9. #13067271C2semidirect
10. #13067265C2semidirect
26. #10622694C22semidirect
27. #10622694C22semidirect
28. #10622683C22semidirect
29. #10622683C22semidirect
43. #10622185C22semidirect
44. #10622182C22semidirect
45. #10622120C22semidirect
46. #10622119C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
404. C11#19142semidirect

Maximal subgroups

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

subgroupindex
#130789382
#130786242
C2×#106226252
#130681892
#130681752
#130681612
#130681472
#130673622
#130672712
#130672652
C11×#31002
#1914211