Finite Group Databasebeta

← #14737802

Subgroups — #14737802

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079171C211yesmaximal, characteristic, complemented
2#13078715C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4#13068193C212yesmaximal, complemented
5#13068175C212yesmaximal, complemented
6#13068117C212yesmaximal, complemented
7#13068079C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067317C211yesmaximal, characteristic, complemented
10#13067311C211yesmaximal, characteristic, complemented
11C11×#3109C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4318—21no—
15#10623001C2211yescharacteristic
16C11×#481—21no—
17C11×#476C2212yes—
18C11×#459C2212yes—
19C11×#447—21no—
20C11×#442—22no—
21C11×#432C2211yescharacteristic
22#10622831—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622706C2211yescharacteristic, complemented
25#10622692C2211yescharacteristic, complemented
26#10622689C2211yescharacteristic, complemented
27#10622683C2211yescharacteristic, complemented
28#10622654—21no—
29#10622654—21no—
30#10622632C2212yes—
31#10622631—22no—
32C4×#4324—21no—
33C4×#4324—21no—
34#10622625—21no—
35#10622625—21no—
36#10622625C2212yes—
37#10622625C2212yes—
38#10622620C2212yes—
39#10622583—21no—
40#10622539C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622184C2212yescomplemented
44#10622182C2212yescomplemented
45#10622124C2212yescomplemented
46#10622120C2212yescomplemented
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—
68C2×#4324—21no—
69C2×#4324—21no—
70#66979—21no—
71#66977—21no—
72#66977—21no—
73C2×#4318—22no—
74C2×#4318—22no—
75C2×#4318—44no—
76C22×C11⋊C8—21no—
77C22×C11⋊C8D411yescharacteristic
78C22×C11⋊C8D411yescharacteristic
79#66923—21no—
80#66922C2311yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×#106—22no—
85C11×C4⋊C8C2312yes—
86C11×#102—22no—
87C11×#102—22no—
88C11×C22⋊C8—21no—
89C11×#97—21no—
90#66896—22no—
91#66896—21no—
92#66896—21no—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)—22no—
96#66874—22no—
97#66874—21no—
98#66874—21no—
99#66872—21no—
100#66872—21no—
101#66871—22no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)C2312yes—
104C4⋊(C11⋊C8)C2312yes—
105#66867—21no—
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110#19282—111nomaximal, Sylow
111C24×C11—21no—
112C11×#41—82no—
113C2×Q8×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—42no—
119C2×D4×C11—41no—
120C2×D4×C11C2×D412yes—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C2×Dic22—21no—
131C2×Dic22—21no—
132C11×D8—44no—
133C2×C8×C11—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4C2×D412yes—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C42×C11C2411yescharacteristic
146C22⋊Dic11—41no—
147#4324—44no—
148#4324—42no—
149#4324—42no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156C4×Dic11—41no—
157#4318—44no—
158#4318—44no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—41no—
163C2×C11⋊C8—42no—
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168#3167—111no—
169#3110—111no—
170#3109D1111yescharacteristic
171C2×#436—111no—
172#1703—112no—
173#1701—112no—
174#1691—112no—
175#1685—112no—
176#1568—111no—
177#1552—111no—
178#1551—111no—
179C23×C11—22no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—41no—
184C23×C11#12111yescharacteristic
185Q8×C11—81no—
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—21no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—82no—
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×Dic11—41no—
212C2×Dic11—41no—
213Dic22—41no—
214Dic22—41no—
215Dic22—42no—
216C8×C11—42no—
217C11⋊C8—21no—
218C11⋊C8—21no—
219C11⋊C8—21no—
220C11⋊C8—42no—
221C11⋊C8—42no—
222C11⋊C8AGL(1,ℤ/8)12yes—
223C22×M16—221no—
224#533—111no—
225#532C2×D1111yescharacteristic
226C2×C4×D4C2×D1111yescharacteristic
227#498—111no—
228#492—111no—
229#487—111no—
230#486—111no—
231#484—221no—
232#481—21no—
233#476C2×D1112yes—
234#474—112no—
235#465—221no—
236#465—221no—
237#461—112no—
238#459C2×D1112yes—
239#450—221no—
240#447—21no—
241#442—22no—
242#440—222no—
243C4×SD16—221no—
244C4×SD16—221no—
245#436—112no—
246#436—112no—
247#436—221no—
248#436—221no—
249#432—111no—
250#432C2×D1111yescharacteristic
251C2×C4⋊C8—111no—
252C2×C22⋊C8—221no—
253C2×C4×C8—111no—
254#335—112no—
255#334—112no—
256#333—112no—
257#332—112no—
258#332—112no—
259#331—112no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—84no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11#47112yes—
270C22×C11C2×#12111yescharacteristic
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—42no—
276C4×C11—81no—
277C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
278C4×C11#57511yescharacteristic
279C4×C11#57512yes—
280Dic11—81no—
281Dic11—81no—
282C2×#41—21no—
283C22×D4C22⋊D1111yescharacteristic
284C23×C4—21no—
285C2×SD16—221no—
286C2×SD16—221no—
287C2×SD16—222no—
288C2×D8—22no—
289C2×M16—222no—
290C2×M16—222no—
291C2×M16—444no—
292C22×C8—111no—
293C22×C8—111no—
294C22×C8—221no—
295C4⋊Q8—111no—
296C4⋊Q8—111no—
297C4⋊Q8C22×D1111yescharacteristic
298#127C22×D1111yescharacteristic
299#125—221no—
300#124—21no—
301C22⋊Q8—221no—
302C22⋊Q8—221no—
303#121—21no—
304#121—21no—
305C4×Q8—221no—
306C4×Q8—221no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4C22⋊D1112yes—
312C4×D4C22×D1112yes—
313#117—221no—
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C22⋊C4—21no—
316C2×C42C22×D1111yescharacteristic
317#107—222no—
318#106—22no—
319#106—221no—
320#106—221no—
321C4⋊C8—112no—
322C4⋊C8—112no—
323C4⋊C8—221no—
324C4⋊C8C22×D1112yes—
325#103—221no—
326#103—221no—
327#103—222no—
328#102—22no—
329#102—22no—
330#102—221no—
331#102—221no—
332#102—222no—
333C22⋊C8—21no—
334C22⋊C8—222no—
335C22⋊C8—222no—
336C22⋊C8—221no—
337#97—21no—
338#97—221no—
339C4×C8—111no—
340C4×C8—111no—
341C4×C8—111no—
342C4×C8—111no—
343C2×C11—22no—
344C2×C11—82no—
345C2×C11—161no—
346C2×C11#303611yescharacteristic
347C2×C11#305411yescharacteristic
348C2×C11C2×#47111yescharacteristic
349C24—21no—
350#41—82no—
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—442no—
371SD16—442no—
372SD16—444no—
373D8—44no—
374M16—444no—
375M16—444no—
376C2×C8—22no—
377C2×C8—111no—
378C2×C8—111no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—441no—
385C2×C8—442no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4C2×C22⋊D1112yes—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—441no—
401C42—441no—
402C42D4×D1111yescharacteristic
403C42#434111yescharacteristic
404C42C2×C22⋊D1111yescharacteristic
405C42C23×D1111yescharacteristic
406C11#1928211yescharacteristic, complemented, Sylow
407C23—22no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—41no—
412C23#6699211yescharacteristic
413Q8—81no—
414Q8—441no—
415Q8—441no—
416Q8—442no—
417D4—22no—
418D4—22no—
419D4—42no—
420D4—41no—
421D4—41no—
422D4—42no—
423D4—81no—
424D4—82no—
425C2×C4—22no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—82no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4#6699211yescharacteristic
439C2×C4#6699211yescharacteristic
440C2×C4#6699211yescharacteristic
441C2×C4C2×D4×D1111yescharacteristic
442C2×C4C2×#434111yescharacteristic
443C2×C4C22×C22⋊D1111yescharacteristic
444C8—42no—
445C8—112no—
446C8—221no—
447C8—221no—
448C8—221no—
449C8—442no—
450C8—442no—
451C22—21no—
452C22—21no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—84no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22#1062281312yes—
461C22C2×#6699211yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—881no—
469C4—881no—
470C4D11×AGL(1,ℤ/8)11yescharacteristic
471C4#1062330411yescharacteristic
472C4#1062335312yes—
473C2—22no—
474C2—82no—
475C2—161no—
476C2#1307807711yescharacteristic
477C2#1307822211yescharacteristic
478C2C2×#1062281311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3109C2
socleC22×C11C2×#121
hypercenter#3109D11
hypocenterC11#19282
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3109

Complements

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

NH ≅ G/Ntype
1. #13079171C2semidirect
2. #13078715C2semidirect
3. C2×#10622625C2semidirect
4. #13068193C2semidirect
5. #13068175C2semidirect
6. #13068117C2semidirect
7. #13068079C2semidirect
8. #13067377C2semidirect
9. #13067317C2semidirect
10. #13067311C2semidirect
24. #10622706C22semidirect
25. #10622692C22semidirect
26. #10622689C22semidirect
27. #10622683C22semidirect
43. #10622184C22semidirect
44. #10622182C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
406. C11#19282semidirect

Maximal subgroups

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

subgroupindex
#130791712
#130787152
C2×#106226252
#130681932
#130681752
#130681172
#130680792
#130673772
#130673172
#130673112
C11×#31092
#1928211