Finite Group Databasebeta

← #14723341

Subgroups — #14723341

Order 2816.

688 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#13077577C211yesmaximal, characteristic, complemented
2#41×C11⋊C8C211yesmaximal, characteristic, complemented
3C4×#67003C211yesmaximal, characteristic
4#13067491C212yesmaximal, complemented
5#13067484C212yesmaximal, complemented
6#13067477C212yesmaximal, complemented
7#13067470C212yesmaximal, complemented
8#13067362C211yesmaximal, characteristic, complemented
9#13066999C211yesmaximal, characteristic, complemented
10C2×#10622093C211yesmaximal, characteristic, complemented
11C11×#1476C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67003C411yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17#10622846C411yescharacteristic
18C4×#4326C411yescharacteristic
19C4×#4326C2211yescharacteristic
20C4×#4325C411yescharacteristic
21C4×#4325C2211yescharacteristic
22Q8×C11⋊C8C2212yes—
23C4×#4324C411yescharacteristic
24C4×#4324C2211yescharacteristic
25C4×#4323C411yescharacteristic
26C4×#4323C2211yescharacteristic
27D4×C11⋊C8—22no—
28D4×C11⋊C8C2212yes—
29#10622615C411yescharacteristic
30#10622611C411yescharacteristic
31#10622538—21no—
32#10622538C2211yescharacteristic
33C2×C4×C11⋊C8—21no—
34C2×C4×C11⋊C8C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622451C2212yes—
37#10622444C2212yes—
38#10622343—22no—
39C4×#4313—21no—
40#10622298—21no—
41C11×Q8⋊C8C2212yes—
42C11×D4⋊C8C2212yes—
43#10622118C2212yes—
44#10622117C2212yes—
45#10622097C2212yes—
46#10622094C2212yes—
47#10622093C2212yes—
48#10622093C2212yes—
49C2×C11×#41C2×C411yescharacteristic
50C2×#4339C2×C411yescharacteristic
51C22×C8×C11—21no—
52C4×Q8×C11C2×C411yescharacteristic
53C4×Q8×C11C2311yescharacteristic
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11C2×C411yescharacteristic
57C4×D4×C11C2311yescharacteristic
58C11×#117—21no—
59C11×#117C2×C411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62#67003—24no—
63C2×#4326C2×C411yescharacteristic
64C2×#4325C2×C411yescharacteristic
65C2×#4324C2×C411yescharacteristic
66C2×#4323C2×C411yescharacteristic
67C4×C22⋊D11—21no—
68C4×C22⋊D11—21no—
69#66979C2×C411yescharacteristic
70C22×C11⋊C8—22no—
71C22×C11⋊C8C2×C411yescharacteristic
72C22×C11⋊C8C2×C411yescharacteristic
73C22×C11⋊C8D412yes—
74C2×#4313—22no—
75C4×D44C2×C411yescharacteristic
76C4×D44C2311yescharacteristic
77#66925—21no—
78C42×D11—21no—
79C4×Dic22C2×C411yescharacteristic
80C4×Dic22C2311yescharacteristic
81C11×C4⋊C8C2312yes—
82C11×C22⋊C8—21no—
83C4×C8×C11—21no—
84C4×C8×C11—21no—
85C4×C8×C11C2312yes—
86#66899C2×C411yescharacteristic
87#66899C2×C411yescharacteristic
88#66896C2×C411yescharacteristic
89#66896C2×C411yescharacteristic
90C22⋊(C11⋊C8)—21no—
91C22⋊(C11⋊C8)—22no—
92(C2×D11)⋊C8—22no—
93#66879—22no—
94Dic11⋊C8—22no—
95#66874C2×C411yescharacteristic
96#66874C2×C411yescharacteristic
97#66873C2×C411yescharacteristic
98#66873C2×C411yescharacteristic
99#66872C2×C411yescharacteristic
100#66872C2×C411yescharacteristic
101#66871C2×C411yescharacteristic
102#66871C2×C411yescharacteristic
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)C2312yes—
105C4×C11⋊C8—21no—
106C4×C11⋊C8—22no—
107C4×C11⋊C8C2×C411yescharacteristic
108C4×C11⋊C8C2×C411yescharacteristic
109C4×C11⋊C8D411yescharacteristic
110C4×C11⋊C8D411yescharacteristic
111C4×C11⋊C8C2311yescharacteristic
112C4×C11⋊C8C2311yescharacteristic
113C4×C11⋊C8C2312yes—
114#17868—111nomaximal, Sylow
115C11×#41—22no—
116C11×#41M1614yescomplemented
117C2×Q8×C11C22×C411yescharacteristic
118C2×D4×C11—21no—
119C2×D4×C11C22×C411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×C22⋊D11—21no—
127#4339—22no—
128#4339—22no—
129C2×D44C22×C411yescharacteristic
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×Dic22C22×C411yescharacteristic
134C2×C8×C11—24no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4C22×C411yescharacteristic
140C11×C4⋊C4C22×C411yescharacteristic
141C11×C22⋊C4—21no—
142C11×C22⋊C4—21no—
143C11×C22⋊C4—21no—
144C42×C11—21no—
145C42×C11—21no—
146C42×C11—21no—
147C42×C11C22×C411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11#4111yescharacteristic
150C42×C11C2411yescharacteristic
151C22⋊Dic11—21no—
152#4326—22no—
153#4325—22no—
154#4324—22no—
155#4323—22no—
156(C2×D11)⋊C4—21no—
157(C2×D11)⋊C4—21no—
158C4⋊Dic11C22×C411yescharacteristic
159C4⋊Dic11C22×C411yescharacteristic
160Dic11⋊C4—21no—
161Dic11⋊C4—21no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—42no—
169C2×C11⋊C8—44no—
170C2×C11⋊C8C22×C411yescharacteristic
171C2×C11⋊C8C22×C411yescharacteristic
172C2×C11⋊C8C22×C411yescharacteristic
173C2×C11⋊C8C22×C411yescharacteristic
174C2×C11⋊C8C2×D412yes—
175C2×C11⋊C8C2×D412yes—
176#4313—44no—
177#2965—111no—
178C8×#41—111no—
179C4×#135—111no—
180#1588—112no—
181#1587—112no—
182#1586—112no—
183#1585—112no—
184#1564—111no—
185#1476—111no—
186#1476D1111yescharacteristic, complemented
187C2×#322—111no—
188C23×C11—21no—
189C23×C11C4×D411yescharacteristic
190C22×D11—21no—
191Q8×C11—21no—
192Q8×C11C2×M1612yes—
193D4×C11—24no—
194D4×C11—21no—
195D4×C11C2×M1612yes—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11C4×D411yescharacteristic
205C2×C4×C11C4×D411yescharacteristic
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11C2×M1612yes—
208C2×C4×C11#13112yes—
209C2×C4×C11C23×C411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C22⋊D11—42no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216D44—21no—
217D44—21no—
218C4×D11—42no—
219C4×D11—42no—
220C4×D11—42no—
221Dic22—21no—
222Dic22—21no—
223C8×C11—24no—
224C8×C11—42no—
225C11⋊C8—21no—
226C11⋊C8—21no—
227C11⋊C8—21no—
228C11⋊C8—21no—
229C11⋊C8—22no—
230C11⋊C8—22no—
231C11⋊C8—42no—
232C2×#135—111no—
233C4×#41—111no—
234C4×#41C2×D1111yescharacteristic
235#446—112no—
236C8×Q8—112no—
237C4×Q16—111no—
238C4×Q16—111no—
239C4×SD16—111no—
240C4×SD16—111no—
241C4×SD16—111no—
242C4×SD16—111no—
243C4×D8—111no—
244C4×D8—111no—
245#436—112no—
246#435—222no—
247C8×D4—112no—
248C8×D4—222no—
249#431—111no—
250#431—221no—
251#431—221no—
252#431C2×D1111yescharacteristic
253#427—111no—
254#416—111no—
255#416—111no—
256C4×M16—221no—
257C2×C4×C8—111no—
258C2×C4×C8—111no—
259C2×C4×C8—221no—
260C2×C4×C8C2×D1111yescharacteristic
261#335—112no—
262#334—112no—
263Q8⋊C8—112no—
264Q8⋊C8C2×D1112yes—
265D4⋊C8—112no—
266D4⋊C8C2×D1112yes—
267#322—112no—
268#322—112no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—22no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11#43512yes—
275C22×C11C2×C4×D411yescharacteristic
276C2×D11—41no—
277C2×D11—41no—
278C2×D11—41no—
279C4×C11—22no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—41no—
283C4×C11—41no—
284C4×C11#43512yes—
285C4×C11#44312yes—
286C4×C11C22×M1611yescharacteristic
287C4×C11C2×#13111yescharacteristic
288C4×C11#57512yes—
289Dic11—41no—
290Dic11—41no—
291Dic11—41no—
292C2×#41—111no—
293C2×#41C4×D1111yescharacteristic
294#135—224no—
295C2×Q16—111no—
296C2×SD16—111no—
297C2×SD16—111no—
298C2×D8—111no—
299C2×M16—222no—
300C22×C8—21no—
301C22×C8—111no—
302C22×C8—111no—
303C22×C8—112no—
304C22×C8—222no—
305C4×Q8—111no—
306C4×Q8—111no—
307C4×Q8C4×D1111yescharacteristic
308C4×Q8C22×D1111yescharacteristic
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—111no—
312C4×D4—111no—
313C4×D4—221no—
314C4×D4—221no—
315C4×D4C4×D1111yescharacteristic
316C4×D4C22×D1111yescharacteristic
317#117—21no—
318#117—111no—
319#117—221no—
320#117C4×D1111yescharacteristic
321C2×C42—21no—
322C2×C42—221no—
323C2×C42C22×D1111yescharacteristic
324#107—111no—
325#107—111no—
326#106—111no—
327#106—111no—
328C4⋊C8—112no—
329C4⋊C8—222no—
330C4⋊C8—222no—
331C4⋊C8C22×D1112yes—
332#103—111no—
333#103—111no—
334#103—111no—
335#103—111no—
336#102—111no—
337#102—111no—
338#102—111no—
339#102—111no—
340C22⋊C8—21no—
341C22⋊C8—222no—
342C22⋊C8—222no—
343C22⋊C8—221no—
344#97—222no—
345C4×C8—21no—
346C4×C8—21no—
347C4×C8—111no—
348C4×C8—111no—
349C4×C8—111no—
350C4×C8—111no—
351C4×C8—111no—
352C4×C8—111no—
353C4×C8—112no—
354C4×C8—222no—
355C4×C8—221no—
356C4×C8C22×D1112yes—
357C2×C11—22no—
358C2×C11—42no—
359C2×C11C2×#43511yescharacteristic
360C2×C11#294311yescharacteristic
361C2×C11C2×#44311yescharacteristic
362D11—81no—
363#41—22no—
364#41—222no—
365#41—222no—
366#41#431314yescomplemented
367C2×Q8—111no—
368C2×Q8C2×C4×D1111yescharacteristic
369C2×D4—21no—
370C2×D4—111no—
371C2×D4—221no—
372C2×D4C2×C4×D1111yescharacteristic
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4C2×C4×D1111yescharacteristic
380C22×C4D4×D1111yescharacteristic
381C22×C4#434111yescharacteristic
382Q16—222no—
383SD16—222no—
384SD16—222no—
385D8—222no—
386M16—444no—
387C2×C8—24no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—111no—
391C2×C8—111no—
392C2×C8—111no—
393C2×C8—111no—
394C2×C8—112no—
395C2×C8—112no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—442no—
400C2×C8—444no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—111no—
404C4⋊C4—111no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4C2×C4×D1111yescharacteristic
408C4⋊C4C2×C4×D1111yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—221no—
413C22⋊C4—221no—
414C22⋊C4—221no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42—221no—
419C42—221no—
420C42—221no—
421C42C2×C4×D1111yescharacteristic
422C42D4×D1111yescharacteristic
423C42#434111yescharacteristic
424C42C23×D1111yescharacteristic
425C11#1786811yescharacteristic, complemented, Sylow
426C23—21no—
427C23—221no—
428C23(C22⋊D11)⋊C411yescharacteristic
429Q8—21no—
430Q8—221no—
431Q8—221no—
432Q8C2×#431312yes—
433D4—24no—
434D4—21no—
435D4—221no—
436D4—221no—
437D4—442no—
438D4C2×#431312yes—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4(C22⋊D11)⋊C411yescharacteristic
454C2×C4(C22⋊D11)⋊C411yescharacteristic
455C2×C4(C22⋊D11)⋊C411yescharacteristic
456C2×C4C2×#431312yes—
457C2×C4#6696012yes—
458C2×C4C22×C4×D1111yescharacteristic
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×#434111yescharacteristic
461C8—24no—
462C8—42no—
463C8—221no—
464C8—221no—
465C8—221no—
466C8—221no—
467C8—222no—
468C8—222no—
469C8—442no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—441no—
476C22—441no—
477C22—441no—
478C22#1062234312yes—
479C22C2×(C22⋊D11)⋊C411yescharacteristic
480C4—22no—
481C4—21no—
482C4—21no—
483C4—41no—
484C4—41no—
485C4—441no—
486C4—441no—
487C4—441no—
488C4#1062234312yes—
489C4#1062243712yes—
490C4C22×#431311yescharacteristic
491C4C2×#6696011yescharacteristic
492C4#1062329912yes—
493C2—22no—
494C2—42no—
495C2—881no—
496C2C2×#1062234311yescharacteristic
497C2#1307741211yescharacteristic
498C2C2×#1062243711yescharacteristic
subgroupG/H
centerC42D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1476C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C4
cosocleC42×C11C24
hypercenter#1476D11
hypocenterC11#17868
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
1. #13077577C2semidirect
2. #41×C11⋊C8C2semidirect
4. #13067491C2semidirect
5. #13067484C2semidirect
6. #13067477C2semidirect
7. #13067470C2semidirect
8. #13067362C2semidirect
9. #13066999C2semidirect
10. C2×#10622093C2semidirect
11. C11×#1476C2semidirect
116. C11×#41M16semidirect
186. #1476D11semidirect
366. #41#4313semidirect
425. C11#17868semidirect

Maximal subgroups

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

subgroupindex
#130775772
#41×C11⋊C82
C4×#670032
#130674912
#130674842
#130674772
#130674702
#130673622
#130669992
C2×#106220932
C11×#14762
#1786811