Finite Group Databasebeta

← #14737794

Subgroups — #14737794

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079198C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic
3C2×#10622625C211yesmaximal, characteristic
4#13068193C212yesmaximal, complemented
5#13068189C212yesmaximal, complemented
6#13068137C212yesmaximal, complemented
7#13068103C212yesmaximal, complemented
8#13067371C211yesmaximal, characteristic, complemented
9#13067307C211yesmaximal, characteristic, complemented
10#13067306C211yesmaximal, characteristic, complemented
11C11×#3077C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4318—21no—
15#10623001C2211yescharacteristic
16C11×#478—22no—
17C11×#476C2212yes—
18C11×#474C2212yes—
19C11×#428—21no—
20C11×#423C2211yescharacteristic
21C11×#418—21no—
22#10622828—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622706C2211yescharacteristic, complemented
25#10622705C2211yescharacteristic, complemented
26#10622694C2211yescharacteristic, complemented
27#10622691C2211yescharacteristic, complemented
28#10622664—21no—
29#10622664—21no—
30C4×#4326—21no—
31C4×#4326—21no—
32#10622625—21no—
33#10622625—21no—
34#10622625C2212yes—
35#10622625C2212yes—
36#10622622—22no—
37#10622621C2212yes—
38#10622620C2212yes—
39#10622577—21no—
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622184C2212yescomplemented
45#10622124C2212yescomplemented
46#10622119C2212yescomplemented
47#10622118C2212yescomplemented
48#10622118C2212yescomplemented
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C2×C11×M16—21no—
52C11×C4⋊Q8C2311yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×#125—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11D412yes—
62C4×D4×C11C2312yes—
63C11×#117—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4326—21no—
68C2×#4326—21no—
69#66979—21no—
70#66977—21no—
71#66977—21no—
72C2×#4318—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×#107—22no—
85C11×#106—22no—
86C11×C4⋊C8—21no—
87C11×C4⋊C8C2312yes—
88C11×#102—22no—
89C11×#102—22no—
90#66899—21no—
91#66899—21no—
92#66896—22no—
93#66896—22no—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)—22no—
96#66874—21no—
97#66874—21no—
98#66872—22no—
99#66871—22no—
100#66871—21no—
101#66871—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)C2312yes—
105C4⋊(C11⋊C8)C2312yes—
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110#19281—111nomaximal, Sylow
111C24×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11C2×D412yes—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×Dic22—21no—
127C2×Dic22—21no—
128C11×M16—42no—
129C2×C8×C11—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4C2×D412yes—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—41no—
141C42×C11—41no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C42×C11C2411yescharacteristic
146C22⋊Dic11—41no—
147#4326—42no—
148#4326—42no—
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—
158#4318—42no—
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#3170—111no—
169#3077—111no—
170#3077D1111yescharacteristic
171C2×#436—111no—
172#1703—112no—
173#1703—112no—
174#1695—112no—
175#1689—112no—
176#1566—111no—
177#1550—111no—
178#1550—111no—
179C23×C11—22no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11#12111yescharacteristic
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—81no—
187D4×C11—22no—
188D4×C11—22no—
189D4×C11—42no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—44no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#13712yes—
204C2×C4×C11#13712yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×Dic11—41no—
209C2×Dic11—41no—
210Dic22—41no—
211Dic22—41no—
212Dic22—81no—
213C8×C11—42no—
214C11⋊C8—21no—
215C11⋊C8—21no—
216C11⋊C8—21no—
217C11⋊C8—42no—
218C11⋊C8—42no—
219C11⋊C8AGL(1,ℤ/8)12yes—
220C22×M16—221no—
221#533—111no—
222#533C2×D1111yescharacteristic
223C2×C4×D4C2×D1111yescharacteristic
224#500—111no—
225#494—111no—
226#487—111no—
227#487—111no—
228#478—22no—
229#478—222no—
230#476—112no—
231#476C2×D1112yes—
232#474—112no—
233#474C2×D1112yes—
234#467—221no—
235#467—221no—
236C4×Q16—221no—
237C4×Q16—221no—
238#436—112no—
239#436—112no—
240#436—221no—
241#436—221no—
242#428—21no—
243#428—221no—
244#423—111no—
245#423C2×D1111yescharacteristic
246C2×C4⋊C8—111no—
247#418—21no—
248#418—221no—
249C2×C22⋊C8—221no—
250C2×C4×C8—111no—
251#334—112no—
252#334—112no—
253#333—112no—
254#333—112no—
255#332—112no—
256#332—112no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—84no—
263C22×C11#47012yes—
264C22×C11C2×#12111yescharacteristic
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—42no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11#47012yes—
272C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C4×C11C2×#13711yescharacteristic
274C4×C11C2×#13711yescharacteristic
275C4×C11#57511yescharacteristic
276Dic11—81no—
277Dic11—81no—
278C22×D4C22⋊D1111yescharacteristic
279C23×C4—21no—
280C2×Q16—221no—
281C2×Q16—221no—
282C2×M16—21no—
283C2×M16—222no—
284C2×M16—222no—
285C2×M16—221no—
286C2×M16—444no—
287C22×C8—111no—
288C22×C8—111no—
289C22×C8—221no—
290C4⋊Q8—111no—
291C4⋊Q8—111no—
292C4⋊Q8C22×D1111yescharacteristic
293C4⋊Q8C22×D1111yescharacteristic
294#125—21no—
295#125—221no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—221no—
299C22⋊Q8—221no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—221no—
303C4×Q8—221no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4C22⋊D1112yes—
307C4×D4C22×D1112yes—
308#117—21no—
309#117—221no—
310C2×C4⋊C4C22⋊D1111yescharacteristic
311C2×C22⋊C4—21no—
312C2×C42C22×D1111yescharacteristic
313#107—22no—
314#107—221no—
315#107—221no—
316#107—222no—
317#106—22no—
318#106—222no—
319C4⋊C8—21no—
320C4⋊C8—112no—
321C4⋊C8—112no—
322C4⋊C8—221no—
323C4⋊C8—221no—
324C4⋊C8C22×D1112yes—
325#103—221no—
326#103—221no—
327#103—221no—
328#103—221no—
329#102—22no—
330#102—22no—
331#102—222no—
332#102—222no—
333C22⋊C8—222no—
334C22⋊C8—222no—
335C4×C8—111no—
336C4×C8—111no—
337C4×C8—111no—
338C4×C8—111no—
339C2×C11—22no—
340C2×C11—82no—
341C2×C11#303611yescharacteristic
342C2×C11C2×#47011yescharacteristic
343C2×C11#306711yescharacteristic
344C24—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—221no—
348C2×Q8—221no—
349C2×D4—21no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4C2×C22⋊D1112yes—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4D4×D1111yescharacteristic
359C22×C4#434111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361Q16—442no—
362Q16—442no—
363M16—42no—
364M16—444no—
365M16—444no—
366M16—442no—
367C2×C8—22no—
368C2×C8—111no—
369C2×C8—111no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—222no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8—441no—
376C2×C8—442no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4C2×C22⋊D1112yes—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—41no—
394C22⋊C4—441no—
395C42—41no—
396C42—441no—
397C42D4×D1111yescharacteristic
398C42#434111yescharacteristic
399C42C2×C22⋊D1111yescharacteristic
400C42C23×D1111yescharacteristic
401C11#1928111yescharacteristic, complemented, Sylow
402C23—22no—
403C23—42no—
404C23—42no—
405C23—42no—
406C23#6699211yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—81no—
410Q8—441no—
411Q8—441no—
412Q8—881no—
413D4—22no—
414D4—22no—
415D4—42no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4#6699211yescharacteristic
429C2×C4#6699211yescharacteristic
430C2×C4#6699211yescharacteristic
431C2×C4#6699512yes—
432C2×C4#6700412yes—
433C2×C4C2×D4×D1111yescharacteristic
434C2×C4C2×#434111yescharacteristic
435C2×C4C22×C22⋊D1111yescharacteristic
436C8—42no—
437C8—112no—
438C8—221no—
439C8—221no—
440C8—221no—
441C8—442no—
442C8—442no—
443C22—21no—
444C22—21no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—84no—
449C22#1062266512yes—
450C22C2×#6699211yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—81no—
457C4—881no—
458C4—881no—
459C4#1062266512yes—
460C4D11×AGL(1,ℤ/8)11yescharacteristic
461C4#1062330411yescharacteristic
462C4C2×#6699511yescharacteristic
463C4C2×#6700411yescharacteristic
464C2—22no—
465C2—82no—
466C2#1307807711yescharacteristic
467C2C2×#1062266511yescharacteristic
468C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3077C2
socleC22×C11C2×#121
prime radicalC22×D4×C11D4
hypercenter#3077D11
hypocenterC11#19281
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #13079198C2semidirect
4. #13068193C2semidirect
5. #13068189C2semidirect
6. #13068137C2semidirect
7. #13068103C2semidirect
8. #13067371C2semidirect
9. #13067307C2semidirect
10. #13067306C2semidirect
24. #10622706C22semidirect
25. #10622705C22semidirect
26. #10622694C22semidirect
27. #10622691C22semidirect
43. #10622185C22semidirect
44. #10622184C22semidirect
45. #10622124C22semidirect
46. #10622119C22semidirect
47. #10622118C22semidirect
48. #10622118C22semidirect
401. C11#19281semidirect

Maximal subgroups

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

subgroupindex
#130791982
#130784132
C2×#106226252
#130681932
#130681892
#130681372
#130681032
#130673712
#130673072
#130673062
C11×#30772
#1928111