Finite Group Databasebeta

← #14737297

Subgroups — #14737297

Order 2816.

704 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#13079932C211yesmaximal, characteristic, complemented
2#13078990C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic, complemented
4#13068175C212yesmaximal, complemented
5#13068147C212yesmaximal, complemented
6#13068051C212yesmaximal, complemented
7#13068023C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067271C211yesmaximal, characteristic, complemented
10C2×#10622182C211yesmaximal, characteristic, complemented
11C11×#3205C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×#67001—21no—
15#10623001C2211yescharacteristic
16C11×#493—21no—
17C11×#486—21no—
18C11×#459C2212yes—
19C11×#459C2212yes—
20C11×#447—22no—
21C11×#431C2211yescharacteristic
22#10622847—21no—
23#10622828—21no—
24#10622828—21no—
25#10622707—21no—
26#10622688—21no—
27#10622684—22no—
28#10622683C2212yes—
29#10622683C2212yes—
30#10622654—22no—
31#10622632C2212yescomplemented
32#10622625C2212yescomplemented
33#10622624—22no—
34D4×C11⋊C8C2212yescomplemented
35#10622621C2212yescomplemented
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622182C2212yes—
40#10622182C2212yes—
41#10622120C2211yescharacteristic, complemented
42#10622120C2211yescharacteristic, complemented
43#10622119C2211yescharacteristic, complemented
44#10622119C2211yescharacteristic, complemented
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47C2×C11×#41—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C2×C11×D8—22no—
52C2×C11×D8—22no—
53C11×C4⋊Q8D411yescharacteristic
54C11×#127—21no—
55C11×#127—21no—
56C11×#127—21no—
57C11×#127D411yescharacteristic
58C11×#127C2312yes—
59C11×#124—21no—
60C11×#121—21no—
61C11×#121D412yes—
62C4×D4×C11—21no—
63C4×D4×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65#67001—44no—
66C2×#4324—22no—
67#66979—21no—
68#66977—21no—
69#66977—21no—
70C2×#4318—22no—
71C2×#4318D411yescharacteristic
72C2×#4318D411yescharacteristic
73C22×C11⋊C8—21no—
74C22×C11⋊C8—21no—
75C22×C11⋊C8—22no—
76#66923—21no—
77#66922C2311yescharacteristic
78#66922C2311yescharacteristic
79C4×Dic22—21no—
80C4×Dic22—21no—
81C11×C4⋊C8C2311yescharacteristic
82C11×C4⋊C8C2311yescharacteristic
83C11×#102—22no—
84C11×#102—22no—
85C11×C22⋊C8—21no—
86C4×C8×C11—21no—
87#66896—22no—
88#66896—22no—
89#66896—22no—
90#66896—22no—
91#66896—22no—
92C22⋊(C11⋊C8)—22no—
93C22⋊(C11⋊C8)—22no—
94#66874—22no—
95#66872—22no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101#66867D412yes—
102C4×C11⋊C8C2312yes—
103#19234—111nomaximal, Sylow
104C24×C11—41no—
105C11×#41—42no—
106C11×#41—42no—
107C2×Q8×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—41no—
115C2×D4×C11—41no—
116C2×D4×C11—41no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—81no—
120C2×D4×C11—81no—
121C2×D4×C11—82no—
122C2×D4×C11C2×D412yes—
123C22×C4×C11—22no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C2×Dic22—21no—
128C2×Dic22—21no—
129C11×D8—82no—
130C11×D8—82no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4C2×D412yes—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—22no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140C42×C11C2411yescharacteristic
141C22⋊Dic11—41no—
142#4324—82no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147Dic11⋊C4—41no—
148Dic11⋊C4—41no—
149C4×Dic11—41no—
150#4318—22no—
151#4318—22no—
152#4318—44no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—44no—
157C2×C11⋊C8—42no—
158C2×C11⋊C8—81no—
159C2×C11⋊C8C2×D412yes—
160C2×C11⋊C8C2×D412yes—
161#3246—111no—
162#3205D1111yescharacteristic
163#3138—111no—
164#2935—111no—
165#1701—112no—
166#1697—112no—
167#1681—112no—
168#1677—112no—
169#1565—111no—
170#1542—111no—
171C2×#331—111no—
172C23×C11—22no—
173C23×C11—42no—
174C23×C11—82no—
175C23×C11—82no—
176C23×C11—82no—
177C23×C11#12111yescharacteristic
178Q8×C11—42no—
179D4×C11—22no—
180D4×C11—22no—
181D4×C11—44no—
182D4×C11—42no—
183D4×C11—42no—
184D4×C11—42no—
185D4×C11—42no—
186D4×C11—42no—
187D4×C11—81no—
188D4×C11—82no—
189D4×C11—82no—
190D4×C11—82no—
191D4×C11—82no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#13512yes—
202C2×C4×C11AGL(1,ℤ/8)12yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×Dic11—41no—
207C2×Dic11—41no—
208Dic22—41no—
209Dic22—41no—
210Dic22—81no—
211C8×C11—41no—
212C8×C11—41no—
213C11⋊C8—22no—
214C11⋊C8—22no—
215C11⋊C8—41no—
216C11⋊C8—41no—
217C11⋊C8—42no—
218C2×#131—221no—
219#533—111no—
220#532C2×D1111yescharacteristic
221C2×#127C2×D1111yescharacteristic
222#493—21no—
223#490—222no—
224#486—21no—
225#486—112no—
226#486—112no—
227#476—112no—
228#475—221no—
229#465—222no—
230#461—112no—
231#460—221no—
232#459C2×D1112yes—
233#459C2×D1112yes—
234#447—22no—
235#436—112no—
236#435—222no—
237C8×D4—112no—
238#431C2×D1111yescharacteristic
239C2×C4⋊C8—111no—
240C2×C4⋊C8—111no—
241#418—221no—
242#418—221no—
243#408—221no—
244C4×M16—111no—
245#335—112no—
246#334—112no—
247#333—111no—
248#333—111no—
249#332—111no—
250#332—111no—
251#331—112no—
252#331—112no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11—164no—
262C22×C11#46312yes—
263C22×C11C2×#12111yescharacteristic
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11#46312yes—
269C4×C11C2×#13511yescharacteristic
270C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
271C4×C11#57611yescharacteristic
272C4×C11#57711yescharacteristic
273Dic11—81no—
274Dic11—81no—
275C2×#41—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C2×SD16—222no—
280C2×D8—22no—
281C2×D8—22no—
282#131—444no—
283C2×M16—111no—
284C2×M16—111no—
285C2×M16—222no—
286C22×C8—222no—
287C22×C8—221no—
288C22×C8—221no—
289C4⋊Q8—111no—
290C4⋊Q8—111no—
291C4⋊Q8C22⋊D1111yescharacteristic
292#127—21no—
293#127—21no—
294#127—21no—
295#127C22⋊D1111yescharacteristic
296#127C22×D1112yes—
297#125—221no—
298#124—21no—
299C22⋊Q8—221no—
300C22⋊Q8—221no—
301#121—21no—
302#121C22⋊D1112yes—
303C4×Q8—221no—
304C4×Q8—221no—
305C4×D4—21no—
306C4×D4C22×D1112yes—
307#117—221no—
308C2×C42C22×D1111yescharacteristic
309#106—222no—
310C4⋊C8—111no—
311C4⋊C8—111no—
312C4⋊C8—112no—
313C4⋊C8—221no—
314C4⋊C8—221no—
315C4⋊C8C22×D1111yescharacteristic
316C4⋊C8C22×D1111yescharacteristic
317#103—222no—
318#102—22no—
319#102—22no—
320#102—222no—
321#102—222no—
322#102—222no—
323#102—222no—
324#102—222no—
325C22⋊C8—21no—
326C22⋊C8—222no—
327C22⋊C8—222no—
328#97—112no—
329C4×C8—21no—
330C4×C8—112no—
331C2×C11—22no—
332C2×C11—82no—
333C2×C11—162no—
334C2×C11C2×#46311yescharacteristic
335C2×C11#306211yescharacteristic
336C2×C11#306811yescharacteristic
337C24—41no—
338#41—42no—
339#41—42no—
340C2×Q8—21no—
341C2×Q8—221no—
342C2×Q8—221no—
343C2×D4—22no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—42no—
350C2×D4—42no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—81no—
355C2×D4—81no—
356C2×D4—82no—
357C2×D4C2×C22⋊D1112yes—
358C22×C4—22no—
359C22×C4D4×D1111yescharacteristic
360C22×C4#434111yescharacteristic
361C22×C4C2×C22⋊D1111yescharacteristic
362SD16—882no—
363D8—82no—
364D8—82no—
365M16—222no—
366M16—222no—
367M16—444no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—112no—
371C2×C8—112no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—222no—
375C2×C8—444no—
376C2×C8—442no—
377C2×C8—881no—
378C4⋊C4—21no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4C2×C22⋊D1112yes—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—441no—
389C42—441no—
390C42D4×D1111yescharacteristic
391C42#434111yescharacteristic
392C42C2×C22⋊D1111yescharacteristic
393C42C23×D1111yescharacteristic
394C11#1923411yescharacteristic, complemented, Sylow
395C23—22no—
396C23—42no—
397C23—82no—
398C23—82no—
399C23—82no—
400C23#6699211yescharacteristic
401Q8—42no—
402Q8—441no—
403Q8—441no—
404Q8—881no—
405D4—22no—
406D4—22no—
407D4—44no—
408D4—42no—
409D4—42no—
410D4—42no—
411D4—42no—
412D4—42no—
413D4—81no—
414D4—82no—
415D4—82no—
416D4—82no—
417D4—82no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4#6696412yes—
427C2×C4#6696512yes—
428C2×C4#6699211yescharacteristic
429C2×C4#6699211yescharacteristic
430C2×C4#6699211yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C2×C4C2×#434111yescharacteristic
433C2×C4C22×C22⋊D1111yescharacteristic
434C8—41no—
435C8—41no—
436C8—222no—
437C8—222no—
438C8—441no—
439C8—441no—
440C8—442no—
441C22—21no—
442C22—21no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—82no—
447C22—82no—
448C22—82no—
449C22—164no—
450C22#1062276612yes—
451C22C2×#6699211yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—881no—
457C4—881no—
458C4#1062276612yes—
459C4C2×#6696411yescharacteristic
460C4C2×#6696511yescharacteristic
461C4#1062336611yescharacteristic
462C4#1062336711yescharacteristic
463C2—22no—
464C2—82no—
465C2—162no—
466C2C2×#1062276611yescharacteristic
467C2#1307829211yescharacteristic
468C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3205C2
socleC22×C11C2×#121
hypercenter#3205D11
hypocenterC11#19234
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #13079932C2semidirect
2. #13078990C2semidirect
3. #13077360C2semidirect
4. #13068175C2semidirect
5. #13068147C2semidirect
6. #13068051C2semidirect
7. #13068023C2semidirect
8. #13067369C2semidirect
9. #13067271C2semidirect
10. C2×#10622182C2semidirect
31. #10622632C22semidirect
32. #10622625C22semidirect
34. D4×C11⋊C8C22semidirect
35. #10622621C22semidirect
41. #10622120C22semidirect
42. #10622120C22semidirect
43. #10622119C22semidirect
44. #10622119C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
394. C11#19234semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130789902
#130773602
#130681752
#130681472
#130680512
#130680232
#130673692
#130672712
C2×#106221822
C11×#32052
#1923411