Finite Group Databasebeta

← #14737666

Subgroups — #14737666

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622686C211yesmaximal, characteristic, complemented
2#13078096C211yesmaximal, characteristic, complemented
3#41×C11⋊C8C211yesmaximal, characteristic, complemented
4#13067974C214yesmaximal, complemented
5#13067969C214yesmaximal, complemented
6#13067374C211yesmaximal, characteristic, complemented
7#13067285C211yesmaximal, characteristic, complemented
8#13067284C211yesmaximal, characteristic, complemented
9C11×#3038C211yesmaximal, characteristic, complemented
10C2×C11×AGL(1,ℤ/8)—21no—
11C2×C11×#127C2211yescharacteristic
12C4×C11×#41C2211yescharacteristic
13C2×#67002—21no—
14C22×#4323—22no—
15C2×#66927C2211yescharacteristic
16C11×#460—21no—
17C11×#460C2212yescomplemented
18C11×#459—21no—
19C11×#459C2212yescomplemented
20C11×#423C2211yescharacteristic
21C11×#418—21no—
22#10622686—21no—
23#10622686—21no—
24#10622686C2214yes—
25#10622640—21no—
26#10622640C2212yescomplemented
27Q8×C11⋊C8C2212yescomplemented
28#10622628—21no—
29#10622628C2212yescomplemented
30D4×C11⋊C8—22no—
31D4×C11⋊C8C2212yescomplemented
32#10622614—21no—
33#10622538—21no—
34#10622538C2211yescharacteristic
35#10622537C2211yescharacteristic
36C2×C4×C11⋊C8—21no—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622182C2214yescomplemented
39#10622123C2214yescomplemented
40#10622117C2214yescomplemented
41C2×C11×#41D411yescharacteristic
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D44—21no—
46C22×D44—21no—
47C22×D44—21no—
48C11×AGL(1,ℤ/8)—44no—
49C2×C11×SD16—22no—
50C2×C11×D8—22no—
51C2×C11×M16—21no—
52C11×#127—21no—
53C11×#127—21no—
54C11×#127—21no—
55C11×#127C2312yes—
56C4×Q8×C11D411yescharacteristic
57C4×Q8×C11C2311yescharacteristic
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11D411yescharacteristic
61C4×D4×C11C2311yescharacteristic
62C11×#117—21no—
63C11×#117D411yescharacteristic
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66#67002—44no—
67C2×#4325—22no—
68C2×#4323—22no—
69C2×#4323—24no—
70C2×#4323—24no—
71C2×#4323—48no—
72C2×#4318—21no—
73C22×C11⋊C8—22no—
74C22×C11⋊C8D412yes—
75#66927—21no—
76#66927—21no—
77#66927—21no—
78#66927C2312yes—
79C11×C4⋊C8—21no—
80C11×C4⋊C8C2312yes—
81C11×#102—22no—
82C11×#102—22no—
83C22⋊(C11⋊C8)—21no—
84C22⋊(C11⋊C8)—22no—
85#66873—22no—
86#66873—22no—
87C4⋊(C11⋊C8)—21no—
88C4⋊(C11⋊C8)—22no—
89C4⋊(C11⋊C8)C2312yes—
90C4⋊(C11⋊C8)C2312yes—
91C4×C11⋊C8—21no—
92C4×C11⋊C8—22no—
93C4×C11⋊C8D411yescharacteristic
94C4×C11⋊C8D411yescharacteristic
95C4×C11⋊C8C2312yes—
96#19267—111nomaximal, Sylow
97C24×C11—41no—
98C23×D11—41no—
99C11×#41—22no—
100C11×#41D814yescomplemented
101C2×Q8×C11C2×D411yescharacteristic
102C2×D4×C11—21no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—44no—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11—82no—
113C2×D4×C11C2×D411yescharacteristic
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—44no—
124C2×D44—41no—
125C2×D44—41no—
126C2×D44—41no—
127C2×D44—42no—
128C2×D44—42no—
129C2×D44—82no—
130C11×SD16—44no—
131C11×D8—44no—
132C11×M16—42no—
133C2×C8×C11—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4C2×D411yescharacteristic
137C11×C4⋊C4C2×D411yescharacteristic
138C11×C22⋊C4—21no—
139C11×C22⋊C4—21no—
140C11×C22⋊C4—21no—
141C42×C11—21no—
142C42×C11—21no—
143C42×C11—21no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148#4325—44no—
149#4323—48no—
150#4323—48no—
151#4323—44no—
152#4318—42no—
153C2×C11⋊C8—24no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—44no—
157C2×C11⋊C8C2×D412yes—
158C2×C11⋊C8C2×D412yes—
159C2×#493—111no—
160#3038—111no—
161#3038D1111yescharacteristic, complemented
162C8×#41—111no—
163#1668—114no—
164#1667—114no—
165#1567—111no—
166#1545—111no—
167#1545—111no—
168C23×C11—21no—
169C23×C11—42no—
170C23×C11—82no—
171C23×C11—82no—
172C23×C11—82no—
173C23×C11#12111yescharacteristic
174C22×D11—42no—
175C22×D11—82no—
176C22×D11—82no—
177C22×D11—82no—
178Q8×C11—21no—
179Q8×C11C2×D812yescomplemented
180D4×C11—24no—
181D4×C11—21no—
182D4×C11—42no—
183D4×C11—42no—
184D4×C11—44no—
185D4×C11—82no—
186D4×C11—82no—
187D4×C11—82no—
188D4×C11—82no—
189D4×C11C2×D812yescomplemented
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11C2×D812yes—
202C2×C4×C11#13512yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206D44—42no—
207D44—42no—
208D44—44no—
209D44—82no—
210D44—82no—
211D44—82no—
212D44—82no—
213C8×C11—42no—
214C11⋊C8—22no—
215C11⋊C8—42no—
216C11⋊C8—42no—
217C11⋊C8AGL(1,ℤ/8)14yescomplemented
218C2×AGL(1,ℤ/8)—21no—
219C2×AGL(1,ℤ/8)—221no—
220C22×D8—222no—
221C2×#127—111no—
222C2×#127C2×D1111yescharacteristic
223C4×#41C2×D1111yescharacteristic
224#493—114no—
225#493—221no—
226#493—221no—
227#460—21no—
228#460—112no—
229#460—221no—
230#460C2×D1112yescomplemented
231#459—21no—
232#459—112no—
233#459—221no—
234#459C2×D1112yescomplemented
235C8×Q8—112no—
236C8×D4—112no—
237C8×D4—222no—
238#431—111no—
239#431—221no—
240#423—111no—
241#423C2×D1111yescharacteristic
242#418—21no—
243#418—221no—
244C2×C4×C8—111no—
245C2×C4×C8—221no—
246#335—114no—
247#331—114no—
248#331—114no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—22no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—82no—
255C22×C11—82no—
256C22×C11—82no—
257C22×C11—164no—
258C22×C11#46612yes—
259C22×C11C2×#12111yescharacteristic
260C2×D11—82no—
261C2×D11—82no—
262C2×D11—82no—
263C2×D11—164no—
264C4×C11—21no—
265C4×C11—22no—
266C4×C11—21no—
267C4×C11—41no—
268C4×C11—41no—
269C4×C11#46612yes—
270C4×C11#47212yes—
271C4×C11C22×D811yescharacteristic
272C4×C11C2×#13511yescharacteristic
273C4×C11C2×AGL(1,ℤ/8)12yes—
274C2×#41C22⋊D1111yescharacteristic
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—221no—
279C22×D4—221no—
280C22×D4—221no—
281AGL(1,ℤ/8)—44no—
282AGL(1,ℤ/8)—444no—
283C2×SD16—22no—
284C2×SD16—222no—
285C2×D8—22no—
286C2×D8—224no—
287C2×D8—224no—
288C2×D8—222no—
289C2×D8—448no—
290C2×M16—21no—
291C2×M16—221no—
292C22×C8—112no—
293C22×C8—222no—
294#127—21no—
295#127—21no—
296#127—21no—
297#127—112no—
298#127—221no—
299#127—221no—
300#127—221no—
301#127C22×D1112yes—
302C4×Q8C22⋊D1111yescharacteristic
303C4×Q8C22×D1111yescharacteristic
304C4×D4—21no—
305C4×D4—21no—
306C4×D4C22⋊D1111yescharacteristic
307C4×D4C22×D1111yescharacteristic
308#117—21no—
309#117C22⋊D1111yescharacteristic
310C2×C42—21no—
311C2×C42C22×D1111yescharacteristic
312C4⋊C8—21no—
313C4⋊C8—112no—
314C4⋊C8—112no—
315C4⋊C8—222no—
316C4⋊C8—221no—
317C4⋊C8C22×D1112yes—
318#102—22no—
319#102—22no—
320#102—222no—
321#102—222no—
322C22⋊C8—222no—
323C22⋊C8—221no—
324C4×C8—111no—
325C4×C8—111no—
326C4×C8—112no—
327C4×C8—222no—
328C4×C8—221no—
329C2×C11—22no—
330C2×C11—42no—
331C2×C11—162no—
332C2×C11#303811yescharacteristic
333C2×C11C2×#46611yescharacteristic
334C2×C11C2×#47211yescharacteristic
335D11—162no—
336C24—41no—
337C24—441no—
338#41—22no—
339#41#432314yescomplemented
340C2×Q8C2×C22⋊D1111yescharacteristic
341C2×D4—21no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—44no—
346C2×D4—42no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—42no—
351C2×D4—82no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—444no—
356C2×D4—442no—
357C2×D4—441no—
358C2×D4—441no—
359C2×D4—441no—
360C2×D4—442no—
361C2×D4—882no—
362C2×D4C2×C22⋊D1111yescharacteristic
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4D4×D1111yescharacteristic
367C22×C4#434111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369SD16—44no—
370SD16—444no—
371D8—44no—
372D8—448no—
373D8—448no—
374D8—444no—
375M16—42no—
376M16—442no—
377C2×C8—22no—
378C2×C8—112no—
379C2×C8—112no—
380C2×C8—224no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—444no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4C2×C22⋊D1111yescharacteristic
387C4⋊C4C2×C22⋊D1111yescharacteristic
388C22⋊C4—21no—
389C22⋊C4—21no—
390C22⋊C4—21no—
391C42—21no—
392C42—21no—
393C42—21no—
394C42D4×D1111yescharacteristic
395C42#434111yescharacteristic
396C42C2×C22⋊D1111yescharacteristic
397C42C23×D1111yescharacteristic
398C11#1926711yescharacteristic, complemented, Sylow
399C23—21no—
400C23—42no—
401C23—82no—
402C23—82no—
403C23—82no—
404C23—442no—
405C23—882no—
406C23—882no—
407C23—882no—
408C23#6699211yescharacteristic
409Q8—21no—
410Q8C2×#432312yescomplemented
411D4—24no—
412D4—21no—
413D4—44no—
414D4—42no—
415D4—42no—
416D4—82no—
417D4—82no—
418D4—82no—
419D4—82no—
420D4—444no—
421D4—442no—
422D4—442no—
423D4—882no—
424D4—882no—
425D4—882no—
426D4—882no—
427D4C2×#432312yescomplemented
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4C2×#432312yes—
437C2×C4#6699211yescharacteristic
438C2×C4#6699211yescharacteristic
439C2×C4#6699211yescharacteristic
440C2×C4#6700312yes—
441C2×C4C2×D4×D1111yescharacteristic
442C2×C4C2×#434111yescharacteristic
443C2×C4C22×C22⋊D1111yescharacteristic
444C8—42no—
445C8—114no—
446C8—222no—
447C8—442no—
448C8—442no—
449C22—21no—
450C22—21no—
451C22—22no—
452C22—41no—
453C22—41no—
454C22—82no—
455C22—82no—
456C22—82no—
457C22—164no—
458C22—882no—
459C22—882no—
460C22—882no—
461C22—1764no—
462C22#1062265112yes—
463C22C2×#6699211yescharacteristic
464C4—21no—
465C4—21no—
466C4—22no—
467C4—41no—
468C4—41no—
469C4#1062265112yes—
470C4#1062281212yes—
471C4D11×AGL(1,ℤ/8)12yes—
472C4C22×#432311yescharacteristic
473C4C2×#6700311yescharacteristic
474C2—22no—
475C2—42no—
476C2—162no—
477C2—1762no—
478C2#1307809411yescharacteristic
479C2C2×#1062265111yescharacteristic
480C2C2×#1062281211yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3038C2
socleC22×C11C2×#121
hypercenter#3038D11
hypocenterC11#19267
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. C2×#10622686C2semidirect
2. #13078096C2semidirect
3. #41×C11⋊C8C2semidirect
4. #13067974C2semidirect
5. #13067969C2semidirect
6. #13067374C2semidirect
7. #13067285C2semidirect
8. #13067284C2semidirect
9. C11×#3038C2semidirect
17. C11×#460C22semidirect
19. C11×#459C22semidirect
26. #10622640C22semidirect
27. Q8×C11⋊C8C22semidirect
29. #10622628C22semidirect
31. D4×C11⋊C8C22semidirect
38. #10622182C22semidirect
39. #10622123C22semidirect
40. #10622117C22semidirect
100. C11×#41D8semidirect
161. #3038D11semidirect
179. Q8×C11C2×D8semidirect
189. D4×C11C2×D8semidirect
217. C11⋊C8AGL(1,ℤ/8)semidirect
230. #460C2×D11semidirect
234. #459C2×D11semidirect
339. #41#4323semidirect
398. C11#19267semidirect
410. Q8C2×#4323semidirect
427. D4C2×#4323semidirect

Maximal subgroups

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

subgroupindex
C2×#106226862
#130780962
#41×C11⋊C82
#130679742
#130679692
#130673742
#130672852
#130672842
C11×#30382
#1926711