Finite Group Databasebeta

← #14736977

Subgroups — #14736977

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079554C211yesmaximal, characteristic, complemented
2C2×#10622686C211yesmaximal, characteristic
3#13077551C211yesmaximal, characteristic, complemented
4#13068098C214yesmaximal, complemented
5#13067974C214yesmaximal, complemented
6#13067362C211yesmaximal, characteristic, complemented
7#13067284C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic, complemented
9C11×#3208C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C22×#4323—21no—
13C22×#4323—21no—
14C2×#66927C2211yescharacteristic
15C11×#492—21no—
16C11×#486—21no—
17C11×#460C2214yescomplemented
18C11×#450—22no—
19C11×#431C2211yescharacteristic
20#10622701—21no—
21#10622698—21no—
22#10622686—21no—
23#10622686—21no—
24#10622686C2212yes—
25#10622686C2212yes—
26#10622659—22no—
27#10622640C2214yescomplemented
28#10622637—21no—
29#10622637C2212yescomplemented
30Q8×C11⋊C8—21no—
31Q8×C11⋊C8C2212yescomplemented
32#10622612—21no—
33#10622610—21no—
34#10622538C2211yescharacteristic
35#10622537C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622182C2214yescomplemented
38#10622123C2214yescomplemented
39#10622118C2212yescomplemented
40#10622117C2212yescomplemented
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44—21no—
47C2×C11×SD16—24no—
48C11×C4⋊Q8D411yescharacteristic
49C11×C4⋊Q8D411yescharacteristic
50C11×#127—21no—
51C11×#127—21no—
52C11×#127—21no—
53C11×#127C2312yes—
54C11×#125—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8D412yes—
57C4×Q8×C11—21no—
58C4×Q8×C11C2312yes—
59C11×#117—21no—
60C2×C42×C11C2311yescharacteristic
61C2×#4325—24no—
62C2×#4323—22no—
63C2×#4323—22no—
64C2×#4323—22no—
65C2×#4323—22no—
66C2×#4323—44no—
67C2×#4323—44no—
68C2×#4318—21no—
69C22×C11⋊C8D411yescharacteristic
70C22×C11⋊C8D411yescharacteristic
71#66927—21no—
72#66927—21no—
73#66927—21no—
74#66927C2312yes—
75C11×C4⋊C8C2312yes—
76C11×#102—24no—
77C11×C22⋊C8—21no—
78C4×C8×C11—21no—
79C22⋊(C11⋊C8)—21no—
80#66873—24no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)—22no—
83C4⋊(C11⋊C8)—22no—
84C4⋊(C11⋊C8)C2312yes—
85C4⋊(C11⋊C8)C2312yes—
86#66867—22no—
87C4×C11⋊C8—21no—
88C4×C11⋊C8—22no—
89C4×C11⋊C8D411yescharacteristic
90C4×C11⋊C8D411yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93#19203—111nomaximal, Sylow
94C24×C11—41no—
95C23×D11—41no—
96C2×Q8×C11—21no—
97C2×Q8×C11C2×D412yes—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—82no—
107C2×D4×C11—82no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—41no—
115C2×D44—41no—
116C2×D44—41no—
117C2×D44—42no—
118C2×D44—42no—
119C2×D44—82no—
120C2×D44—82no—
121C11×SD16—84no—
122C2×C8×C11—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4C2×D412yes—
129C11×C22⋊C4—22no—
130C42×C11—22no—
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134C42×C11C2411yescharacteristic
135#4325—84no—
136#4323—44no—
137#4323—44no—
138#4323—44no—
139#4323—44no—
140#4318—42no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8SD1614yescomplemented
145C2×C11⋊C8C2×D411yescharacteristic
146C2×C11⋊C8C2×D411yescharacteristic
147C2×C11⋊C8C2×D411yescharacteristic
148C2×C11⋊C8C2×D411yescharacteristic
149#3208—111no—
150#3208D1111yescharacteristic, complemented
151C2×#493—111no—
152#2960—111no—
153#1688—114no—
154#1668—114no—
155#1564—111no—
156#1545—111no—
157#1545—111no—
158C23×C11—42no—
159C23×C11—82no—
160C23×C11—82no—
161C23×C11—82no—
162C23×C11#12111yescharacteristic
163C22×D11—42no—
164C22×D11—82no—
165C22×D11—82no—
166C22×D11—82no—
167Q8×C11—24no—
168Q8×C11—42no—
169D4×C11—42no—
170D4×C11—42no—
171D4×C11—44no—
172D4×C11—82no—
173D4×C11—82no—
174D4×C11—82no—
175D4×C11—82no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11C2×SD1612yes—
184C2×C4×C11AGL(1,ℤ/8)12yes—
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188D44—42no—
189D44—42no—
190D44—44no—
191D44—82no—
192D44—82no—
193D44—82no—
194D44—82no—
195C8×C11—42no—
196C11⋊C8—21no—
197C11⋊C8—21no—
198C11⋊C8—42no—
199C11⋊C8—42no—
200C11⋊C8C2×SD1612yes—
201C11⋊C8C2×SD1612yes—
202C22×D8—221no—
203C22×D8—221no—
204#533C2×D1111yescharacteristic
205C2×#127—111no—
206C2×#127C2×D1111yescharacteristic
207#493—112no—
208#493—112no—
209#493—221no—
210#493—221no—
211#492—21no—
212#492—221no—
213#486—21no—
214#486—221no—
215#460—114no—
216#460C2×D1114yescomplemented
217#450—22no—
218#450—222no—
219#446—112no—
220#446—221no—
221C8×Q8—112no—
222C8×Q8—221no—
223#431—111no—
224#431C2×D1111yescharacteristic
225#424—221no—
226#423—111no—
227#405—221no—
228C2×C4×C8—111no—
229#335—112no—
230#334—112no—
231#331—114no—
232#331—114no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—82no—
236C22×C11—82no—
237C22×C11—82no—
238C22×C11—164no—
239C22×C11#46012yes—
240C22×C11C2×#12111yescharacteristic
241C2×D11—82no—
242C2×D11—82no—
243C2×D11—82no—
244C2×D11—164no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11#46012yes—
250C4×C11#47212yes—
251C4×C11C22×SD1611yescharacteristic
252C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
253C4×C11#57612yes—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4—221no—
258C22×D4—221no—
259C22×D4—221no—
260C2×SD16—24no—
261C2×SD16—224no—
262C2×D8—222no—
263C2×D8—222no—
264C2×D8—222no—
265C2×D8—222no—
266C2×D8—444no—
267C2×D8—444no—
268C2×M16—221no—
269C22×C8—111no—
270C22×C8—111no—
271C4⋊Q8C22⋊D1111yescharacteristic
272C4⋊Q8C22⋊D1111yescharacteristic
273#127—21no—
274#127—21no—
275#127—21no—
276#127—112no—
277#127—221no—
278#127—221no—
279#127—221no—
280#127C22×D1112yes—
281#125—21no—
282C22⋊Q8—21no—
283C22⋊Q8C22⋊D1112yes—
284C4×Q8—21no—
285C4×Q8C22×D1112yes—
286#117—21no—
287C2×C42C22×D1111yescharacteristic
288C4⋊C8—112no—
289C4⋊C8—112no—
290C4⋊C8—222no—
291C4⋊C8—222no—
292C4⋊C8—221no—
293C4⋊C8C22×D1112yes—
294#102—24no—
295#102—224no—
296C22⋊C8—21no—
297C22⋊C8—221no—
298#97—222no—
299C4×C8—21no—
300C4×C8—111no—
301C4×C8—111no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8—222no—
305C4×C8—221no—
306C2×C11—22no—
307C2×C11—162no—
308C2×C11C2×#46011yescharacteristic
309C2×C11#305811yescharacteristic
310C2×C11C2×#47211yescharacteristic
311D11—162no—
312C24—41no—
313C24—441no—
314C2×Q8—21no—
315C2×Q8C2×C22⋊D1112yes—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—42no—
320C2×D4—42no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—82no—
325C2×D4—82no—
326C2×D4—222no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—442no—
330C2×D4—442no—
331C2×D4—441no—
332C2×D4—441no—
333C2×D4—441no—
334C2×D4—882no—
335C2×D4—882no—
336C22×C4D4×D1111yescharacteristic
337C22×C4#434111yescharacteristic
338C22×C4C2×C22⋊D1111yescharacteristic
339SD16—84no—
340SD16—884no—
341D8—444no—
342D8—444no—
343D8—444no—
344D8—444no—
345M16—442no—
346C2×C8—22no—
347C2×C8—114no—
348C2×C8—111no—
349C2×C8—111no—
350C2×C8—111no—
351C2×C8—111no—
352C2×C8—222no—
353C2×C8—222no—
354C2×C8—222no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4C2×C22⋊D1112yes—
361C22⋊C4—22no—
362C42—22no—
363C42D4×D1111yescharacteristic
364C42#434111yescharacteristic
365C42C2×C22⋊D1111yescharacteristic
366C42C23×D1111yescharacteristic
367C11#1920311yescharacteristic, complemented, Sylow
368C23—42no—
369C23—82no—
370C23—82no—
371C23—82no—
372C23—442no—
373C23—882no—
374C23—882no—
375C23—882no—
376C23#6699211yescharacteristic
377Q8—24no—
378Q8—42no—
379D4—42no—
380D4—42no—
381D4—44no—
382D4—82no—
383D4—82no—
384D4—82no—
385D4—82no—
386D4—442no—
387D4—442no—
388D4—444no—
389D4—882no—
390D4—882no—
391D4—882no—
392D4—882no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4SD16×D1112yes—
398C2×C4#6696712yes—
399C2×C4#6699211yescharacteristic
400C2×C4#6699211yescharacteristic
401C2×C4#6699211yescharacteristic
402C2×C4C2×D4×D1111yescharacteristic
403C2×C4C2×#434111yescharacteristic
404C2×C4C22×C22⋊D1111yescharacteristic
405C8—42no—
406C8—112no—
407C8—112no—
408C8—221no—
409C8—221no—
410C8—442no—
411C8—442no—
412C22—21no—
413C22—21no—
414C22—82no—
415C22—82no—
416C22—82no—
417C22—164no—
418C22—882no—
419C22—882no—
420C22—882no—
421C22—1764no—
422C22#1062277612yes—
423C22C2×#6699211yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4#1062277612yes—
429C4#1062281212yes—
430C4C2×SD16×D1111yescharacteristic
431C4C2×#6696711yescharacteristic
432C4#1062336612yes—
433C2—22no—
434C2—162no—
435C2—1762no—
436C2C2×#1062277611yescharacteristic
437C2#1307826111yescharacteristic
438C2C2×#1062281211yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3208C2
socleC22×C11C2×#121
prime radicalC2×#10622686C2
hypercenter#3208D11
hypocenterC11#19203
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #13079554C2semidirect
3. #13077551C2semidirect
4. #13068098C2semidirect
5. #13067974C2semidirect
6. #13067362C2semidirect
7. #13067284C2semidirect
8. #13067283C2semidirect
9. C11×#3208C2semidirect
17. C11×#460C22semidirect
27. #10622640C22semidirect
29. #10622637C22semidirect
31. Q8×C11⋊C8C22semidirect
37. #10622182C22semidirect
38. #10622123C22semidirect
39. #10622118C22semidirect
40. #10622117C22semidirect
144. C2×C11⋊C8SD16semidirect
150. #3208D11semidirect
216. #460C2×D11semidirect
367. C11#19203semidirect

Maximal subgroups

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

subgroupindex
#130795542
C2×#106226862
#130775512
#130680982
#130679742
#130673622
#130672842
#130672832
C11×#32082
#1920311