Finite Group Databasebeta

← #14737743

Subgroups — #14737743

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622683C211yesmaximal, characteristic, complemented
2#13078103C211yesmaximal, characteristic, complemented
3#41×C11⋊C8C211yesmaximal, characteristic, complemented
4#13068058C214yesmaximal, complemented
5#13068051C214yesmaximal, complemented
6#13067374C211yesmaximal, characteristic, complemented
7#13067289C211yesmaximal, characteristic, complemented
8#13067284C211yesmaximal, characteristic, complemented
9C11×#3038C211yesmaximal, characteristic
10C2×C11×AGL(1,ℤ/8)—21no—
11C2×C11×#127C2211yescharacteristic
12C4×C11×#41C2211yescharacteristic
13C2×#67004—21no—
14C2×#66922C2211yescharacteristic
15C11×#460—21no—
16C11×#460C2212yes—
17C11×#459—21no—
18C11×#459C2212yes—
19C11×#423C2211yescharacteristic
20C11×#418—21no—
21C2×#66896—22no—
22#10622683—21no—
23#10622683—21no—
24#10622683C2214yes—
25#10622644—21no—
26#10622644C2212yescomplemented
27Q8×C11⋊C8C2212yescomplemented
28#10622632—21no—
29#10622632C2212yescomplemented
30D4×C11⋊C8—22no—
31D4×C11⋊C8C2212yescomplemented
32#10622617—21no—
33#10622538—21no—
34#10622538C2211yescharacteristic
35#10622537C2211yescharacteristic
36C2×C4×C11⋊C8—21no—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622182C2214yes—
39#10622120C2214yescomplemented
40#10622117C2214yescomplemented
41C2×C11×#41D411yescharacteristic
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×Dic22—21no—
46C11×AGL(1,ℤ/8)—44no—
47C2×C11×SD16—22no—
48C2×C11×D8—22no—
49C2×C11×M16—21no—
50C11×#127—21no—
51C11×#127—21no—
52C11×#127—21no—
53C11×#127C2312yes—
54C4×Q8×C11D411yescharacteristic
55C4×Q8×C11C2311yescharacteristic
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11D411yescharacteristic
59C4×D4×C11C2311yescharacteristic
60C11×#117—21no—
61C11×#117D411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64#67004—44no—
65C2×#4326—22no—
66C2×#4324—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×#4318—21no—
70C22×C11⋊C8—22no—
71C22×C11⋊C8D412yes—
72#66922—21no—
73#66922—21no—
74#66922—21no—
75#66922C2312yes—
76C11×C4⋊C8—21no—
77C11×C4⋊C8C2312yes—
78C11×#102—22no—
79C11×#102—22no—
80#66896—24no—
81#66896—24no—
82C22⋊(C11⋊C8)—21no—
83C22⋊(C11⋊C8)—22no—
84#66874—22no—
85#66874—22no—
86C4⋊(C11⋊C8)—21no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)C2312yes—
89C4⋊(C11⋊C8)C2312yes—
90C4×C11⋊C8—21no—
91C4×C11⋊C8—22no—
92C4×C11⋊C8D411yescharacteristic
93C4×C11⋊C8D411yescharacteristic
94C4×C11⋊C8C2312yes—
95#19276—111nomaximal, Sylow
96C24×C11—41no—
97C11×#41—22no—
98C11×#41D814yes—
99C2×Q8×C11C2×D411yescharacteristic
100C2×D4×C11—21no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—44no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C2×D4×C11—41no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—82no—
111C2×D4×C11C2×D411yescharacteristic
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×Dic11—41no—
119C2×Dic22—22no—
120C2×Dic22—41no—
121C2×Dic22—42no—
122C2×Dic22—42no—
123C11×SD16—44no—
124C11×D8—44no—
125C11×M16—42no—
126C2×C8×C11—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4C2×D411yescharacteristic
130C11×C4⋊C4C2×D411yescharacteristic
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C11×C22⋊C4—21no—
134C42×C11—21no—
135C42×C11—21no—
136C42×C11—21no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140C42×C11C2411yescharacteristic
141#4326—44no—
142#4324—44no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—41no—
146C4⋊Dic11—41no—
147#4318—42no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—42no—
151C2×C11⋊C8—44no—
152C2×C11⋊C8C2×D412yes—
153C2×C11⋊C8C2×D412yes—
154C2×#486—111no—
155#3039—111no—
156#3038D1111yescharacteristic
157C8×#41—111no—
158#1682—114no—
159#1681—114no—
160#1567—111no—
161#1546—111no—
162#1545—111no—
163C23×C11—21no—
164C23×C11—42no—
165C23×C11—82no—
166C23×C11—82no—
167C23×C11—82no—
168C23×C11#12111yescharacteristic
169Q8×C11—21no—
170Q8×C11C2×D812yes—
171D4×C11—24no—
172D4×C11—21no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—44no—
176D4×C11—82no—
177D4×C11—82no—
178D4×C11—82no—
179D4×C11—82no—
180D4×C11C2×D812yes—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11C2×D812yes—
193C2×C4×C11#13512yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×Dic11—42no—
198C2×Dic11—82no—
199Dic22—42no—
200Dic22—42no—
201Dic22—82no—
202C8×C11—42no—
203C11⋊C8—22no—
204C11⋊C8—22no—
205C11⋊C8—42no—
206C11⋊C8—42no—
207C2×#137—221no—
208C2×AGL(1,ℤ/8)—21no—
209C2×C4⋊Q8—111no—
210C2×#127C2×D1111yescharacteristic
211C4×#41C2×D1111yescharacteristic
212#486—114no—
213#486—221no—
214#486—221no—
215#462—112no—
216#462—221no—
217#461—112no—
218#461—221no—
219#460—21no—
220#460C2×D1112yes—
221#459—21no—
222#459C2×D1112yes—
223C8×Q8—112no—
224C8×D4—112no—
225C8×D4—222no—
226#431—111no—
227#431—221no—
228#423—111no—
229#423C2×D1111yescharacteristic
230#419—221no—
231#418—21no—
232C2×#102—222no—
233C2×C4×C8—111no—
234C2×C4×C8—221no—
235#335—114no—
236#332—114no—
237#331—114no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—22no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11—164no—
247C22×C11#46612yes—
248C22×C11C2×#12111yescharacteristic
249C4×C11—21no—
250C4×C11—22no—
251C4×C11—21no—
252C4×C11—41no—
253C4×C11—41no—
254C4×C11#46612yes—
255C4×C11#47112yes—
256C4×C11C22×D811yescharacteristic
257C4×C11C2×#13511yescharacteristic
258C4×C11#57512yes—
259Dic11—82no—
260C2×#41C22⋊D1111yescharacteristic
261C22×Q8—221no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265#137—444no—
266AGL(1,ℤ/8)—44no—
267C2×Q16—222no—
268C2×SD16—22no—
269C2×SD16—222no—
270C2×D8—22no—
271C2×M16—21no—
272C2×M16—221no—
273C22×C8—112no—
274C22×C8—222no—
275C4⋊Q8—112no—
276C4⋊Q8—221no—
277C4⋊Q8—221no—
278C4⋊Q8—221no—
279#127—21no—
280#127—21no—
281#127—21no—
282#127C22×D1112yes—
283C4×Q8C22⋊D1111yescharacteristic
284C4×Q8C22×D1111yescharacteristic
285C4×D4—21no—
286C4×D4—21no—
287C4×D4C22⋊D1111yescharacteristic
288C4×D4C22×D1111yescharacteristic
289#117—21no—
290#117C22⋊D1111yescharacteristic
291C2×C4⋊C4—221no—
292C2×C4⋊C4—221no—
293C2×C42—21no—
294C2×C42C22×D1111yescharacteristic
295C4⋊C8—21no—
296C4⋊C8—112no—
297C4⋊C8—112no—
298C4⋊C8—222no—
299C4⋊C8—221no—
300C4⋊C8C22×D1112yes—
301#103—222no—
302#103—222no—
303#102—22no—
304#102—22no—
305#102—224no—
306#102—224no—
307C22⋊C8—222no—
308C22⋊C8—221no—
309C4×C8—111no—
310C4×C8—111no—
311C4×C8—112no—
312C4×C8—222no—
313C4×C8—221no—
314C2×C11—22no—
315C2×C11—42no—
316C2×C11—162no—
317C2×C11#304011yescharacteristic
318C2×C11C2×#46611yescharacteristic
319C2×C11C2×#47111yescharacteristic
320C24—41no—
321#41—22no—
322#41#432314yes—
323C2×Q8—222no—
324C2×Q8—441no—
325C2×Q8—442no—
326C2×Q8—442no—
327C2×Q8C2×C22⋊D1111yescharacteristic
328C2×D4—21no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—44no—
333C2×D4—42no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—42no—
338C2×D4—82no—
339C2×D4C2×C22⋊D1111yescharacteristic
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—441no—
344C22×C4D4×D1111yescharacteristic
345C22×C4#434111yescharacteristic
346C22×C4C2×C22⋊D1111yescharacteristic
347Q16—444no—
348SD16—44no—
349SD16—444no—
350D8—44no—
351M16—42no—
352M16—442no—
353C2×C8—22no—
354C2×C8—112no—
355C2×C8—112no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—442no—
359C2×C8—444no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—222no—
363C4⋊C4—222no—
364C4⋊C4—441no—
365C4⋊C4—441no—
366C4⋊C4C2×C22⋊D1111yescharacteristic
367C4⋊C4C2×C22⋊D1111yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C42—21no—
372C42—21no—
373C42—21no—
374C42D4×D1111yescharacteristic
375C42#434111yescharacteristic
376C42C2×C22⋊D1111yescharacteristic
377C42C23×D1111yescharacteristic
378C11#1927611yescharacteristic, complemented, Sylow
379C23—21no—
380C23—42no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23#6699211yescharacteristic
385Q8—21no—
386Q8—442no—
387Q8—442no—
388Q8—882no—
389Q8C2×#432312yes—
390D4—24no—
391D4—21no—
392D4—44no—
393D4—42no—
394D4—42no—
395D4—82no—
396D4—82no—
397D4—82no—
398D4—82no—
399D4C2×#432312yes—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—442no—
409C2×C4—882no—
410C2×C4C2×#432312yes—
411C2×C4#6699211yescharacteristic
412C2×C4#6699211yescharacteristic
413C2×C4#6699211yescharacteristic
414C2×C4#6700312yes—
415C2×C4C2×D4×D1111yescharacteristic
416C2×C4C2×#434111yescharacteristic
417C2×C4C22×C22⋊D1111yescharacteristic
418C8—42no—
419C8—222no—
420C8—222no—
421C8—442no—
422C8—442no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—41no—
427C22—41no—
428C22—82no—
429C22—82no—
430C22—82no—
431C22—164no—
432C22#1062265112yes—
433C22C2×#6699211yescharacteristic
434C4—21no—
435C4—21no—
436C4—22no—
437C4—41no—
438C4—41no—
439C4—882no—
440C4#1062265112yes—
441C4#1062281312yes—
442C4#1062330412yes—
443C4C22×#432311yescharacteristic
444C4C2×#6700311yescharacteristic
445C2—22no—
446C2—42no—
447C2—162no—
448C2#1307810811yescharacteristic
449C2C2×#1062265111yescharacteristic
450C2C2×#1062281311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3038C2
socleC22×C11C2×#121
hypercenter#3038D11
hypocenterC11#19276
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×#10622683C2semidirect
2. #13078103C2semidirect
3. #41×C11⋊C8C2semidirect
4. #13068058C2semidirect
5. #13068051C2semidirect
6. #13067374C2semidirect
7. #13067289C2semidirect
8. #13067284C2semidirect
26. #10622644C22semidirect
27. Q8×C11⋊C8C22semidirect
29. #10622632C22semidirect
31. D4×C11⋊C8C22semidirect
39. #10622120C22semidirect
40. #10622117C22semidirect
378. C11#19276semidirect

Maximal subgroups

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

subgroupindex
C2×#106226832
#130781032
#41×C11⋊C82
#130680582
#130680512
#130673742
#130672892
#130672842
C11×#30382
#1927611