Finite Group Databasebeta

← #13078555

Subgroups — #13078555

Order 1408.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#121C211yesmaximal, characteristic
2D11×#117C211yesmaximal, characteristic, complemented
3C11×#482C211yesmaximal, characteristic, complemented
4#10622648C211yesmaximal, characteristic, complemented
5#10622616C211yesmaximal, characteristic, complemented
6#10622495C211yesmaximal, characteristic, complemented
7#10622494C211yesmaximal, characteristic, complemented
8#10622476C211yesmaximal, characteristic, complemented
9#10622474C211yesmaximal, characteristic, complemented
10#10622390C211yesmaximal, characteristic, complemented
11#10622387C211yesmaximal, characteristic, complemented
12#10622383C211yesmaximal, characteristic, complemented
13#10622383C211yesmaximal, characteristic, complemented
14#10622350C211yesmaximal, characteristic, complemented
15#10622339C211yesmaximal, characteristic, complemented
16C2×D4×D11—21no—
17C2×D4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C11×#121C2211yescharacteristic
20C11×#117C2211yescharacteristic, complemented
21#66992—21no—
22#66991C2211yescharacteristic
23#66983C2211yescharacteristic
24#66979C2211yescharacteristic, complemented
25C2×#4313C2211yescharacteristic
26C2×#4313C2211yescharacteristic
27#66948C2211yescharacteristic
28#66945C2211yescharacteristic
29#66945C2211yescharacteristic
30C4⋊C4×D11C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic, complemented
32C4⋊C4×D11C2211yescharacteristic, complemented
33#66937—21no—
34C22⋊C4×D11—21no—
35C22⋊C4×D11—21no—
36#66930—21no—
37#66925—21no—
38C42×D11—21no—
39C11×#107C2211yescharacteristic, complemented
40C11×#106C2211yescharacteristic, complemented
41C11×#102C2211yescharacteristic, complemented
42C11×#102C2211yescharacteristic, complemented
43C11×C22⋊C8C2211yescharacteristic, complemented
44#66896C2211yescharacteristic, complemented
45#66896C2211yescharacteristic, complemented
46C22⋊(C11⋊C8)C2211yescharacteristic, complemented
47#66885C2211yescharacteristic, complemented
48#66885C2211yescharacteristic, complemented
49(C2×D11)⋊C8C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic, complemented
51#66882C2211yescharacteristic, complemented
52#66881C2211yescharacteristic, complemented
53#66873C2211yescharacteristic, complemented
54#66873C2211yescharacteristic, complemented
55#66872C2211yescharacteristic, complemented
56#66872C2211yescharacteristic, complemented
57#66871C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11—21no—
60C23×D11D411yescharacteristic
61C2×D4×C11—21no—
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11D411yescharacteristic
68D4×D11—22no—
69D4×D11—22no—
70D4×D11—44no—
71C2×D44—21no—
72C2×D44C2311yescharacteristic
73C2×C4×D11—22no—
74C2×C4×D11—22no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11D411yescharacteristic
79C2×C4×D11D411yescharacteristic
80C2×C4×D11C2311yescharacteristic
81C2×C4×D11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C4⋊C4C2311yescharacteristic
87C11×C22⋊C4—21no—
88C11×C22⋊C4—21no—
89C42×C11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107#4313—22no—
108#4313—22no—
109#3094—111nomaximal, Sylow
110C23×C11—21no—
111C23×C11C2×D411yescharacteristic
112C22×D11—22no—
113C22×D11—22no—
114C22×D11—21no—
115C22×D11—41no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—42no—
119C22×D11C2×D411yescharacteristic
120C22×D11C2×D411yescharacteristic
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—42no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—42no—
132C22⋊D11—42no—
133C22⋊D11—42no—
134C2×Dic11—22no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140D44—21no—
141D44—21no—
142D44—42no—
143C4×D11—22no—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—22no—
147C4×D11—42no—
148C4×D11—42no—
149C4×D11—42no—
150C4×D11#4112yes—
151C4×D11#4112yes—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156C2×#121—111no—
157C2×#117—111no—
158#482—111no—
159#482—111no—
160#482—111no—
161#482D1111yescharacteristic, complemented
162#481—111no—
163#481—111no—
164#480—111no—
165#480—111no—
166#428—111no—
167#428—111no—
168#418—111no—
169#418—111no—
170#407—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—44no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—84no—
187C2×D11#12312yes—
188C2×D11AGL(1,ℤ/8)12yes—
189C4×C11—21no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11C2×#4111yescharacteristic
194C4×C11C2×#4111yescharacteristic
195Dic11—21no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199Dic11#12312yes—
200C22×D4—111no—
201C22×D4—221no—
202C23×C4—111no—
203C2×M16—111no—
204C2×M16—111no—
205#121—111no—
206#121—111no—
207#121—111no—
208#121—221no—
209#121—221no—
210#121C2×D1111yescharacteristic
211#117—111no—
212#117—111no—
213#117—111no—
214#117—221no—
215#117—221no—
216#117C2×D1111yescharacteristic, complemented
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C42—221no—
223#107—111no—
224#107—111no—
225#107—111no—
226#107C2×D1111yescharacteristic, complemented
227#106—111no—
228#106—111no—
229#106—111no—
230#106C2×D1111yescharacteristic, complemented
231#102—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102C2×D1111yescharacteristic, complemented
238#102C2×D1111yescharacteristic, complemented
239C22⋊C8—111no—
240C22⋊C8—111no—
241C22⋊C8—111no—
242C22⋊C8C2×D1111yescharacteristic, complemented
243C2×C11—41no—
244C2×C11—81no—
245C2×C11C2×#12311yescharacteristic
246C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
247C2×C11#57511yescharacteristic
248D11—22no—
249D11—22no—
250D11—81no—
251C24—111no—
252C24—221no—
253C2×D4—21no—
254C2×D4—111no—
255C2×D4—221no—
256C2×D4—222no—
257C2×D4—222no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—444no—
262C2×D4C22×D1111yescharacteristic
263C22×C4—111no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—222no—
269C22×C4—222no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4C22×D1111yescharacteristic
274M16—222no—
275M16—222no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8C22×D1111yescharacteristic
279C2×C8C22×D1111yescharacteristic
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—111no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4C22×D1111yescharacteristic
287C4⋊C4C22×D1111yescharacteristic
288C4⋊C4C22×D1111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C42—21no—
298C42—221no—
299C42—221no—
300C42—221no—
301C11#309411yescharacteristic, complemented, Sylow
302C23—21no—
303C23—111no—
304C23—111no—
305C23—222no—
306C23—222no—
307C23—221no—
308C23—441no—
309C23—442no—
310C23—442no—
311C23—442no—
312C23D4×D1111yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—221no—
317D4—221no—
318D4—442no—
319D4—442no—
320D4—442no—
321D4—442no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—111no—
328C2×C4—112no—
329C2×C4—112no—
330C2×C4—111no—
331C2×C4—222no—
332C2×C4—222no—
333C2×C4—222no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4D4×D1111yescharacteristic
343C2×C4C23×D1111yescharacteristic
344C8—21no—
345C8—21no—
346C8—221no—
347C8—221no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—112no—
355C22—112no—
356C22—221no—
357C22—221no—
358C22—221no—
359C22—221no—
360C22—444no—
361C22—441no—
362C22—441no—
363C22—441no—
364C22—884no—
365C22C2×D4×D1111yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—112no—
371C4—221no—
372C4—441no—
373C4—441no—
374C4—441no—
375C4#41×D1111yescharacteristic
376C4#41×D1111yescharacteristic
377C2—41no—
378C2—81no—
379C2—222no—
380C2—222no—
381C2—881no—
382C2D11×#12311yescharacteristic
383C2#1062329911yescharacteristic
384C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#482C2
socleC22×C11C22×D4
prime radicalD11×#121C2
hypercenter#482D11
hypocenterC11#3094
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. D11×#117C2semidirect
3. C11×#482C2semidirect
4. #10622648C2semidirect
5. #10622616C2semidirect
6. #10622495C2semidirect
7. #10622494C2semidirect
8. #10622476C2semidirect
9. #10622474C2semidirect
10. #10622390C2semidirect
11. #10622387C2semidirect
12. #10622383C2semidirect
13. #10622383C2semidirect
14. #10622350C2semidirect
15. #10622339C2semidirect
20. C11×#117C22semidirect
24. #66979C22semidirect
31. C4⋊C4×D11C22semidirect
32. C4⋊C4×D11C22semidirect
39. C11×#107C22semidirect
40. C11×#106C22semidirect
41. C11×#102C22semidirect
42. C11×#102C22semidirect
43. C11×C22⋊C8C22semidirect
44. #66896C22semidirect
45. #66896C22semidirect
46. C22⋊(C11⋊C8)C22semidirect
47. #66885C22semidirect
48. #66885C22semidirect
49. (C2×D11)⋊C8C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. #66882C22semidirect
52. #66881C22semidirect
53. #66873C22semidirect
54. #66873C22semidirect
55. #66872C22semidirect
56. #66872C22semidirect
57. #66871C22semidirect
58. #66871C22semidirect
161. #482D11semidirect
216. #117C2×D11semidirect
226. #107C2×D11semidirect
230. #106C2×D11semidirect
237. #102C2×D11semidirect
238. #102C2×D11semidirect
242. C22⋊C8C2×D11semidirect
301. C11#3094semidirect

Maximal subgroups

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

subgroupindex
D11×#1212
D11×#1172
C11×#4822
#106226482
#106226162
#106224952
#106224942
#106224762
#106224742
#106223902
#106223872
#106223832
#106223502
#106223392
#309411