Finite Group Databasebeta

← #13079434

Subgroups — #13079434

Order 1408.

466 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#121C211yesmaximal, characteristic, complemented
2#10623055C211yesmaximal, characteristic, complemented
3C11×#482C211yesmaximal, characteristic, complemented
4#10622650C211yesmaximal, characteristic, complemented
5#10622616C211yesmaximal, characteristic, complemented
6#10622499C211yesmaximal, characteristic, complemented
7#10622495C211yesmaximal, characteristic, complemented
8#10622478C211yesmaximal, characteristic, complemented
9#10622475C211yesmaximal, characteristic, complemented
10#10622395C211yesmaximal, characteristic, complemented
11#10622393C211yesmaximal, characteristic, complemented
12#10622389C211yesmaximal, characteristic, complemented
13#10622386C211yesmaximal, characteristic, complemented
14#10622347C211yesmaximal, characteristic, complemented
15#10622339C211yesmaximal, characteristic, complemented
16C2×D4×D11—21no—
17C2×D4×D11C2211yescharacteristic
18C2×#4339C2211yescharacteristic, complemented
19C22×C4×D11C2211yescharacteristic
20C11×#121C2211yescharacteristic
21C11×#117C2211yescharacteristic, complemented
22#66992—21no—
23#66991C2211yescharacteristic
24C2×#4324C2211yescharacteristic, complemented
25C2×#4323C2211yescharacteristic, complemented
26#66983C2211yescharacteristic
27C2×D88C2211yescharacteristic, complemented
28C2×#4314C2211yescharacteristic, complemented
29C2×#4313C2211yescharacteristic, complemented
30C2×#4313C2211yescharacteristic, complemented
31#66950C2211yescharacteristic
32#66950C2211yescharacteristic, complemented
33#66948C2211yescharacteristic
34#66948C2211yescharacteristic
35#66948C2211yescharacteristic, complemented
36C4⋊C4×D11C2211yescharacteristic
37#66939—21no—
38#66937—21no—
39#66935—21no—
40C22⋊C4×D11—21no—
41C4×D44—21no—
42C4×D44—21no—
43C11×#107C2211yescharacteristic, complemented
44C11×#106C2211yescharacteristic, complemented
45C11×#102C2211yescharacteristic, complemented
46C11×#102C2211yescharacteristic, complemented
47C11×C22⋊C8C2211yescharacteristic, complemented
48C22⋊(C11⋊C8)C2211yescharacteristic, complemented
49#66885C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66880C2211yescharacteristic, complemented
53#66874C2211yescharacteristic, complemented
54#66873C2211yescharacteristic, complemented
55#66873C2211yescharacteristic, complemented
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, 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—
67C2×C22⋊D11—21no—
68C22×Dic11D411yescharacteristic
69D4×D11—41no—
70D4×D11—41no—
71D4×D11—44no—
72#4339—41no—
73#4339—41no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44C2311yescharacteristic
78C2×D44C2311yescharacteristic
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11D411yescharacteristic
84C2×C4×D11D411yescharacteristic
85C2×C4×D11C2311yescharacteristic
86C2×C4×D11C2311yescharacteristic
87C2×Dic22C2311yescharacteristic
88C2×C8×C11C2311yescharacteristic
89C2×C8×C11C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C4⋊C4C2311yescharacteristic
92C11×C4⋊C4C2311yescharacteristic
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C42×C11—21no—
96C22⋊Dic11—21no—
97#4324—41no—
98#4323—41no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11C2311yescharacteristic
108Dic11⋊C4—21no—
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111D88—41no—
112#4314—41no—
113#4313—41no—
114#4313—41no—
115#3194—111nomaximal, Sylow
116C23×C11—21no—
117C23×C11C2×D411yescharacteristic
118C22×D11—22no—
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—42no—
124C22×D11—42no—
125C22×D11—42no—
126C22×D11C2×D411yescharacteristic
127C22×D11C2×D411yescharacteristic
128D4×C11—21no—
129D4×C11—21no—
130D4×C11—42no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2411yescharacteristic
138C22⋊D11—42no—
139C22⋊D11—42no—
140C22⋊D11—42no—
141C22⋊D11—42no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—41no—
145C2×Dic11C2×D411yescharacteristic
146C2×Dic11C2×D411yescharacteristic
147D44—21no—
148D44—21no—
149D44—21no—
150D44—21no—
151D44—42no—
152D44—42no—
153D44—42no—
154C4×D11—21no—
155C4×D11—21no—
156C4×D11—21no—
157C4×D11—21no—
158C4×D11—41no—
159C4×D11—41no—
160C4×D11—42no—
161C4×D11—42no—
162Dic22—21no—
163Dic22—21no—
164C8×C11—21no—
165C8×C11—21no—
166C11⋊C8—21no—
167C11⋊C8—21no—
168#525—111no—
169C2×#121—111no—
170#483—111no—
171#482—111no—
172#482D1111yescharacteristic, complemented
173#480—111no—
174#469—111no—
175#469—111no—
176#468—111no—
177#468—111no—
178#450—111no—
179#449—111no—
180#449—111no—
181#447—111no—
182#407—111no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11C22×D411yescharacteristic
190C2×D11—21no—
191C2×D11—21no—
192C2×D11—21no—
193C2×D11—21no—
194C2×D11—21no—
195C2×D11—44no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—84no—
203C2×D11AGL(1,ℤ/8)12yes—
204C4×C11—21no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11H(5,𝔽2)11yescharacteristic
209C4×C11H(5,𝔽2)11yescharacteristic
210Dic11—21no—
211Dic11—21no—
212Dic11—41no—
213Dic11—41no—
214C2×#41—111no—
215C22×D4—111no—
216C22×D4—221no—
217C23×C4—111no—
218C2×SD16—111no—
219C2×SD16—111no—
220C2×D8—111no—
221C2×D8—111no—
222C2×M16—111no—
223C2×M16—111no—
224#123—221no—
225C22⋊Q8—111no—
226C22⋊Q8—111no—
227#121—111no—
228#121—111no—
229#121—111no—
230#121—111no—
231#121—111no—
232#121—221no—
233#121—221no—
234#121C2×D1111yescharacteristic
235#120—221no—
236C4×D4—221no—
237C4×D4—221no—
238#117C2×D1111yescharacteristic, complemented
239C2×C4⋊C4—111no—
240C2×C22⋊C4—221no—
241#107—111no—
242#107C2×D1111yescharacteristic, complemented
243#106—111no—
244#106C2×D1111yescharacteristic, complemented
245#103—111no—
246#103—111no—
247#102—111no—
248#102—111no—
249#102—111no—
250#102—111no—
251#102C2×D1111yescharacteristic, complemented
252#102C2×D1111yescharacteristic, complemented
253C22⋊C8—111no—
254C22⋊C8—111no—
255C22⋊C8—111no—
256C22⋊C8C2×D1111yescharacteristic, complemented
257C2×C11—41no—
258C2×C11—81no—
259C2×C11#53411yescharacteristic
260C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C2×C11#57511yescharacteristic
262D11—22no—
263D11—41no—
264D11—81no—
265D11—81no—
266C24—111no—
267C24—221no—
268#41—441no—
269#41—441no—
270C2×Q8—111no—
271C2×D4—21no—
272C2×D4—111no—
273C2×D4—111no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—441no—
282C2×D4—441no—
283C2×D4—444no—
284C2×D4C22×D1111yescharacteristic
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4C22×D1111yescharacteristic
295SD16—441no—
296SD16—441no—
297D8—441no—
298D8—441no—
299M16—441no—
300M16—441no—
301C2×C8—111no—
302C2×C8—111no—
303C2×C8C22×D1111yescharacteristic
304C2×C8C22×D1111yescharacteristic
305C4⋊C4—111no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4C22×D1111yescharacteristic
310C4⋊C4C22×D1111yescharacteristic
311C4⋊C4C22×D1111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C22⋊C4—221no—
319C22⋊C4—221no—
320C22⋊C4—221no—
321C42—21no—
322C11#319411yescharacteristic, complemented, Sylow
323C23—21no—
324C23—111no—
325C23—111no—
326C23—222no—
327C23—221no—
328C23—221no—
329C23—441no—
330C23—441no—
331C23—442no—
332C23—442no—
333C23—442no—
334C23D4×D1111yescharacteristic
335Q8—221no—
336Q8—221no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—221no—
341D4—221no—
342D4—221no—
343D4—221no—
344D4—442no—
345D4—442no—
346D4—442no—
347D4—442no—
348D4—442no—
349D4—442no—
350D4—442no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—111no—
357C2×C4—111no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—441no—
369C2×C4D4×D1111yescharacteristic
370C2×C4C23×D1111yescharacteristic
371C8—21no—
372C8—21no—
373C8—221no—
374C8—221no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—112no—
382C22—221no—
383C22—221no—
384C22—221no—
385C22—221no—
386C22—221no—
387C22—444no—
388C22—441no—
389C22—441no—
390C22—441no—
391C22—441no—
392C22—441no—
393C22—441no—
394C22—884no—
395C22C2×D4×D1111yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—221no—
401C4—221no—
402C4—441no—
403C4—441no—
404C4#6704211yescharacteristic
405C4#6704211yescharacteristic
406C2—41no—
407C2—81no—
408C2—222no—
409C2—441no—
410C2—881no—
411C2—881no—
412C2#1062318411yescharacteristic
413C2#1062329911yescharacteristic
414C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#482C2
socleC22×C11C22×D4
hypercenter#482D11
hypocenterC11#3194
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
1. D11×#121C2semidirect
2. #10623055C2semidirect
3. C11×#482C2semidirect
4. #10622650C2semidirect
5. #10622616C2semidirect
6. #10622499C2semidirect
7. #10622495C2semidirect
8. #10622478C2semidirect
9. #10622475C2semidirect
10. #10622395C2semidirect
11. #10622393C2semidirect
12. #10622389C2semidirect
13. #10622386C2semidirect
14. #10622347C2semidirect
15. #10622339C2semidirect
18. C2×#4339C22semidirect
21. C11×#117C22semidirect
24. C2×#4324C22semidirect
25. C2×#4323C22semidirect
27. C2×D88C22semidirect
28. C2×#4314C22semidirect
29. C2×#4313C22semidirect
30. C2×#4313C22semidirect
32. #66950C22semidirect
35. #66948C22semidirect
43. C11×#107C22semidirect
44. C11×#106C22semidirect
45. C11×#102C22semidirect
46. C11×#102C22semidirect
47. C11×C22⋊C8C22semidirect
48. C22⋊(C11⋊C8)C22semidirect
49. #66885C22semidirect
52. #66880C22semidirect
53. #66874C22semidirect
54. #66873C22semidirect
55. #66873C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
172. #482D11semidirect
238. #117C2×D11semidirect
242. #107C2×D11semidirect
244. #106C2×D11semidirect
251. #102C2×D11semidirect
252. #102C2×D11semidirect
256. C22⋊C8C2×D11semidirect
322. C11#3194semidirect

Maximal subgroups

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

subgroupindex
D11×#1212
#106230552
C11×#4822
#106226502
#106226162
#106224992
#106224952
#106224782
#106224752
#106223952
#106223932
#106223892
#106223862
#106223472
#106223392
#319411