Finite Group Databasebeta

← #13080576

Subgroups — #13080576

Order 1408.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623257C211yesmaximal, characteristic, complemented
2#10623207C211yesmaximal, characteristic, complemented
3C11×#489C211yesmaximal, characteristic, complemented
4#10622697C211yesmaximal, characteristic, complemented
5#10622670C211yesmaximal, characteristic, complemented
6#10622424C211yesmaximal, characteristic, complemented
7#10622420C211yesmaximal, characteristic, complemented
8#10622418C211yesmaximal, characteristic, complemented
9#10622416C211yesmaximal, characteristic, complemented
10#10622395C211yesmaximal, characteristic, complemented
11#10622390C211yesmaximal, characteristic, complemented
12#10622386C211yesmaximal, characteristic, complemented
13D11×#102C211yesmaximal, characteristic, complemented
14#10622324C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C2×#4343—21no—
17C2×#4343C2211yescharacteristic
18C2×D4×D11C2211yescharacteristic
19C11×C4⋊Q8C2211yescharacteristic, complemented
20C11×#124C2211yescharacteristic
21#66999—21no—
22#66999C2211yescharacteristic
23C2×#4325C2211yescharacteristic, complemented
24#66991C2211yescharacteristic
25C2×#4323C2211yescharacteristic
26C2×D88C2211yescharacteristic
27C2×#4313C2211yescharacteristic, complemented
28C2×C8×D11C2211yescharacteristic
29#66948C2211yescharacteristic
30#66948C2211yescharacteristic, complemented
31#66947—21no—
32#66947—21no—
33C4⋊C4×D11C2211yescharacteristic
34C4⋊C4×D11C2211yescharacteristic, complemented
35#66937—21no—
36#66936—21no—
37#66935—21no—
38C22⋊C4×D11—21no—
39C4×D44C2211yescharacteristic
40C4×D44C2211yescharacteristic
41C4×D44C2211yescharacteristic, complemented
42C11×#103C2211yescharacteristic, complemented
43C11×#103C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C11×#97C2211yescharacteristic, complemented
47#66899C2211yescharacteristic, complemented
48#66896C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic, complemented
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53#66881C2211yescharacteristic, complemented
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65#4343—22no—
66#4343—41no—
67#4343—44no—
68D4×D11—22no—
69D4×D11—41no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44D411yescharacteristic
74C2×D44C2311yescharacteristic
75C2×D44C2311yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11C2311yescharacteristic
82C2×C4×D11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C11×C4⋊C4—21no—
86C11×C4⋊C4C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C22⋊C4—21no—
89C11×C22⋊C4—21no—
90C42×C11C2311yescharacteristic
91C22⋊Dic11—21no—
92#4325—41no—
93#4323—41no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4D411yescharacteristic
100(C2×D11)⋊C4D411yescharacteristic
101C4⋊Dic11D411yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103C4⋊Dic11C2311yescharacteristic
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109D88—22no—
110#4313—41no—
111C8×D11—41no—
112#3306—111nomaximal, Sylow
113C23×C11—21no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—81no—
119C22×D11C2×D411yescharacteristic
120C22×D11C2×D411yescharacteristic
121Q8×C11—21no—
122Q8×C11—21no—
123Q8×C11—42no—
124D4×C11—21no—
125D4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—42no—
133C22⋊D11—81no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138D44—22no—
139D44—21no—
140D44—21no—
141D44—21no—
142D44—42no—
143D44—42no—
144D44—42no—
145D44#4112yescomplemented
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—21no—
149C4×D11—21no—
150C4×D11—42no—
151C4×D11—42no—
152C4×D11—42no—
153C4×D11—42no—
154C4×D11—81no—
155C8×C11—21no—
156C8×C11—21no—
157C11⋊C8—21no—
158C11⋊C8—21no—
159#547—111no—
160#546—111no—
161#489D1111yescharacteristic, complemented
162#483—111no—
163#481—111no—
164#476—111no—
165#469—111no—
166#465—111no—
167#463—111no—
168#449—111no—
169#447—111no—
170#442—111no—
171#435—111no—
172#417—111no—
173C2×#102—111no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—22no—
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—84no—
190C2×D11AGL(1,ℤ/8)12yes—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11C2×#4111yescharacteristic
197C4×C11H(5,𝔽2)11yescharacteristic
198Dic11—21no—
199Dic11—21no—
200Dic11—41no—
201Dic11—41no—
202C2×#41—111no—
203C2×#41—221no—
204C22×D4—111no—
205C2×SD16—111no—
206C2×D8—111no—
207C2×D8—111no—
208C2×M16—111no—
209C22×C8—111no—
210C4⋊Q8C2×D1111yescharacteristic, complemented
211#124C2×D1111yescharacteristic
212#123—221no—
213#123—221no—
214#123—221no—
215C22⋊Q8—111no—
216C22⋊Q8—221no—
217#121—111no—
218#121—111no—
219#121—111no—
220#121—221no—
221#120—221no—
222C4×D4—111no—
223C4×D4—111no—
224C4×D4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C22⋊C4—221no—
228#106—111no—
229#106—111no—
230#106—111no—
231C4⋊C8—111no—
232#103—111no—
233#103C2×D1111yescharacteristic, complemented
234#103C2×D1111yescharacteristic, complemented
235#102—111no—
236#102—111no—
237#102—111no—
238#102—111no—
239#102—111no—
240#102C2×D1111yescharacteristic
241#102C2×D1111yescharacteristic
242C22⋊C8—111no—
243C22⋊C8—111no—
244#97C2×D1111yescharacteristic, complemented
245C2×C11—81no—
246C2×C11#54611yescharacteristic
247C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
248C2×C11#57711yescharacteristic
249D11—22no—
250D11—41no—
251D11—42no—
252D11—81no—
253C24—221no—
254#41—222no—
255#41—441no—
256#41—444no—
257C2×Q8—21no—
258C2×Q8C22×D1111yescharacteristic
259C2×D4—111no—
260C2×D4—111no—
261C2×D4—111no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—222no—
267C2×D4—221no—
268C2×D4—441no—
269C2×D4C22×D1111yescharacteristic
270C22×C4—111no—
271C22×C4—111no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277SD16—441no—
278D8—222no—
279D8—441no—
280M16—441no—
281C2×C8—111no—
282C2×C8—111no—
283C2×C8—441no—
284C2×C8C22×D1111yescharacteristic
285C2×C8C22×D1111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—111no—
288C4⋊C4—111no—
289C4⋊C4—111no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4C22×D1111yescharacteristic
294C4⋊C4C22×D1111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—111no—
298C22⋊C4—111no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C42C22×D1111yescharacteristic
306C11#330611yescharacteristic, complemented, Sylow
307C23—21no—
308C23—111no—
309C23—111no—
310C23—221no—
311C23—221no—
312C23—442no—
313C23—442no—
314C23—881no—
315Q8—21no—
316Q8—21no—
317Q8—42no—
318D4—21no—
319D4—21no—
320D4—112no—
321D4—222no—
322D4—221no—
323D4—221no—
324D4—221no—
325D4—442no—
326D4—442no—
327D4—442no—
328D4—442no—
329D4—881no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—111no—
334C2×C4—111no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—881no—
346C2×C4D4×D1111yescharacteristic
347C2×C4D4×D1111yescharacteristic
348C2×C4C23×D1111yescharacteristic
349C8—21no—
350C8—21no—
351C8—221no—
352C8—221no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—112no—
357C22—221no—
358C22—221no—
359C22—221no—
360C22—221no—
361C22—221no—
362C22—222no—
363C22—441no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22—884no—
369C22C2×D4×D1111yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—221no—
376C4—221no—
377C4—441no—
378C4—441no—
379C4#41×D1111yescharacteristic
380C4#6704211yescharacteristic
381C2—81no—
382C2—222no—
383C2—441no—
384C2—442no—
385C2—881no—
386C2#1062320711yescharacteristic
387C2D11×AGL(1,ℤ/8)11yescharacteristic
388C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#489C2
socleC22×C11C22×D4
hypercenter#489D11
hypocenterC11#3306
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #10623257C2semidirect
2. #10623207C2semidirect
3. C11×#489C2semidirect
4. #10622697C2semidirect
5. #10622670C2semidirect
6. #10622424C2semidirect
7. #10622420C2semidirect
8. #10622418C2semidirect
9. #10622416C2semidirect
10. #10622395C2semidirect
11. #10622390C2semidirect
12. #10622386C2semidirect
13. D11×#102C2semidirect
14. #10622324C2semidirect
15. #10622319C2semidirect
19. C11×C4⋊Q8C22semidirect
23. C2×#4325C22semidirect
27. C2×#4313C22semidirect
30. #66948C22semidirect
34. C4⋊C4×D11C22semidirect
41. C4×D44C22semidirect
42. C11×#103C22semidirect
43. C11×#103C22semidirect
46. C11×#97C22semidirect
47. #66899C22semidirect
50. #66885C22semidirect
52. (C2×D11)⋊C8C22semidirect
53. #66881C22semidirect
56. #66872C22semidirect
57. #66872C22semidirect
58. C4⋊(C11⋊C8)C22semidirect
145. D44#41semidirect
161. #489D11semidirect
210. C4⋊Q8C2×D11semidirect
233. #103C2×D11semidirect
234. #103C2×D11semidirect
244. #97C2×D11semidirect
306. C11#3306semidirect

Maximal subgroups

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

subgroupindex
#106232572
#106232072
C11×#4892
#106226972
#106226702
#106224242
#106224202
#106224182
#106224162
#106223952
#106223902
#106223862
D11×#1022
#106223242
#106223192
#330611