Finite Group Databasebeta

← #13080768

Subgroups — #13080768

Order 1408.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623360C211yesmaximal, characteristic, complemented
2#10623063C211yesmaximal, characteristic, complemented
3C11×#416C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic, complemented
5#10622728C211yesmaximal, characteristic, complemented
6#10622724C211yesmaximal, characteristic, complemented
7#10622616C211yesmaximal, characteristic, complemented
8#10622432C211yesmaximal, characteristic, complemented
9#10622427C211yesmaximal, characteristic, complemented
10#10622425C211yesmaximal, characteristic, complemented
11#10622408C211yesmaximal, characteristic, complemented
12#10622398C211yesmaximal, characteristic, complemented
13#10622386C211yesmaximal, characteristic, complemented
14#10622383C211yesmaximal, characteristic, complemented
15#10622372C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C22×C8×C11C2211yescharacteristic, complemented
19C11×#117C2211yescharacteristic, complemented
20#67000C2211yescharacteristic
21#66999C2211yescharacteristic
22C2×#4325C2211yescharacteristic, complemented
23#66992—21no—
24#66990—21no—
25D4×Dic11C2211yescharacteristic
26C2×#4323C2211yescharacteristic
27#66983C2211yescharacteristic
28#66983C2211yescharacteristic, complemented
29#66982—21no—
30C4×C22⋊D11C2211yescharacteristic
31C2×(C2×D11)⋊C4—21no—
32C2×D88C2211yescharacteristic
33C2×#4313C2211yescharacteristic
34#66948C2211yescharacteristic
35#66946C2211yescharacteristic, complemented
36#66945C2211yescharacteristic
37#66941C2211yescharacteristic, complemented
38#66938—21no—
39#66937—21no—
40#66928—21no—
41#66925—21no—
42C11×#103C2211yescharacteristic, complemented
43C11×#103C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic, complemented
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic, complemented
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic, complemented
51(C2×D11)⋊C8C2211yescharacteristic
52#66882C2211yescharacteristic, complemented
53#66879C2211yescharacteristic, complemented
54Dic11⋊C8C2211yescharacteristic, complemented
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11—21no—
60C11×#41—22no—
61C11×#41—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11D411yescharacteristic
71C22×Dic11—21no—
72D4×D11—22no—
73D4×D11—41no—
74C2×D44—21no—
75C2×D44C2311yescharacteristic
76C2×D44C2311yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22—21no—
80C2×C8×C11—41no—
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C42×C11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11D411yescharacteristic
89#4325—41no—
90#4323—22no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
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
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109D88—41no—
110#4313—41no—
111#3319—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—81no—
119C22×D11C2×D411yescharacteristic
120Q8×C11—21no—
121Q8×C11—21no—
122D4×C11—21no—
123D4×C11—42no—
124D4×C11#4112yes—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—42no—
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2411yescharacteristic
133C22⋊D11—41no—
134C22⋊D11—42no—
135C22⋊D11—81no—
136C22⋊D11—81no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—81no—
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143D44—21no—
144D44—21no—
145D44—21no—
146D44—21no—
147D44—81no—
148C4×D11—21no—
149C4×D11—21no—
150C4×D11—42no—
151Dic22—81no—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#555—111no—
157#546—111no—
158#489—111no—
159#485—111no—
160#482—111no—
161#474—111no—
162#468—111no—
163#466—111no—
164#463—111no—
165#449—111no—
166#447—111no—
167#442—111no—
168#435—111no—
169#418—111no—
170#416D1111yescharacteristic, complemented
171C22×C11—21no—
172C22×C11—22no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—84no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11C2×#4111yescharacteristic
193C4×C11H(5,𝔽2)11yescharacteristic
194Dic11—21no—
195Dic11—21no—
196Dic11—21no—
197Dic11—41no—
198Dic11—41no—
199C2×#41C2×D1111yescharacteristic
200C22×D4—111no—
201C2×SD16—111no—
202C2×D8—111no—
203C2×D8—111no—
204C2×M16—111no—
205C22×C8C2×D1111yescharacteristic, complemented
206C4⋊Q8—111no—
207#124—111no—
208#124—221no—
209#124—221no—
210#123—221no—
211C22⋊Q8—111no—
212#121—111no—
213#121—111no—
214#121—111no—
215#121—221no—
216#121—221no—
217#120—221no—
218C4×D4—111no—
219C4×D4—111no—
220C4×D4—111no—
221#117—111no—
222#117—221no—
223#117C2×D1111yescharacteristic, complemented
224C2×C22⋊C4—221no—
225#107—111no—
226#107—111no—
227#106—111no—
228C4⋊C8—111no—
229#103—111no—
230#103C2×D1111yescharacteristic, complemented
231#103C2×D1111yescharacteristic, complemented
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102C2×D1111yescharacteristic
238#102C2×D1111yescharacteristic
239C22⋊C8—111no—
240C22⋊C8—111no—
241#97—111no—
242C2×C11—42no—
243C2×C11—41no—
244C2×C11#54611yescharacteristic
245C2×C11#57511yescharacteristic
246C2×C11#57611yescharacteristic
247D11—41no—
248D11—81no—
249D11—81no—
250C24—221no—
251#41—22no—
252#41—41no—
253C2×Q8—221no—
254C2×Q8C22×D1111yescharacteristic
255C2×D4—21no—
256C2×D4—111no—
257C2×D4—111no—
258C2×D4—111no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—222no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—441no—
265C2×D4C22×D1111yescharacteristic
266C22×C4—21no—
267C22×C4—111no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4C22×D1111yescharacteristic
271SD16—441no—
272D8—222no—
273D8—441no—
274M16—441no—
275C2×C8—41no—
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⋊C4C22×D1111yescharacteristic
286C4⋊C4C22×D1111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—111no—
289C22⋊C4—111no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C42—21no—
300C42—111no—
301C42—221no—
302C11#331911yescharacteristic, complemented, Sylow
303C23—21no—
304C23—111no—
305C23—221no—
306C23—221no—
307C23—442no—
308C23—442no—
309C23—881no—
310C23D4×D1111yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—881no—
314D4—21no—
315D4—42no—
316D4—221no—
317D4—221no—
318D4—221no—
319D4—221no—
320D4—441no—
321D4—442no—
322D4—881no—
323D4—881no—
324D4—881no—
325D4#433912yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—111no—
333C2×C4—111no—
334C2×C4—111no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—442no—
340C2×C4—881no—
341C2×C4D4×D1111yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—221no—
346C8—221no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—221no—
354C22—221no—
355C22—221no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22—441no—
362C22—884no—
363C22C2×D4×D1111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—221no—
369C4—221no—
370C4—221no—
371C4—441no—
372C4—441no—
373C4C2×#433911yescharacteristic
374C4#6703711yescharacteristic
375C2—41no—
376C2—42no—
377C2—441no—
378C2—881no—
379C2—881no—
380C2#1062302111yescharacteristic
381C2#1062329911yescharacteristic
382C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#416C2
socleC22×C11C22×D4
hypercenter#416D11
hypocenterC11#3319
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #10623360C2semidirect
2. #10623063C2semidirect
3. C11×#416C2semidirect
4. #10622851C2semidirect
5. #10622728C2semidirect
6. #10622724C2semidirect
7. #10622616C2semidirect
8. #10622432C2semidirect
9. #10622427C2semidirect
10. #10622425C2semidirect
11. #10622408C2semidirect
12. #10622398C2semidirect
13. #10622386C2semidirect
14. #10622383C2semidirect
15. #10622372C2semidirect
18. C22×C8×C11C22semidirect
19. C11×#117C22semidirect
22. C2×#4325C22semidirect
28. #66983C22semidirect
35. #66946C22semidirect
37. #66941C22semidirect
42. C11×#103C22semidirect
43. C11×#103C22semidirect
46. #66899C22semidirect
48. C22⋊(C11⋊C8)C22semidirect
50. #66885C22semidirect
52. #66882C22semidirect
53. #66879C22semidirect
54. Dic11⋊C8C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
170. #416D11semidirect
205. C22×C8C2×D11semidirect
223. #117C2×D11semidirect
230. #103C2×D11semidirect
231. #103C2×D11semidirect
302. C11#3319semidirect

Maximal subgroups

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

subgroupindex
#106233602
#106230632
C11×#4162
#106228512
#106227282
#106227242
#106226162
#106224322
#106224272
#106224252
#106224082
#106223982
#106223862
#106223832
#106223722
#331911