Finite Group Databasebeta

← #13079617

Subgroups — #13079617

Order 1408.

400 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#124C211yesmaximal, characteristic
2#10623109C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic, complemented
4#10622803C211yesmaximal, characteristic, complemented
5#10622799C211yesmaximal, characteristic, complemented
6#10622782C211yesmaximal, characteristic
7#10622780C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622641C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic, complemented
11#10622448C211yesmaximal, characteristic, complemented
12#10622421C211yesmaximal, characteristic, complemented
13#10622408C211yesmaximal, characteristic, complemented
14#10622389C211yesmaximal, characteristic
15#10622378C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic, complemented
19C2×C11×SD16C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C4×Q8×C11C2211yescharacteristic, complemented
22#67000C2211yescharacteristic
23#66999C2211yescharacteristic
24#66997C2211yescharacteristic, complemented
25C2×#4326C2211yescharacteristic, complemented
26C2×#4326C2211yescharacteristic, complemented
27C2×#4325C2211yescharacteristic
28#66989C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30C2×Dic44C2211yescharacteristic, complemented
31C2×#4314C2211yescharacteristic
32#66950C2211yescharacteristic
33#66949—21no—
34#66942—21no—
35#66941C2211yescharacteristic, complemented
36#66938—21no—
37#66938—21no—
38C22⋊C4×D11—21no—
39C22⋊C4×D11—21no—
40#66928C2211yescharacteristic
41#66925—21no—
42C42×D11C2211yescharacteristic
43C4×Dic22—21no—
44C4×Dic22C2211yescharacteristic, complemented
45C11×C4⋊C8C2211yescharacteristic, complemented
46C11×#103C2211yescharacteristic, complemented
47C11×#102C2211yescharacteristic
48#66899C2211yescharacteristic, complemented
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66880C2211yescharacteristic, complemented
54#66879C2211yescharacteristic, complemented
55#66879C2211yescharacteristic, complemented
56#66874C2211yescharacteristic, complemented
57#66873C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64Q8×D11—41no—
65Q8×D11—41no—
66D4×D11—41no—
67D4×D11—41no—
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11D411yescharacteristic
71C2×C4×D11D411yescharacteristic
72C2×C4×D11C2311yescharacteristic
73C2×Dic22—21no—
74C2×Dic22—21no—
75C2×Dic22C2311yescharacteristic
76C2×Dic22C2311yescharacteristic
77C11×Q16—41no—
78C11×SD16—41no—
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C42×C11—21no—
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89#4326—41no—
90#4326—41no—
91#4325—41no—
92#4324—41no—
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—
99C4⋊Dic11—21no—
100C4⋊Dic11C2311yescharacteristic
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C4×Dic11D411yescharacteristic
108C4×Dic11D411yescharacteristic
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112Dic44—41no—
113#4314—41no—
114#3215—111nomaximal, Sylow
115C23×C11—21no—
116C22×D11—21no—
117C22×D11—42no—
118C22×D11—42no—
119C22×D11—42no—
120C22×D11C2×D411yescharacteristic
121Q8×C11—21no—
122Q8×C11—21no—
123Q8×C11—21no—
124Q8×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2411yescharacteristic
133C22⋊D11—42no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140D44—21no—
141D44—21no—
142C4×D11—22no—
143C4×D11—21no—
144C4×D11—21no—
145C4×D11—41no—
146C4×D11—42no—
147Dic22—21no—
148Dic22—21no—
149Dic22—21no—
150Dic22—21no—
151Dic22—42no—
152Dic22—42no—
153C8×C11—21no—
154C8×C11—21no—
155C11⋊C8—21no—
156C11⋊C8—21no—
157#533—111no—
158C2×#124—111no—
159#497—111no—
160#497—111no—
161#489—111no—
162#489—111no—
163#464—111no—
164#464—111no—
165#464—111no—
166#464D1111yescharacteristic, complemented
167#451—111no—
168#451—111no—
169#450—111no—
170#450—111no—
171#432—111no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11C22×D411yescharacteristic
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—84no—
182C2×D11#13712yes—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11H(5,𝔽2)11yescharacteristic
189C4×C11H(5,𝔽2)11yescharacteristic
190Dic11—21no—
191Dic11—21no—
192Dic11—21no—
193Dic11—41no—
194Dic11—41no—
195Dic11—41no—
196C22×Q8—111no—
197C22×D4—111no—
198C2×Q16—111no—
199C2×Q16—111no—
200C2×Q16—111no—
201C2×Q16C2×D1111yescharacteristic, complemented
202C2×SD16—111no—
203C2×SD16—111no—
204C2×SD16—111no—
205C2×SD16C2×D1111yescharacteristic
206C4⋊Q8—111no—
207C4⋊Q8—111no—
208#125—221no—
209#124—111no—
210#124—111no—
211#124—111no—
212#124—221no—
213#124—221no—
214#124C2×D1111yescharacteristic
215C22⋊Q8—111no—
216C22⋊Q8—111no—
217C22⋊Q8—221no—
218C4×Q8—111no—
219C4×Q8—221no—
220C4×Q8C2×D1111yescharacteristic, complemented
221#117—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C42—111no—
225C4⋊C8—111no—
226C4⋊C8C2×D1111yescharacteristic, complemented
227#103—111no—
228#103—111no—
229#103—111no—
230#103C2×D1111yescharacteristic, complemented
231#102—111no—
232#102—111no—
233#102—111no—
234#102C2×D1111yescharacteristic
235C22⋊C8—111no—
236C22⋊C8—111no—
237#97—111no—
238#97—111no—
239C2×C11—81no—
240C2×C11#53511yescharacteristic
241C2×C11C2×#13711yescharacteristic
242C2×C11#57511yescharacteristic
243D11—22no—
244D11—81no—
245C24—221no—
246C2×Q8—111no—
247C2×Q8—111no—
248C2×Q8—221no—
249C2×Q8—221no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×Q8C22×D1111yescharacteristic
253C2×Q8C22×D1111yescharacteristic
254C2×D4—111no—
255C2×D4—221no—
256C2×D4—441no—
257C2×D4—441no—
258C2×D4C22×D1111yescharacteristic
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—221no—
263Q16—41no—
264Q16—441no—
265Q16—441no—
266Q16—441no—
267SD16—41no—
268SD16—441no—
269SD16—441no—
270SD16—441no—
271C2×C8—111no—
272C2×C8—111no—
273C2×C8C22×D1111yescharacteristic
274C2×C8C22×D1111yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—111no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4C22×D1111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C42—21no—
295C42—111no—
296C42—111no—
297C42—111no—
298C42—221no—
299C42C22×D1111yescharacteristic
300C11#321511yescharacteristic, complemented, Sylow
301C23—21no—
302C23—111no—
303C23—221no—
304C23—442no—
305C23—442no—
306C23—442no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—221no—
312Q8—221no—
313Q8—221no—
314Q8—221no—
315Q8—442no—
316Q8—442no—
317D4—21no—
318D4—21no—
319D4—221no—
320D4—221no—
321D4—442no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—111no—
326C2×C4—111no—
327C2×C4—111no—
328C2×C4—222no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—441no—
335C2×C4—442no—
336C2×C4D4×D1111yescharacteristic
337C2×C4D4×D1111yescharacteristic
338C2×C4C23×D1111yescharacteristic
339C8—21no—
340C8—21no—
341C8—221no—
342C8—221no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—112no—
347C22—221no—
348C22—221no—
349C22—441no—
350C22—441no—
351C22—441no—
352C22—884no—
353C22C2×D4×D1111yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—221no—
360C4—221no—
361C4—221no—
362C4—441no—
363C4—441no—
364C4—441no—
365C4#6703711yescharacteristic
366C4#6704211yescharacteristic
367C2—81no—
368C2—222no—
369C2—881no—
370C2#1062313811yescharacteristic
371C2#1062329911yescharacteristic
372C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radicalC2×D4×D11C22
hypercenter#464D11
hypocenterC11#3215
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #10623109C2semidirect
3. C11×#464C2semidirect
4. #10622803C2semidirect
5. #10622799C2semidirect
7. #10622780C2semidirect
8. #10622667C2semidirect
9. #10622641C2semidirect
10. #10622458C2semidirect
11. #10622448C2semidirect
12. #10622421C2semidirect
13. #10622408C2semidirect
15. #10622378C2semidirect
18. C2×C11×Q16C22semidirect
21. C4×Q8×C11C22semidirect
24. #66997C22semidirect
25. C2×#4326C22semidirect
26. C2×#4326C22semidirect
30. C2×Dic44C22semidirect
35. #66941C22semidirect
44. C4×Dic22C22semidirect
45. C11×C4⋊C8C22semidirect
46. C11×#103C22semidirect
48. #66899C22semidirect
53. #66880C22semidirect
54. #66879C22semidirect
55. #66879C22semidirect
56. #66874C22semidirect
58. C4⋊(C11⋊C8)C22semidirect
166. #464D11semidirect
201. C2×Q16C2×D11semidirect
220. C4×Q8C2×D11semidirect
226. C4⋊C8C2×D11semidirect
230. #103C2×D11semidirect
300. C11#3215semidirect

Maximal subgroups

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

subgroupindex
D11×#1242
#106231092
C11×#4642
#106228032
#106227992
#106227822
#106227802
#106226672
#106226412
#106224582
#106224482
#106224212
#106224082
#106223892
#106223782
#321511