Finite Group Databasebeta

← #13080646

Subgroups — #13080646

Order 1408.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#556C211yesmaximal, characteristic, complemented
2#10623081C211yesmaximal, characteristic
3#10622702C211yesmaximal, characteristic, complemented
4#10622697C211yesmaximal, characteristic, complemented
5#10622665C211yesmaximal, characteristic, complemented
6#10622661C211yesmaximal, characteristic, complemented
7#10622660C211yesmaximal, characteristic, complemented
8#10622659C211yesmaximal, characteristic, complemented
9#10622641C211yesmaximal, characteristic, complemented
10#10622639C211yesmaximal, characteristic, complemented
11#10622624C211yesmaximal, characteristic, complemented
12#10622616C211yesmaximal, characteristic, complemented
13#10622615C211yesmaximal, characteristic, complemented
14#10622614C211yesmaximal, characteristic, complemented
15#10622609C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C11×C4⋊Q8C2211yescharacteristic, complemented
19C11×#126—21no—
20C11×#126—21no—
21C11×#124—21no—
22C11×C22⋊Q8C2211yescharacteristic
23C11×C22⋊Q8C2211yescharacteristic, complemented
24C4×Q8×C11—21no—
25C4×Q8×C11C2211yescharacteristic, complemented
26C4×D4×C11C2211yescharacteristic
27C11×#117C2211yescharacteristic
28C11×#117C2211yescharacteristic, complemented
29C2×#4326C2211yescharacteristic, complemented
30C2×#4325C2211yescharacteristic
31C2×#4325C2211yescharacteristic
32#66990—21no—
33#66983C2211yescharacteristic
34#66977C2211yescharacteristic
35C2×#4318C2211yescharacteristic
36C22×C11⋊C8C2211yescharacteristic, complemented
37#66947—21no—
38#66937—21no—
39C22⋊C4×D11—21no—
40#66928C2211yescharacteristic
41C4×D44C2211yescharacteristic
42#66899C2211yescharacteristic, complemented
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic, complemented
45#66874C2211yescharacteristic, complemented
46#66874C2211yescharacteristic, complemented
47#66874C2211yescharacteristic, complemented
48#66873C2211yescharacteristic
49#66873C2211yescharacteristic
50#66873C2211yescharacteristic
51#66873C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic, complemented
55#66872C2211yescharacteristic, complemented
56#66871C2211yescharacteristic, complemented
57C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11D411yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67#4339—22no—
68#4339—41no—
69C2×D44—22no—
70C2×D44—21no—
71C2×D44—41no—
72C2×D44C2311yescharacteristic
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×Dic22C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4D411yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C11×C22⋊C4—21no—
89C11×C22⋊C4D411yescharacteristic
90C11×C22⋊C4D411yescharacteristic
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—21no—
94C42×C11C2311yescharacteristic
95C22⋊Dic11—21no—
96#4326—41no—
97#4325—22no—
98#4325—41no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103C4⋊Dic11C2311yescharacteristic
104Dic11⋊C4—21no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#3311—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—81no—
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—42no—
122D4×C11—41no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2411yescharacteristic
136C22⋊D11—42no—
137C22⋊D11—81no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140D44—21no—
141D44—21no—
142D44—21no—
143D44—42no—
144D44#4112yes—
145C4×D11—42no—
146C4×D11—81no—
147Dic22—21no—
148Dic22—21no—
149C11⋊C8—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#556D1111yescharacteristic, complemented
154#546—111no—
155#489—111no—
156#485—111no—
157#482—111no—
158#476—111no—
159#470—111no—
160#465—111no—
161#464—111no—
162#452—111no—
163#450—111no—
164#440—111no—
165#435—111no—
166#418—111no—
167#416—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11C22×D411yescharacteristic
175C2×D11—22no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—84no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11C2×#4111yescharacteristic
191C4×C11H(5,𝔽2)11yescharacteristic
192Dic11—41no—
193Dic11—41no—
194C2×#41—111no—
195C22×D4—111no—
196C2×Q16—111no—
197C2×SD16—111no—
198C2×SD16—111no—
199C2×M16—111no—
200C22×C8—111no—
201C4⋊Q8C2×D1111yescharacteristic, complemented
202#126—21no—
203#126—21no—
204#124—21no—
205#124—111no—
206#123—221no—
207C22⋊Q8—111no—
208C22⋊Q8C2×D1111yescharacteristic
209C22⋊Q8C2×D1111yescharacteristic, complemented
210#121—111no—
211#121—221no—
212#120—221no—
213C4×Q8—21no—
214C4×Q8C2×D1111yescharacteristic, complemented
215C4×D4—111no—
216C4×D4C2×D1111yescharacteristic
217#117C2×D1111yescharacteristic
218#117C2×D1111yescharacteristic, complemented
219C2×C22⋊C4—221no—
220#107—111no—
221#106—111no—
222#106—111no—
223C4⋊C8—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#103—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102—111no—
233#102—111no—
234C22⋊C8—111no—
235C22⋊C8—111no—
236#97—111no—
237C2×C11—41no—
238C2×C11—41no—
239C2×C11#54611yescharacteristic
240C2×C11#57511yescharacteristic
241C2×C11#57711yescharacteristic
242D11—42no—
243D11—81no—
244C24—221no—
245#41—222no—
246#41—441no—
247C2×Q8—21no—
248C2×Q8—111no—
249C2×Q8C22×D1111yescharacteristic
250C2×D4—111no—
251C2×D4—111no—
252C2×D4—222no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—441no—
257C2×D4C22⋊D1111yescharacteristic
258C22×C4—221no—
259C22×C4—221no—
260C22×C4C22×D1111yescharacteristic
261C22×C4C22×D1111yescharacteristic
262Q16—441no—
263SD16—222no—
264SD16—441no—
265M16—441no—
266C2×C8—111no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8—441no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—111no—
276C4⋊C4—221no—
277C4⋊C4C22⋊D1111yescharacteristic
278C4⋊C4C22×D1111yescharacteristic
279C4⋊C4C22×D1111yescharacteristic
280C4⋊C4C22×D1111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4C22⋊D1111yescharacteristic
291C22⋊C4C22⋊D1111yescharacteristic
292C42—21no—
293C42—21no—
294C42—21no—
295C42C22×D1111yescharacteristic
296C11#331111yescharacteristic, complemented, Sylow
297C23—221no—
298C23—221no—
299C23—442no—
300C23—442no—
301C23—881no—
302C23C2×C22⋊D1111yescharacteristic
303C23C2×C22⋊D1111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—42no—
307Q8—221no—
308Q8—221no—
309D4—41no—
310D4—112no—
311D4—221no—
312D4—221no—
313D4—221no—
314D4—442no—
315D4—442no—
316D4—881no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—442no—
328C2×C4—881no—
329C2×C4C2×C22⋊D1111yescharacteristic
330C2×C4C2×C22⋊D1111yescharacteristic
331C2×C4C2×C22⋊D1111yescharacteristic
332C2×C4C2×C22⋊D1111yescharacteristic
333C2×C4C23×D1111yescharacteristic
334C8—221no—
335C8—221no—
336C8—221no—
337C8—221no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—222no—
345C22—441no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22—441no—
350C22—884no—
351C22C22×C22⋊D1111yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—441no—
361C4—441no—
362C4#41×D1111yescharacteristic
363C4#6704211yescharacteristic
364C2—41no—
365C2—41no—
366C2—442no—
367C2—881no—
368C2#1062335311yescharacteristic
369C2#1062336011yescharacteristic
370C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#556C2
socleC22×C11C22×D4
prime radical#10623081C2
hypercenter#556D11
hypocenterC11#3311
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C11×#556C2semidirect
3. #10622702C2semidirect
4. #10622697C2semidirect
5. #10622665C2semidirect
6. #10622661C2semidirect
7. #10622660C2semidirect
8. #10622659C2semidirect
9. #10622641C2semidirect
10. #10622639C2semidirect
11. #10622624C2semidirect
12. #10622616C2semidirect
13. #10622615C2semidirect
14. #10622614C2semidirect
15. #10622609C2semidirect
18. C11×C4⋊Q8C22semidirect
23. C11×C22⋊Q8C22semidirect
25. C4×Q8×C11C22semidirect
28. C11×#117C22semidirect
29. C2×#4326C22semidirect
36. C22×C11⋊C8C22semidirect
42. #66899C22semidirect
44. C22⋊(C11⋊C8)C22semidirect
45. #66874C22semidirect
46. #66874C22semidirect
47. #66874C22semidirect
54. #66872C22semidirect
55. #66872C22semidirect
56. #66871C22semidirect
57. C4⋊(C11⋊C8)C22semidirect
58. #66867C22semidirect
153. #556D11semidirect
201. C4⋊Q8C2×D11semidirect
209. C22⋊Q8C2×D11semidirect
214. C4×Q8C2×D11semidirect
218. #117C2×D11semidirect
296. C11#3311semidirect

Maximal subgroups

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

subgroupindex
C11×#5562
#106230812
#106227022
#106226972
#106226652
#106226612
#106226602
#106226592
#106226412
#106226392
#106226242
#106226162
#106226152
#106226142
#106226092
#331111