Finite Group Databasebeta

← #13080766

Subgroups — #13080766

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
1C11×#555C211yesmaximal, characteristic, complemented
2#10623081C211yesmaximal, characteristic, complemented
3#10622702C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic, complemented
5#10622655C211yesmaximal, characteristic, complemented
6#10622651C211yesmaximal, characteristic, complemented
7#10622650C211yesmaximal, characteristic, complemented
8#10622649C211yesmaximal, characteristic, complemented
9#10622629C211yesmaximal, characteristic, complemented
10#10622627C211yesmaximal, 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×#124—21no—
20C11×#124—21no—
21C11×#121—21no—
22C11×#121C2211yescharacteristic
23C11×#121C2211yescharacteristic, complemented
24C4×D4×C11C2211yescharacteristic
25C4×D4×C11C2211yescharacteristic, complemented
26C11×#117—21no—
27C11×#117C2211yescharacteristic
28C11×#117C2211yescharacteristic, complemented
29#66990—21no—
30C2×#4324C2211yescharacteristic, complemented
31C2×#4323C2211yescharacteristic
32C2×#4323C2211yescharacteristic
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#66896C2211yescharacteristic, 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#66871C2211yescharacteristic, complemented
56#66871C2211yescharacteristic, complemented
57C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11D411yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70#4339—22no—
71#4339—41no—
72C2×D44—22no—
73C2×D44—21no—
74C2×D44—41no—
75C2×D44C2311yescharacteristic
76C2×D44C2311yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×Dic22C2311yescharacteristic
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⋊C4—21no—
90C11×C22⋊C4D411yescharacteristic
91C11×C22⋊C4D411yescharacteristic
92C42×C11—21no—
93C42×C11—21no—
94C42×C11C2311yescharacteristic
95C22⋊Dic11—21no—
96#4324—41no—
97#4323—22no—
98#4323—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#3319—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C23×C11C2×D411yescharacteristic
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—42no—
118C22×D11—42no—
119C22×D11—81no—
120Q8×C11—81no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—41no—
124D4×C11—81no—
125D4×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2411yescharacteristic
139C22⋊D11—42no—
140C22⋊D11—81no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143D44—21no—
144D44—21no—
145D44—21no—
146D44—42no—
147D44#4112yes—
148C4×D11—42no—
149C4×D11—81no—
150Dic22—21no—
151Dic22—21no—
152C11⋊C8—21no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#555D1111yescharacteristic, complemented
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#416—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11C22×D411yescharacteristic
181C2×D11—22no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—84no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11C2×#4111yescharacteristic
196C4×C11H(5,𝔽2)11yescharacteristic
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C22×D4—111no—
201C2×SD16—111no—
202C2×D8—111no—
203C2×D8—111no—
204C2×M16—111no—
205C22×C8—111no—
206C4⋊Q8C2×D1111yescharacteristic, complemented
207#124—21no—
208#124—21no—
209#124—111no—
210#123—221no—
211C22⋊Q8—111no—
212#121—21no—
213#121—111no—
214#121—221no—
215#121C2×D1111yescharacteristic
216#121C2×D1111yescharacteristic, complemented
217#120—221no—
218C4×D4—111no—
219C4×D4C2×D1111yescharacteristic
220C4×D4C2×D1111yescharacteristic, complemented
221#117—21no—
222#117C2×D1111yescharacteristic
223#117C2×D1111yescharacteristic, complemented
224C2×C22⋊C4—221no—
225#107—111no—
226#107—111no—
227#106—111no—
228C4⋊C8—111no—
229#103—111no—
230#103—111no—
231#103—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102—111no—
239C22⋊C8—111no—
240C22⋊C8—111no—
241#97—111no—
242C2×C11—41no—
243C2×C11—41no—
244C2×C11—81no—
245C2×C11#54611yescharacteristic
246C2×C11#57511yescharacteristic
247C2×C11#57611yescharacteristic
248D11—42no—
249D11—81no—
250C24—221no—
251#41—222no—
252#41—441no—
253C2×Q8—21no—
254C2×Q8—111no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—111no—
258C2×D4—111no—
259C2×D4—222no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—441no—
264C2×D4C22⋊D1111yescharacteristic
265C2×D4C22×D1111yescharacteristic
266C22×C4—21no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4C22×D1111yescharacteristic
270C22×C4C22×D1111yescharacteristic
271SD16—441no—
272D8—222no—
273D8—441no—
274M16—441no—
275C2×C8—111no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8—111no—
279C2×C8—441no—
280C4⋊C4—21no—
281C4⋊C4—111no—
282C4⋊C4—221no—
283C4⋊C4C22⋊D1111yescharacteristic
284C4⋊C4C22×D1111yescharacteristic
285C4⋊C4C22×D1111yescharacteristic
286C4⋊C4C22×D1111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4C22⋊D1111yescharacteristic
298C22⋊C4C22⋊D1111yescharacteristic
299C42—21no—
300C42—21no—
301C42C22×D1111yescharacteristic
302C11#331911yescharacteristic, complemented, Sylow
303C23—21no—
304C23—221no—
305C23—221no—
306C23—442no—
307C23—442no—
308C23—881no—
309C23C2×C22⋊D1111yescharacteristic
310C23C2×C22⋊D1111yescharacteristic
311Q8—81no—
312Q8—221no—
313Q8—221no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—81no—
318D4—81no—
319D4—112no—
320D4—221no—
321D4—221no—
322D4—221no—
323D4—442no—
324D4—442no—
325D4—881no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—442no—
337C2×C4—881no—
338C2×C4C2×C22⋊D1111yescharacteristic
339C2×C4C2×C22⋊D1111yescharacteristic
340C2×C4C2×C22⋊D1111yescharacteristic
341C2×C4C2×C22⋊D1111yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—221no—
344C8—221no—
345C8—221no—
346C8—221no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—222no—
357C22—441no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22—441no—
362C22—884no—
363C22C22×C22⋊D1111yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—441no—
372C4—441no—
373C4#41×D1111yescharacteristic
374C4#6704211yescharacteristic
375C2—41no—
376C2—41no—
377C2—81no—
378C2—442no—
379C2—881no—
380C2#1062335311yescharacteristic
381C2#1062336011yescharacteristic
382C2#1062336611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#555C2
socleC22×C11C22×D4
hypercenter#555D11
hypocenterC11#3319
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. C11×#555C2semidirect
2. #10623081C2semidirect
3. #10622702C2semidirect
4. #10622700C2semidirect
5. #10622655C2semidirect
6. #10622651C2semidirect
7. #10622650C2semidirect
8. #10622649C2semidirect
9. #10622629C2semidirect
10. #10622627C2semidirect
11. #10622624C2semidirect
12. #10622616C2semidirect
13. #10622615C2semidirect
14. #10622614C2semidirect
15. #10622609C2semidirect
18. C11×C4⋊Q8C22semidirect
23. C11×#121C22semidirect
25. C4×D4×C11C22semidirect
28. C11×#117C22semidirect
30. C2×#4324C22semidirect
36. C22×C11⋊C8C22semidirect
42. #66896C22semidirect
44. C22⋊(C11⋊C8)C22semidirect
45. #66874C22semidirect
46. #66874C22semidirect
47. #66874C22semidirect
54. #66872C22semidirect
55. #66871C22semidirect
56. #66871C22semidirect
57. C4⋊(C11⋊C8)C22semidirect
58. #66867C22semidirect
156. #555D11semidirect
206. C4⋊Q8C2×D11semidirect
216. #121C2×D11semidirect
220. C4×D4C2×D11semidirect
223. #117C2×D11semidirect
302. C11#3319semidirect

Maximal subgroups

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

subgroupindex
C11×#5552
#106230812
#106227022
#106227002
#106226552
#106226512
#106226502
#106226492
#106226292
#106226272
#106226242
#106226162
#106226152
#106226142
#106226092
#331911