Finite Group Databasebeta

← #13080821

Subgroups — #13080821

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#10623337C211yesmaximal, characteristic, complemented
2#10623145C211yesmaximal, characteristic, complemented
3C11×#447C211yesmaximal, characteristic, complemented
4#10622828C211yesmaximal, characteristic, complemented
5#10622772C211yesmaximal, characteristic, complemented
6#10622771C211yesmaximal, characteristic, complemented
7#10622766C211yesmaximal, characteristic, complemented
8D8×Dic11C211yesmaximal, characteristic, complemented
9#10622655C211yesmaximal, characteristic, complemented
10#10622387C211yesmaximal, characteristic, complemented
11#10622384C211yesmaximal, characteristic, complemented
12#10622381C211yesmaximal, characteristic, complemented
13#10622376C211yesmaximal, characteristic, complemented
14#10622342C211yesmaximal, characteristic, complemented
15#10622336C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×C11×D8C2211yescharacteristic
19C2×C11×D8C2211yescharacteristic
20C11×#121C2211yescharacteristic
21#67006—21no—
22C2×C22⋊Dic11—21no—
23#66992—21no—
24#66991—21no—
25#66991C2211yescharacteristic
26#66991C2211yescharacteristic, complemented
27#66989C2211yescharacteristic
28#66988—21no—
29#66988—21no—
30D4×Dic11C2211yescharacteristic
31D4×Dic11C2211yescharacteristic, complemented
32C2×#4324C2211yescharacteristic, complemented
33C4×C22⋊D11C2211yescharacteristic
34#66979C2211yescharacteristic
35#66977C2211yescharacteristic
36C2×#4318C2211yescharacteristic
37C2×#4313C2211yescharacteristic, complemented
38C4⋊C4×D11C2211yescharacteristic, complemented
39#66943C2211yescharacteristic, complemented
40(C22⋊D11)⋊C4—21no—
41#66932—21no—
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic, complemented
51#66882C2211yescharacteristic, complemented
52#66881C2211yescharacteristic, complemented
53#66880C2211yescharacteristic, complemented
54#66880C2211yescharacteristic, complemented
55Dic11⋊C8C2211yescharacteristic, complemented
56C8×Dic11C2211yescharacteristic, complemented
57#66874C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C24×C11—21no—
60C2×D4×C11—22no—
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C2×D4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75#4341—22no—
76#4341—41no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22C2311yescharacteristic
80C11×D8—22no—
81C11×D8—41no—
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11D411yescharacteristic
95#4324—41no—
96(C2×D11)⋊C4D411yescharacteristic
97C4⋊Dic11—21no—
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107#4318—41no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#3322—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—42no—
116C23×C11—42no—
117C23×C11—81no—
118C23×C11C2×D411yescharacteristic
119C22×D11C2×D411yescharacteristic
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—42no—
126D4×C11—81no—
127D4×C11#4112yes—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2411yescharacteristic
133C22⋊D11—41no—
134C22⋊D11—42no—
135C22⋊D11—42no—
136C22⋊D11—81no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—42no—
142C2×Dic11—81no—
143C2×Dic11—81no—
144C2×Dic11C2×D411yescharacteristic
145C2×Dic11C2×D411yescharacteristic
146C2×Dic11C2×D411yescharacteristic
147C4×D11—21no—
148C4×D11—21no—
149C4×D11—81no—
150Dic22—21no—
151Dic22—21no—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#553—111no—
157#546—111no—
158#488—111no—
159#485—111no—
160#480—111no—
161#478—111no—
162#469—111no—
163#468—111no—
164#463—111no—
165#449—111no—
166#447D1111yescharacteristic, complemented
167C4×D8—111no—
168#436—111no—
169#418—111no—
170#417—111no—
171C22×C11—21no—
172C22×C11—22no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—84no—
184C22×C11C22×D411yescharacteristic
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—21no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11C2×#4111yescharacteristic
191C4×C11H(5,𝔽2)11yescharacteristic
192Dic11—21no—
193Dic11—21no—
194Dic11—21no—
195Dic11—41no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C22×D4C2×D1111yescharacteristic
201C2×SD16—111no—
202C2×D8C2×D1111yescharacteristic
203C2×D8C2×D1111yescharacteristic
204C2×M16—111no—
205C2×M16—111no—
206#126—221no—
207#125—111no—
208#124—111no—
209#123—221no—
210#123—221no—
211C22⋊Q8—111no—
212#121—111no—
213#121—111no—
214#121—221no—
215#121—221no—
216#121C2×D1111yescharacteristic
217#120—221no—
218C4×D4—111no—
219C4×D4—111no—
220C4×D4—111no—
221C4×D4—221no—
222#117—111no—
223C2×C4⋊C4—111no—
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#102C2×D1111yescharacteristic
238#102C2×D1111yescharacteristic
239C22⋊C8—111no—
240C22⋊C8C2×D1111yescharacteristic
241C4×C8—111no—
242C2×C11—41no—
243C2×C11—42no—
244C2×C11—81no—
245C2×C11—81no—
246C2×C11#54611yescharacteristic
247C2×C11#57511yescharacteristic
248C2×C11#57611yescharacteristic
249D11—41no—
250C24—21no—
251#41—222no—
252#41—441no—
253C2×Q8—111no—
254C2×D4—22no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—111no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4C22×D1111yescharacteristic
263C2×D4C22×D1111yescharacteristic
264C2×D4C22×D1111yescharacteristic
265C22×C4—111no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4C22×D1111yescharacteristic
271SD16—441no—
272D8—22no—
273D8—41no—
274M16—441no—
275M16—441no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8C22×D1111yescharacteristic
279C2×C8C22×D1111yescharacteristic
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—111no—
283C4⋊C4—111no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4C22×D1111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—111no—
291C22⋊C4—111no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C42—111no—
301C42—221no—
302C11#332211yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—21no—
306C23—42no—
307C23—42no—
308C23—81no—
309C23—111no—
310C23D4×D1111yescharacteristic
311Q8—221no—
312Q8—221no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—81no—
320D4—441no—
321D4—442no—
322D4—442no—
323D4—881no—
324D4#434112yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—111no—
329C2×C4—111no—
330C2×C4—111no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—442no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4D4×D1111yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—221no—
346C8—221no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—84no—
360C22—221no—
361C22—221no—
362C22—221no—
363C22C2×D4×D1111yescharacteristic
364C4—21no—
365C4—41no—
366C4—221no—
367C4—221no—
368C4—221no—
369C4—441no—
370C4—441no—
371C4—441no—
372C4—441no—
373C4C2×#434111yescharacteristic
374C4#6703711yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2—441no—
380C2#1062312211yescharacteristic
381C2#1062328811yescharacteristic
382C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#447C2
socleC22×C11C22×D4
hypercenter#447D11
hypocenterC11#3322
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #10623337C2semidirect
2. #10623145C2semidirect
3. C11×#447C2semidirect
4. #10622828C2semidirect
5. #10622772C2semidirect
6. #10622771C2semidirect
7. #10622766C2semidirect
8. D8×Dic11C2semidirect
9. #10622655C2semidirect
10. #10622387C2semidirect
11. #10622384C2semidirect
12. #10622381C2semidirect
13. #10622376C2semidirect
14. #10622342C2semidirect
15. #10622336C2semidirect
26. #66991C22semidirect
31. D4×Dic11C22semidirect
32. C2×#4324C22semidirect
37. C2×#4313C22semidirect
38. C4⋊C4×D11C22semidirect
39. #66943C22semidirect
49. #66896C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. #66882C22semidirect
52. #66881C22semidirect
53. #66880C22semidirect
54. #66880C22semidirect
55. Dic11⋊C8C22semidirect
56. C8×Dic11C22semidirect
57. #66874C22semidirect
58. #66871C22semidirect
166. #447D11semidirect
302. C11#3322semidirect

Maximal subgroups

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

subgroupindex
#106233372
#106231452
C11×#4472
#106228282
#106227722
#106227712
#106227662
D8×Dic112
#106226552
#106223872
#106223842
#106223812
#106223762
#106223422
#106223362
#332211