Finite Group Databasebeta

← #13080639

Subgroups — #13080639

Order 1408.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D44C211yesmaximal, characteristic
2#10623072C211yesmaximal, characteristic, complemented
3C11×#435C211yesmaximal, characteristic, complemented
4#10622747C211yesmaximal, characteristic, complemented
5#10622744C211yesmaximal, characteristic, complemented
6#10622727C211yesmaximal, characteristic, complemented
7C2×#66885C211yesmaximal, characteristic, complemented
8#10622461C211yesmaximal, characteristic, complemented
9#10622460C211yesmaximal, characteristic, complemented
10#10622350C211yesmaximal, characteristic, complemented
11#10622349C211yesmaximal, characteristic, complemented
12#10622344C211yesmaximal, characteristic, complemented
13#10622344C211yesmaximal, characteristic, complemented
14#10622326C211yesmaximal, characteristic, complemented
15#10622323C211yesmaximal, characteristic, complemented
16C2×D4×D11—21no—
17C22×D44C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C2×C11×M16C2211yescharacteristic, complemented
20C22×C8×C11C2211yescharacteristic, complemented
21C4×D4×C11C2211yescharacteristic
22#66988—21no—
23#66983C2211yescharacteristic
24#66983C2211yescharacteristic
25#66979C2211yescharacteristic, complemented
26C2×C4⋊Dic11C2211yescharacteristic, complemented
27#66977C2211yescharacteristic, complemented
28#66977C2211yescharacteristic, complemented
29C2×#4314C2211yescharacteristic
30C2×#4314C2211yescharacteristic, complemented
31C2×#4314C2211yescharacteristic, complemented
32#66948—21no—
33#66942—21no—
34#66935—21no—
35#66935—21no—
36#66932—21no—
37#66930—21no—
38#66927C2211yescharacteristic
39C4×D44C2211yescharacteristic
40#66923C2211yescharacteristic, complemented
41C4×Dic22C2211yescharacteristic, complemented
42C11×C4⋊C8C2211yescharacteristic, complemented
43C11×C22⋊C8C2211yescharacteristic, complemented
44C11×C22⋊C8C2211yescharacteristic, complemented
45C11×#97C2211yescharacteristic, complemented
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic, complemented
50#66885C2211yescharacteristic, complemented
51#66885C2211yescharacteristic, complemented
52#66885C2211yescharacteristic, complemented
53#66885C2211yescharacteristic, complemented
54#66885C2211yescharacteristic, complemented
55#66882C2211yescharacteristic, complemented
56#66882C2211yescharacteristic, complemented
57#66881C2211yescharacteristic, complemented
58#66880C2211yescharacteristic, complemented
59C23×D11—21no—
60C23×D11—21no—
61C2×D4×C11D411yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67D4×D11—44no—
68C2×D44—22no—
69C2×D44—22no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—41no—
75C2×D44—41no—
76C2×D44C2311yescharacteristic
77C2×D44C2311yescharacteristic
78C2×D44C2311yescharacteristic
79C2×C4×D11—21no—
80C2×Dic22C2311yescharacteristic
81C11×M16—41no—
82C2×C8×C11—41no—
83C2×C8×C11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C11×C4⋊C4D411yescharacteristic
88C11×C22⋊C4D411yescharacteristic
89C11×C22⋊C4D411yescharacteristic
90C42×C11C2311yescharacteristic
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109#4314—22no—
110#4314—41no—
111#4314—41no—
112#3310—111nomaximal, Sylow
113C23×C11C2×D411yescharacteristic
114C23×C11C2×D411yescharacteristic
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—42no—
119C22×D11—42no—
120C22×D11—42no—
121C22×D11—42no—
122C22×D11—81no—
123C22×D11—81no—
124D4×C11—22no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2411yescharacteristic
134C22⋊D11—42no—
135C22⋊D11—42no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—42no—
142D44—21no—
143D44—21no—
144D44—21no—
145D44—21no—
146D44—21no—
147D44—42no—
148D44—42no—
149D44—42no—
150D44—81no—
151D44#4112yes—
152C4×D11—42no—
153Dic22—21no—
154Dic22—21no—
155C8×C11—21no—
156C8×C11—21no—
157C8×C11—21no—
158C8×C11—21no—
159#552—111no—
160D42—111no—
161#490—111no—
162#482—111no—
163#480—111no—
164#478—111no—
165#468—111no—
166#465—111no—
167#460—111no—
168#450—111no—
169#450—111no—
170#440—111no—
171#435D1111yescharacteristic, complemented
172#418—111no—
173C2×#102—111no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11AGL(1,ℤ/8)12yes—
180C22×C11C22×D411yescharacteristic
181C2×D11—22no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—84no—
191C2×D11—84no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11C2×#4111yescharacteristic
197C4×C11H(5,𝔽2)11yescharacteristic
198Dic11—41no—
199Dic11—41no—
200Dic11—41no—
201Dic11—41no—
202Dic11—41no—
203C22×D4—111no—
204C22×D4—111no—
205C22×D4—221no—
206C2×SD16—111no—
207C2×SD16—111no—
208C2×SD16—111no—
209C2×M16C2×D1111yescharacteristic, complemented
210C22×C8C2×D1111yescharacteristic, complemented
211#127—111no—
212#126—221no—
213#125—111no—
214#125—221no—
215#123—221no—
216C22⋊Q8—111no—
217C22⋊Q8—111no—
218#121—111no—
219#121—111no—
220#121—221no—
221#120—221no—
222#120—221no—
223C4×Q8—111no—
224C4×D4—111no—
225C4×D4C2×D1111yescharacteristic
226#117—111no—
227#117—221no—
228C2×C4⋊C4—111no—
229#107—111no—
230#107—111no—
231#106—111no—
232C4⋊C8C2×D1111yescharacteristic, complemented
233#103—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102—111no—
239#102—111no—
240#102—111no—
241#102—111no—
242#102—111no—
243C22⋊C8C2×D1111yescharacteristic, complemented
244C22⋊C8C2×D1111yescharacteristic, complemented
245#97C2×D1111yescharacteristic, complemented
246C2×C11—22no—
247C2×C11—41no—
248C2×C11#54611yescharacteristic
249C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
250C2×C11#57711yescharacteristic
251D11—42no—
252D11—81no—
253D11—81no—
254C24—221no—
255C24—221no—
256C2×Q8—111no—
257C2×D4—111no—
258C2×D4—111no—
259C2×D4—111no—
260C2×D4—222no—
261C2×D4—222no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—441no—
269C2×D4—441no—
270C2×D4—444no—
271C2×D4D4411yescharacteristic
272C22×C4—221no—
273C22×C4—221no—
274C22×C4C22×D1111yescharacteristic
275C22×C4C22×D1111yescharacteristic
276SD16—222no—
277SD16—441no—
278SD16—441no—
279M16—41no—
280C2×C8—41no—
281C2×C8C22×D1111yescharacteristic
282C2×C8C22×D1111yescharacteristic
283C2×C8C22×D1111yescharacteristic
284C2×C8C22×D1111yescharacteristic
285C4⋊C4—111no—
286C4⋊C4—111no—
287C4⋊C4—111no—
288C4⋊C4—111no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4D4411yescharacteristic
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4D4411yescharacteristic
303C22⋊C4D4411yescharacteristic
304C42—221no—
305C42—221no—
306C42C22×D1111yescharacteristic
307C11#331011yescharacteristic, complemented, Sylow
308C23—221no—
309C23—221no—
310C23—221no—
311C23—442no—
312C23—442no—
313C23—442no—
314C23—442no—
315C23—881no—
316C23—881no—
317C23C2×D4411yescharacteristic
318C23C2×D4411yescharacteristic
319Q8—221no—
320Q8—221no—
321D4—22no—
322D4—112no—
323D4—221no—
324D4—221no—
325D4—221no—
326D4—221no—
327D4—221no—
328D4—442no—
329D4—442no—
330D4—442no—
331D4—442no—
332D4—442no—
333D4—881no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4C2×D4411yescharacteristic
346C2×C4C2×D4411yescharacteristic
347C2×C4C2×D4411yescharacteristic
348C2×C4C2×D4411yescharacteristic
349C2×C4C23×D1111yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—222no—
360C22—441no—
361C22—441no—
362C22—441no—
363C22—441no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22—884no—
369C22—884no—
370C22#6696112yes—
371C22C22×D4411yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—441no—
377C4—441no—
378C4—441no—
379C4—441no—
380C4—441no—
381C4#6703711yescharacteristic
382C4#41×D1111yescharacteristic
383C2—22no—
384C2—41no—
385C2—442no—
386C2—881no—
387C2—881no—
388C2#1062308511yescharacteristic
389C2C2×#6696111yescharacteristic
390C2#1062328211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#435C2
socleC22×C11C22×D4
prime radicalD4×D44C2
hypercenter#435D11
hypocenterC11#3310
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #10623072C2semidirect
3. C11×#435C2semidirect
4. #10622747C2semidirect
5. #10622744C2semidirect
6. #10622727C2semidirect
7. C2×#66885C2semidirect
8. #10622461C2semidirect
9. #10622460C2semidirect
10. #10622350C2semidirect
11. #10622349C2semidirect
12. #10622344C2semidirect
13. #10622344C2semidirect
14. #10622326C2semidirect
15. #10622323C2semidirect
19. C2×C11×M16C22semidirect
20. C22×C8×C11C22semidirect
25. #66979C22semidirect
26. C2×C4⋊Dic11C22semidirect
27. #66977C22semidirect
28. #66977C22semidirect
30. C2×#4314C22semidirect
31. C2×#4314C22semidirect
40. #66923C22semidirect
41. C4×Dic22C22semidirect
42. C11×C4⋊C8C22semidirect
43. C11×C22⋊C8C22semidirect
44. C11×C22⋊C8C22semidirect
45. C11×#97C22semidirect
49. #66885C22semidirect
50. #66885C22semidirect
51. #66885C22semidirect
52. #66885C22semidirect
53. #66885C22semidirect
54. #66885C22semidirect
55. #66882C22semidirect
56. #66882C22semidirect
57. #66881C22semidirect
58. #66880C22semidirect
171. #435D11semidirect
209. C2×M16C2×D11semidirect
210. C22×C8C2×D11semidirect
232. C4⋊C8C2×D11semidirect
243. C22⋊C8C2×D11semidirect
244. C22⋊C8C2×D11semidirect
245. #97C2×D11semidirect
307. C11#3310semidirect

Maximal subgroups

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

subgroupindex
D4×D442
#106230722
C11×#4352
#106227472
#106227442
#106227272
C2×#668852
#106224612
#106224602
#106223502
#106223492
#106223442
#106223262
#106223232
#331011