Finite Group Databasebeta

← #13077445

Subgroups — #13077445

Order 1408.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66964C211yesmaximal, characteristic
2#10623077C211yesmaximal, characteristic, complemented
3#10623076C211yesmaximal, characteristic, complemented
4C11×#442C211yesmaximal, characteristic, complemented
5D8×Dic11C211yesmaximal, characteristic, complemented
6C4×#4324C211yesmaximal, characteristic, complemented
7C4×#4323C211yesmaximal, characteristic, complemented
8#10622474C211yesmaximal, characteristic, complemented
9#10622465C211yesmaximal, characteristic, complemented
10#10622398C211yesmaximal, characteristic, complemented
11#10622385C211yesmaximal, characteristic, complemented
12D11×#102C211yesmaximal, characteristic, complemented
13#10622370C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622321C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×C11×D8C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic, complemented
21D4×Dic11C2211yescharacteristic
22D4×Dic11C2211yescharacteristic, complemented
23C2×#4324C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25C4×C22⋊D11—21no—
26C4×C22⋊D11—21no—
27C2×(C2×D11)⋊C4—21no—
28C2×Dic11⋊C4—21no—
29#66964C418yescomplemented
30C2×#4314C2211yescharacteristic
31C2×#4313C2211yescharacteristic
32C2×C8×D11C2211yescharacteristic
33#66946C2211yescharacteristic
34#66945C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic
36#66940C2211yescharacteristic, complemented
37(C22⋊D11)⋊C4—21no—
38(C22⋊D11)⋊C4—21no—
39C22⋊C4×D11—21no—
40#66930—21no—
41C4×D44C2211yescharacteristic
42#66925C2211yescharacteristic
43C4×Dic22C2211yescharacteristic, complemented
44C11×#106C2211yescharacteristic, complemented
45C11×#102C2211yescharacteristic
46C11×#102C2211yescharacteristic, complemented
47C11×#97C2211yescharacteristic, complemented
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic, complemented
50#66885C2211yescharacteristic
51#66882C2211yescharacteristic, complemented
52#66880C2211yescharacteristic, complemented
53#66879C2211yescharacteristic, complemented
54C8×Dic11C2211yescharacteristic, complemented
55#66874C2211yescharacteristic, complemented
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C4×C11⋊C8C2211yescharacteristic, complemented
60C23×D11—21no—
61C2×D4×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70#4341—22no—
71#4341C2×C414yescomplemented
72D4×D11—22no—
73D4×D11C2×C414yescomplemented
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22C2311yescharacteristic
80C11×D8C2×C414yescomplemented
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C42×C11C2311yescharacteristic
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90#4324C2×C414yescomplemented
91#4323C2×C414yescomplemented
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4D411yescharacteristic
96(C2×D11)⋊C4D411yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103Dic11⋊C4D411yescharacteristic
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4314C2×C414yescomplemented
111#4313C2×C414yescomplemented
112C8×D11—22no—
113#2946—111nomaximal, Sylow
114C23×C11—21no—
115C23×C11—21no—
116C22×D11—21no—
117C22×D11—24no—
118C22×D11—81no—
119C22×D11—81no—
120C22×D11C2×D411yescharacteristic
121D4×C11—21no—
122D4×C11—21no—
123D4×C11C22×C412yes—
124D4×C11C22×C412yes—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—24no—
133C22⋊D11—24no—
134C2×Dic11—21no—
135C2×Dic11—24no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143D44—21no—
144D44C22×C412yes—
145C4×D11—81no—
146C4×D11—81no—
147C4×D11—81no—
148C4×D11C22×C412yes—
149C4×D11#4112yes—
150Dic22—21no—
151Dic22C22×C412yes—
152C8×C11—21no—
153C8×C11C22×C412yes—
154C11⋊C8—21no—
155C11⋊C8C22×C412yes—
156C2×AGL(1,ℤ/8)—111no—
157#520—111no—
158#518—111no—
159#442—111no—
160#442D1111yescharacteristic, complemented
161#440—111no—
162#440—111no—
163C4×SD16—111no—
164C4×SD16—111no—
165C4×D8—111no—
166C4×D8—111no—
167#428—111no—
168#416—111no—
169C2×#102—111no—
170#405—111no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—22no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—84no—
184C2×D11C4×D412yes—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11C23×C411yescharacteristic
190C4×C11C2×#4111yescharacteristic
191Dic11—22no—
192Dic11—21no—
193Dic11—21no—
194Dic11—41no—
195Dic11—41no—
196Dic11C4×D412yes—
197C2×#41—111no—
198C22×D4—111no—
199AGL(1,ℤ/8)—118no—
200C2×SD16—111no—
201C2×SD16—111no—
202C2×D8—111no—
203C2×D8C2×D1111yescharacteristic
204C2×M16—111no—
205C22×C8—111no—
206C4×Q8—111no—
207C4×Q8—111no—
208C4×D4—111no—
209C4×D4—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—221no—
213C4×D4—221no—
214C4×D4—221no—
215C4×D4—221no—
216C4×D4C2×D1111yescharacteristic
217C4×D4C2×D1111yescharacteristic, complemented
218#117—111no—
219#117—111no—
220#117—221no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225#107—111no—
226#107—111no—
227#106—111no—
228#106C2×D1111yescharacteristic, complemented
229#103—111no—
230#103—111no—
231#102—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#102C2×D1111yescharacteristic
236#102C2×D1111yescharacteristic, complemented
237#97—111no—
238#97C2×D1111yescharacteristic, complemented
239C4×C8—111no—
240C4×C8—111no—
241C2×C11—42no—
242C2×C11—42no—
243C2×C11C2×C4×D411yescharacteristic
244C2×C11#57611yescharacteristic
245C2×C11#57711yescharacteristic
246D11—22no—
247D11—42no—
248C24—221no—
249#41—114no—
250#41—222no—
251C2×Q8—111no—
252C2×D4—114no—
253C2×D4—111no—
254C2×D4—222no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4C22×D1111yescharacteristic
258C2×D4C22×D1111yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—111no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268SD16—114no—
269SD16—114no—
270D8—114no—
271D8C4×D1114yescomplemented
272M16—114no—
273C2×C8—111no—
274C2×C8—111no—
275C2×C8—222no—
276C2×C8C22×D1111yescharacteristic
277C2×C8C22×D1111yescharacteristic
278C4⋊C4—111no—
279C4⋊C4—111no—
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4C22×D1111yescharacteristic
286C4⋊C4C22×D1111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—111no—
290C22⋊C4—111no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C42—111no—
297C42—221no—
298C42—221no—
299C42—221no—
300C42C22×D1111yescharacteristic
301C11#294611yescharacteristic, complemented, Sylow
302C23—21no—
303C23—21no—
304C23—111no—
305C23—224no—
306C23—221no—
307C23—881no—
308C23—881no—
309Q8—112no—
310Q8—221no—
311D4—21no—
312D4—21no—
313D4—112no—
314D4—224no—
315D4—224no—
316D4—221no—
317D4C2×C4×D1112yes—
318D4C2×C4×D1112yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—111no—
324C2×C4—112no—
325C2×C4—112no—
326C2×C4—111no—
327C2×C4—111no—
328C2×C4—224no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—881no—
333C2×C4—881no—
334C2×C4—881no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4D4×D1111yescharacteristic
338C2×C4D4×D1111yescharacteristic
339C2×C4C23×D1111yescharacteristic
340C8—21no—
341C8—112no—
342C8—221no—
343C8C2×C4×D1112yes—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—112no—
351C22—221no—
352C22—221no—
353C22—222no—
354C22—441no—
355C22—441no—
356C22—884no—
357C22C2×D4×D1111yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—112no—
363C4—221no—
364C4—221no—
365C4—222no—
366C4—441no—
367C4—441no—
368C4C22×C4×D1111yescharacteristic
369C4#41×D1111yescharacteristic
370C2—42no—
371C2—42no—
372C2—222no—
373C2—442no—
374C2C4×D4×D1111yescharacteristic
375C2#1062330511yescharacteristic
376C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutatorC4×C11C23×C4
FrattiniC2×C4C23×D11
FittingC11×#442C2
socleC22×C11C22×D4
prime radicalC2×#66964C2
cosocleC2×C4×C11C24
hypercenter#442D11
hypocenterC11#2946
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #10623077C2semidirect
3. #10623076C2semidirect
4. C11×#442C2semidirect
5. D8×Dic11C2semidirect
6. C4×#4324C2semidirect
7. C4×#4323C2semidirect
8. #10622474C2semidirect
9. #10622465C2semidirect
10. #10622398C2semidirect
11. #10622385C2semidirect
12. D11×#102C2semidirect
13. #10622370C2semidirect
14. #10622323C2semidirect
15. #10622321C2semidirect
20. C4×D4×C11C22semidirect
22. D4×Dic11C22semidirect
29. #66964C4semidirect
36. #66940C22semidirect
43. C4×Dic22C22semidirect
44. C11×#106C22semidirect
46. C11×#102C22semidirect
47. C11×#97C22semidirect
49. #66896C22semidirect
51. #66882C22semidirect
52. #66880C22semidirect
53. #66879C22semidirect
54. C8×Dic11C22semidirect
55. #66874C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
59. C4×C11⋊C8C22semidirect
71. #4341C2×C4semidirect
73. D4×D11C2×C4semidirect
80. C11×D8C2×C4semidirect
90. #4324C2×C4semidirect
91. #4323C2×C4semidirect
110. #4314C2×C4semidirect
111. #4313C2×C4semidirect
160. #442D11semidirect
217. C4×D4C2×D11semidirect
228. #106C2×D11semidirect
236. #102C2×D11semidirect
238. #97C2×D11semidirect
271. D8C4×D11semidirect
301. C11#2946semidirect

Maximal subgroups

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

subgroupindex
C2×#669642
#106230772
#106230762
C11×#4422
D8×Dic112
C4×#43242
C4×#43232
#106224742
#106224652
#106223982
#106223852
D11×#1022
#106223702
#106223232
#106223212
#294611