Finite Group Databasebeta

← #13078135

Subgroups — #13078135

Order 1408.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66971C211yesmaximal, characteristic, complemented
2C2×SD16×D11C211yesmaximal, characteristic, complemented
3#10623205C211yesmaximal, characteristic
4#10623103C211yesmaximal, characteristic, complemented
5C11×#464C211yesmaximal, characteristic, complemented
6#10622798C211yesmaximal, characteristic, complemented
7#10622776C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622640C211yesmaximal, characteristic, complemented
10#10622461C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622417C211yesmaximal, characteristic, complemented
13#10622411C211yesmaximal, characteristic, complemented
14#10622383C211yesmaximal, characteristic, complemented
15#10622375C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×D4×D11C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic, complemented
20C2×C11×SD16C2211yescharacteristic
21C11×#124C2211yescharacteristic
22C4×Q8×C11C2211yescharacteristic, complemented
23#67000C2211yescharacteristic
24Q8×Dic11C2211yescharacteristic, complemented
25C2×#4326C2211yescharacteristic, complemented
26C2×#4325C2211yescharacteristic
27C2×#4325C2211yescharacteristic, complemented
28#66993C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30#66971—24no—
31SD16×D11—24no—
32C2×#4314C2211yescharacteristic
33C2×#4314C2211yescharacteristic, complemented
34C2×#4313C2211yescharacteristic
35C2×C8×D11C2211yescharacteristic
36#66945—21no—
37#66945C2211yescharacteristic
38#66940—21no—
39#66940C2211yescharacteristic, complemented
40#66937—21no—
41#66937—21no—
42#66935—21no—
43#66935—21no—
44#66927C2211yescharacteristic
45#66925—21no—
46#66925C2211yescharacteristic
47C4×Dic22—21no—
48C4×Dic22C2211yescharacteristic, complemented
49C11×C4⋊C8C2211yescharacteristic, complemented
50C11×#103C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic
52#66899C2211yescharacteristic, complemented
53#66896C2211yescharacteristic
54#66885C2211yescharacteristic
55#66885C2211yescharacteristic, complemented
56Dic11⋊C8C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58#66873C2211yescharacteristic
59#66873C2211yescharacteristic, complemented
60C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C23×D11—21no—
62C2×Q8×C11C2311yescharacteristic
63C2×Q8×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68#4343—22no—
69#4343—22no—
70Q8×D11—22no—
71Q8×D11D414yescomplemented
72D4×D11—22no—
73D4×D11—22no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44C2311yescharacteristic
78C2×D44C2311yescharacteristic
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11C2311yescharacteristic
82C2×Dic22—21no—
83C2×Dic22C2311yescharacteristic
84C11×Q16—22no—
85C11×SD16—22no—
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C11×C4⋊C4—21no—
89C11×C4⋊C4C2311yescharacteristic
90C11×C22⋊C4—21no—
91C11×C22⋊C4—21no—
92C42×C11—21no—
93C42×C11C2311yescharacteristic
94#4326—22no—
95#4325—22no—
96#4325—22no—
97#4324—22no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4D411yescharacteristic
102(C2×D11)⋊C4D411yescharacteristic
103C4⋊Dic11—21no—
104C4⋊Dic11C2311yescharacteristic
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4D411yescharacteristic
108Dic11⋊C4D411yescharacteristic
109C4×Dic11—21no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11C2311yescharacteristic
114C2×C11⋊C8C2311yescharacteristic
115C2×C11⋊C8C2311yescharacteristic
116#4314—22no—
117#4314—22no—
118#4313—22no—
119C8×D11—22no—
120#3043—111nomaximal, Sylow
121C23×C11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—42no—
125C22×D11—81no—
126C22×D11—81no—
127C22×D11C2×D411yescharacteristic
128Q8×C11—21no—
129Q8×C11—21no—
130Q8×C11—21no—
131Q8×C11C2×D412yes—
132D4×C11—21no—
133D4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2411yescharacteristic
140C22⋊D11—42no—
141C22⋊D11—81no—
142C22⋊D11—81no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11C2×D411yescharacteristic
146C2×Dic11C2×D411yescharacteristic
147C2×Dic11C2×D411yescharacteristic
148D44—21no—
149D44—21no—
150D44—21no—
151D44—21no—
152D44—42no—
153D44—81no—
154D44—81no—
155C4×D11—24no—
156C4×D11—42no—
157C4×D11C2×D412yes—
158C4×D11#4112yes—
159Dic22—21no—
160Dic22—24no—
161Dic22C2×D412yes—
162C8×C11—21no—
163C8×C11—21no—
164C11⋊C8—21no—
165C11⋊C8—21no—
166C2×#137—111no—
167C22×SD16—111no—
168#535—111no—
169#519—111no—
170#464—111no—
171#464—111no—
172#464—111no—
173#464D1111yescharacteristic, complemented
174#460—111no—
175#460—111no—
176#460—111no—
177#460—111no—
178#424—111no—
179#418—111no—
180#416—111no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11C22×D411yescharacteristic
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—84no—
194C2×D11#12112yes—
195C4×C11—22no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11C22×D411yescharacteristic
201C4×C11C2×#4111yescharacteristic
202Dic11—22no—
203Dic11—21no—
204Dic11—21no—
205Dic11—41no—
206Dic11#12112yes—
207C2×#41—111no—
208C22×Q8—111no—
209C22×D4—111no—
210#137—224no—
211C2×Q16—111no—
212C2×Q16C2×D1111yescharacteristic, complemented
213C2×SD16—111no—
214C2×SD16—111no—
215C2×SD16—111no—
216C2×SD16—111no—
217C2×SD16—111no—
218C2×SD16—224no—
219C2×SD16C2×D1111yescharacteristic
220C2×M16—111no—
221C22×C8—111no—
222#127—111no—
223#127—111no—
224#124—111no—
225#124C2×D1111yescharacteristic
226#121—221no—
227#121—221no—
228#120—221no—
229#120—221no—
230C4×Q8—111no—
231C4×Q8—111no—
232C4×Q8—111no—
233C4×Q8—221no—
234C4×Q8—221no—
235C4×Q8C2×D1111yescharacteristic, complemented
236#117—111no—
237#117—111no—
238#117—221no—
239#117—221no—
240C4⋊C8—111no—
241C4⋊C8—111no—
242C4⋊C8—111no—
243C4⋊C8C2×D1111yescharacteristic, complemented
244#103—111no—
245#103C2×D1111yescharacteristic, complemented
246#102—111no—
247#102—111no—
248#102—111no—
249#102—111no—
250#102—111no—
251#102C2×D1111yescharacteristic
252C2×C11—81no—
253C2×C11C2×#12111yescharacteristic
254C2×C11#57711yescharacteristic
255C2×C11#57711yescharacteristic
256D11—22no—
257D11—81no—
258D11—81no—
259C24—221no—
260#41—222no—
261#41—222no—
262C2×Q8—114no—
263C2×Q8—111no—
264C2×Q8—221no—
265C2×Q8—222no—
266C2×Q8C22×D1111yescharacteristic
267C2×Q8C22×D1111yescharacteristic
268C2×D4—111no—
269C2×D4—111no—
270C2×D4—221no—
271C2×D4—222no—
272C2×D4—222no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4C22×D1111yescharacteristic
279C22×C4—111no—
280C22×C4—221no—
281C22×C4—221no—
282Q16—22no—
283Q16—222no—
284SD16—22no—
285SD16—222no—
286SD16—222no—
287SD16—222no—
288SD16—222no—
289SD16—222no—
290M16—222no—
291C2×C8—111no—
292C2×C8—111no—
293C2×C8—222no—
294C2×C8C22×D1111yescharacteristic
295C2×C8C22×D1111yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—111no—
298C4⋊C4—111no—
299C4⋊C4—111no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4C22×D1111yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—111no—
307C22⋊C4—111no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C42—21no—
312C42—111no—
313C42—221no—
314C42—221no—
315C42—221no—
316C42—221no—
317C42C22×D1111yescharacteristic
318C11#304311yescharacteristic, complemented, Sylow
319C23—21no—
320C23—111no—
321C23—221no—
322C23—221no—
323C23—442no—
324C23—881no—
325C23—881no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—112no—
330Q8—224no—
331Q8—221no—
332Q8D4×D1112yes—
333D4—21no—
334D4—21no—
335D4—221no—
336D4—221no—
337D4—221no—
338D4—221no—
339D4—442no—
340D4—442no—
341D4—881no—
342D4—881no—
343D4—881no—
344D4—881no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—111no—
349C2×C4—112no—
350C2×C4—112no—
351C2×C4—111no—
352C2×C4—111no—
353C2×C4—224no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—442no—
357C2×C4D4×D1111yescharacteristic
358C2×C4D4×D1111yescharacteristic
359C2×C4C23×D1111yescharacteristic
360C8—21no—
361C8—21no—
362C8—221no—
363C8—221no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—112no—
368C22—221no—
369C22—221no—
370C22—441no—
371C22—441no—
372C22—441no—
373C22—441no—
374C22—441no—
375C22—441no—
376C22—884no—
377C22C2×D4×D1111yescharacteristic
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—112no—
384C4—221no—
385C4—221no—
386C4—222no—
387C4—441no—
388C4C2×D4×D1111yescharacteristic
389C4#41×D1111yescharacteristic
390C2—81no—
391C2—222no—
392C2—881no—
393C2—881no—
394C2D11×#12111yescharacteristic
395C2#1062330111yescharacteristic
396C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radical#10623205C2
hypercenter#464D11
hypocenterC11#3043
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#66971C2semidirect
2. C2×SD16×D11C2semidirect
4. #10623103C2semidirect
5. C11×#464C2semidirect
6. #10622798C2semidirect
7. #10622776C2semidirect
8. #10622667C2semidirect
9. #10622640C2semidirect
10. #10622461C2semidirect
11. #10622452C2semidirect
12. #10622417C2semidirect
13. #10622411C2semidirect
14. #10622383C2semidirect
15. #10622375C2semidirect
19. C2×C11×Q16C22semidirect
22. C4×Q8×C11C22semidirect
24. Q8×Dic11C22semidirect
25. C2×#4326C22semidirect
27. C2×#4325C22semidirect
33. C2×#4314C22semidirect
39. #66940C22semidirect
48. C4×Dic22C22semidirect
49. C11×C4⋊C8C22semidirect
50. C11×#103C22semidirect
52. #66899C22semidirect
55. #66885C22semidirect
56. Dic11⋊C8C22semidirect
57. Dic11⋊C8C22semidirect
59. #66873C22semidirect
60. C4⋊(C11⋊C8)C22semidirect
71. Q8×D11D4semidirect
173. #464D11semidirect
212. C2×Q16C2×D11semidirect
235. C4×Q8C2×D11semidirect
243. C4⋊C8C2×D11semidirect
245. #103C2×D11semidirect
318. C11#3043semidirect

Maximal subgroups

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

subgroupindex
C2×#669712
C2×SD16×D112
#106232052
#106231032
C11×#4642
#106227982
#106227762
#106226672
#106226402
#106224612
#106224522
#106224172
#106224112
#106223832
#106223752
#304311