Finite Group Databasebeta

← #13078126

Subgroups — #13078126

Order 1408.

494 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×SD16×D11C211yesmaximal, characteristic, complemented
2C2×#66964C211yesmaximal, characteristic
3#10623206C211yesmaximal, characteristic, complemented
4#10623076C211yesmaximal, characteristic, complemented
5C11×#463C211yesmaximal, characteristic, complemented
6#10622775C211yesmaximal, characteristic, complemented
7#10622766C211yesmaximal, characteristic, complemented
8#10622670C211yesmaximal, characteristic, complemented
9#10622632C211yesmaximal, characteristic, complemented
10#10622454C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622431C211yesmaximal, characteristic, complemented
13#10622415C211yesmaximal, characteristic, complemented
14#10622400C211yesmaximal, characteristic, complemented
15#10622385C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×D4×D11C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C11×#124C2211yescharacteristic, complemented
22C4×D4×C11C2211yescharacteristic
23#66997C2211yescharacteristic, complemented
24C2×#4325C2211yescharacteristic
25#66989C2211yescharacteristic, complemented
26D4×Dic11C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C2×#4324C2211yescharacteristic
29C2×#4323C2211yescharacteristic
30C4×C22⋊D11—21no—
31C2×(C2×D11)⋊C4—21no—
32SD16×D11—24no—
33#66964—24no—
34C2×#4314C2211yescharacteristic
35C2×#4314C2211yescharacteristic
36C2×#4313C2211yescharacteristic
37C2×C8×D11C2211yescharacteristic
38#66946C2211yescharacteristic
39#66945C2211yescharacteristic
40#66936—21no—
41#66936—21no—
42(C22⋊D11)⋊C4—21no—
43C22⋊C4×D11—21no—
44#66931—21no—
45#66931—21no—
46C4×D44C2211yescharacteristic
47#66925C2211yescharacteristic
48#66922C2211yescharacteristic, complemented
49C11×C4⋊C8C2211yescharacteristic, complemented
50C11×#103C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic, complemented
52#66899C2211yescharacteristic, complemented
53#66896C2211yescharacteristic, complemented
54#66880C2211yescharacteristic, complemented
55#66880C2211yescharacteristic, complemented
56Dic11⋊C8C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58#66874C2211yescharacteristic, complemented
59#66874C2211yescharacteristic, complemented
60C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C23×D11—21no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70Q8×D11—22no—
71Q8×D11—22no—
72#4341—22no—
73#4341—22no—
74D4×D11—22no—
75D4×D11D414yes—
76C2×D44C2311yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11C2311yescharacteristic
81C2×Dic22—21no—
82C2×Dic22C2311yescharacteristic
83C2×Dic22C2311yescharacteristic
84C11×SD16—22no—
85C11×D8—22no—
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C22⋊C4—21no—
90C11×C22⋊C4—21no—
91C11×C22⋊C4—21no—
92C42×C11C2311yescharacteristic
93C22⋊Dic11—21no—
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
96#4325—22no—
97#4324—22no—
98#4324—22no—
99#4323—22no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4D411yescharacteristic
104(C2×D11)⋊C4D411yescharacteristic
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11C2311yescharacteristic
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110Dic11⋊C4D411yescharacteristic
111Dic11⋊C4D411yescharacteristic
112C4×Dic11—21no—
113C4×Dic11C2311yescharacteristic
114C2×C11⋊C8C2311yescharacteristic
115C2×C11⋊C8C2311yescharacteristic
116#4314—22no—
117#4314—22no—
118#4313—22no—
119C8×D11—22no—
120#3042—111nomaximal, Sylow
121C23×C11—21no—
122C23×C11—21no—
123C22×D11—21no—
124C22×D11—24no—
125C22×D11—81no—
126C22×D11—81no—
127C22×D11C2×D411yescharacteristic
128Q8×C11—21no—
129Q8×C11—21no—
130D4×C11—21no—
131D4×C11—21no—
132D4×C11—21no—
133D4×C11C2×D412yes—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—81no—
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2411yescharacteristic
140C22⋊D11—24no—
141C22⋊D11—42no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—42no—
146C2×Dic11—81no—
147C2×Dic11C2×D411yescharacteristic
148C2×Dic11C2×D411yescharacteristic
149C2×Dic11C2×D411yescharacteristic
150D44—21no—
151D44C2×D412yes—
152C4×D11—42no—
153C4×D11—81no—
154C4×D11—81no—
155C4×D11C2×D412yes—
156C4×D11#4112yes—
157Dic22—21no—
158Dic22—21no—
159Dic22—21no—
160Dic22—21no—
161Dic22—42no—
162C8×C11—21no—
163C8×C11—21no—
164C11⋊C8—21no—
165C11⋊C8—21no—
166C2×AGL(1,ℤ/8)—111no—
167C22×SD16—111no—
168#536—111no—
169#518—111no—
170#463—111no—
171#463—111no—
172#463—111no—
173#463D1111yescharacteristic, complemented
174#461—111no—
175#461—111no—
176#461—111no—
177#461—111no—
178#424—111no—
179#419—111no—
180#416—111no—
181C22×C11—22no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11C22×D411yescharacteristic
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—22no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—84no—
194C2×D11#12112yes—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11C22×D411yescharacteristic
200C4×C11C2×#4111yescharacteristic
201Dic11—21no—
202Dic11—21no—
203Dic11—41no—
204Dic11—41no—
205Dic11—41no—
206Dic11#12112yes—
207C2×#41—111no—
208C22×Q8—111no—
209C22×D4—111no—
210AGL(1,ℤ/8)—224no—
211C2×SD16—111no—
212C2×SD16—111no—
213C2×SD16—111no—
214C2×SD16—111no—
215C2×SD16—111no—
216C2×SD16—224no—
217C2×SD16C2×D1111yescharacteristic
218C2×D8—111no—
219C2×D8C2×D1111yescharacteristic
220C2×M16—111no—
221C22×C8—111no—
222C4⋊Q8—111no—
223C4⋊Q8—111no—
224#124—111no—
225#124C2×D1111yescharacteristic, complemented
226#123—221no—
227#123—221no—
228C22⋊Q8—221no—
229C22⋊Q8—221no—
230C4×D4—111no—
231C4×D4—111no—
232C4×D4—111no—
233C4×D4—221no—
234C4×D4—221no—
235C4×D4C2×D1111yescharacteristic
236#117—111no—
237#117—111no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C4⋊C8—111no—
241C4⋊C8—111no—
242C4⋊C8—111no—
243C4⋊C8C2×D1111yescharacteristic, complemented
244#103—111no—
245#103—111no—
246#103—111no—
247#103—111no—
248#103—111no—
249#103C2×D1111yescharacteristic, complemented
250#102—111no—
251#102C2×D1111yescharacteristic, complemented
252C2×C11—42no—
253C2×C11—81no—
254C2×C11C2×#12111yescharacteristic
255C2×C11#57711yescharacteristic
256C2×C11#57711yescharacteristic
257D11—22no—
258D11—42no—
259C24—221no—
260#41—222no—
261#41—222no—
262C2×Q8—111no—
263C2×Q8—111no—
264C2×Q8—221no—
265C2×Q8—222no—
266C2×Q8—222no—
267C2×Q8C22×D1111yescharacteristic
268C2×D4—114no—
269C2×D4—111no—
270C2×D4—222no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4C22×D1111yescharacteristic
274C2×D4C22×D1111yescharacteristic
275C22×C4—21no—
276C22×C4—111no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282SD16—22no—
283SD16—222no—
284SD16—222no—
285SD16—222no—
286SD16—222no—
287SD16—222no—
288D8—22no—
289D8—222no—
290M16—222no—
291C2×C8—111no—
292C2×C8—111no—
293C2×C8—222no—
294C2×C8C22×D1111yescharacteristic
295C2×C8C22×D1111yescharacteristic
296C4⋊C4—111no—
297C4⋊C4—111no—
298C4⋊C4—111no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4C22×D1111yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—111no—
308C22⋊C4—111no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C22⋊C4—221no—
315C42—111no—
316C42—221no—
317C42C22×D1111yescharacteristic
318C11#304211yescharacteristic, complemented, Sylow
319C23—21no—
320C23—21no—
321C23—111no—
322C23—224no—
323C23—221no—
324C23—881no—
325C23—881no—
326Q8—21no—
327Q8—21no—
328Q8—221no—
329Q8—221no—
330Q8—221no—
331Q8—221no—
332Q8—442no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—112no—
337D4—224no—
338D4—221no—
339D4—442no—
340D4D4×D1112yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—81no—
344C2×C4—111no—
345C2×C4—112no—
346C2×C4—112no—
347C2×C4—111no—
348C2×C4—111no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—881no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4D4×D1111yescharacteristic
358C2×C4D4×D1111yescharacteristic
359C2×C4C23×D1111yescharacteristic
360C8—21no—
361C8—21no—
362C8—221no—
363C8—221no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—112no—
371C22—221no—
372C22—221no—
373C22—222no—
374C22—441no—
375C22—441no—
376C22—884no—
377C22C2×D4×D1111yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—112no—
383C4—221no—
384C4—221no—
385C4—441no—
386C4—441no—
387C4—441no—
388C4C2×D4×D1111yescharacteristic
389C4#41×D1111yescharacteristic
390C2—42no—
391C2—81no—
392C2—222no—
393C2—442no—
394C2D11×#12111yescharacteristic
395C2#1062330111yescharacteristic
396C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
prime radicalC2×#66964C2
hypercenter#463D11
hypocenterC11#3042
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D11C2semidirect
3. #10623206C2semidirect
4. #10623076C2semidirect
5. C11×#463C2semidirect
6. #10622775C2semidirect
7. #10622766C2semidirect
8. #10622670C2semidirect
9. #10622632C2semidirect
10. #10622454C2semidirect
11. #10622452C2semidirect
12. #10622431C2semidirect
13. #10622415C2semidirect
14. #10622400C2semidirect
15. #10622385C2semidirect
21. C11×#124C22semidirect
23. #66997C22semidirect
25. #66989C22semidirect
48. #66922C22semidirect
49. C11×C4⋊C8C22semidirect
50. C11×#103C22semidirect
51. C11×#102C22semidirect
52. #66899C22semidirect
53. #66896C22semidirect
54. #66880C22semidirect
55. #66880C22semidirect
56. Dic11⋊C8C22semidirect
57. Dic11⋊C8C22semidirect
58. #66874C22semidirect
59. #66874C22semidirect
60. C4⋊(C11⋊C8)C22semidirect
173. #463D11semidirect
225. #124C2×D11semidirect
243. C4⋊C8C2×D11semidirect
249. #103C2×D11semidirect
251. #102C2×D11semidirect
318. C11#3042semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D112
C2×#669642
#106232062
#106230762
C11×#4632
#106227752
#106227662
#106226702
#106226322
#106224542
#106224522
#106224312
#106224152
#106224002
#106223852
#304211