Finite Group Databasebeta

← #13078567

Subgroups — #13078567

Order 1408.

418 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
1#10623138C211yesmaximal, characteristic
2#10623035C211yesmaximal, characteristic, complemented
3C11×#480C211yesmaximal, characteristic, complemented
4#10622648C211yesmaximal, characteristic, complemented
5#10622581C211yesmaximal, characteristic, complemented
6#10622498C211yesmaximal, characteristic, complemented
7#10622495C211yesmaximal, characteristic, complemented
8#10622494C211yesmaximal, characteristic, complemented
9#10622493C211yesmaximal, characteristic, complemented
10#10622397C211yesmaximal, characteristic, complemented
11#10622390C211yesmaximal, characteristic, complemented
12#10622383C211yesmaximal, characteristic, complemented
13D11×#102C211yesmaximal, characteristic, complemented
14#10622350C211yesmaximal, characteristic, complemented
15#10622340C211yesmaximal, characteristic, complemented
16C2×D4×D11C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C11×#121C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic, complemented
20#66993—21no—
21#66991C2211yescharacteristic
22#66990—21no—
23#66983C2211yescharacteristic
24C4×C22⋊D11—21no—
25C4×C22⋊D11—21no—
26#66979C2211yescharacteristic, complemented
27C2×#4313C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic
29#66948C2211yescharacteristic
30#66946—21no—
31#66945C2211yescharacteristic
32#66945C2211yescharacteristic
33#66945C2211yescharacteristic, complemented
34C4⋊C4×D11C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic, complemented
36#66940—21no—
37#66938—21no—
38#66935—21no—
39C11×#107C2211yescharacteristic, complemented
40C11×#107C2211yescharacteristic, complemented
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic, complemented
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic, complemented
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic, complemented
51#66882C2211yescharacteristic, complemented
52#66881C2211yescharacteristic, complemented
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66872C2211yescharacteristic, complemented
56#66872C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11D411yescharacteristic
68C2×C22⋊D11D411yescharacteristic
69D4×D11—22no—
70D4×D11—22no—
71#4339—22no—
72#4339—22no—
73C2×D44—21no—
74C2×D44D411yescharacteristic
75C2×D44C2311yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×C4×D11C2311yescharacteristic
80C2×Dic22D411yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C4⋊C4—21no—
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C4⋊C4C2311yescharacteristic
87C11×C22⋊C4—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—22no—
107C8×D11—22no—
108#3096—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111C22×D11—21no—
112C22×D11—42no—
113C22×D11—81no—
114C22×D11—81no—
115C22×D11C2×D411yescharacteristic
116C22×D11C2×D411yescharacteristic
117D4×C11—21no—
118D4×C11—21no—
119D4×C11—81no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—81no—
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—22no—
129C22⋊D11—22no—
130C22⋊D11—42no—
131C22⋊D11—81no—
132C22⋊D11—81no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138D44—22no—
139D44—21no—
140D44—21no—
141D44—81no—
142C4×D11—21no—
143C4×D11—21no—
144C4×D11—81no—
145C4×D11—81no—
146C4×D11#4112yes—
147C4×D11#4112yes—
148Dic22—22no—
149C8×C11—21no—
150C8×C11—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#535—111no—
154#520—111no—
155#482—111no—
156#482—111no—
157#482—111no—
158#482—111no—
159#481—111no—
160#481—111no—
161#480—111no—
162#480D1111yescharacteristic, complemented
163#428—111no—
164#427—111no—
165#418—111no—
166C2×#102—111no—
167#408—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11C22×D411yescharacteristic
175C2×D11—21no—
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—84no—
184C2×D11#12312yes—
185C4×C11—21no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11C2×#4111yescharacteristic
190C4×C11C2×#4111yescharacteristic
191Dic11—21no—
192Dic11—41no—
193Dic11—41no—
194Dic11—41no—
195Dic11#12312yes—
196C2×#41—111no—
197C22×D4—111no—
198C2×M16—111no—
199C22×C8—111no—
200#127—221no—
201#124—221no—
202#121—111no—
203#121—111no—
204#121—111no—
205#121C2×D1111yescharacteristic
206#120—221no—
207#120—221no—
208C4×Q8—221no—
209C4×D4—221no—
210C4×D4—221no—
211C4×D4—221no—
212#117—111no—
213#117—111no—
214#117—111no—
215#117—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4C2×D1111yescharacteristic, complemented
219#107—111no—
220#107—111no—
221#107C2×D1111yescharacteristic, complemented
222#107C2×D1111yescharacteristic, complemented
223#106—111no—
224#106—111no—
225#106—111no—
226#106—111no—
227#102—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102—111no—
233#102C2×D1111yescharacteristic
234#102C2×D1111yescharacteristic
235C22⋊C8—111no—
236C22⋊C8—111no—
237C22⋊C8—111no—
238C22⋊C8C2×D1111yescharacteristic, complemented
239C2×C11—41no—
240C2×C11—81no—
241C2×C11C2×#12311yescharacteristic
242C2×C11#57611yescharacteristic
243C2×C11#57711yescharacteristic
244D11—22no—
245D11—41no—
246D11—81no—
247C24—221no—
248#41—222no—
249#41—222no—
250C2×Q8—111no—
251C2×D4—21no—
252C2×D4—111no—
253C2×D4—111no—
254C2×D4—111no—
255C2×D4—111no—
256C2×D4—221no—
257C2×D4—222no—
258C2×D4—222no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4C22×D1111yescharacteristic
263C22×C4—21no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4C22×D1111yescharacteristic
269M16—222no—
270C2×C8—111no—
271C2×C8—111no—
272C2×C8—222no—
273C2×C8C22×D1111yescharacteristic
274C2×C8C22×D1111yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—111no—
277C4⋊C4—111no—
278C4⋊C4—111no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4C22×D1111yescharacteristic
282C4⋊C4C22×D1111yescharacteristic
283C4⋊C4C22×D1111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C42—221no—
293C42—221no—
294C42—221no—
295C42—221no—
296C11#309611yescharacteristic, complemented, Sylow
297C23—21no—
298C23—111no—
299C23—111no—
300C23—221no—
301C23—442no—
302C23—881no—
303C23—881no—
304C23D4×D1111yescharacteristic
305Q8—222no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—222no—
310D4—222no—
311D4—222no—
312D4—221no—
313D4—221no—
314D4—442no—
315D4—881no—
316D4—881no—
317D4—881no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—111no—
325C2×C4—112no—
326C2×C4—112no—
327C2×C4—111no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—881no—
334C2×C4—881no—
335C2×C4D4×D1111yescharacteristic
336C2×C4C23×D1111yescharacteristic
337C8—21no—
338C8—21no—
339C8—221no—
340C8—221no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—112no—
348C22—221no—
349C22—221no—
350C22—221no—
351C22—221no—
352C22—221no—
353C22—441no—
354C22—441no—
355C22—441no—
356C22—884no—
357C22C2×D4×D1111yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—112no—
363C4—221no—
364C4—441no—
365C4—441no—
366C4—441no—
367C4#41×D1111yescharacteristic
368C4#41×D1111yescharacteristic
369C2—41no—
370C2—81no—
371C2—222no—
372C2—441no—
373C2—881no—
374C2D11×#12311yescharacteristic
375C2#1062328811yescharacteristic
376C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#480C2
socleC22×C11C22×D4
prime radical#10623138C2
hypercenter#480D11
hypocenterC11#3096
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #10623035C2semidirect
3. C11×#480C2semidirect
4. #10622648C2semidirect
5. #10622581C2semidirect
6. #10622498C2semidirect
7. #10622495C2semidirect
8. #10622494C2semidirect
9. #10622493C2semidirect
10. #10622397C2semidirect
11. #10622390C2semidirect
12. #10622383C2semidirect
13. D11×#102C2semidirect
14. #10622350C2semidirect
15. #10622340C2semidirect
19. C2×C11×C4⋊C4C22semidirect
26. #66979C22semidirect
33. #66945C22semidirect
35. C4⋊C4×D11C22semidirect
39. C11×#107C22semidirect
40. C11×#107C22semidirect
43. C11×C22⋊C8C22semidirect
46. C22⋊(C11⋊C8)C22semidirect
49. (C2×D11)⋊C8C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. #66882C22semidirect
52. #66881C22semidirect
55. #66872C22semidirect
56. #66872C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
162. #480D11semidirect
218. C2×C4⋊C4C2×D11semidirect
221. #107C2×D11semidirect
222. #107C2×D11semidirect
238. C22⋊C8C2×D11semidirect
296. C11#3096semidirect

Maximal subgroups

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

subgroupindex
#106231382
#106230352
C11×#4802
#106226482
#106225812
#106224982
#106224952
#106224942
#106224932
#106223972
#106223902
#106223832
D11×#1022
#106223502
#106223402
#309611