Finite Group Databasebeta

← #13078705

Subgroups — #13078705

Order 1408.

488 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623079C211yesmaximal, characteristic, complemented
2C4×D4×D11C211yesmaximal, characteristic, complemented
3C11×#442C211yesmaximal, characteristic, complemented
4#10622769C211yesmaximal, characteristic, complemented
5#10622763C211yesmaximal, characteristic, complemented
6#10622627C211yesmaximal, characteristic, complemented
7#10622627C211yesmaximal, characteristic, complemented
8#10622483C211yesmaximal, characteristic, complemented
9#10622476C211yesmaximal, characteristic, complemented
10#10622399C211yesmaximal, characteristic, complemented
11#10622390C211yesmaximal, characteristic, complemented
12#10622386C211yesmaximal, characteristic, complemented
13#10622374C211yesmaximal, characteristic, complemented
14#10622324C211yesmaximal, characteristic, complemented
15#10622318C211yesmaximal, characteristic, complemented
16C2×D4×D11C2211yescharacteristic
17C2×#4339—21no—
18C22×C4×D11—21no—
19C2×C11×D8C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic
21C4×D4×C11C2211yescharacteristic, complemented
22#66993C2211yescharacteristic, complemented
23#66991C2211yescharacteristic
24D4×Dic11C2211yescharacteristic
25C2×#4323C2211yescharacteristic
26C2×#4323C2211yescharacteristic
27C4×C22⋊D11—21no—
28C4×C22⋊D11—21no—
29C2×D88C2211yescharacteristic
30#66948C2211yescharacteristic
31#66946C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33#66941C2211yescharacteristic, complemented
34#66938—21no—
35#66937—21no—
36(C22⋊D11)⋊C4—21no—
37C22⋊C4×D11—21no—
38C4×D44C2211yescharacteristic
39C4×D44C2211yescharacteristic, complemented
40C42×D11C2211yescharacteristic
41C11×#106C2211yescharacteristic, complemented
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic, complemented
44C11×#97C2211yescharacteristic, complemented
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic, complemented
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic, complemented
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66881C2211yescharacteristic, complemented
52Dic11⋊C8C2211yescharacteristic, complemented
53Dic11⋊C8C2211yescharacteristic, complemented
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic, complemented
56#66872C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×D4×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C22×Dic11—21no—
69D4×D11—22no—
70D4×D11—22no—
71#4339—44no—
72C2×D44—21no—
73C2×D44C2311yescharacteristic
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—44no—
80C2×C4×D11D411yescharacteristic
81C2×C4×D11D411yescharacteristic
82C2×C4×D11C2311yescharacteristic
83C2×Dic22—21no—
84C11×D8—22no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C22⋊C4—21no—
90C11×C22⋊C4—21no—
91C42×C11C2311yescharacteristic
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94#4323—22no—
95#4323—22no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104C4×Dic11D411yescharacteristic
105C4×Dic11D411yescharacteristic
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109D88—22no—
110#3109—111nomaximal, Sylow
111C23×C11—21no—
112C23×C11—21no—
113C22×D11—24no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11C2×D411yescharacteristic
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11#4112yescomplemented
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—24no—
131C22⋊D11—42no—
132C22⋊D11—42no—
133C22⋊D11—42no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—42no—
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140D44—21no—
141D44—21no—
142D44—21no—
143D44—42no—
144D44#4112yescomplemented
145C4×D11—22no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—22no—
149C4×D11—42no—
150C4×D11—42no—
151C4×D11—42no—
152C4×D11—42no—
153Dic22—42no—
154C8×C11—21no—
155C8×C11—21no—
156C11⋊C8—21no—
157C11⋊C8—21no—
158#532—111no—
159C2×C4×D4—111no—
160#481—111no—
161#481—111no—
162#476—111no—
163#476—111no—
164#459—111no—
165#459—111no—
166#447—111no—
167#447—111no—
168#442—111no—
169#442—111no—
170#442—111no—
171#442D1111yescharacteristic, complemented
172#432—111no—
173C22×C11—22no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11C22×D411yescharacteristic
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—22no—
183C2×D11—48no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11AGL(1,ℤ/8)12yes—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11C2×#4111yescharacteristic
195C4×C11C2×#4111yescharacteristic
196Dic11—21no—
197Dic11—21no—
198Dic11—41no—
199Dic11—41no—
200Dic11AGL(1,ℤ/8)12yes—
201C2×#41—221no—
202C22×D4—111no—
203C23×C4—221no—
204C2×D8—111no—
205C2×D8—111no—
206C2×D8—111no—
207C2×D8C2×D1111yescharacteristic
208C4⋊Q8—111no—
209#127—111no—
210#124—221no—
211#121—111no—
212#121—111no—
213#121—221no—
214C4×D4—111no—
215C4×D4—111no—
216C4×D4—111no—
217C4×D4—111no—
218C4×D4—221no—
219C4×D4—221no—
220C4×D4—221no—
221C4×D4C2×D1111yescharacteristic
222C4×D4C2×D1111yescharacteristic, complemented
223C2×C4⋊C4—111no—
224C2×C22⋊C4—221no—
225C2×C42—111no—
226#106—111no—
227#106—111no—
228#106—111no—
229#106C2×D1111yescharacteristic, complemented
230C4⋊C8—111no—
231C4⋊C8—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102C2×D1111yescharacteristic
239#102C2×D1111yescharacteristic, complemented
240C22⋊C8—111no—
241C22⋊C8—111no—
242#97—111no—
243#97C2×D1111yescharacteristic, complemented
244C2×C11—42no—
245C2×C11—81no—
246C2×C11#52511yescharacteristic
247C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
248C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
249D11—22no—
250D11—42no—
251D11—81no—
252C24—221no—
253#41—444no—
254C2×Q8—221no—
255C2×D4—111no—
256C2×D4—111no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—222no—
262C2×D4—222no—
263C2×D4—221no—
264C2×D4C22×D1111yescharacteristic
265C2×D4C22×D1111yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—111no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—444no—
277D8—22no—
278D8—222no—
279D8—222no—
280D8—222no—
281C2×C8—111no—
282C2×C8—111no—
283C2×C8C22×D1111yescharacteristic
284C2×C8C22×D1111yescharacteristic
285C4⋊C4—111no—
286C4⋊C4—111no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4C22×D1111yescharacteristic
290C4⋊C4C22×D1111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C42—111no—
300C42—111no—
301C42—111no—
302C42C22×D1111yescharacteristic
303C11#310911yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—111no—
307C23—224no—
308C23—221no—
309C23—221no—
310C23—442no—
311C23—442no—
312Q8—442no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—112no—
317D4—224no—
318D4—221no—
319D4—221no—
320D4—221no—
321D4—442no—
322D4—442no—
323D4—442no—
324D4—442no—
325D4#433912yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—111no—
331C2×C4—111no—
332C2×C4—111no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4D4×D1111yescharacteristic
345C2×C4D4×D1111yescharacteristic
346C2×C4C23×D1111yescharacteristic
347C8—21no—
348C8—21no—
349C8—221no—
350C8—221no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—112no—
358C22—221no—
359C22—221no—
360C22—222no—
361C22—448no—
362C22—441no—
363C22—441no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22C2×D4×D1111yescharacteristic
368C4—21no—
369C4—21no—
370C4—41no—
371C4—41no—
372C4—112no—
373C4—221no—
374C4—221no—
375C4—441no—
376C4—441no—
377C4C2×#433911yescharacteristic
378C4#41×D1111yescharacteristic
379C2—42no—
380C2—81no—
381C2—222no—
382C2—442no—
383C2—881no—
384C2#1062307811yescharacteristic
385C2D11×AGL(1,ℤ/8)11yescharacteristic
386C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#442C2
socleC22×C11C22×D4
hypercenter#442D11
hypocenterC11#3109
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #10623079C2semidirect
2. C4×D4×D11C2semidirect
3. C11×#442C2semidirect
4. #10622769C2semidirect
5. #10622763C2semidirect
6. #10622627C2semidirect
7. #10622627C2semidirect
8. #10622483C2semidirect
9. #10622476C2semidirect
10. #10622399C2semidirect
11. #10622390C2semidirect
12. #10622386C2semidirect
13. #10622374C2semidirect
14. #10622324C2semidirect
15. #10622318C2semidirect
21. C4×D4×C11C22semidirect
22. #66993C22semidirect
33. #66941C22semidirect
39. C4×D44C22semidirect
41. C11×#106C22semidirect
43. C11×#102C22semidirect
44. C11×#97C22semidirect
46. #66896C22semidirect
48. #66885C22semidirect
51. #66881C22semidirect
52. Dic11⋊C8C22semidirect
53. Dic11⋊C8C22semidirect
55. #66873C22semidirect
56. #66872C22semidirect
57. #66872C22semidirect
58. #66867C22semidirect
122. D4×C11#41semidirect
144. D44#41semidirect
171. #442D11semidirect
222. C4×D4C2×D11semidirect
229. #106C2×D11semidirect
239. #102C2×D11semidirect
243. #97C2×D11semidirect
303. C11#3109semidirect
325. D4#4339semidirect

Maximal subgroups

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

subgroupindex
#106230792
C4×D4×D112
C11×#4422
#106227692
#106227632
#106226272
#106224832
#106224762
#106223992
#106223902
#106223862
#106223742
#106223242
#106223182
#310911