Finite Group Databasebeta

← #13080642

Subgroups — #13080642

Order 1408.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623112C211yesmaximal, characteristic, complemented
2D4×D44C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622782C211yesmaximal, characteristic, complemented
5#10622782C211yesmaximal, characteristic, complemented
6#10622640C211yesmaximal, characteristic, complemented
7#10622622C211yesmaximal, characteristic, complemented
8#10622498C211yesmaximal, characteristic, complemented
9#10622495C211yesmaximal, characteristic, complemented
10#10622425C211yesmaximal, characteristic, complemented
11#10622420C211yesmaximal, characteristic, complemented
12#10622383C211yesmaximal, characteristic, complemented
13D11×#102C211yesmaximal, characteristic, complemented
14#10622326C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C2×D4×D11C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C22×D44—21no—
19C2×C11×SD16C2211yescharacteristic
20C4×Q8×C11C2211yescharacteristic, complemented
21C4×D4×C11C2211yescharacteristic
22#66999C2211yescharacteristic, complemented
23#66999C2211yescharacteristic, complemented
24C2×#4325C2211yescharacteristic, complemented
25C2×#4325C2211yescharacteristic, complemented
26#66983—21no—
27C2×#4313C2211yescharacteristic, complemented
28C2×C8×D11C2211yescharacteristic, complemented
29#66948C2211yescharacteristic
30#66948C2211yescharacteristic
31#66947—21no—
32#66945C2211yescharacteristic, complemented
33C4⋊C4×D11C2211yescharacteristic, complemented
34#66942—21no—
35#66935—21no—
36#66935—21no—
37#66929—21no—
38#66927C2211yescharacteristic
39C4×D44C2211yescharacteristic
40#66925—21no—
41#66923C2211yescharacteristic, complemented
42C11×#107C2211yescharacteristic, complemented
43C11×#103C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic
45C11×#97C2211yescharacteristic, complemented
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic, complemented
49#66885C2211yescharacteristic, complemented
50#66885C2211yescharacteristic, complemented
51#66885C2211yescharacteristic, complemented
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53(C2×D11)⋊C8C2211yescharacteristic, complemented
54#66873C2211yescharacteristic, complemented
55#66873C2211yescharacteristic, complemented
56#66872C2211yescharacteristic, complemented
57#66871C2211yescharacteristic, complemented
58C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C23×D11—21no—
60C23×D11—21no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66D4×D11—22no—
67D4×D11—22no—
68D4×D11—41no—
69D4×D11—41no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—44no—
75C2×D44D411yescharacteristic
76C2×D44C2311yescharacteristic
77C2×D44C2311yescharacteristic
78C2×C4×D11—21no—
79C2×C4×D11C2311yescharacteristic
80C2×C4×D11C2311yescharacteristic
81C11×SD16—22no—
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4—21no—
85C11×C4⋊C4C2311yescharacteristic
86C11×C4⋊C4C2311yescharacteristic
87C11×C22⋊C4—21no—
88C42×C11—21no—
89C42×C11C2311yescharacteristic
90#4325—41no—
91#4325—41no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4D411yescharacteristic
98(C2×D11)⋊C4D411yescharacteristic
99C4⋊Dic11D411yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111C8×D11—41no—
112#3310—111nomaximal, Sylow
113C23×C11—21no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—42no—
119C22×D11—42no—
120C22×D11—81no—
121C22×D11—81no—
122C22×D11C2×D411yescharacteristic
123C22×D11C2×D411yescharacteristic
124Q8×C11—21no—
125Q8×C11—21no—
126D4×C11—21no—
127D4×C11#4112yes—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—42no—
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2411yescharacteristic
135C22⋊D11—42no—
136C22⋊D11—42no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141D44—22no—
142D44—21no—
143D44—21no—
144D44—21no—
145D44—21no—
146D44—42no—
147D44—42no—
148D44—42no—
149D44—81no—
150C4×D11—21no—
151C4×D11—21no—
152C4×D11—21no—
153C4×D11—21no—
154C4×D11—42no—
155C8×C11—21no—
156C8×C11—21no—
157C11⋊C8—21no—
158C11⋊C8—21no—
159#552—111no—
160D42—111no—
161#490—111no—
162#482—111no—
163#480—111no—
164#478—111no—
165#468—111no—
166#465—111no—
167#460—111no—
168#450—111no—
169#450—111no—
170#440D1111yescharacteristic, complemented
171#435—111no—
172#418—111no—
173C2×#102—111no—
174C22×C11—22no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—84no—
190C2×D11—84no—
191C2×D11AGL(1,ℤ/8)12yes—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11C2×#4111yescharacteristic
198C4×C11H(5,𝔽2)11yescharacteristic
199Dic11—21no—
200Dic11—21no—
201Dic11—41no—
202Dic11—41no—
203C22×D4—111no—
204C22×D4—111no—
205C22×D4—221no—
206C2×SD16—111no—
207C2×SD16—111no—
208C2×SD16C2×D1111yescharacteristic
209C2×M16—111no—
210C22×C8—111no—
211#127—111no—
212#126—221no—
213#125—111no—
214#125—221no—
215#123—221no—
216C22⋊Q8—111no—
217C22⋊Q8—111no—
218#121—111no—
219#121—111no—
220#121—221no—
221#120—221no—
222#120—221no—
223C4×Q8C2×D1111yescharacteristic, complemented
224C4×D4—111no—
225C4×D4C2×D1111yescharacteristic
226#117—111no—
227#117—221no—
228C2×C4⋊C4—111no—
229#107—111no—
230#107C2×D1111yescharacteristic, complemented
231#106—111no—
232C4⋊C8—111no—
233#103C2×D1111yescharacteristic, complemented
234#102—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102—111no—
239#102—111no—
240#102—111no—
241#102—111no—
242#102C2×D1111yescharacteristic
243C22⋊C8—111no—
244C22⋊C8—111no—
245#97C2×D1111yescharacteristic, complemented
246C2×C11—42no—
247C2×C11#54611yescharacteristic
248C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
249C2×C11#57711yescharacteristic
250D11—22no—
251D11—41no—
252D11—81no—
253D11—81no—
254C24—221no—
255C24—221no—
256C2×Q8C22×D1111yescharacteristic
257C2×D4—111no—
258C2×D4—111no—
259C2×D4—111no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—222no—
265C2×D4—222no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—444no—
269C2×D4—441no—
270C2×D4—441no—
271C2×D4C22×D1111yescharacteristic
272C22×C4—21no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—221no—
276SD16—22no—
277SD16—441no—
278SD16—441no—
279M16—441no—
280C2×C8—111no—
281C2×C8—111no—
282C2×C8—441no—
283C2×C8C22×D1111yescharacteristic
284C2×C8C22×D1111yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—111no—
287C4⋊C4—111no—
288C4⋊C4—111no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4C22×D1111yescharacteristic
295C4⋊C4C22×D1111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—111no—
298C22⋊C4—111no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C42—21no—
305C42—221no—
306C42C22×D1111yescharacteristic
307C11#331011yescharacteristic, complemented, Sylow
308C23—21no—
309C23—111no—
310C23—111no—
311C23—221no—
312C23—221no—
313C23—442no—
314C23—442no—
315C23—442no—
316C23—442no—
317C23—881no—
318C23—881no—
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—222no—
323D4—221no—
324D4—221no—
325D4—221no—
326D4—221no—
327D4—442no—
328D4—442no—
329D4—442no—
330D4—442no—
331D4—442no—
332D4—881no—
333D4#433912yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—111no—
339C2×C4—111no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—442no—
347C2×C4D4×D1111yescharacteristic
348C2×C4D4×D1111yescharacteristic
349C2×C4C23×D1111yescharacteristic
350C8—21no—
351C8—21no—
352C8—221no—
353C8—221no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—112no—
358C22—221no—
359C22—221no—
360C22—221no—
361C22—221no—
362C22—221no—
363C22—441no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22—441no—
369C22—884no—
370C22—884no—
371C22C2×D4×D1111yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—221no—
378C4—221no—
379C4—441no—
380C4—441no—
381C4C2×#433911yescharacteristic
382C4#6704211yescharacteristic
383C2—42no—
384C2—222no—
385C2—441no—
386C2—881no—
387C2—881no—
388C2#1062308111yescharacteristic
389C2D11×AGL(1,ℤ/8)11yescharacteristic
390C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radicalD4×D44C2
hypercenter#440D11
hypocenterC11#3310
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10623112C2semidirect
3. C11×#440C2semidirect
4. #10622782C2semidirect
5. #10622782C2semidirect
6. #10622640C2semidirect
7. #10622622C2semidirect
8. #10622498C2semidirect
9. #10622495C2semidirect
10. #10622425C2semidirect
11. #10622420C2semidirect
12. #10622383C2semidirect
13. D11×#102C2semidirect
14. #10622326C2semidirect
15. #10622319C2semidirect
20. C4×Q8×C11C22semidirect
22. #66999C22semidirect
23. #66999C22semidirect
24. C2×#4325C22semidirect
25. C2×#4325C22semidirect
27. C2×#4313C22semidirect
28. C2×C8×D11C22semidirect
32. #66945C22semidirect
33. C4⋊C4×D11C22semidirect
41. #66923C22semidirect
42. C11×#107C22semidirect
43. C11×#103C22semidirect
45. C11×#97C22semidirect
48. #66885C22semidirect
49. #66885C22semidirect
50. #66885C22semidirect
51. #66885C22semidirect
52. (C2×D11)⋊C8C22semidirect
53. (C2×D11)⋊C8C22semidirect
54. #66873C22semidirect
55. #66873C22semidirect
56. #66872C22semidirect
57. #66871C22semidirect
58. C4⋊(C11⋊C8)C22semidirect
170. #440D11semidirect
223. C4×Q8C2×D11semidirect
230. #107C2×D11semidirect
233. #103C2×D11semidirect
245. #97C2×D11semidirect
307. C11#3310semidirect

Maximal subgroups

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

subgroupindex
#106231122
D4×D442
C11×#4402
#106227822
#106226402
#106226222
#106224982
#106224952
#106224252
#106224202
#106223832
D11×#1022
#106223262
#106223192
#331011