Finite Group Databasebeta

← #13079077

Subgroups — #13079077

Order 1408.

572 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66971C211yesmaximal, characteristic, complemented
2C2×#66968C211yesmaximal, characteristic, complemented
3C2×#66967C211yesmaximal, characteristic, complemented
4C2×#66964C211yesmaximal, characteristic, complemented
5D11×#124C211yesmaximal, characteristic, complemented
6#10623199C211yesmaximal, characteristic, complemented
7C11×#495C211yesmaximal, characteristic, complemented
8#10622803C211yesmaximal, characteristic, complemented
9#10622789C211yesmaximal, characteristic, complemented
10#10622780C211yesmaximal, characteristic, complemented
11#10622767C211yesmaximal, characteristic, complemented
12#10622672C211yesmaximal, characteristic, complemented
13#10622672C211yesmaximal, characteristic, complemented
14#10622309C211yesmaximal, characteristic, complemented
15C4×#4313C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×#4341C2211yescharacteristic
19C2×D4×D11C2211yescharacteristic
20C2×C11×Q16C2211yescharacteristic, complemented
21C2×C11×SD16C2211yescharacteristic
22C2×C11×SD16C2211yescharacteristic, complemented
23C2×C11×D8C2211yescharacteristic
24C11×#124C2211yescharacteristic
25C11×#124C2211yescharacteristic, complemented
26#67000C2211yescharacteristic
27#66997C2211yescharacteristic, complemented
28C2×#4326C2211yescharacteristic, complemented
29C2×#4326C2211yescharacteristic, complemented
30C2×#4325C2211yescharacteristic
31C2×#4325C2211yescharacteristic, complemented
32#66993C2211yescharacteristic, complemented
33#66989C2211yescharacteristic
34C2×#4324C2211yescharacteristic
35C2×#4324C2211yescharacteristic, complemented
36C2×#4323C2211yescharacteristic
37C2×#4323C2211yescharacteristic
38#66971—24no—
39#66968—24no—
40#66967—24no—
41#66964—24no—
42C2×Dic44C2211yescharacteristic, complemented
43C2×D88C2211yescharacteristic
44C2×#4314C2211yescharacteristic
45C2×#4314C2211yescharacteristic, complemented
46C2×#4313C2211yescharacteristic
47C2×#4313C2211yescharacteristic
48#66938—22no—
49#66937—22no—
50(C22⋊D11)⋊C4—22no—
51C22⋊C4×D11—22no—
52#66928C2211yescharacteristic
53#66928C2211yescharacteristic, complemented
54C42×D11C2211yescharacteristic
55C4×C8×C11C2211yescharacteristic, complemented
56#66879C2211yescharacteristic, complemented
57#66879C2211yescharacteristic, complemented
58C4×C11⋊C8C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×C22⋊D11—22no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68#4343—22no—
69#4343—22no—
70Q8×D11—22no—
71Q8×D11—22no—
72#4341—22no—
73#4341—22no—
74D4×D11—22no—
75D4×D11—22no—
76C2×D44—21no—
77C2×D44C2311yescharacteristic
78C2×D44C2311yescharacteristic
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11D412yes—
82C2×C4×D11C2311yescharacteristic
83C2×Dic22—21no—
84C2×Dic22C2311yescharacteristic
85C2×Dic22C2311yescharacteristic
86C11×Q16—22no—
87C11×SD16—22no—
88C11×SD16—22no—
89C11×D8—22no—
90C2×C8×C11C2311yescharacteristic
91C2×C8×C11C2311yescharacteristic
92C11×C22⋊C4—22no—
93C11×C22⋊C4—22no—
94C42×C11C2311yescharacteristic
95C22⋊Dic11—22no—
96#4326—22no—
97#4326—22no—
98#4325—22no—
99#4325—22no—
100#4324—22no—
101#4324—22no—
102#4323—22no—
103#4323—22no—
104(C2×D11)⋊C4—22no—
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4—22no—
107Dic11⋊C4—22no—
108C4×Dic11D412yes—
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112Dic44—22no—
113D88—22no—
114#4314—22no—
115#4314—22no—
116#4313D414yescomplemented
117#4313D414yescomplemented
118#3153—111nomaximal, Sylow
119C23×C11—21no—
120C23×C11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—44no—
124C22×D11—42no—
125C22×D11C2×D411yescharacteristic
126Q8×C11—21no—
127Q8×C11—21no—
128Q8×C11—21no—
129Q8×C11—21no—
130D4×C11—21no—
131D4×C11—21no—
132D4×C11—21no—
133D4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11C2×D412yes—
137C2×C4×C11C2411yescharacteristic
138C22⋊D11—44no—
139C22⋊D11—42no—
140C22⋊D11—42no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—42no—
144C2×Dic11C2×D412yes—
145C2×Dic11C2×D411yescharacteristic
146D44—21no—
147D44—21no—
148D44—21no—
149D44—21no—
150D44—42no—
151C4×D11—42no—
152C4×D11—42no—
153C4×D11—42no—
154C4×D11C2×D412yes—
155C4×D11C2×D412yes—
156Dic22—21no—
157Dic22—21no—
158Dic22—21no—
159Dic22—21no—
160Dic22—42no—
161C8×C11C2×D412yes—
162C8×C11C2×D412yes—
163C11⋊C8C2×D412yes—
164C11⋊C8C2×D412yes—
165C2×#137—111no—
166C2×#137—111no—
167C2×AGL(1,ℤ/8)—111no—
168C2×AGL(1,ℤ/8)—111no—
169#532—111no—
170C2×#124—111no—
171#497—111no—
172#497—111no—
173#496—111no—
174#496—111no—
175#495—111no—
176#495—111no—
177#495—111no—
178#495D1111yescharacteristic, complemented
179C4×M16—111no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11C22×D411yescharacteristic
185C2×D11—22no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—42no—
189C2×D11—42no—
190C2×D11—84no—
191C2×D11#12712yes—
192C4×C11—22no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11C22×D411yescharacteristic
196C4×C11C22×D411yescharacteristic
197Dic11—22no—
198Dic11—41no—
199Dic11—41no—
200Dic11#12712yes—
201C2×#41—111no—
202C2×#41—111no—
203C22×Q8—111no—
204C22×D4—111no—
205#137—224no—
206#137—224no—
207AGL(1,ℤ/8)—224no—
208AGL(1,ℤ/8)—224no—
209C2×Q16—111no—
210C2×Q16—111no—
211C2×Q16—111no—
212C2×Q16C2×D1111yescharacteristic, complemented
213C2×SD16—111no—
214C2×SD16—111no—
215C2×SD16—111no—
216C2×SD16—111no—
217C2×SD16—111no—
218C2×SD16—111no—
219C2×SD16C2×D1111yescharacteristic
220C2×SD16C2×D1111yescharacteristic, complemented
221C2×D8—111no—
222C2×D8—111no—
223C2×D8—111no—
224C2×D8C2×D1111yescharacteristic
225C2×M16—111no—
226C2×M16—111no—
227C4⋊Q8—111no—
228#127—111no—
229#124—111no—
230#124—111no—
231#124—111no—
232#124—111no—
233#124—222no—
234#124C2×D1111yescharacteristic
235#124C2×D1111yescharacteristic, complemented
236#121—222no—
237C4×D4—222no—
238C2×C22⋊C4—222no—
239C2×C42—111no—
240#97—111no—
241#97—111no—
242C4×C8—111no—
243C4×C8C2×D1111yescharacteristic, complemented
244C2×C11—81no—
245C2×C11—81no—
246C2×C11C2×#12711yescharacteristic
247C2×C11#57512yes—
248D11—22no—
249D11—81no—
250D11—81no—
251C24—221no—
252#41—222no—
253#41—222no—
254#41—222no—
255#41—222no—
256C2×Q8—111no—
257C2×Q8—111no—
258C2×Q8—221no—
259C2×Q8—222no—
260C2×Q8—222no—
261C2×Q8C22×D1111yescharacteristic
262C2×Q8C22×D1111yescharacteristic
263C2×D4—111no—
264C2×D4—111no—
265C2×D4—221no—
266C2×D4—222no—
267C2×D4—222no—
268C2×D4—222no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4C22×D1111yescharacteristic
272C2×D4C22×D1111yescharacteristic
273C22×C4—111no—
274C22×C4—112no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278Q16—22no—
279Q16—222no—
280Q16—222no—
281Q16—222no—
282SD16—22no—
283SD16—22no—
284SD16—222no—
285SD16—222no—
286SD16—222no—
287SD16—222no—
288SD16—222no—
289SD16—222no—
290D8—22no—
291D8—222no—
292D8—222no—
293D8—222no—
294M16—114no—
295M16—114no—
296C2×C8—111no—
297C2×C8—111no—
298C2×C8C22×D1111yescharacteristic
299C2×C8C22×D1111yescharacteristic
300C4⋊C4—222no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—222no—
304C22⋊C4—222no—
305C22⋊C4—222no—
306C22⋊C4—222no—
307C42—112no—
308C42—111no—
309C42C22×D1111yescharacteristic
310C11#315311yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—111no—
314C23—221no—
315C23—221no—
316C23—442no—
317C23—444no—
318Q8—21no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—221no—
323Q8—221no—
324Q8—221no—
325Q8—221no—
326Q8—442no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—221no—
332D4—221no—
333D4—221no—
334D4—221no—
335D4—442no—
336D4—442no—
337D4—444no—
338D4—442no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—111no—
342C2×C4—112no—
343C2×C4—112no—
344C2×C4—112no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4D4×D1112yes—
352C2×C4C23×D1111yescharacteristic
353C8—112no—
354C8—112no—
355C8D4×D1112yes—
356C8D4×D1112yes—
357C22—41no—
358C22—41no—
359C22—42no—
360C22—42no—
361C22—112no—
362C22—222no—
363C22—441no—
364C22—441no—
365C22—442no—
366C22—442no—
367C22—884no—
368C22C2×D4×D1111yescharacteristic
369C4—22no—
370C4—41no—
371C4—41no—
372C4—112no—
373C4—222no—
374C4—441no—
375C4—441no—
376C4C2×D4×D1111yescharacteristic
377C4C2×D4×D1111yescharacteristic
378C2—81no—
379C2—81no—
380C2—222no—
381C2—881no—
382C2—881no—
383C2D11×#12711yescharacteristic
384C2#1062329912yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#495C2
socleC22×C11C22×D4
hypercenter#495D11
hypocenterC11#3153
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#66971C2semidirect
2. C2×#66968C2semidirect
3. C2×#66967C2semidirect
4. C2×#66964C2semidirect
5. D11×#124C2semidirect
6. #10623199C2semidirect
7. C11×#495C2semidirect
8. #10622803C2semidirect
9. #10622789C2semidirect
10. #10622780C2semidirect
11. #10622767C2semidirect
12. #10622672C2semidirect
13. #10622672C2semidirect
14. #10622309C2semidirect
15. C4×#4313C2semidirect
20. C2×C11×Q16C22semidirect
22. C2×C11×SD16C22semidirect
25. C11×#124C22semidirect
27. #66997C22semidirect
28. C2×#4326C22semidirect
29. C2×#4326C22semidirect
31. C2×#4325C22semidirect
32. #66993C22semidirect
35. C2×#4324C22semidirect
42. C2×Dic44C22semidirect
45. C2×#4314C22semidirect
53. #66928C22semidirect
55. C4×C8×C11C22semidirect
56. #66879C22semidirect
57. #66879C22semidirect
58. C4×C11⋊C8C22semidirect
116. #4313D4semidirect
117. #4313D4semidirect
178. #495D11semidirect
212. C2×Q16C2×D11semidirect
220. C2×SD16C2×D11semidirect
235. #124C2×D11semidirect
243. C4×C8C2×D11semidirect
310. C11#3153semidirect

Maximal subgroups

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

subgroupindex
C2×#669712
C2×#669682
C2×#669672
C2×#669642
D11×#1242
#106231992
C11×#4952
#106228032
#106227892
#106227802
#106227672
#106226722
#106223092
C4×#43132
#315311