Finite Group Databasebeta

← #13079085

Subgroups — #13079085

Order 1408.

564 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×#66969C211yesmaximal, characteristic, complemented
2C2×#66968C211yesmaximal, characteristic, complemented
3C2×#66967C211yesmaximal, characteristic, complemented
4C2×SD16×D11C211yesmaximal, characteristic, complemented
5#10623255C211yesmaximal, characteristic, complemented
6#10623246C211yesmaximal, characteristic, complemented
7C11×#492C211yesmaximal, characteristic, complemented
8#10622789C211yesmaximal, characteristic, complemented
9#10622788C211yesmaximal, characteristic, complemented
10#10622781C211yesmaximal, characteristic, complemented
11#10622780C211yesmaximal, characteristic, complemented
12#10622699C211yesmaximal, characteristic, complemented
13#10622687C211yesmaximal, characteristic, complemented
14#10622309C211yesmaximal, characteristic, complemented
15#10622302C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×#4341C2211yescharacteristic
19C2×D4×D11C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic
21C2×C11×SD16C2211yescharacteristic
22C2×C11×SD16C2211yescharacteristic, complemented
23C2×C11×SD16C2211yescharacteristic, complemented
24C11×C4⋊Q8C2211yescharacteristic, complemented
25C11×#127C2211yescharacteristic
26#67000C2211yescharacteristic, complemented
27#66997C2211yescharacteristic, complemented
28C2×#4326C2211yescharacteristic, complemented
29C2×#4326C2211yescharacteristic, complemented
30C2×#4325C2211yescharacteristic
31C2×#4325C2211yescharacteristic
32#66993C2211yescharacteristic
33#66992—22no—
34#66990—22no—
35#66989C2211yescharacteristic
36C2×#4324C2211yescharacteristic
37C2×#4324C2211yescharacteristic, complemented
38C2×#4323C2211yescharacteristic
39C2×#4323C2211yescharacteristic, complemented
40#66969—24no—
41#66968—24no—
42#66967—24no—
43SD16×D11—24no—
44C2×Dic44C2211yescharacteristic, complemented
45C2×D88C2211yescharacteristic
46C2×#4314C2211yescharacteristic
47C2×#4314C2211yescharacteristic, complemented
48C2×#4313C2211yescharacteristic
49C2×C8×D11C2211yescharacteristic
50#66949—22no—
51#66947—22no—
52#66928C2211yescharacteristic
53#66928C2211yescharacteristic, complemented
54#66925C2211yescharacteristic
55C4×C8×C11C2211yescharacteristic, complemented
56#66879C2211yescharacteristic, complemented
57C8×Dic11C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—22no—
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11—22no—
67C2×C22⋊D11—21no—
68C22×Dic11—21no—
69#4343—22no—
70#4343—22no—
71Q8×D11—22no—
72Q8×D11—22no—
73#4341—22no—
74#4341—22no—
75D4×D11—22no—
76D4×D11—22no—
77C2×D44—21no—
78C2×D44C2311yescharacteristic
79C2×D44C2311yescharacteristic
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11C2311yescharacteristic
83C2×Dic22—21no—
84C2×Dic22C2311yescharacteristic
85C2×Dic22C2311yescharacteristic
86C11×SD16—22no—
87C11×SD16—22no—
88C11×SD16—22no—
89C11×SD16—22no—
90C2×C8×C11C2311yescharacteristic
91C2×C8×C11C2311yescharacteristic
92C11×C4⋊C4—22no—
93C42×C11C2311yescharacteristic
94C22⋊Dic11—22no—
95#4326—22no—
96#4326—22no—
97#4325—22no—
98#4325—22no—
99#4324—22no—
100#4324—22no—
101#4323—22no—
102#4323—22no—
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—22no—
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4D412yes—
107Dic11⋊C4—22no—
108Dic11⋊C4D412yes—
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112Dic44—22no—
113D88—22no—
114#4314—22no—
115#4314—22no—
116#4313D414yescomplemented
117C8×D11D414yescomplemented
118#3154—111nomaximal, Sylow
119C23×C11—21no—
120C23×C11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—42no—
124C22×D11—82no—
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—
134D4×C11—82no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11C2×D412yes—
138C2×C4×C11C2411yescharacteristic
139C22⋊D11—42no—
140C22⋊D11—42no—
141C22⋊D11—82no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—42no—
145C2×Dic11C2×D412yes—
146C2×Dic11C2×D411yescharacteristic
147D44—21no—
148D44—21no—
149D44—21no—
150D44—21no—
151D44—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×AGL(1,ℤ/8)—111no—
167C2×#135—111no—
168C22×SD16—111no—
169#536—111no—
170#535—111no—
171#497—111no—
172#497—111no—
173#496—111no—
174#496—111no—
175#495—111no—
176#495—111no—
177#492—111no—
178#492D1111yescharacteristic, complemented
179#405—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—
206AGL(1,ℤ/8)—224no—
207#135—224no—
208C2×Q16—111no—
209C2×Q16—111no—
210C2×Q16—111no—
211C2×SD16—111no—
212C2×SD16—111no—
213C2×SD16—111no—
214C2×SD16—111no—
215C2×SD16—111no—
216C2×SD16—111no—
217C2×SD16—224no—
218C2×SD16C2×D1111yescharacteristic
219C2×SD16C2×D1111yescharacteristic
220C2×SD16C2×D1111yescharacteristic, complemented
221C2×SD16C2×D1111yescharacteristic, complemented
222C2×D8—111no—
223C2×D8—111no—
224C2×D8—111no—
225C2×M16—111no—
226C22×C8—111no—
227C4⋊Q8—111no—
228C4⋊Q8C2×D1111yescharacteristic, complemented
229#127—111no—
230#127C2×D1111yescharacteristic
231#124—111no—
232#124—111no—
233#124—111no—
234#124—111no—
235#123—222no—
236C22⋊Q8—222no—
237#121—222no—
238#120—222no—
239#117—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#57712yes—
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—22no—
264C2×D4—111no—
265C2×D4—111no—
266C2×D4—221no—
267C2×D4—222no—
268C2×D4—222no—
269C2×D4—221no—
270C2×D4—222no—
271C2×D4—221no—
272C2×D4C22×D1111yescharacteristic
273C2×D4C22×D1111yescharacteristic
274C22×C4—111no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278Q16—222no—
279Q16—222no—
280Q16—222no—
281SD16—22no—
282SD16—22no—
283SD16—22no—
284SD16—22no—
285SD16—222no—
286SD16—222no—
287SD16—222no—
288SD16—222no—
289SD16—222no—
290SD16—222no—
291D8—222no—
292D8—222no—
293D8—222no—
294M16—114no—
295C2×C8—111no—
296C2×C8—111no—
297C2×C8—114no—
298C2×C8C22×D1111yescharacteristic
299C2×C8C22×D1111yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—112no—
302C4⋊C4—222no—
303C22⋊C4—112no—
304C22⋊C4—222no—
305C22⋊C4—222no—
306C22⋊C4—222no—
307C22⋊C4—222no—
308C42—111no—
309C42C22×D1111yescharacteristic
310C11#315411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—111no—
314C23—221no—
315C23—221no—
316C23—442no—
317C23—882no—
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—82no—
332D4—221no—
333D4—221no—
334D4—221no—
335D4—221no—
336D4—442no—
337D4—442no—
338D4—442no—
339D4—882no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—111no—
343C2×C4—112no—
344C2×C4—112no—
345C2×C4—112no—
346C2×C4—221no—
347C2×C4—221no—
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#1062329312yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#492C2
socleC22×C11C22×D4
hypercenter#492D11
hypocenterC11#3154
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#66969C2semidirect
2. C2×#66968C2semidirect
3. C2×#66967C2semidirect
4. C2×SD16×D11C2semidirect
5. #10623255C2semidirect
6. #10623246C2semidirect
7. C11×#492C2semidirect
8. #10622789C2semidirect
9. #10622788C2semidirect
10. #10622781C2semidirect
11. #10622780C2semidirect
12. #10622699C2semidirect
13. #10622687C2semidirect
14. #10622309C2semidirect
15. #10622302C2semidirect
22. C2×C11×SD16C22semidirect
23. C2×C11×SD16C22semidirect
24. C11×C4⋊Q8C22semidirect
26. #67000C22semidirect
27. #66997C22semidirect
28. C2×#4326C22semidirect
29. C2×#4326C22semidirect
37. C2×#4324C22semidirect
39. C2×#4323C22semidirect
44. C2×Dic44C22semidirect
47. C2×#4314C22semidirect
53. #66928C22semidirect
55. C4×C8×C11C22semidirect
56. #66879C22semidirect
57. C8×Dic11C22semidirect
58. #66867C22semidirect
116. #4313D4semidirect
117. C8×D11D4semidirect
178. #492D11semidirect
220. C2×SD16C2×D11semidirect
221. C2×SD16C2×D11semidirect
228. C4⋊Q8C2×D11semidirect
243. C4×C8C2×D11semidirect
310. C11#3154semidirect

Maximal subgroups

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

subgroupindex
C2×#669692
C2×#669682
C2×#669672
C2×SD16×D112
#106232552
#106232462
C11×#4922
#106227892
#106227882
#106227812
#106227802
#106226992
#106226872
#106223092
#106223022
#315411