Finite Group Databasebeta

← #13079087

Subgroups — #13079087

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×#66971C211yesmaximal, characteristic, complemented
2C2×#66969C211yesmaximal, characteristic, complemented
3C2×SD16×D11C211yesmaximal, characteristic, complemented
4C2×#66964C211yesmaximal, characteristic, complemented
5#10623206C211yesmaximal, characteristic, complemented
6#10623205C211yesmaximal, characteristic, complemented
7C11×#495C211yesmaximal, characteristic, complemented
8#10622803C211yesmaximal, characteristic, complemented
9#10622788C211yesmaximal, characteristic, complemented
10#10622781C211yesmaximal, characteristic, complemented
11#10622767C211yesmaximal, characteristic, complemented
12#10622673C211yesmaximal, characteristic, complemented
13#10622671C211yesmaximal, characteristic, complemented
14#10622306C211yesmaximal, characteristic, complemented
15#10622302C211yesmaximal, 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
33#66989C2211yescharacteristic, complemented
34C2×#4324C2211yescharacteristic
35C2×#4324C2211yescharacteristic
36C2×#4323C2211yescharacteristic
37C2×#4323C2211yescharacteristic, complemented
38#66971—24no—
39#66969—24no—
40SD16×D11—24no—
41#66964—24no—
42C2×#4314C2211yescharacteristic
43C2×#4314C2211yescharacteristic
44C2×#4314C2211yescharacteristic, complemented
45C2×#4314C2211yescharacteristic, complemented
46C2×#4313C2211yescharacteristic
47C2×C8×D11C2211yescharacteristic
48#66937—22no—
49#66936—22no—
50#66935—22no—
51#66931—22no—
52#66927C2211yescharacteristic
53#66925C2211yescharacteristic
54#66922C2211yescharacteristic, complemented
55C4×C8×C11C2211yescharacteristic, complemented
56#66879C2211yescharacteristic, complemented
57C8×Dic11C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—22no—
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×D44—22no—
78C2×D44C2311yescharacteristic
79C2×D44C2311yescharacteristic
80C2×C4×D11—21no—
81C2×C4×D11—21no—
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)⋊C4D412yes—
106C4⋊Dic11—22no—
107Dic11⋊C4—22no—
108Dic11⋊C4D412yes—
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112#4314—22no—
113#4314—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—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11C2×D412yes—
137C2×C4×C11C2411yescharacteristic
138C22⋊D11—42no—
139C22⋊D11—42no—
140C22⋊D11—82no—
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—
151D44—82no—
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#495D1111yescharacteristic, complemented
177#492—111no—
178#492—111no—
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×Q16C2×D1111yescharacteristic, complemented
211C2×SD16—111no—
212C2×SD16—111no—
213C2×SD16—111no—
214C2×SD16—111no—
215C2×SD16—111no—
216C2×SD16—111no—
217C2×SD16—111no—
218C2×SD16—111no—
219C2×SD16—224no—
220C2×SD16C2×D1111yescharacteristic
221C2×SD16C2×D1111yescharacteristic, complemented
222C2×D8—111no—
223C2×D8—111no—
224C2×D8C2×D1111yescharacteristic
225C2×M16—111no—
226C22×C8—111no—
227C4⋊Q8—111no—
228C4⋊Q8—111no—
229#127—111no—
230#127—111no—
231#124—111no—
232#124—111no—
233#124C2×D1111yescharacteristic
234#124C2×D1111yescharacteristic, complemented
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—111no—
264C2×D4—111no—
265C2×D4—221no—
266C2×D4—222no—
267C2×D4—222no—
268C2×D4—221no—
269C2×D4—222no—
270C2×D4—221no—
271C2×D4—222no—
272C2×D4C22×D1111yescharacteristic
273C2×D4C22×D1111yescharacteristic
274C22×C4—111no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278Q16—22no—
279Q16—222no—
280Q16—222no—
281SD16—22no—
282SD16—22no—
283SD16—222no—
284SD16—222no—
285SD16—222no—
286SD16—222no—
287SD16—222no—
288SD16—222no—
289SD16—222no—
290SD16—222no—
291D8—22no—
292D8—222no—
293D8—222no—
294M16—114no—
295C2×C8—111no—
296C2×C8—111no—
297C2×C8—114no—
298C2×C8C22×D1111yescharacteristic
299C2×C8C22×D1111yescharacteristic
300C4⋊C4—112no—
301C4⋊C4—222no—
302C4⋊C4—222no—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—112no—
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—221no—
332D4—221no—
333D4—221no—
334D4—221no—
335D4—442no—
336D4—442no—
337D4—442no—
338D4—882no—
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#1062330112yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#495C2
socleC22×C11C22×D4
hypercenter#495D11
hypocenterC11#3154
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×#66969C2semidirect
3. C2×SD16×D11C2semidirect
4. C2×#66964C2semidirect
5. #10623206C2semidirect
6. #10623205C2semidirect
7. C11×#495C2semidirect
8. #10622803C2semidirect
9. #10622788C2semidirect
10. #10622781C2semidirect
11. #10622767C2semidirect
12. #10622673C2semidirect
13. #10622671C2semidirect
14. #10622306C2semidirect
15. #10622302C2semidirect
20. C2×C11×Q16C22semidirect
22. C2×C11×SD16C22semidirect
25. C11×#124C22semidirect
27. #66997C22semidirect
28. C2×#4326C22semidirect
29. C2×#4326C22semidirect
31. C2×#4325C22semidirect
33. #66989C22semidirect
37. C2×#4323C22semidirect
44. C2×#4314C22semidirect
45. C2×#4314C22semidirect
54. #66922C22semidirect
55. C4×C8×C11C22semidirect
56. #66879C22semidirect
57. C8×Dic11C22semidirect
58. #66867C22semidirect
116. #4313D4semidirect
117. C8×D11D4semidirect
176. #495D11semidirect
210. C2×Q16C2×D11semidirect
221. C2×SD16C2×D11semidirect
234. #124C2×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×#669712
C2×#669692
C2×SD16×D112
C2×#669642
#106232062
#106232052
C11×#4952
#106228032
#106227882
#106227812
#106227672
#106226732
#106226712
#106223062
#106223022
#315411