Finite Group Databasebeta

← #13080237

Subgroups — #13080237

Order 1408.

556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66967C212yesmaximal, complemented
2#10623108C211yesmaximal, characteristic, complemented
3D4×D44C211yesmaximal, characteristic, complemented
4C4×C11×SD16C211yesmaximal, characteristic, complemented
5#10622640C211yesmaximal, characteristic, complemented
6#10622628C211yesmaximal, characteristic, complemented
7#10622478C212yesmaximal, complemented
8#10622424C212yesmaximal, complemented
9#10622386C212yesmaximal, complemented
10#10622308C211yesmaximal, characteristic, complemented
11#10622301C211yesmaximal, characteristic, complemented
12C2×#4343C2212yescomplemented
13C2×D4×D11C2212yes—
14C22×D44—21no—
15C2×C11×SD16C2211yescharacteristic
16C4×Q8×C11C2211yescharacteristic, complemented
17C4×D4×C11C2211yescharacteristic
18C2×#4325C2212yescomplemented
19C2×#4323C2212yes—
20#66983—21no—
21#66967—28no—
22C2×D88C2212yescomplemented
23C2×D88C2212yescomplemented
24C2×#4313C2212yescomplemented
25#66948—22no—
26#66948C2212yes—
27#66948C2212yescomplemented
28#66935—22no—
29#66927—21no—
30#66927C2211yescharacteristic
31#66927C2211yescharacteristic, complemented
32C4×D44—21no—
33C4×D44C2211yescharacteristic
34C11×#106C2211yescharacteristic, complemented
35C11×#103C2211yescharacteristic, complemented
36C11×#102C2211yescharacteristic
37C4×C8×C11C2211yescharacteristic, complemented
38(C2×D11)⋊C8C2212yescomplemented
39#66873C2212yescomplemented
40#66873C2212yescomplemented
41C4⋊(C11⋊C8)C2211yescharacteristic, complemented
42C23×D11—22no—
43C2×Q8×C11C2311yescharacteristic
44C2×D4×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C2×C22⋊D11—22no—
47#4343—24no—
48#4343—42no—
49D4×D11—24no—
50D4×D11—42no—
51C2×D44—22no—
52C2×D44—22no—
53C2×D44—22no—
54C2×D44—21no—
55C2×D44—21no—
56C2×D44—21no—
57C2×D44—21no—
58C2×D44—44no—
59C2×D44D411yescharacteristic
60C2×D44C2312yes—
61C2×D44C2312yes—
62C2×C4×D11—22no—
63C2×C4×D11C2312yes—
64C11×SD16D414yescomplemented
65C2×C8×C11C2311yescharacteristic
66C2×C8×C11C2311yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4C2311yescharacteristic
69C11×C4⋊C4C2311yescharacteristic
70C11×C22⋊C4—21no—
71C42×C11—21no—
72C42×C11C2311yescharacteristic
73#4325—24no—
74#4323—24no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—22no—
77(C2×D11)⋊C4D412yes—
78C4⋊Dic11D411yescharacteristic
79C2×C11⋊C8C2312yes—
80D88—24no—
81D88—42no—
82#4313—24no—
83#3274—111nomaximal, Sylow
84C23×C11—21no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—44no—
88C22×D11—44no—
89C22×D11—82no—
90C22×D11C2×D412yes—
91Q8×C11—21no—
92Q8×C11C2×D412yescomplemented
93D4×C11—21no—
94D4×C11C2×D412yes—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—42no—
99C2×C4×C11C2×D411yescharacteristic
100C2×C4×C11C2×D411yescharacteristic
101C2×C4×C11C2411yescharacteristic
102C22⋊D11—44no—
103C2×Dic11C2×D412yes—
104D44—22no—
105D44—22no—
106D44—22no—
107D44—22no—
108D44—22no—
109D44—44no—
110D44—44no—
111D44—42no—
112D44—42no—
113D44—81no—
114D44—81no—
115D44—82no—
116C4×D11—22no—
117C4×D11—22no—
118C4×D11—44no—
119C8×C11—21no—
120C8×C11C2×D412yescomplemented
121C11⋊C8—22no—
122C2×AGL(1,ℤ/8)—112no—
123#550—111no—
124D42—111no—
125#493—111no—
126#469—112no—
127#460—111no—
128#459—111no—
129#449—112no—
130#447—112no—
131C4×SD16D1111yescharacteristic, complemented
132#436—111no—
133C22×C11—22no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11C22×D411yescharacteristic
137C2×D11—22no—
138C2×D11—22no—
139C2×D11—22no—
140C2×D11—42no—
141C2×D11—42no—
142C2×D11—42no—
143C2×D11—42no—
144C2×D11—42no—
145C2×D11—42no—
146C2×D11—88no—
147C4×C11—22no—
148C4×C11—21no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11AGL(1,ℤ/8)12yescomplemented
152C4×C11C22×D411yescharacteristic
153C4×C11H(5,𝔽2)11yescharacteristic
154Dic11—22no—
155C2×#41—112no—
156C22×D4—112no—
157C22×D4—221no—
158AGL(1,ℤ/8)—228no—
159C2×SD16—112no—
160C2×SD16C2×D1111yescharacteristic
161C2×D8—112no—
162C2×D8—112no—
163C2×D8—112no—
164C2×M16—112no—
165#127—111no—
166#127—111no—
167#127—221no—
168#121—112no—
169#121—112no—
170#121—222no—
171#121—221no—
172#120—222no—
173C4×Q8C2×D1111yescharacteristic, complemented
174C4×D4—111no—
175C4×D4—221no—
176C4×D4C2×D1111yescharacteristic
177#106C2×D1111yescharacteristic, complemented
178C4⋊C8—111no—
179#103C2×D1111yescharacteristic, complemented
180#102—112no—
181#102—112no—
182#102C2×D1111yescharacteristic
183C22⋊C8—112no—
184C4×C8C2×D1111yescharacteristic, complemented
185C2×C11—42no—
186C2×C11D4211yescharacteristic
187C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C11#57611yescharacteristic
189D11—42no—
190D11—82no—
191D11—82no—
192C24—222no—
193#41—224no—
194#41—442no—
195C2×Q8C22×D1111yescharacteristic
196C2×D4—111no—
197C2×D4—112no—
198C2×D4—112no—
199C2×D4—222no—
200C2×D4—222no—
201C2×D4—222no—
202C2×D4—222no—
203C2×D4—224no—
204C2×D4—221no—
205C2×D4—221no—
206C2×D4—221no—
207C2×D4—221no—
208C2×D4—444no—
209C2×D4—442no—
210C2×D4C22×D1111yescharacteristic
211C22×C4—21no—
212C22×C4—112no—
213C22×C4—222no—
214SD16—224no—
215SD16D4414yescomplemented
216D8—224no—
217D8—224no—
218D8—442no—
219M16—224no—
220C2×C8—112no—
221C2×C8C22×D1111yescharacteristic
222C2×C8C22×D1111yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—111no—
225C4⋊C4C22×D1111yescharacteristic
226C4⋊C4C22×D1111yescharacteristic
227C22⋊C4—21no—
228C22⋊C4—112no—
229C22⋊C4—222no—
230C22⋊C4—222no—
231C42—21no—
232C42C22×D1111yescharacteristic
233C11#327411yescharacteristic, complemented, Sylow
234C23—21no—
235C23—112no—
236C23—222no—
237C23—222no—
238C23—444no—
239C23—444no—
240C23—882no—
241Q8—21no—
242Q8C2×D4412yescomplemented
243D4—21no—
244D4—222no—
245D4—222no—
246D4—222no—
247D4—222no—
248D4—222no—
249D4—444no—
250D4—444no—
251D4—444no—
252D4—442no—
253D4—442no—
254D4—881no—
255D4—881no—
256D4—882no—
257D4C2×D4412yes—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—112no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—444no—
266C2×C4D4×D1111yescharacteristic
267C2×C4D4×D1111yescharacteristic
268C2×C4C23×D1111yescharacteristic
269C8—21no—
270C8—222no—
271C8C2×D4412yescomplemented
272C22—22no—
273C22—41no—
274C22—41no—
275C22—222no—
276C22—222no—
277C22—222no—
278C22—442no—
279C22—442no—
280C22—442no—
281C22—442no—
282C22—442no—
283C22—442no—
284C22—888no—
285C22C2×D4×D1111yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—222no—
291C4#6696712yescomplemented
292C4C22×D4411yescharacteristic
293C4#6704211yescharacteristic
294C2—42no—
295C2—442no—
296C2—882no—
297C2—882no—
298C2D4×D4411yescharacteristic
299C2C2×#6696711yescharacteristic
300C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×SD16C2
socleC22×C11C22×D4
hypercenterC4×SD16D11
hypocenterC11#3274
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#66967C2semidirect
2. #10623108C2semidirect
3. D4×D44C2semidirect
4. C4×C11×SD16C2semidirect
5. #10622640C2semidirect
6. #10622628C2semidirect
7. #10622478C2semidirect
8. #10622424C2semidirect
9. #10622386C2semidirect
10. #10622308C2semidirect
11. #10622301C2semidirect
12. C2×#4343C22semidirect
16. C4×Q8×C11C22semidirect
18. C2×#4325C22semidirect
22. C2×D88C22semidirect
23. C2×D88C22semidirect
24. C2×#4313C22semidirect
27. #66948C22semidirect
31. #66927C22semidirect
34. C11×#106C22semidirect
35. C11×#103C22semidirect
37. C4×C8×C11C22semidirect
38. (C2×D11)⋊C8C22semidirect
39. #66873C22semidirect
40. #66873C22semidirect
41. C4⋊(C11⋊C8)C22semidirect
64. C11×SD16D4semidirect
92. Q8×C11C2×D4semidirect
120. C8×C11C2×D4semidirect
131. C4×SD16D11semidirect
151. C4×C11AGL(1,ℤ/8)semidirect
173. C4×Q8C2×D11semidirect
177. #106C2×D11semidirect
179. #103C2×D11semidirect
184. C4×C8C2×D11semidirect
215. SD16D44semidirect
233. C11#3274semidirect
242. Q8C2×D44semidirect
271. C8C2×D44semidirect
291. C4#66967semidirect

Maximal subgroups

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

subgroupindex
C2×#669672
#106231082
D4×D442
C4×C11×SD162
#106226402
#106226282
#106224782
#106224242
#106223862
#106223082
#106223012
#327411