Finite Group Databasebeta

← #13078554

Subgroups — #13078554

Order 1408.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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×#66991C211yesmaximal, characteristic
2D11×#117C211yesmaximal, characteristic, complemented
3C11×#418C211yesmaximal, characteristic, complemented
4#10622828C211yesmaximal, characteristic, complemented
5#10622739C211yesmaximal, characteristic, complemented
6#10622734C211yesmaximal, characteristic, complemented
7#10622608C211yesmaximal, characteristic, complemented
8#10622397C212yesmaximal, complemented
9#10622392C212yesmaximal, complemented
10#10622390C212yesmaximal, complemented
11#10622387C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C22×C22⋊D11—21no—
14C22×C4×D11C2211yescharacteristic
15C2×C11×M16C2211yescharacteristic
16C11×#117C2211yescharacteristic
17C2×C22⋊Dic11—21no—
18#66991—21no—
19#66991—21no—
20#66991C2212yes—
21#66991C2212yes—
22#66979C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×#4318C2211yescharacteristic
25#66945C2211yescharacteristic, complemented
26#66945C2211yescharacteristic, complemented
27C4⋊C4×D11C2211yescharacteristic, complemented
28C4⋊C4×D11C2211yescharacteristic, complemented
29C22⋊C4×D11—21no—
30#66930—21no—
31#66925—21no—
32C42×D11—21no—
33C11×#102C2212yescomplemented
34C11×#102C2212yescomplemented
35#66896C2212yescomplemented
36#66896C2212yescomplemented
37(C2×D11)⋊C8C2212yescomplemented
38(C2×D11)⋊C8C2212yescomplemented
39#66882C2212yescomplemented
40#66881C2212yescomplemented
41#66872C2212yescomplemented
42#66871C2212yescomplemented
43C24×C11—21no—
44C23×D11D411yescharacteristic
45C2×D4×C11—21no—
46C2×D4×C11—22no—
47C2×D4×C11—22no—
48C2×D4×C11C2312yes—
49C22×C4×C11C2311yescharacteristic
50C2×C22⋊D11—22no—
51C2×C22⋊D11—22no—
52C2×C22⋊D11—44no—
53C22×Dic11—21no—
54C22×Dic11D411yescharacteristic
55C2×C4×D11—21no—
56C2×C4×D11—21no—
57C2×C4×D11—22no—
58C2×C4×D11—22no—
59C2×C4×D11D411yescharacteristic
60C2×C4×D11D411yescharacteristic
61C2×C4×D11C2311yescharacteristic
62C2×C4×D11C2311yescharacteristic
63C11×M16—22no—
64C2×C8×C11C2312yes—
65C11×C4⋊C4C2311yescharacteristic
66C11×C4⋊C4C2311yescharacteristic
67C11×C22⋊C4—21no—
68C42×C11—21no—
69C22⋊Dic11—22no—
70C22⋊Dic11—22no—
71C22⋊Dic11—21no—
72(C2×D11)⋊C4—21no—
73(C2×D11)⋊C4—21no—
74C4⋊Dic11—21no—
75C4⋊Dic11C2312yes—
76C4⋊Dic11C2311yescharacteristic
77C4⋊Dic11C2311yescharacteristic
78Dic11⋊C4—21no—
79Dic11⋊C4—21no—
80C4×Dic11—21no—
81C4×Dic11—21no—
82C4×Dic11—21no—
83#4318—22no—
84C2×C11⋊C8C2312yes—
85#3094—111nomaximal, Sylow
86C23×C11—22no—
87C23×C11—42no—
88C23×C11—42no—
89C23×C11—42no—
90C23×C11C2×D411yescharacteristic
91C22×D11—22no—
92C22×D11—22no—
93C22×D11—41no—
94C22×D11C2×D411yescharacteristic
95C22×D11C2×D411yescharacteristic
96D4×C11—22no—
97D4×C11—22no—
98D4×C11—42no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11C2×D411yescharacteristic
102C2×C4×C11#4112yes—
103C2×C4×C11#4112yes—
104C2×C4×C11C2411yescharacteristic
105C22⋊D11—44no—
106C22⋊D11—44no—
107C2×Dic11—22no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—22no—
111C2×Dic11—42no—
112C2×Dic11C2×D411yescharacteristic
113C2×Dic11C2×D411yescharacteristic
114C4×D11—22no—
115C4×D11—22no—
116C4×D11—21no—
117C4×D11—21no—
118C4×D11—21no—
119C4×D11—21no—
120C4×D11—42no—
121C4×D11—42no—
122C8×C11—22no—
123C11⋊C8—22no—
124C2×#121—111no—
125C2×#117—111no—
126#482—112no—
127#482—112no—
128#481—112no—
129#480—112no—
130#428—111no—
131#428—111no—
132#418—111no—
133#418D1111yescharacteristic, complemented
134#407—111no—
135C22×C11—21no—
136C22×C11—21no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11—42no—
140C22×C11—84no—
141C22×C11#12312yes—
142C22×C11C22×D411yescharacteristic
143C2×D11—21no—
144C2×D11—21no—
145C2×D11—21no—
146C2×D11—21no—
147C2×D11—21no—
148C2×D11—44no—
149C2×D11AGL(1,ℤ/8)12yes—
150C4×C11—41no—
151C4×C11—41no—
152C4×C11#12312yes—
153C4×C11C2×#4111yescharacteristic
154C4×C11C2×#4111yescharacteristic
155Dic11—21no—
156Dic11—21no—
157Dic11—41no—
158Dic11—42no—
159Dic11—41no—
160C22×D4—221no—
161C22×D4C2×D1111yescharacteristic
162C23×C4—111no—
163C2×M16—111no—
164C2×M16C2×D1111yescharacteristic
165#121—112no—
166#121—112no—
167#121—221no—
168#121—221no—
169#117—111no—
170#117—111no—
171#117—111no—
172#117—221no—
173#117—221no—
174#117C2×D1111yescharacteristic
175C2×C4⋊C4—111no—
176C2×C4⋊C4—111no—
177C2×C4⋊C4—111no—
178C2×C22⋊C4—221no—
179C2×C22⋊C4—221no—
180C2×C42—221no—
181#107—112no—
182#107—112no—
183#106—112no—
184#106—112no—
185#102—112no—
186#102—112no—
187#102C2×D1112yescomplemented
188#102C2×D1112yescomplemented
189C22⋊C8—112no—
190C22⋊C8—112no—
191C2×C11—22no—
192C2×C11—82no—
193C2×C11C2×#12311yescharacteristic
194C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C11#57511yescharacteristic
196D11—22no—
197D11—41no—
198C24—21no—
199C24—111no—
200C2×D4—22no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—222no—
204C2×D4—222no—
205C2×D4—444no—
206C2×D4C22×D1112yes—
207C22×C4—111no—
208C22×C4—111no—
209C22×C4—111no—
210C22×C4—111no—
211C22×C4—111no—
212C22×C4—221no—
213C22×C4—221no—
214C22×C4—222no—
215C22×C4—222no—
216C22×C4—221no—
217C22×C4C22×D1111yescharacteristic
218M16—22no—
219M16—222no—
220C2×C8—112no—
221C2×C8C22×D1112yes—
222C4⋊C4—111no—
223C4⋊C4—111no—
224C4⋊C4—112no—
225C4⋊C4—221no—
226C4⋊C4—221no—
227C4⋊C4—221no—
228C4⋊C4C22×D1111yescharacteristic
229C4⋊C4C22×D1111yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—221no—
232C22⋊C4—221no—
233C22⋊C4—222no—
234C22⋊C4—222no—
235C22⋊C4—221no—
236C42—21no—
237C42—221no—
238C42—221no—
239C42—221no—
240C11#309411yescharacteristic, complemented, Sylow
241C23—22no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—111no—
246C23—111no—
247C23—222no—
248C23—222no—
249C23—441no—
250C23D4×D1111yescharacteristic
251D4—22no—
252D4—22no—
253D4—42no—
254D4—444no—
255D4—444no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—111no—
259C2×C4—111no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—222no—
263C2×C4—221no—
264C2×C4—221no—
265C2×C4—221no—
266C2×C4—221no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—222no—
270C2×C4—442no—
271C2×C4—442no—
272C2×C4—442no—
273C2×C4#433912yes—
274C2×C4D4×D1111yescharacteristic
275C2×C4#434112yes—
276C2×C4C23×D1111yescharacteristic
277C8—22no—
278C8—222no—
279C22—21no—
280C22—21no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—84no—
285C22—112no—
286C22—221no—
287C22—221no—
288C22—221no—
289C22—221no—
290C22—221no—
291C22—444no—
292C22#6693612yes—
293C22C2×D4×D1111yescharacteristic
294C4—41no—
295C4—41no—
296C4—221no—
297C4—221no—
298C4—442no—
299C4—441no—
300C4—441no—
301C4#6693612yes—
302C4C2×#433911yescharacteristic
303C4C2×#434111yescharacteristic
304C2—22no—
305C2—82no—
306C2—222no—
307C2—441no—
308C2C2×#6693611yescharacteristic
309C2D11×AGL(1,ℤ/8)11yescharacteristic
310C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#418C2
socleC22×C11C22×D4
prime radicalC2×#66991C2
hypercenter#418D11
hypocenterC11#3094
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. D11×#117C2semidirect
3. C11×#418C2semidirect
4. #10622828C2semidirect
5. #10622739C2semidirect
6. #10622734C2semidirect
7. #10622608C2semidirect
8. #10622397C2semidirect
9. #10622392C2semidirect
10. #10622390C2semidirect
11. #10622387C2semidirect
25. #66945C22semidirect
26. #66945C22semidirect
27. C4⋊C4×D11C22semidirect
28. C4⋊C4×D11C22semidirect
33. C11×#102C22semidirect
34. C11×#102C22semidirect
35. #66896C22semidirect
36. #66896C22semidirect
37. (C2×D11)⋊C8C22semidirect
38. (C2×D11)⋊C8C22semidirect
39. #66882C22semidirect
40. #66881C22semidirect
41. #66872C22semidirect
42. #66871C22semidirect
133. #418D11semidirect
187. #102C2×D11semidirect
188. #102C2×D11semidirect
240. C11#3094semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
D11×#1172
C11×#4182
#106228282
#106227392
#106227342
#106226082
#106223972
#106223922
#106223902
#106223872
#309411