Finite Group Databasebeta

← #13079602

Subgroups — #13079602

Order 1408.

444 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 113 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×#67000C211yesmaximal, characteristic, complemented
2#10623127C211yesmaximal, characteristic, complemented
3C11×#448C211yesmaximal, characteristic, complemented
4#10622840C211yesmaximal, characteristic, complemented
5#10622789C212yesmaximal, complemented
6#10622778C212yesmaximal, complemented
7#10622649C211yesmaximal, characteristic, complemented
8#10622432C212yesmaximal, complemented
9#10622408C212yesmaximal, complemented
10#10622345C211yesmaximal, characteristic, complemented
11#10622332C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C2×#4341—21no—
14C22×D44C2211yescharacteristic
15C2×C11×SD16C2212yescomplemented
16C11×#121C2211yescharacteristic
17#67000—21no—
18#67000—21no—
19#67000C2212yes—
20#67000C2212yes—
21C2×#4325C2212yescomplemented
22#66993C2211yescharacteristic, complemented
23#66992—21no—
24D4×Dic11C2211yescharacteristic, complemented
25C2×#4323C2212yes—
26#66983C2211yescharacteristic
27C2×(C2×D11)⋊C4—21no—
28C2×(C2×D11)⋊C4—21no—
29C2×C4×Dic11C2211yescharacteristic
30C2×D88C2212yes—
31#66946C2211yescharacteristic, complemented
32#66941C2211yescharacteristic, complemented
33#66938—21no—
34(C22⋊D11)⋊C4—21no—
35C11×#103C2212yescomplemented
36C11×C22⋊C8C2211yescharacteristic
37#66899C2212yescomplemented
38C22⋊(C11⋊C8)C2211yescharacteristic
39#66885C2212yes—
40#66879C2212yescomplemented
41Dic11⋊C8C2212yescomplemented
42#66873C2212yes—
43C23×D11—21no—
44C2×Q8×C11—21no—
45C2×Q8×C11—42no—
46C2×Q8×C11C2312yes—
47C2×D4×C11—21no—
48C2×D4×C11C2311yescharacteristic
49C22×C4×C11—21no—
50C22×C4×C11C2311yescharacteristic
51C2×C22⋊D11—21no—
52C2×C22⋊D11—21no—
53C2×C22⋊D11—21no—
54C22×Dic11—21no—
55C22×Dic11D411yescharacteristic
56C22×Dic11D411yescharacteristic
57#4341—44no—
58C2×D44—21no—
59C2×D44—42no—
60C2×D44C2312yes—
61C2×D44C2311yescharacteristic
62C2×C4×D11—21no—
63C2×Dic22—21no—
64C11×SD16—42no—
65C2×C8×C11C2312yes—
66C11×C4⋊C4C2311yescharacteristic
67C11×C22⋊C4—21no—
68C22⋊Dic11—21no—
69#4325—42no—
70#4323—42no—
71(C2×D11)⋊C4—21no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—22no—
74(C2×D11)⋊C4—22no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—21no—
77C4⋊Dic11C2311yescharacteristic
78Dic11⋊C4—21no—
79C4×Dic11D411yescharacteristic
80C4×Dic11D411yescharacteristic
81C4×Dic11C2311yescharacteristic
82C4×Dic11C2311yescharacteristic
83C2×C11⋊C8C2312yes—
84D88—42no—
85#3213—111nomaximal, Sylow
86C23×C11—21no—
87C23×C11C2×D411yescharacteristic
88C22×D11—22no—
89C22×D11—21no—
90C22×D11—42no—
91C22×D11—42no—
92C22×D11—42no—
93Q8×C11—22no—
94Q8×C11—22no—
95Q8×C11—42no—
96D4×C11—22no—
97D4×C11—42no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—42no—
102C2×C4×C11C2×D411yescharacteristic
103C2×C4×C11C2411yescharacteristic
104C22⋊D11—42no—
105C22⋊D11—42no—
106C22⋊D11—42no—
107C2×Dic11—22no—
108C2×Dic11—21no—
109C2×Dic11—41no—
110C2×Dic11—42no—
111C2×Dic11C2×D411yescharacteristic
112C2×Dic11C2×D411yescharacteristic
113C2×Dic11C2×D411yescharacteristic
114C2×Dic11C2×D411yescharacteristic
115D44—22no—
116D44—22no—
117D44—22no—
118D44—42no—
119C4×D11—42no—
120Dic22—42no—
121C8×C11—22no—
122C11⋊C8—22no—
123#532—111no—
124C2×#124—111no—
125#496—112no—
126#489—112no—
127#463—112no—
128#463—112no—
129#448—111no—
130#448D1111yescharacteristic, complemented
131#447—111no—
132#447—111no—
133#432—111no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11AGL(1,ℤ/8)12yes—
140C22×C11C22×D411yescharacteristic
141C2×D11—42no—
142C2×D11—41no—
143C2×D11—42no—
144C2×D11—41no—
145C2×D11—42no—
146C2×D11—41no—
147C2×D11—84no—
148C4×C11—21no—
149C4×C11—42no—
150C4×C11—41no—
151C4×C11H(5,𝔽2)12yes—
152Dic11—21no—
153Dic11—21no—
154Dic11—21no—
155Dic11—21no—
156Dic11—41no—
157C2×#41—221no—
158C22×Q8C2×D1111yescharacteristic
159C22×D4—111no—
160C2×SD16—112no—
161C2×SD16C2×D1112yescomplemented
162C2×D8—112no—
163C2×D8—112no—
164C4⋊Q8—111no—
165#127—111no—
166#124—112no—
167#124—112no—
168#124—221no—
169#124—221no—
170#124—221no—
171#121—111no—
172#121—221no—
173#121C2×D1111yescharacteristic
174C4×D4—111no—
175C4×D4—111no—
176C4×D4—221no—
177C2×C22⋊C4—221no—
178C2×C22⋊C4—221no—
179C2×C42—111no—
180C4⋊C8—112no—
181#103—112no—
182#103C2×D1112yescomplemented
183#102—112no—
184#102—112no—
185C22⋊C8—111no—
186C22⋊C8C2×D1111yescharacteristic
187#97—112no—
188C2×C11—22no—
189C2×C11—81no—
190C2×C11#53511yescharacteristic
191C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C11#57511yescharacteristic
193D11—81no—
194D11—82no—
195C24—221no—
196#41—444no—
197C2×Q8—21no—
198C2×Q8—42no—
199C2×Q8—221no—
200C2×Q8C22×D1112yes—
201C2×D4—21no—
202C2×D4—112no—
203C2×D4—111no—
204C2×D4—221no—
205C2×D4—221no—
206C2×D4—221no—
207C2×D4—221no—
208C2×D4—442no—
209C2×D4C22×D1111yescharacteristic
210C22×C4—21no—
211C22×C4—111no—
212C22×C4—111no—
213C22×C4—221no—
214C22×C4—221no—
215C22×C4C22×D1111yescharacteristic
216SD16—42no—
217SD16—442no—
218D8—442no—
219D8—442no—
220C2×C8—112no—
221C2×C8C22×D1112yes—
222C4⋊C4—111no—
223C4⋊C4—221no—
224C4⋊C4C22×D1111yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—222no—
227C22⋊C4—222no—
228C22⋊C4—222no—
229C22⋊C4—222no—
230C22⋊C4—221no—
231C22⋊C4—221no—
232C22⋊C4—221no—
233C42—111no—
234C42—111no—
235C42—111no—
236C42—111no—
237C11#321311yescharacteristic, complemented, Sylow
238C23—21no—
239C23—222no—
240C23—221no—
241C23—442no—
242C23—442no—
243C23—442no—
244C23D4×D1111yescharacteristic
245Q8—22no—
246Q8—22no—
247Q8—42no—
248Q8—442no—
249D4—22no—
250D4—42no—
251D4—222no—
252D4—222no—
253D4—222no—
254D4—442no—
255D4—442no—
256D4—442no—
257D4—442no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—111no—
263C2×C4—111no—
264C2×C4—111no—
265C2×C4—111no—
266C2×C4—222no—
267C2×C4—221no—
268C2×C4—442no—
269C2×C4—441no—
270C2×C4—442no—
271C2×C4D4×D1111yescharacteristic
272C2×C4C23×D1111yescharacteristic
273C8—22no—
274C8—222no—
275C22—21no—
276C22—21no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—441no—
281C22—442no—
282C22—441no—
283C22—442no—
284C22—442no—
285C22—441no—
286C22—884no—
287C22#6696712yes—
288C22C2×D4×D1111yescharacteristic
289C4—21no—
290C4—41no—
291C4—42no—
292C4—221no—
293C4—221no—
294C4—221no—
295C4—221no—
296C4—441no—
297C4#6703712yes—
298C2—22no—
299C2—81no—
300C2—882no—
301C2—881no—
302C2#1062312311yescharacteristic
303C2C2×#6696711yescharacteristic
304C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#448C2
socleC22×C11C22×D4
hypercenter#448D11
hypocenterC11#3213
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#67000C2semidirect
2. #10623127C2semidirect
3. C11×#448C2semidirect
4. #10622840C2semidirect
5. #10622789C2semidirect
6. #10622778C2semidirect
7. #10622649C2semidirect
8. #10622432C2semidirect
9. #10622408C2semidirect
10. #10622345C2semidirect
11. #10622332C2semidirect
15. C2×C11×SD16C22semidirect
21. C2×#4325C22semidirect
22. #66993C22semidirect
24. D4×Dic11C22semidirect
31. #66946C22semidirect
32. #66941C22semidirect
35. C11×#103C22semidirect
37. #66899C22semidirect
40. #66879C22semidirect
41. Dic11⋊C8C22semidirect
130. #448D11semidirect
161. C2×SD16C2×D11semidirect
182. #103C2×D11semidirect
237. C11#3213semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
#106231272
C11×#4482
#106228402
#106227892
#106227782
#106226492
#106224322
#106224082
#106223452
#106223322
#321311