Finite Group Databasebeta

← #13079420

Subgroups — #13079420

Order 1408.

462 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 115 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×#66999C211yesmaximal, characteristic, complemented
2D11×#121C211yesmaximal, characteristic
3C11×#448C211yesmaximal, characteristic, complemented
4#10622840C211yesmaximal, characteristic, complemented
5#10622787C212yesmaximal, complemented
6#10622782C212yesmaximal, complemented
7#10622646C211yesmaximal, characteristic, complemented
8#10622425C212yesmaximal, complemented
9#10622422C212yesmaximal, complemented
10#10622349C211yesmaximal, characteristic, complemented
11#10622339C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic, complemented
13C2×D4×D11—21no—
14C2×D4×D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C2×C11×SD16C2212yescomplemented
17C11×#121C2211yescharacteristic
18#66999—21no—
19#66999—21no—
20#66999C2212yes—
21#66999C2212yescomplemented
22C2×#4325C2212yescomplemented
23#66992—21no—
24#66991C2211yescharacteristic
25#66983C2211yescharacteristic
26C2×(C2×D11)⋊C4—21no—
27C2×C4⋊Dic11C2211yescharacteristic, complemented
28C2×Dic11⋊C4—21no—
29C2×#4313C2212yescomplemented
30#66948C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32#66937—21no—
33C22⋊C4×D11—21no—
34C11×#103C2212yescomplemented
35C11×C22⋊C8C2211yescharacteristic, complemented
36#66899C2212yescomplemented
37#66896C2212yescomplemented
38C22⋊(C11⋊C8)C2211yescharacteristic, complemented
39#66885C2212yescomplemented
40(C2×D11)⋊C8C2212yes—
41#66882C2212yescomplemented
42#66871C2212yescomplemented
43C23×D11—21no—
44C23×D11D411yescharacteristic
45C2×Q8×C11—21no—
46C2×Q8×C11—42no—
47C2×Q8×C11C2312yes—
48C2×D4×C11—21no—
49C2×D4×C11C2311yescharacteristic
50C22×C4×C11—21no—
51C22×C4×C11C2311yescharacteristic
52C2×C22⋊D11—21no—
53C2×C22⋊D11—21no—
54C2×C22⋊D11—21no—
55C22×Dic11—21no—
56C22×Dic11D411yescharacteristic
57D4×D11—42no—
58D4×D11—44no—
59C2×D44—21no—
60C2×D44C2311yescharacteristic
61C2×C4×D11—21no—
62C2×C4×D11—42no—
63C2×C4×D11D411yescharacteristic
64C2×C4×D11D411yescharacteristic
65C2×C4×D11C2311yescharacteristic
66C2×C4×D11C2311yescharacteristic
67C11×SD16—42no—
68C2×C8×C11C2312yes—
69C11×C4⋊C4C2311yescharacteristic
70C11×C22⋊C4—21no—
71C22⋊Dic11—21no—
72#4325—42no—
73(C2×D11)⋊C4—21no—
74(C2×D11)⋊C4—22no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—21no—
77C4⋊Dic11—21no—
78C4⋊Dic11C2312yes—
79C4⋊Dic11C2311yescharacteristic
80Dic11⋊C4—21no—
81Dic11⋊C4—22no—
82Dic11⋊C4—22no—
83C2×C11⋊C8C2312yes—
84#4313—42no—
85#3193—111nomaximal, Sylow
86C23×C11—21no—
87C23×C11C2×D411yescharacteristic
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—21no—
91C22×D11—41no—
92C22×D11—42no—
93C22×D11—42no—
94C22×D11—42no—
95C22×D11C2×D411yescharacteristic
96C22×D11C2×D411yescharacteristic
97Q8×C11—22no—
98Q8×C11—22no—
99Q8×C11—42no—
100D4×C11—22no—
101D4×C11—42no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—42no—
106C2×C4×C11C2×D411yescharacteristic
107C2×C4×C11C2411yescharacteristic
108C22⋊D11—42no—
109C22⋊D11—42no—
110C22⋊D11—42no—
111C2×Dic11—22no—
112C2×Dic11—21no—
113C2×Dic11—41no—
114C2×Dic11—42no—
115C2×Dic11C2×D411yescharacteristic
116C2×Dic11C2×D411yescharacteristic
117D44—22no—
118D44—42no—
119C4×D11—22no—
120C4×D11—22no—
121C4×D11—41no—
122C4×D11—41no—
123C4×D11—42no—
124C8×C11—22no—
125C11⋊C8—22no—
126C2×C22⋊Q8—111no—
127C2×#121—111no—
128#484—112no—
129#480—111no—
130#480—111no—
131#468—112no—
132#468—112no—
133#450—112no—
134#448—111no—
135#448D1111yescharacteristic, complemented
136#407—111no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11AGL(1,ℤ/8)12yes—
143C22×C11C22×D411yescharacteristic
144C2×D11—21no—
145C2×D11—21no—
146C2×D11—21no—
147C2×D11—21no—
148C2×D11—21no—
149C2×D11—44no—
150C2×D11—41no—
151C2×D11—41no—
152C2×D11—41no—
153C2×D11—84no—
154C2×D11#13712yes—
155C4×C11—21no—
156C4×C11—42no—
157C4×C11—41no—
158C4×C11H(5,𝔽2)12yes—
159Dic11—21no—
160Dic11—21no—
161Dic11—41no—
162Dic11—42no—
163C22×Q8C2×D1111yescharacteristic, complemented
164C22×D4—111no—
165C22×D4—221no—
166C23×C4—111no—
167C2×SD16—112no—
168C2×SD16C2×D1112yescomplemented
169C2×M16—112no—
170C22⋊Q8—112no—
171C22⋊Q8—112no—
172C22⋊Q8—221no—
173C22⋊Q8—221no—
174#121—111no—
175#121—111no—
176#121—111no—
177#121—221no—
178#121—221no—
179#121C2×D1111yescharacteristic
180C2×C4⋊C4—111no—
181C2×C4⋊C4—111no—
182C2×C4⋊C4—221no—
183C2×C22⋊C4—221no—
184C2×C22⋊C4—221no—
185#107—112no—
186#107—112no—
187#103—112no—
188#103C2×D1112yescomplemented
189#102—112no—
190#102—112no—
191C22⋊C8—111no—
192C22⋊C8—112no—
193C22⋊C8C2×D1111yescharacteristic, complemented
194C2×C11—22no—
195C2×C11—81no—
196C2×C11#53411yescharacteristic
197C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C11C2×#13711yescharacteristic
199D11—22no—
200D11—41no—
201D11—81no—
202C24—111no—
203C24—221no—
204C2×Q8—21no—
205C2×Q8—42no—
206C2×Q8C22×D1112yes—
207C2×D4—21no—
208C2×D4—111no—
209C2×D4—221no—
210C2×D4—221no—
211C2×D4—221no—
212C2×D4—221no—
213C2×D4—442no—
214C2×D4—444no—
215C2×D4C22×D1111yescharacteristic
216C22×C4—21no—
217C22×C4—111no—
218C22×C4—111no—
219C22×C4—111no—
220C22×C4—111no—
221C22×C4—111no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4—442no—
225C22×C4C22×D1111yescharacteristic
226SD16—42no—
227SD16—442no—
228M16—442no—
229C2×C8—112no—
230C2×C8C22×D1112yes—
231C4⋊C4—112no—
232C4⋊C4—111no—
233C4⋊C4—221no—
234C4⋊C4—222no—
235C4⋊C4—222no—
236C4⋊C4—221no—
237C4⋊C4C22×D1111yescharacteristic
238C22⋊C4—21no—
239C22⋊C4—221no—
240C22⋊C4—222no—
241C22⋊C4—222no—
242C22⋊C4—221no—
243C22⋊C4—221no—
244C11#319311yescharacteristic, complemented, Sylow
245C23—21no—
246C23—111no—
247C23—111no—
248C23—222no—
249C23—222no—
250C23—221no—
251C23—441no—
252C23—442no—
253C23—442no—
254C23—442no—
255C23D4×D1111yescharacteristic
256Q8—22no—
257Q8—22no—
258Q8—42no—
259D4—22no—
260D4—42no—
261D4—222no—
262D4—442no—
263D4—442no—
264D4—442no—
265D4—442no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—111no—
271C2×C4—111no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—221no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—442no—
279C2×C4—441no—
280C2×C4—442no—
281C2×C4D4×D1111yescharacteristic
282C2×C4C23×D1111yescharacteristic
283C8—22no—
284C8—222no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—112no—
291C22—221no—
292C22—221no—
293C22—221no—
294C22—221no—
295C22—221no—
296C22—444no—
297C22—441no—
298C22—441no—
299C22—441no—
300C22—884no—
301C22#6696712yes—
302C22C2×D4×D1111yescharacteristic
303C4—21no—
304C4—41no—
305C4—42no—
306C4—221no—
307C4—221no—
308C4—441no—
309C4—442no—
310C4#6703712yes—
311C2—22no—
312C2—81no—
313C2—222no—
314C2—441no—
315C2—881no—
316C2#1062312011yescharacteristic
317C2C2×#6696711yescharacteristic
318C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#448C2
socleC22×C11C22×D4
prime radicalD11×#121C2
hypercenter#448D11
hypocenterC11#3193
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×#66999C2semidirect
3. C11×#448C2semidirect
4. #10622840C2semidirect
5. #10622787C2semidirect
6. #10622782C2semidirect
7. #10622646C2semidirect
8. #10622425C2semidirect
9. #10622422C2semidirect
10. #10622349C2semidirect
11. #10622339C2semidirect
12. C22×Q8×C11C22semidirect
16. C2×C11×SD16C22semidirect
21. #66999C22semidirect
22. C2×#4325C22semidirect
27. C2×C4⋊Dic11C22semidirect
29. C2×#4313C22semidirect
34. C11×#103C22semidirect
35. C11×C22⋊C8C22semidirect
36. #66899C22semidirect
37. #66896C22semidirect
38. C22⋊(C11⋊C8)C22semidirect
39. #66885C22semidirect
41. #66882C22semidirect
42. #66871C22semidirect
135. #448D11semidirect
163. C22×Q8C2×D11semidirect
168. C2×SD16C2×D11semidirect
188. #103C2×D11semidirect
193. C22⋊C8C2×D11semidirect
244. C11#3193semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
D11×#1212
C11×#4482
#106228402
#106227872
#106227822
#106226462
#106224252
#106224222
#106223492
#106223392
#319311