Finite Group Databasebeta

← #13078159

Subgroups — #13078159

Order 1408.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#10623358C211yesmaximal, characteristic, complemented
3C2×#67003C211yesmaximal, characteristic, complemented
4#10623336C211yesmaximal, characteristic, complemented
5C2×#66896C211yesmaximal, characteristic, complemented
6#10622779C212yesmaximal, complemented
7#10622776C212yesmaximal, complemented
8#10622766C212yesmaximal, complemented
9#10622763C212yesmaximal, complemented
10#10622746C211yesmaximal, characteristic, complemented
11#10622732C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C2×#4339C2211yescharacteristic
15C11×AGL(1,ℤ/8)—24no—
16C2×C11×SD16C2212yes—
17C2×C11×D8C2212yes—
18C2×C11×M16C2211yescharacteristic
19#67006—22no—
20#67003—24no—
21Q8×Dic11C2212yescomplemented
22C2×#4326C2211yescharacteristic, complemented
23C2×#4325C2211yescharacteristic, complemented
24#66993C2212yes—
25#66991—21no—
26#66991—21no—
27#66989C2212yes—
28D4×Dic11—22no—
29D4×Dic11C2212yescomplemented
30C2×#4324C2211yescharacteristic, complemented
31C2×#4323C2211yescharacteristic, complemented
32#66979—21no—
33#66979C2211yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2211yescharacteristic
36C22×C11⋊C8C2211yescharacteristic
37#66896C2212yes—
38#66896C2212yes—
39#66885C2212yescomplemented
40#66880C2212yescomplemented
41Dic11⋊C8C2212yescomplemented
42Dic11⋊C8C2212yescomplemented
43C24×C11—21no—
44C11×#41—22no—
45C11×#41D414yescomplemented
46C2×Q8×C11C2311yescharacteristic
47C2×D4×C11—21no—
48C2×D4×C11—22no—
49C2×D4×C11—21no—
50C2×D4×C11—22no—
51C2×D4×C11C2312yes—
52C2×D4×C11C2311yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11C2311yescharacteristic
55C2×C22⋊D11—22no—
56C2×C22⋊D11—22no—
57C2×C22⋊D11—21no—
58C22×Dic11—22no—
59C22×Dic11—21no—
60#4339—22no—
61#4339—22no—
62C2×D44C2311yescharacteristic
63C2×C4×D11—21no—
64C2×Dic22C2311yescharacteristic
65C11×SD16—24no—
66C11×D8—24no—
67C11×M16—22no—
68C2×C8×C11C2312yes—
69C22⋊Dic11—22no—
70C22⋊Dic11—22no—
71C22⋊Dic11—22no—
72C22⋊Dic11D412yes—
73#4326—22no—
74#4325—22no—
75#4324—22no—
76#4323—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11—21no—
79C4⋊Dic11D411yescharacteristic
80C4⋊Dic11D411yescharacteristic
81C4⋊Dic11C2312yes—
82C4×Dic11—22no—
83C4×Dic11C2312yes—
84C2×C11⋊C8—22no—
85C2×C11⋊C8C2311yescharacteristic
86C2×C11⋊C8C2311yescharacteristic
87#3045—111nomaximal, Sylow
88C23×C11—21no—
89C23×C11—22no—
90C23×C11—42no—
91C23×C11—81no—
92C23×C11—81no—
93C23×C11C2×D411yescharacteristic
94C22×D11—21no—
95Q8×C11—21no—
96Q8×C11C2×D412yes—
97D4×C11—24no—
98D4×C11—22no—
99D4×C11—21no—
100D4×C11—22no—
101D4×C11—42no—
102D4×C11C2×D412yes—
103C2×C4×C11—21no—
104C2×C4×C11—24no—
105C2×C4×C11C2×D411yescharacteristic
106C2×C4×C11C2×D412yes—
107C2×C4×C11#4112yes—
108C2×C4×C11C2411yescharacteristic
109C22⋊D11—42no—
110C22⋊D11—82no—
111C22⋊D11—82no—
112C2×Dic11—22no—
113C2×Dic11—21no—
114C2×Dic11—82no—
115C2×Dic11—81no—
116C2×Dic11C2×D412yes—
117C2×Dic11C2×D412yes—
118D44—21no—
119D44—21no—
120C4×D11—42no—
121Dic22—21no—
122Dic22—21no—
123C8×C11—22no—
124C11⋊C8—21no—
125C11⋊C8—21no—
126C2×AGL(1,ℤ/8)D1111yescharacteristic, complemented
127C2×#135—111no—
128#535—111no—
129#520—111no—
130#464—112no—
131#463—112no—
132#460—112no—
133#459—112no—
134#424—111no—
135#417—111no—
136C2×#102—111no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—22no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—84no—
146C22×C11#12112yes—
147C22×C11C22×D411yescharacteristic
148C2×D11—41no—
149C2×D11—41no—
150C2×D11—41no—
151C4×C11—22no—
152C4×C11#12112yes—
153C4×C11C22×D411yescharacteristic
154C4×C11C2×#4111yescharacteristic
155Dic11—22no—
156Dic11—22no—
157Dic11—41no—
158Dic11—42no—
159C2×#41—111no—
160C2×#41C2×D1111yescharacteristic
161C22×D4C2×D1111yescharacteristic
162AGL(1,ℤ/8)—24no—
163#135—224no—
164C2×Q16—111no—
165C2×SD16—111no—
166C2×SD16—111no—
167C2×SD16C2×D1112yes—
168C2×D8—111no—
169C2×D8C2×D1112yes—
170C2×M16C2×D1111yescharacteristic
171C22×C8—111no—
172#127—112no—
173#124—112no—
174#121—221no—
175#121—221no—
176#120—222no—
177C4×Q8—112no—
178C4×D4—112no—
179C4×D4—222no—
180#117—111no—
181#117—221no—
182C2×C4⋊C4—111no—
183C2×C4⋊C4—221no—
184C4⋊C8—112no—
185C4⋊C8—112no—
186#103—112no—
187#102—112no—
188#102—112no—
189#102—112no—
190C2×C11—22no—
191C2×C11—42no—
192C2×C11—82no—
193C2×C11C2×#12111yescharacteristic
194C2×C11#57611yescharacteristic
195C2×C11#57711yescharacteristic
196D11—81no—
197C24—21no—
198#41—22no—
199#41—222no—
200#41—222no—
201#41C22⋊D1114yescomplemented
202C2×Q8—111no—
203C2×Q8C22×D1111yescharacteristic
204C2×D4—21no—
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—111no—
209C2×D4—222no—
210C2×D4—222no—
211C2×D4—221no—
212C2×D4C22×D1112yes—
213C2×D4C22×D1111yescharacteristic
214C22×C4—21no—
215C22×C4—222no—
216C22×C4—221no—
217C22×C4—221no—
218C22×C4C22×D1111yescharacteristic
219Q16—222no—
220SD16—24no—
221SD16—222no—
222SD16—222no—
223D8—24no—
224D8—222no—
225M16—22no—
226C2×C8—111no—
227C2×C8—111no—
228C2×C8—222no—
229C2×C8C22×D1112yes—
230C4⋊C4—111no—
231C4⋊C4—111no—
232C4⋊C4—112no—
233C4⋊C4—222no—
234C4⋊C4—221no—
235C22⋊C4—112no—
236C22⋊C4—222no—
237C22⋊C4—222no—
238C22⋊C4—222no—
239C42—112no—
240C42—222no—
241C11#304511yescharacteristic, complemented, Sylow
242C23—21no—
243C23—22no—
244C23—42no—
245C23—81no—
246C23—81no—
247C23—221no—
248C23D4×D1111yescharacteristic
249Q8—21no—
250Q8—221no—
251Q8—221no—
252Q8C2×C22⋊D1112yes—
253D4—24no—
254D4—21no—
255D4—22no—
256D4—22no—
257D4—42no—
258D4—221no—
259D4—221no—
260D4—442no—
261D4—882no—
262D4—882no—
263D4C2×C22⋊D1112yes—
264C2×C4—21no—
265C2×C4—24no—
266C2×C4—112no—
267C2×C4—112no—
268C2×C4—222no—
269C2×C4—221no—
270C2×C4—442no—
271C2×C4—882no—
272C2×C4—881no—
273C2×C4D4×D1111yescharacteristic
274C2×C4#434112yes—
275C2×C4C2×C22⋊D1112yes—
276C2×C4C23×D1111yescharacteristic
277C8—22no—
278C8—221no—
279C8—221no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—84no—
289C22—441no—
290C22—441no—
291C22—441no—
292C22#6699212yes—
293C22C2×D4×D1111yescharacteristic
294C4—22no—
295C4—222no—
296C4—222no—
297C4—442no—
298C4—441no—
299C4#6699212yes—
300C4C2×#434111yescharacteristic
301C4C22×C22⋊D1111yescharacteristic
302C2—22no—
303C2—42no—
304C2—82no—
305C2—881no—
306C2#1062330511yescharacteristic
307C2#1062330611yescharacteristic
308C2C2×#6699211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×AGL(1,ℤ/8)C2
socleC22×C11C22×D4
hypercenterC2×AGL(1,ℤ/8)D11
hypocenterC11#3045
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C11×AGL(1,ℤ/8)C2semidirect
2. #10623358C2semidirect
3. C2×#67003C2semidirect
4. #10623336C2semidirect
5. C2×#66896C2semidirect
6. #10622779C2semidirect
7. #10622776C2semidirect
8. #10622766C2semidirect
9. #10622763C2semidirect
10. #10622746C2semidirect
11. #10622732C2semidirect
21. Q8×Dic11C22semidirect
22. C2×#4326C22semidirect
23. C2×#4325C22semidirect
29. D4×Dic11C22semidirect
30. C2×#4324C22semidirect
31. C2×#4323C22semidirect
39. #66885C22semidirect
40. #66880C22semidirect
41. Dic11⋊C8C22semidirect
42. Dic11⋊C8C22semidirect
45. C11×#41D4semidirect
126. C2×AGL(1,ℤ/8)D11semidirect
201. #41C22⋊D11semidirect
241. C11#3045semidirect

Maximal subgroups

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

subgroupindex
C2×C11×AGL(1,ℤ/8)2
#106233582
C2×#670032
#106233362
C2×#668962
#106227792
#106227762
#106227662
#106227632
#106227462
#106227322
#304511