Finite Group Databasebeta

← #13078449

Subgroups — #13078449

Order 1408.

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

normal subgroups only

This group has 398 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
1#10623329C211yesmaximal, characteristic
2#10623050C211yesmaximal, characteristic, complemented
3C11×#418C211yesmaximal, characteristic
4C2×#66896C211yesmaximal, characteristic
5#10622734C211yesmaximal, characteristic, complemented
6#10622732C211yesmaximal, characteristic, complemented
7#10622611C211yesmaximal, characteristic, complemented
8#10622379C212yesmaximal, complemented
9#10622376C212yesmaximal, complemented
10#10622374C212yesmaximal, complemented
11#10622372C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C11×#117C2211yescharacteristic
15C2×C22⋊Dic11—22no—
16D4×Dic11—21no—
17D4×Dic11—21no—
18D4×Dic11C2212yes—
19D4×Dic11C2212yes—
20#66979C2211yescharacteristic
21#66979C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C22×C11⋊C8C2211yescharacteristic
24#66943C2212yescomplemented
25#66941C2212yescomplemented
26#66931—22no—
27#66923—21no—
28#66922—21no—
29C11×#102C2212yes—
30C11×#102C2212yes—
31#66896C2212yes—
32#66896C2212yes—
33#66882C2212yescomplemented
34#66881C2212yescomplemented
35Dic11⋊C8C2212yescomplemented
36Dic11⋊C8C2212yescomplemented
37#66872C2211yescharacteristic, complemented
38#66872C2211yescharacteristic, complemented
39#66871C2211yescharacteristic, complemented
40#66871C2211yescharacteristic, complemented
41C24×C11—21no—
42C2×D4×C11—21no—
43C2×D4×C11—22no—
44C2×D4×C11Q814yescomplemented
45C2×D4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×Dic11—22no—
48C22×Dic11—22no—
49C22×Dic11—21no—
50C2×Dic22—22no—
51C11×M16—22no—
52C2×C8×C11C2312yes—
53C11×C4⋊C4C2311yescharacteristic
54C11×C4⋊C4C2311yescharacteristic
55C11×C22⋊C4—21no—
56C42×C11—21no—
57C22⋊Dic11—22no—
58C22⋊Dic11—22no—
59C22⋊Dic11—21no—
60C22⋊Dic11D412yes—
61C4⋊Dic11—22no—
62C4⋊Dic11—21no—
63C4⋊Dic11D411yescharacteristic
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11C2311yescharacteristic
66C4⋊Dic11C2311yescharacteristic
67C4⋊Dic11C2312yes—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70C4×Dic11—21no—
71C4×Dic11C2312yes—
72C2×C11⋊C8—22no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75#3081—111nomaximal, Sylow
76C23×C11—22no—
77C23×C11—24no—
78C23×C11—81no—
79C23×C11—81no—
80C23×C11C2×D411yescharacteristic
81D4×C11—24no—
82D4×C11—22no—
83D4×C11C2×Q814yes—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×Q812yes—
88C2×C4×C11#4112yes—
89C2×C4×C11C2411yescharacteristic
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—82no—
94C2×Dic11—82no—
95C2×Dic11—81no—
96C2×Dic11C2×D412yes—
97C2×Dic11C2×D412yes—
98Dic22—82no—
99C8×C11—22no—
100C11⋊C8—21no—
101C11⋊C8—21no—
102#544—111no—
103#518—111no—
104#478—112no—
105#478—112no—
106#476—112no—
107#474—112no—
108#428—111no—
109#427—111no—
110#424—111no—
111#418D1111yescharacteristic
112C2×#102—111no—
113C22×C11—21no—
114C22×C11—21no—
115C22×C11—24no—
116C22×C11—42no—
117C22×C11—42no—
118C22×C11—84no—
119C22×C11C22⋊Q812yes—
120C22×C11C22×D411yescharacteristic
121C4×C11—41no—
122C4×C11—41no—
123C4×C11C22⋊Q812yes—
124C4×C11C22×Q811yescharacteristic
125C4×C11C2×#4111yescharacteristic
126Dic11—22no—
127Dic11—22no—
128Dic11—42no—
129Dic11—41no—
130Dic11—41no—
131C22×D4C2×D1111yescharacteristic
132C2×M16C2×D1111yescharacteristic
133C22×C8—111no—
134C4⋊Q8—112no—
135C4⋊Q8—221no—
136#125—112no—
137#125—221no—
138C22⋊Q8—222no—
139C4×D4—112no—
140C4×D4—112no—
141C4×D4—221no—
142C4×D4—221no—
143#117—111no—
144#117—111no—
145#117C2×D1111yescharacteristic
146C2×C4⋊C4—111no—
147C2×C22⋊C4—222no—
148#107—112no—
149#107—111no—
150#107—111no—
151#106—112no—
152#106—111no—
153#106—111no—
154C4⋊C8—112no—
155C4⋊C8—112no—
156#102—112no—
157#102—112no—
158#102C2×D1112yes—
159#102C2×D1112yes—
160C2×C11—22no—
161C2×C11—44no—
162C2×C11C2×C22⋊Q811yescharacteristic
163C2×C11#57611yescharacteristic
164C2×C11#57711yescharacteristic
165C24—21no—
166C2×Q8—222no—
167C2×D4—21no—
168C2×D4—22no—
169C2×D4Dic2214yescomplemented
170C2×D4C22×D1112yes—
171C22×C4—222no—
172C22×C4—222no—
173C22×C4—221no—
174C22×C4C22×D1111yescharacteristic
175M16—22no—
176C2×C8—111no—
177C2×C8—111no—
178C2×C8—222no—
179C2×C8C22×D1112yes—
180C4⋊C4—111no—
181C4⋊C4—111no—
182C4⋊C4—112no—
183C4⋊C4—111no—
184C4⋊C4—111no—
185C4⋊C4—222no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—221no—
189C4⋊C4C22×D1111yescharacteristic
190C4⋊C4C22×D1111yescharacteristic
191C22⋊C4—21no—
192C22⋊C4—112no—
193C22⋊C4—222no—
194C22⋊C4—222no—
195C22⋊C4—221no—
196C42—21no—
197C42—112no—
198C42—221no—
199C11#308111yescharacteristic, complemented, Sylow
200C23—22no—
201C23—24no—
202C23—81no—
203C23—81no—
204C23D4×D1111yescharacteristic
205Q8—882no—
206D4—24no—
207D4—22no—
208D4C2×Dic2214yes—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—112no—
212C2×C4—112no—
213C2×C4—221no—
214C2×C4—221no—
215C2×C4—222no—
216C2×C4—882no—
217C2×C4—882no—
218C2×C4—881no—
219C2×C4C2×Dic2212yes—
220C2×C4D4×D1111yescharacteristic
221C2×C4#434112yes—
222C2×C4C23×D1111yescharacteristic
223C8—22no—
224C8—221no—
225C8—221no—
226C22—21no—
227C22—21no—
228C22—24no—
229C22—42no—
230C22—42no—
231C22—84no—
232C22#6693112yes—
233C22C2×D4×D1111yescharacteristic
234C4—41no—
235C4—41no—
236C4—222no—
237C4—222no—
238C4—441no—
239C4—442no—
240C4—441no—
241C4#6693112yes—
242C4C22×Dic2211yescharacteristic
243C4C2×#434111yescharacteristic
244C2—22no—
245C2—44no—
246C2C2×#6693111yescharacteristic
247C2#1062330511yescharacteristic
248C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#418C2
socleC22×C11C22×D4
prime radicalC22×D4×C11C22
hypercenter#418D11
hypocenterC11#3081
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. #10623050C2semidirect
5. #10622734C2semidirect
6. #10622732C2semidirect
7. #10622611C2semidirect
8. #10622379C2semidirect
9. #10622376C2semidirect
10. #10622374C2semidirect
11. #10622372C2semidirect
24. #66943C22semidirect
25. #66941C22semidirect
33. #66882C22semidirect
34. #66881C22semidirect
35. Dic11⋊C8C22semidirect
36. Dic11⋊C8C22semidirect
37. #66872C22semidirect
38. #66872C22semidirect
39. #66871C22semidirect
40. #66871C22semidirect
44. C2×D4×C11Q8semidirect
169. C2×D4Dic22semidirect
199. C11#3081semidirect

Maximal subgroups

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

subgroupindex
#106233292
#106230502
C11×#4182
C2×#668962
#106227342
#106227322
#106226112
#106223792
#106223762
#106223742
#106223722
#308111