Finite Group Databasebeta

← #13079080

Subgroups — #13079080

Order 1408.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#124C211yesmaximal, characteristic, complemented
2C2×#66995C212yesmaximal, complemented
3C2×#66985C212yesmaximal, complemented
4#10623008C211yesmaximal, characteristic, complemented
5#10622673C212yesmaximal, complemented
6#10622672C214yesmaximal, complemented
7#10622671C212yesmaximal, complemented
8C4×#4318C211yesmaximal, characteristic, complemented
9C22×Q8×C11C2211yescharacteristic
10C22×D4×C11C2211yescharacteristic
11C2×#4339C2212yes—
12C11×#124—22no—
13C11×#124C2212yes—
14C11×#124C2212yes—
15C2×C11×C22⋊C4—22no—
16C2×C42×C11C2211yescharacteristic
17C2×#4326C2214yescomplemented
18#66995—28no—
19C2×#4325C2214yescomplemented
20C2×#4324C2214yes—
21#66985—28no—
22C2×#4323C2214yes—
23#66983—22no—
24C2×#4318C2212yes—
25#66928C2212yescomplemented
26#66927C2211yescharacteristic, complemented
27C4×D44—22no—
28#66922C2211yescharacteristic, complemented
29#66867C2212yescomplemented
30C4×C11⋊C8C2212yescomplemented
31C24×C11—21no—
32C2×Q8×C11—21no—
33C2×Q8×C11—24no—
34C2×Q8×C11C2312yes—
35C2×D4×C11—24no—
36C2×D4×C11—21no—
37C2×D4×C11C2312yes—
38C22×C4×C11—21no—
39C22×C4×C11D412yes—
40C22×C4×C11C2311yescharacteristic
41C2×C22⋊D11—22no—
42#4339—24no—
43#4339—24no—
44C2×D44—22no—
45C2×D44C2312yes—
46C2×C4×D11—22no—
47C2×Dic22C2312yes—
48C11×C22⋊C4—24no—
49C11×C22⋊C4—24no—
50C42×C11D412yes—
51C42×C11C2311yescharacteristic
52C42×C11C2311yescharacteristic
53#4326—28no—
54#4325—28no—
55#4324—28no—
56#4323—28no—
57(C2×D11)⋊C4—24no—
58C4⋊Dic11—22no—
59#4318D418yescomplemented
60C2×C11⋊C8C2314yes—
61#3153—111nomaximal, Sylow
62C23×C11—22no—
63C23×C11—44no—
64C23×C11—42no—
65C23×C11C2×D411yescharacteristic
66C22×D11—22no—
67Q8×C11—24no—
68Q8×C11—42no—
69D4×C11—24no—
70D4×C11—42no—
71C2×C4×C11—22no—
72C2×C4×C11—42no—
73C2×C4×C11—42no—
74C2×C4×C11C2×D414yes—
75C2×C4×C11C2×D412yes—
76C2×C4×C11C2×D412yes—
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2411yescharacteristic
79C22⋊D11—44no—
80C2×Dic11—22no—
81D44—22no—
82D44—22no—
83D44—44no—
84C4×D11—44no—
85Dic22—22no—
86Dic22—22no—
87C11⋊C8C2×D418yes—
88C2×#137—112no—
89C2×AGL(1,ℤ/8)—112no—
90#532—111no—
91C2×#124D1111yescharacteristic, complemented
92#497—112no—
93#496—112no—
94#495—114no—
95C4×M16—111no—
96C22×C11—22no—
97C22×C11—42no—
98C22×C11—44no—
99C22×C11—84no—
100C22×C11#12712yes—
101C22×C11C22×D411yescharacteristic
102C2×D11—42no—
103C2×D11—44no—
104C4×C11—22no—
105C4×C11—22no—
106C4×C11—42no—
107C4×C11#12712yes—
108C4×C11C22×D412yes—
109Dic11—42no—
110C2×#41—112no—
111C22×Q8C2×D1111yescharacteristic
112C22×D4C2×D1111yescharacteristic
113#137—228no—
114AGL(1,ℤ/8)—228no—
115C2×Q16—114no—
116C2×SD16—114no—
117C2×SD16—114no—
118C2×D8—114no—
119C2×M16—112no—
120C4⋊Q8—111no—
121#127—111no—
122#124—22no—
123#124—112no—
124#124C2×D1112yes—
125#124C2×D1112yes—
126#121—222no—
127C4×D4—222no—
128C2×C22⋊C4—22no—
129C2×C42C2×D1111yescharacteristic
130#97—112no—
131C4×C8—112no—
132C2×C11—22no—
133C2×C11—82no—
134C2×C11C2×#12711yescharacteristic
135C2×C11#57512yes—
136D11—82no—
137C24—21no—
138#41—224no—
139#41—224no—
140C2×Q8—21no—
141C2×Q8—24no—
142C2×Q8—112no—
143C2×Q8C22×D1112yes—
144C2×D4—24no—
145C2×D4—21no—
146C2×D4—112no—
147C2×D4—222no—
148C2×D4—222no—
149C2×D4C22×D1112yes—
150C22×C4—21no—
151C22×C4—222no—
152C22×C4C22⋊D1112yes—
153C22×C4C22×D1111yescharacteristic
154Q16—228no—
155SD16—228no—
156SD16—228no—
157D8—228no—
158M16—118no—
159C2×C8—114no—
160C4⋊C4—222no—
161C22⋊C4—24no—
162C22⋊C4—24no—
163C22⋊C4—224no—
164C42C22⋊D1112yes—
165C42C22×D1111yescharacteristic
166C42C22×D1111yescharacteristic
167C11#315311yescharacteristic, complemented, Sylow
168C23—22no—
169C23—44no—
170C23—42no—
171C23—222no—
172C23C2×C22⋊D1111yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—222no—
176Q8—222no—
177D4—24no—
178D4—42no—
179D4—222no—
180D4—222no—
181D4—444no—
182D4—444no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—222no—
187C2×C4—444no—
188C2×C4D4×D1114yes—
189C2×C4C2×C22⋊D1112yes—
190C2×C4C2×C22⋊D1112yes—
191C2×C4C2×C22⋊D1111yescharacteristic
192C2×C4C23×D1111yescharacteristic
193C8—118no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—442no—
199C22—444no—
200C22#6699312yes—
201C22C22×C22⋊D1111yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—442no—
206C4#6699312yes—
207C4C2×D4×D1112yes—
208C2—22no—
209C2—82no—
210C2—882no—
211C2C2×#6699311yescharacteristic
212C2#1062335312yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#124C2
socleC22×C11C22×D4
hypercenterC2×#124D11
hypocenterC11#3153
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C11×#124C2semidirect
2. C2×#66995C2semidirect
3. C2×#66985C2semidirect
4. #10623008C2semidirect
5. #10622673C2semidirect
6. #10622672C2semidirect
7. #10622671C2semidirect
8. C4×#4318C2semidirect
17. C2×#4326C22semidirect
19. C2×#4325C22semidirect
25. #66928C22semidirect
26. #66927C22semidirect
28. #66922C22semidirect
29. #66867C22semidirect
30. C4×C11⋊C8C22semidirect
59. #4318D4semidirect
91. C2×#124D11semidirect
167. C11#3153semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#669952
C2×#669852
#106230082
#106226732
#106226722
#106226712
C4×#43182
#315311