Finite Group Databasebeta

← #13079103

Subgroups — #13079103

Order 1408.

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

normal subgroups only

This group has 596 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×#135C211yesmaximal, characteristic, complemented
2#10623361C212yesmaximal, complemented
3C2×#67002C212yesmaximal, complemented
4C22×D88C211yesmaximal, characteristic, complemented
5#10622804C212yesmaximal, complemented
6#10622789C214yesmaximal, complemented
7#10622764C212yesmaximal, complemented
8#10622714C211yesmaximal, characteristic, complemented
9C2×C11×#41C2212yes—
10C22×D44C2212yes—
11C11×#135—24no—
12C2×C11×Q16C2211yescharacteristic, complemented
13C2×C11×SD16C2212yescomplemented
14C2×C11×D8C2211yescharacteristic, complemented
15C22×C8×C11C2211yescharacteristic
16#67002—28no—
17#67000C2214yescomplemented
18C2×#4325C2214yescomplemented
19#66993C2214yescomplemented
20#66990—24no—
21C2×#4323C2214yescomplemented
22#66983—24no—
23#66979C2211yescharacteristic
24C2×#4318C2211yescharacteristic
25C2×D88—24no—
26C2×D88C2212yes—
27C2×D88C2212yes—
28#66879C2212yescomplemented
29C8×Dic11C2212yescomplemented
30C23×D11—22no—
31C11×#41—24no—
32C11×#41—24no—
33C2×Q8×C11C2312yes—
34C2×D4×C11—22no—
35C2×D4×C11C2312yes—
36C22×C4×C11—22no—
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—28no—
39C2×D44—22no—
40C2×D44—24no—
41C2×D44—24no—
42C2×D44C2314yes—
43C11×Q16—22no—
44C11×SD16—24no—
45C11×D8—22no—
46C2×C8×C11D414yescomplemented
47C2×C8×C11C2311yescharacteristic
48C2×C8×C11C2311yescharacteristic
49C22⋊Dic11D412yes—
50#4325—28no—
51#4323—28no—
52(C2×D11)⋊C4—28no—
53C4⋊Dic11D412yes—
54C4×Dic11C2312yes—
55#4318D414yescomplemented
56C2×C11⋊C8C2312yes—
57D88—24no—
58D88—24no—
59#3155—111nomaximal, Sylow
60C23×C11—22no—
61C23×C11C2×D411yescharacteristic
62C22×D11—24no—
63C22×D11—44no—
64C22×D11—84no—
65Q8×C11—22no—
66Q8×C11—22no—
67D4×C11—22no—
68D4×C11—22no—
69D4×C11—44no—
70C2×C4×C11—22no—
71C2×C4×C11—44no—
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D412yes—
74C2×C4×C11C2×D412yes—
75C2×C4×C11C2411yescharacteristic
76C22⋊D11—88no—
77C2×Dic11C2×D414yes—
78D44—24no—
79D44—24no—
80D44—44no—
81C8×C11C2×D412yes—
82C8×C11C2×D412yes—
83C11⋊C8C2×D414yes—
84C2×AGL(1,ℤ/8)—112no—
85C2×#135D1111yescharacteristic, complemented
86C22×D8—111no—
87#535—112no—
88#496—114no—
89#495—112no—
90#493—112no—
91#405—111no—
92C22×C11—22no—
93C22×C11—42no—
94C22×C11—44no—
95C22×C11#12712yes—
96C22×C11C22×D411yescharacteristic
97C2×D11—44no—
98C2×D11—48no—
99C2×D11—88no—
100C4×C11—42no—
101C4×C11#12712yes—
102C4×C11C22×D411yescharacteristic
103C4×C11C22×D411yescharacteristic
104Dic11—24no—
105C2×#41C2×D1112yes—
106C22×D4—112no—
107AGL(1,ℤ/8)—228no—
108#135—24no—
109C2×Q16C2×D1111yescharacteristic, complemented
110C2×SD16—114no—
111C2×SD16C2×D1112yescomplemented
112C2×D8—114no—
113C2×D8—112no—
114C2×D8—112no—
115C2×D8—224no—
116C2×D8C2×D1111yescharacteristic, complemented
117C2×M16—111no—
118C22×C8C2×D1111yescharacteristic
119#127—114no—
120#124—114no—
121#121—224no—
122#120—224no—
123#117—111no—
124#97—112no—
125C4×C8—112no—
126C2×C11—22no—
127C2×C11—82no—
128C2×C11C2×#12711yescharacteristic
129C2×C11#57612yes—
130D11—84no—
131C24—222no—
132#41—24no—
133#41—24no—
134C2×Q8C22×D1112yes—
135C2×D4—22no—
136C2×D4—114no—
137C2×D4—228no—
138C2×D4—224no—
139C2×D4—222no—
140C2×D4—224no—
141C2×D4C22×D1112yes—
142C22×C4—22no—
143C22×C4C22×D1111yescharacteristic
144Q16—22no—
145SD16—24no—
146SD16—228no—
147D8—22no—
148D8—228no—
149D8—224no—
150D8—224no—
151M16—114no—
152C2×C8—112no—
153C2×C8C22⋊D1114yescomplemented
154C2×C8C22×D1111yescharacteristic
155C2×C8C22×D1111yescharacteristic
156C4⋊C4—112no—
157C22⋊C4—112no—
158C22⋊C4—228no—
159C42—112no—
160C11#315511yescharacteristic, complemented, Sylow
161C23—22no—
162C23—224no—
163C23—444no—
164C23—884no—
165C23D4×D1111yescharacteristic
166Q8—22no—
167Q8—22no—
168D4—22no—
169D4—22no—
170D4—44no—
171D4—224no—
172D4—224no—
173D4—444no—
174D4—888no—
175C2×C4—22no—
176C2×C4—44no—
177C2×C4—114no—
178C2×C4D4×D1111yescharacteristic
179C2×C4D4×D1112yes—
180C2×C4C2×C22⋊D1112yes—
181C2×C4C23×D1111yescharacteristic
182C8—114no—
183C8C2×C22⋊D1112yes—
184C8C2×C22⋊D1112yes—
185C22—22no—
186C22—44no—
187C22—42no—
188C22—448no—
189C22—444no—
190C22—888no—
191C22#6699312yes—
192C22C2×D4×D1111yescharacteristic
193C4—42no—
194C4—224no—
195C4#6699312yes—
196C4C2×D4×D1111yescharacteristic
197C4C22×C22⋊D1111yescharacteristic
198C2—22no—
199C2—82no—
200C2—884no—
201C2#1062330012yes—
202C2C2×#6699311yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#135C2
socleC22×C11C22×D4
hypercenterC2×#135D11
hypocenterC11#3155
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C11×#135C2semidirect
2. #10623361C2semidirect
3. C2×#67002C2semidirect
4. C22×D88C2semidirect
5. #10622804C2semidirect
6. #10622789C2semidirect
7. #10622764C2semidirect
8. #10622714C2semidirect
12. C2×C11×Q16C22semidirect
13. C2×C11×SD16C22semidirect
14. C2×C11×D8C22semidirect
17. #67000C22semidirect
18. C2×#4325C22semidirect
19. #66993C22semidirect
21. C2×#4323C22semidirect
28. #66879C22semidirect
29. C8×Dic11C22semidirect
46. C2×C8×C11D4semidirect
55. #4318D4semidirect
85. C2×#135D11semidirect
109. C2×Q16C2×D11semidirect
111. C2×SD16C2×D11semidirect
116. C2×D8C2×D11semidirect
153. C2×C8C22⋊D11semidirect
160. C11#3155semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1352
#106233612
C2×#670022
C22×D882
#106228042
#106227892
#106227642
#106227142
#315511