Finite Group Databasebeta

← #13078859

Subgroups — #13078859

Order 1408.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C11×#518C211yesmaximal, characteristic, complemented
2#10623066C211yesmaximal, characteristic, complemented
3#10622830C212yesmaximal, complemented
4#10622628C212yesmaximal, complemented
5#10622627C212yesmaximal, complemented
6C4×#4323C212yesmaximal, complemented
7#10622622C212yesmaximal, complemented
8#10622616C212yesmaximal, complemented
9#10622613C211yesmaximal, characteristic, complemented
10C22×D4×C11C2211yescharacteristic
11C4×D4×C11—22no—
12C4×D4×C11C2212yes—
13C4×D4×C11C2212yes—
14C11×#117C2211yescharacteristic
15C11×#117C2211yescharacteristic
16C2×C11×C22⋊C4—22no—
17C2×#4323C2212yes—
18C2×#4323C2212yes—
19#66983C2212yes—
20#66947—22no—
21#66937—22no—
22#66927C2211yescharacteristic, complemented
23C4×D44C2212yescomplemented
24#66923C2211yescharacteristic, complemented
25#66896C2212yes—
26#66896C2212yes—
27C22⋊(C11⋊C8)C2212yes—
28#66873C2212yescomplemented
29#66873C2212yescomplemented
30#66872C2212yescomplemented
31#66871C2212yescomplemented
32C4⋊(C11⋊C8)C2212yescomplemented
33#66867C2211yescharacteristic, complemented
34C4×C11⋊C8C2211yescharacteristic, complemented
35C24×C11—21no—
36C2×D4×C11—24no—
37C2×D4×C11—21no—
38C2×D4×C11C2312yes—
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11—22no—
43C2×D44—22no—
44C2×D44C2312yes—
45C2×C4×D11—22no—
46C11×C4⋊C4D412yes—
47C11×C4⋊C4C2312yes—
48C11×C22⋊C4—21no—
49C11×C22⋊C4—22no—
50C11×C22⋊C4—22no—
51C11×C22⋊C4D412yes—
52C42×C11—21no—
53C42×C11C2311yescharacteristic
54C42×C11C2311yescharacteristic
55#4323—24no—
56#4323—24no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—22no—
59C4⋊Dic11C2312yes—
60Dic11⋊C4—22no—
61C2×C11⋊C8C2312yes—
62C2×C11⋊C8C2312yes—
63#3122—111nomaximal, Sylow
64C23×C11—24no—
65C23×C11—22no—
66C23×C11—82no—
67C23×C11C2×D411yescharacteristic
68C22×D11—22no—
69D4×C11—24no—
70D4×C11—22no—
71D4×C11#4114yes—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—82no—
75C2×C4×C11—82no—
76C2×C4×C11C2×D412yes—
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D412yes—
79C2×C4×C11C2411yescharacteristic
80C22⋊D11—82no—
81C2×Dic11—22no—
82D44—22no—
83D44—22no—
84D44—82no—
85C4×D11—82no—
86C11⋊C8—22no—
87C11⋊C8—22no—
88#540—111no—
89#518D1111yescharacteristic, complemented
90#482—112no—
91#478—112no—
92#459—112no—
93#447—112no—
94#442—112no—
95C4×D8—112no—
96#433—111no—
97C22×C11—21no—
98C22×C11—24no—
99C22×C11—22no—
100C22×C11—42no—
101C22×C11—42no—
102C22×C11—84no—
103C22×C11C22×D411yescharacteristic
104C2×D11—42no—
105C2×D11—42no—
106C2×D11—42no—
107C4×C11—21no—
108C4×C11—22no—
109C4×C11—22no—
110C4×C11—42no—
111C4×C11C2×#4112yes—
112Dic11—42no—
113C22×D4C2×D1111yescharacteristic
114C2×D8—112no—
115C2×D8—112no—
116#127—111no—
117#125—111no—
118#123—222no—
119#121—112no—
120#121—222no—
121C4×D4—22no—
122C4×D4—112no—
123C4×D4C2×D1112yes—
124C4×D4C2×D1112yes—
125#117C2×D1111yescharacteristic
126#117C2×D1111yescharacteristic
127C2×C22⋊C4—22no—
128#107—112no—
129#106—112no—
130C4⋊C8—112no—
131#102—112no—
132#102—112no—
133#102—112no—
134#102—112no—
135C22⋊C8—112no—
136#97—111no—
137C4×C8—111no—
138C2×C11—41no—
139C2×C11—44no—
140C2×C11#52511yescharacteristic
141C2×C11#57612yes—
142D11—82no—
143C24—21no—
144C2×D4—24no—
145C2×D4—21no—
146C2×D4—112no—
147C2×D4—222no—
148C2×D4—222no—
149C2×D4C22×D1112yes—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—222no—
153C22×C4C22×D1111yescharacteristic
154D8—224no—
155D8—224no—
156C2×C8—112no—
157C2×C8—112no—
158C4⋊C4—112no—
159C4⋊C4—222no—
160C4⋊C4C22⋊D1112yes—
161C4⋊C4C22×D1112yes—
162C22⋊C4—21no—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—222no—
166C22⋊C4—222no—
167C22⋊C4C22⋊D1112yes—
168C42—21no—
169C42C22×D1111yescharacteristic
170C42C22×D1111yescharacteristic
171C11#312211yescharacteristic, complemented, Sylow
172C23—24no—
173C23—22no—
174C23—82no—
175C23—222no—
176C23C2×C22⋊D1111yescharacteristic
177D4—24no—
178D4—22no—
179D4—222no—
180D4—222no—
181D4—882no—
182D4—882no—
183D4#433914yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—222no—
189C2×C4—882no—
190C2×C4C2×C22⋊D1111yescharacteristic
191C2×C4C2×C22⋊D1112yes—
192C2×C4C2×C22⋊D1112yes—
193C2×C4C23×D1111yescharacteristic
194C8—222no—
195C8—222no—
196C22—21no—
197C22—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—442no—
203C22—442no—
204C22—442no—
205C22C22×C22⋊D1111yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—442no—
211C4C2×#433912yes—
212C2—41no—
213C2—44no—
214C2—882no—
215C2#1062332211yescharacteristic
216C2#1062336612yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#518C2
socleC22×C11C22×D4
hypercenter#518D11
hypocenterC11#3122
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C11×#518C2semidirect
2. #10623066C2semidirect
3. #10622830C2semidirect
4. #10622628C2semidirect
5. #10622627C2semidirect
6. C4×#4323C2semidirect
7. #10622622C2semidirect
8. #10622616C2semidirect
9. #10622613C2semidirect
22. #66927C22semidirect
23. C4×D44C22semidirect
24. #66923C22semidirect
28. #66873C22semidirect
29. #66873C22semidirect
30. #66872C22semidirect
31. #66871C22semidirect
32. C4⋊(C11⋊C8)C22semidirect
33. #66867C22semidirect
34. C4×C11⋊C8C22semidirect
89. #518D11semidirect
171. C11#3122semidirect

Maximal subgroups

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

subgroupindex
C11×#5182
#106230662
#106228302
#106226282
#106226272
C4×#43232
#106226222
#106226162
#106226132
#312211