Finite Group Databasebeta

← #13069286

Subgroups — #13069286

Order 1408.

216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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#10622745C211yesmaximal, characteristic
2#10622738C211yesmaximal, characteristic, complemented
3#10622618C211yesmaximal, characteristic
4C2×#66869C211yesmaximal, characteristic
5C4×#4318C211yesmaximal, characteristic, complemented
6C11×#339C211yesmaximal, characteristic, complemented
7#10622171C211yesmaximal, characteristic, complemented
8C2×#4339C2211yescharacteristic
9C2×C11×M16C2211yescharacteristic
10C11×#117C2211yescharacteristic
11C2×C42×C11C2211yescharacteristic
12C2×#4318C2211yescharacteristic
13C2×#4318C2211yescharacteristic
14C2×#4318C2211yescharacteristic
15#66888C412yescomplemented
16#66887C412yescomplemented
17#66883—22no—
18#66869—21no—
19#66869—21no—
20#66869—22no—
21#66867—21no—
22C4×C11⋊C8—21no—
23C22×C4×C11—21no—
24C22×C4×C11C2311yescharacteristic
25C2×C22⋊D11—21no—
26#4339—21no—
27#4339—21no—
28#4339—21no—
29#4339—21no—
30C2×D44C2×C411yescharacteristic
31C2×C4×D11—21no—
32C2×Dic22C2×C411yescharacteristic
33C11×M16—21no—
34C11×M16C2×C412yes—
35C2×C8×C11—21no—
36C11×C4⋊C4—21no—
37C11×C22⋊C4—21no—
38C42×C11—21no—
39C42×C11—21no—
40C42×C11D411yescharacteristic
41C42×C11D411yescharacteristic
42#4318—21no—
43#4318—21no—
44#4318—21no—
45#4318—21no—
46#4318C2×C412yes—
47#4318D412yes—
48C2×C11⋊C8—21no—
49C2×C11⋊C8—21no—
50C2×C11⋊C8—21no—
51#1932—111nomaximal, Sylow
52C23×C11#4111yescharacteristic
53C22×D11—21no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11—42no—
57C2×C4×C11—41no—
58C2×C4×C11C22×C411yescharacteristic
59C2×C4×C11C2×D411yescharacteristic
60C2×C4×C11C2×D411yescharacteristic
61C2×C4×C11#4111yescharacteristic
62C2×C4×C11#4111yescharacteristic
63C2×C4×C11#4111yescharacteristic
64C22⋊D11—41no—
65C22⋊D11—41no—
66C2×Dic11—21no—
67D44—21no—
68D44—21no—
69C4×D11—41no—
70C4×D11—41no—
71Dic22—21no—
72Dic22—21no—
73C8×C11—22no—
74C11⋊C8—22no—
75C11⋊C8—22no—
76C11⋊C8—41no—
77#430—111no—
78#421—111no—
79C2×#104—111no—
80#413—111no—
81C4×M16—111no—
82#344—111no—
83#339D1111yescharacteristic, complemented
84C22×C11—41no—
85C22×C11#11711yescharacteristic
86C22×C11#12311yescharacteristic
87C22×C11#12411yescharacteristic
88C2×D11—41no—
89C2×D11—81no—
90C4×C11—22no—
91C4×C11—41no—
92C4×C11—81no—
93C4×C11C4×D411yescharacteristic
94C4×C11C4×D411yescharacteristic
95C4×C11#12111yescharacteristic
96C4×C11#12611yescharacteristic
97Dic11—41no—
98C2×#41—111no—
99C2×M16—111no—
100C2×M16—111no—
101C2×M16—111no—
102C2×M16C2×D1111yescharacteristic
103#117C2×D1111yescharacteristic
104C2×C42C2×D1111yescharacteristic
105#108—222no—
106#104—222no—
107#104—221no—
108#104—221no—
109#101—112no—
110#100—112no—
111#97—221no—
112C4×C8—221no—
113C2×C11—21no—
114C2×C11—21no—
115C2×C11—21no—
116C2×C11#38811yescharacteristic
117D11—81no—
118#41—221no—
119#41—221no—
120#41—221no—
121#41—221no—
122C2×Q8—111no—
123C2×D4—111no—
124C2×D4—221no—
125C22×C4—21no—
126C22×C4—221no—
127C22×C4C22×D1111yescharacteristic
128M16—21no—
129M16—112no—
130M16—112no—
131M16—221no—
132M16—221no—
133M16—221no—
134M16—221no—
135M16C4×D1112yes—
136C2×C8—21no—
137C2×C8—221no—
138C2×C8—221no—
139C2×C8—221no—
140C4⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42—21no—
144C42D4411yescharacteristic
145C42D4411yescharacteristic
146C11#193211yescharacteristic, complemented, Sylow
147C23—221no—
148C23#434111yescharacteristic
149Q8—221no—
150Q8—221no—
151D4—221no—
152D4—221no—
153D4—441no—
154D4—441no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—42no—
158C2×C4—41no—
159C2×C4—221no—
160C2×C4—441no—
161C2×C4—441no—
162C2×C4C2×C4×D1111yescharacteristic
163C2×C4C2×D4411yescharacteristic
164C2×C4#433911yescharacteristic
165C2×C4D4×D1111yescharacteristic
166C2×C4#434111yescharacteristic
167C2×C4#434311yescharacteristic
168C8—22no—
169C8—222no—
170C8—222no—
171C8—441no—
172C22—41no—
173C22—441no—
174C22—881no—
175C22#6693811yescharacteristic
176C22#6693911yescharacteristic
177C22#6694511yescharacteristic
178C4—22no—
179C4—41no—
180C4—81no—
181C4—441no—
182C4C4×D4411yescharacteristic
183C4(C22⋊D11)⋊C411yescharacteristic
184C4#6694811yescharacteristic
185C4#6695111yescharacteristic
186C2—21no—
187C2—21no—
188C2—21no—
189C2—881no—
190C2#1062228311yescharacteristic
subgroupG/H
centerC4#66948
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#339C2
socleC2×C11#388
prime radicalC2×#4339C22
cosocleC22×C4×C11C23
hypercenter#339D11
hypocenterC11#1932
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #10622738C2semidirect
5. C4×#4318C2semidirect
6. C11×#339C2semidirect
7. #10622171C2semidirect
15. #66888C4semidirect
16. #66887C4semidirect
83. #339D11semidirect
146. C11#1932semidirect

Maximal subgroups

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

subgroupindex
#106227452
#106227382
#106226182
C2×#668692
C4×#43182
C11×#3392
#106221712
#193211