Finite Group Databasebeta

← #13068698

Subgroups — #13068698

Order 1408.

272 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 77 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×#66945C211yesmaximal, characteristic
2#10622739C212yesmaximal
3C11×#343C211yesmaximal, characteristic, complemented
4#10622192C212yesmaximal, complemented
5#10622168C211yesmaximal, characteristic, complemented
6C22×C4×D11C2211yescharacteristic
7C2×C11×M16C2212yes—
8C2×C11×C4⋊C4C2211yescharacteristic
9C2×(C2×D11)⋊C4C412yes—
10C2×C4⋊Dic11C2211yescharacteristic
11C2×C4×Dic11C412yes—
12C2×#4318C2212yes—
13#66945—24no—
14(C2×D11)⋊C8—24no—
15C23×D11C2×C411yescharacteristic
16C22×C4×C11C2×C412yes—
17C22×C4×C11C2311yescharacteristic
18C22×Dic11C2×C411yescharacteristic
19C22×Dic11C2×C412yes—
20C2×C4×D11—22no—
21C2×C4×D11—21no—
22C2×C4×D11—21no—
23C2×C4×D11D414yes—
24C11×M16—22no—
25C11×M16—22no—
26C2×C8×C11—22no—
27C11×C4⋊C4—22no—
28(C2×D11)⋊C4—24no—
29C4⋊Dic11—22no—
30C4×Dic11—24no—
31#4318—22no—
32#4318—22no—
33C2×C11⋊C8—22no—
34#1822—111nomaximal, Sylow
35C23×C11C22×C411yescharacteristic
36C22×D11—21no—
37C22×D11—21no—
38C22×D11—41no—
39C22×D11—41no—
40C22×D11C22⋊C412yes—
41C2×C4×C11—22no—
42C2×C4×C11—42no—
43C2×C4×C11C2×D412yes—
44C2×C4×C11#4112yes—
45C2×C4×C11#4111yescharacteristic
46C2×C4×C11#4111yescharacteristic
47C2×Dic11—21no—
48C2×Dic11—21no—
49C2×Dic11—22no—
50C2×Dic11—42no—
51C2×Dic11C22⋊C412yes—
52C4×D11—24no—
53C4×D11—24no—
54C8×C11—42no—
55C11⋊C8—42no—
56C2×#117—111no—
57#407—112no—
58#343—112no—
59#343—111no—
60#343D1111yescharacteristic, complemented
61C22×C11—21no—
62C22×C11—21no—
63C22×C11C2×C22⋊C411yescharacteristic
64C22×C11#11711yescharacteristic
65C22×C11#11711yescharacteristic
66C2×D11—22no—
67C2×D11—22no—
68C2×D11—22no—
69C2×D11—42no—
70C2×D11—42no—
71C4×C11—42no—
72C4×C11#12312yes—
73C4×C11#12312yes—
74Dic11—22no—
75Dic11—42no—
76C23×C4—111no—
77C2×M16—112no—
78C2×M16C2×D1112yes—
79#117—224no—
80C2×C4⋊C4—111no—
81C2×C4⋊C4C2×D1111yescharacteristic
82C2×C22⋊C4—112no—
83C2×C42—112no—
84C22⋊C8—224no—
85C2×C11—21no—
86C2×C11—21no—
87C2×C11#38111yescharacteristic
88C2×C11#41311yescharacteristic
89C2×C11#41311yescharacteristic
90D11—42no—
91C24—111no—
92C22×C4—111no—
93C22×C4—114no—
94C22×C4—112no—
95C22×C4—222no—
96C22×C4—221no—
97C22×C4—221no—
98C22×C4C4×D1112yes—
99C22×C4C22×D1111yescharacteristic
100M16—22no—
101M16—22no—
102M16—222no—
103M16—222no—
104C2×C8—22no—
105C2×C8—222no—
106C4⋊C4—22no—
107C4⋊C4—222no—
108C22⋊C4—224no—
109C42—224no—
110C11#182211yescharacteristic, complemented, Sylow
111C23—112no—
112C23—221no—
113C23—221no—
114C23—441no—
115C23—441no—
116C23C2×C4×D1111yescharacteristic
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—112no—
120C2×C4—221no—
121C2×C4—221no—
122C2×C4—224no—
123C2×C4—224no—
124C2×C4—222no—
125C2×C4—442no—
126C2×C4#433912yes—
127C2×C4D4×D1112yes—
128C2×C4#434111yescharacteristic
129C2×C4#434311yescharacteristic
130C8—42no—
131C8—442no—
132C22—21no—
133C22—21no—
134C22—222no—
135C22—222no—
136C22—222no—
137C22—442no—
138C22—442no—
139C22#6692511yescharacteristic
140C22C22⋊C4×D1111yescharacteristic
141C22#6694511yescharacteristic
142C4—42no—
143C4—222no—
144C4—442no—
145C4#6693612yes—
146C4#6694712yes—
147C2—21no—
148C2—21no—
149C2—442no—
150C2#1062227711yescharacteristic
151C2#1062235811yescharacteristic
152C2#1062236411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D11
commutatorC23×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#343C2
socleC22×C11C2×C22⋊C4
prime radicalC23×D11C2×C4
cosocleC22×C4×C11C23
hypercenter#343D11
hypocenterC11#1822
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. C11×#343C2semidirect
4. #10622192C2semidirect
5. #10622168C2semidirect
60. #343D11semidirect
110. C11#1822semidirect

Maximal subgroups

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

subgroupindex
C2×#669452
#106227392
C11×#3432
#106221922
#106221682
#182211