Finite Group Databasebeta

← #13069774

Subgroups — #13069774

Order 1408.

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

normal subgroups only

This group has 246 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
1C11×#544C211yesmaximal, characteristic
2#10622617C212yesmaximal
3#10622587C211yesmaximal, characteristic
4#10622170C212yesmaximal
5#10622168C211yesmaximal, characteristic
6C22×Dic22C2211yescharacteristic
7C11×C4⋊Q8—22no—
8C11×#125—22no—
9C11×C22⋊Q8—22no—
10C11×#117C2212yes—
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C4×Dic11C2211yescharacteristic
13C2×#4318C2212yes—
14C11⋊#95—22no—
15#66874—22no—
16#66874—22no—
17C2×Q8×C11—22no—
18C22×C4×C11D412yes—
19C22×C4×C11C2311yescharacteristic
20C22×Dic11—21no—
21C22×Dic11—21no—
22C2×Dic22—22no—
23C2×Dic22—22no—
24C2×Dic22—21no—
25C2×Dic22Q812yescomplemented
26C11×C4⋊C4—22no—
27C11×C4⋊C4—24no—
28C11×C4⋊C4—22no—
29C11×C4⋊C4D412yes—
30C11×C4⋊C4D412yes—
31C11×C22⋊C4—22no—
32C42×C11—22no—
33C4×Dic11—22no—
34#4318—22no—
35#4318—22no—
36C2×C11⋊C8—22no—
37#2028—111nomaximal, Sylow
38C23×C11C2×D411yescharacteristic
39Q8×C11—82no—
40C2×C4×C11—22no—
41C2×C4×C11—22no—
42C2×C4×C11—22no—
43C2×C4×C11—42no—
44C2×C4×C11C2×D412yes—
45C2×C4×C11C2×Q811yescharacteristic
46C2×C4×C11#4112yes—
47C2×C4×C11#4111yescharacteristic
48C2×Dic11—22no—
49C2×Dic11—22no—
50C2×Dic11—41no—
51C2×Dic11—41no—
52C2×Dic11—41no—
53C2×Dic11—41no—
54Dic22—24no—
55Dic22—42no—
56C11⋊C8—42no—
57#544D1111yescharacteristic
58#419—112no—
59#391—111no—
60#343—111no—
61#339—112no—
62C22×C11—21no—
63C22×C11—21no—
64C22×C11#12011yescharacteristic
65C22×C11C22⋊Q811yescharacteristic
66C22×C11#12411yescharacteristic
67C4×C11—42no—
68C4×C11—42no—
69C4×C11—42no—
70C4×C11C22⋊Q812yes—
71C4×C11#12412yes—
72Dic11—42no—
73Dic11—42no—
74C22×Q8—111no—
75C2×M16—112no—
76C4⋊Q8—22no—
77#125—22no—
78C22⋊Q8—22no—
79#117C2×D1112yes—
80C2×C4⋊C4C2×D1111yescharacteristic
81C2×C42—111no—
82#103—222no—
83#103—222no—
84#95—222no—
85C2×C11—21no—
86C2×C11—21no—
87C2×C11#39311yescharacteristic
88C2×C11#45511yescharacteristic
89C2×C11#45611yescharacteristic
90C2×Q8—22no—
91C2×Q8—112no—
92C2×Q8—221no—
93C2×Q8—222no—
94C2×Q8—222no—
95C22×C4—221no—
96C22×C4—221no—
97C22×C4C22⋊D1112yes—
98C22×C4C22×D1111yescharacteristic
99M16—222no—
100M16—222no—
101C2×C8—222no—
102C4⋊C4—22no—
103C4⋊C4—24no—
104C4⋊C4—22no—
105C4⋊C4C22⋊D1112yes—
106C4⋊C4C22⋊D1112yes—
107C22⋊C4—22no—
108C42—22no—
109C42—222no—
110C11#202811yescharacteristic, complemented, Sylow
111C23C2×C22⋊D1111yescharacteristic
112Q8—82no—
113Q8—224no—
114Q8—442no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—222no—
120C2×C4—222no—
121C2×C4—441no—
122C2×C4—441no—
123C2×C4—441no—
124C2×C4—441no—
125C2×C4Q8×D1111yescharacteristic
126C2×C4#434312yes—
127C2×C4#434311yescharacteristic
128C2×C4C2×C22⋊D1112yes—
129C8—442no—
130C22—21no—
131C22—21no—
132C22#6699911yescharacteristic
133C22#6700011yescharacteristic
134C22#6700611yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—442no—
139C4—442no—
140C4#6699912yes—
141C4#6700012yes—
142C2—21no—
143C2—21no—
144C2#1062284411yescharacteristic
145C2#1062285511yescharacteristic
146C2#1062285911yescharacteristic
subgroupG/H
centerC22#67006
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#544C2
socleC22×C11#120
prime radicalC23×C11C2×D4
hypercenter#544D11
hypocenterC11#2028
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
25. C2×Dic22Q8semidirect
110. C11#2028semidirect

Maximal subgroups

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

subgroupindex
C11×#5442
#106226172
#106225872
#106221702
#106221682
#202811