Finite Group Databasebeta

← #13069769

Subgroups — #13069769

Order 1408.

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

normal subgroups only

This group has 282 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, complemented
2#10622614C212yesmaximal
3#10622601C211yesmaximal, characteristic
4#10622170C212yesmaximal, complemented
5#10622168C211yesmaximal, characteristic, complemented
6C22×D44C2211yescharacteristic
7C11×C4⋊Q8—22no—
8C11×#125—22no—
9C11×C22⋊Q8—22no—
10C11×#117C2212yes—
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×(C2×D11)⋊C4—22no—
13C2×C4×Dic11C2211yescharacteristic
14C2×#4318C2212yes—
15#66873—22no—
16#66873—22no—
17C23×D11—21no—
18C2×Q8×C11—22no—
19C22×C4×C11D412yes—
20C22×C4×C11C2311yescharacteristic
21C22×Dic11—21no—
22C2×D44—22no—
23C2×D44—21no—
24C2×D44—22no—
25C2×D44Q812yescomplemented
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—
33(C2×D11)⋊C4—44no—
34C4×Dic11—22no—
35#4318—22no—
36#4318—22no—
37C2×C11⋊C8—22no—
38#2027—111nomaximal, Sylow
39C23×C11C2×D411yescharacteristic
40C22×D11—22no—
41C22×D11—42no—
42C22×D11—42no—
43C22×D11—41no—
44C22×D11—41no—
45Q8×C11—82no—
46C2×C4×C11—22no—
47C2×C4×C11—22no—
48C2×C4×C11—22no—
49C2×C4×C11—42no—
50C2×C4×C11C2×D412yes—
51C2×C4×C11C2×Q811yescharacteristic
52C2×C4×C11#4112yes—
53C2×C4×C11#4111yescharacteristic
54C2×Dic11—22no—
55C2×Dic11—41no—
56C2×Dic11—41no—
57D44—24no—
58D44—42no—
59C11⋊C8—42no—
60#544D1111yescharacteristic, complemented
61#418—112no—
62#390—111no—
63#343—111no—
64#339—112no—
65C22×C11—21no—
66C22×C11—21no—
67C22×C11#12011yescharacteristic
68C22×C11C22⋊Q811yescharacteristic
69C22×C11#12411yescharacteristic
70C2×D11—44no—
71C2×D11—42no—
72C2×D11—82no—
73C2×D11—81no—
74C2×D11—81no—
75C4×C11—42no—
76C4×C11—42no—
77C4×C11—42no—
78C4×C11C22⋊Q812yes—
79C4×C11#12412yes—
80Dic11—42no—
81C22×D4—111no—
82C2×M16—112no—
83C4⋊Q8—22no—
84#125—22no—
85C22⋊Q8—22no—
86#117C2×D1112yes—
87C2×C4⋊C4C2×D1111yescharacteristic
88C2×C22⋊C4—222no—
89C2×C42—111no—
90#102—222no—
91#102—222no—
92C2×C11—21no—
93C2×C11—21no—
94C2×C11#39311yescharacteristic
95C2×C11#45311yescharacteristic
96C2×C11#45411yescharacteristic
97D11—82no—
98C24—221no—
99C2×Q8—22no—
100C2×D4—112no—
101C2×D4—222no—
102C2×D4—221no—
103C2×D4—222no—
104C22×C4—221no—
105C22×C4C22⋊D1112yes—
106C22×C4C22×D1111yescharacteristic
107M16—222no—
108M16—222no—
109C2×C8—222no—
110C4⋊C4—22no—
111C4⋊C4—24no—
112C4⋊C4—22no—
113C4⋊C4C22⋊D1112yes—
114C4⋊C4C22⋊D1112yes—
115C22⋊C4—22no—
116C22⋊C4—444no—
117C42—22no—
118C42—222no—
119C11#202711yescharacteristic, complemented, Sylow
120C23—222no—
121C23—442no—
122C23—442no—
123C23—441no—
124C23—441no—
125C23C2×C22⋊D1111yescharacteristic
126Q8—82no—
127D4—224no—
128D4—442no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—42no—
133C2×C4—222no—
134C2×C4—441no—
135C2×C4—441no—
136C2×C4Q8×D1111yescharacteristic
137C2×C4#434312yes—
138C2×C4#434311yescharacteristic
139C2×C4C2×C22⋊D1112yes—
140C8—442no—
141C22—21no—
142C22—21no—
143C22—444no—
144C22—442no—
145C22—882no—
146C22—881no—
147C22—881no—
148C22#6699911yescharacteristic
149C22#6700011yescharacteristic
150C22#6700611yescharacteristic
151C4—42no—
152C4—42no—
153C4—42no—
154C4—442no—
155C4#6699912yes—
156C4#6700012yes—
157C2—21no—
158C2—21no—
159C2—882no—
160C2#1062284411yescharacteristic
161C2#1062285411yescharacteristic
162C2#1062285811yescharacteristic
subgroupG/H
centerC22#67006
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#544C2
socleC22×C11#120
prime radicalC22×D44C22
hypercenter#544D11
hypocenterC11#2027
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
1. C11×#544C2semidirect
4. #10622170C2semidirect
5. #10622168C2semidirect
25. C2×D44Q8semidirect
60. #544D11semidirect
119. C11#2027semidirect

Maximal subgroups

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

subgroupindex
C11×#5442
#106226142
#106226012
#106221702
#106221682
#202711