Finite Group Databasebeta

← #13069773

Subgroups — #13069773

Order 1408.

282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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#10623031C211yesmaximal, characteristic, complemented
2#10622744C212yesmaximal
3#10622601C211yesmaximal, characteristic
4C11×#343C211yesmaximal, characteristic, complemented
5#10622193C212yesmaximal, complemented
6C22×D44C2211yescharacteristic
7C2×C11×M16C2212yes—
8C2×C11×C4⋊C4C2211yescharacteristic
9C2×(C2×D11)⋊C4—22no—
10#66979C2212yes—
11#66977—22no—
12C2×C4×Dic11C2211yescharacteristic
13#66943—22no—
14#66941—22no—
15#66885—22no—
16#66885—22no—
17C23×D11—21no—
18C22×C4×C11D412yes—
19C22×C4×C11C2311yescharacteristic
20C22×Dic11—21no—
21C2×D44—22no—
22C2×D44—21no—
23C2×D44—22no—
24C2×D44Q812yescomplemented
25C2×Dic22—22no—
26C11×M16—22no—
27C11×M16—22no—
28C2×C8×C11—22no—
29C11×C4⋊C4—22no—
30C22⋊Dic11—22no—
31(C2×D11)⋊C4—44no—
32C4⋊Dic11—22no—
33C4⋊Dic11D412yes—
34C4⋊Dic11D412yes—
35Dic11⋊C4—24no—
36C4×Dic11—22no—
37C4×Dic11—22no—
38#2027—111nomaximal, Sylow
39C23×C11C2×D411yescharacteristic
40C22×D11—22no—
41C22×D11—42no—
42C22×D11—42no—
43C22×D11—41no—
44C22×D11—41no—
45C2×C4×C11—22no—
46C2×C4×C11—42no—
47C2×C4×C11C2×D412yes—
48C2×C4×C11C2×Q811yescharacteristic
49C2×C4×C11#4112yes—
50C2×C4×C11#4111yescharacteristic
51C2×Dic11—22no—
52C2×Dic11—22no—
53C2×Dic11—22no—
54C2×Dic11—41no—
55C2×Dic11—41no—
56D44—24no—
57D44—42no—
58Dic22—82no—
59C8×C11—42no—
60#544—111no—
61#418—112no—
62#390—111no—
63#343D1111yescharacteristic, complemented
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×C11C22⋊Q812yes—
77C4×C11#12412yes—
78Dic11—42no—
79Dic11—42no—
80Dic11—42no—
81C22×D4—111no—
82C2×M16C2×D1112yes—
83C4⋊Q8—222no—
84#125—222no—
85C22⋊Q8—222no—
86#117—112no—
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—222no—
100C2×D4—112no—
101C2×D4—222no—
102C2×D4—222no—
103C2×D4—221no—
104C22×C4—221no—
105C22×C4D4412yes—
106C22×C4C22×D1111yescharacteristic
107M16—22no—
108M16—22no—
109C2×C8—22no—
110C4⋊C4—22no—
111C4⋊C4—112no—
112C4⋊C4—112no—
113C4⋊C4—222no—
114C4⋊C4—224no—
115C22⋊C4—222no—
116C22⋊C4—444no—
117C42—222no—
118C42—222no—
119C11#202711yescharacteristic, complemented, Sylow
120C23—222no—
121C23—442no—
122C23—442no—
123C23—441no—
124C23—441no—
125C23C2×D4411yescharacteristic
126Q8—882no—
127D4—224no—
128D4—442no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—222no—
132C2×C4—222no—
133C2×C4—222no—
134C2×C4—441no—
135C2×C4—441no—
136C2×C4#433912yes—
137C2×C4D4×D1112yes—
138C2×C4#434111yescharacteristic
139C2×C4Q8×D1111yescharacteristic
140C8—42no—
141C22—21no—
142C22—21no—
143C22—444no—
144C22—442no—
145C22—882no—
146C22—881no—
147C22—881no—
148C22#6692811yescharacteristic
149C22#6693511yescharacteristic
150C22#6695011yescharacteristic
151C4—42no—
152C4—442no—
153C4—442no—
154C4—442no—
155C4#6693812yes—
156C4#6694912yes—
157C2—21no—
158C2—21no—
159C2—882no—
160C2#1062228611yescharacteristic
161C2#1062236011yescharacteristic
162C2#1062236611yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#343C2
socleC22×C11#120
prime radicalC22×D44C22
hypercenter#343D11
hypocenterC11#2027
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. #10623031C2semidirect
4. C11×#343C2semidirect
5. #10622193C2semidirect
24. C2×D44Q8semidirect
63. #343D11semidirect
119. C11#2027semidirect

Maximal subgroups

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

subgroupindex
#106230312
#106227442
#106226012
C11×#3432
#106221932
#202711