Finite Group Databasebeta

← #1828×C211 #41009448

Subgroups — #1828×C211 #41009448

Order 27008.

296 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 100 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#518×C211C211yesmaximal, characteristic
2C2×#99×C211C212yesmaximal
3#342×C211C214yesmaximal, complemented
4C22×D4×C211C2211yescharacteristic
5C4×D4×C211—24no—
6#117×C211C412yescomplemented
7C2×C22⋊C4×C211C412yescomplemented
8C2×C22⋊C4×C211C2214yes—
9C2×C22⋊C4×C211C2212yes—
10#99×C211—24no—
11C24×C211C2×C411yescharacteristic
12C24×C211C2311yescharacteristic
13C2×D4×C211—24no—
14C2×D4×C211D414yes—
15C22×C4×C211—22no—
16C22×C4×C211—22no—
17C22×C4×C211—24no—
18C22×C4×C211C2×C411yescharacteristic
19C4⋊C4×C211—22no—
20C22⋊C4×C211—22no—
21C22⋊C4×C211—22no—
22C22⋊C4×C211—24no—
23C22⋊C4×C211—24no—
24C22⋊C4×C211C2×C414yes—
25C42×C211—22no—
26C23×C211—22no—
27C23×C211—81no—
28C23×C211—81no—
29C23×C211C22⋊C412yes—
30C23×C211C22×C411yescharacteristic
31C23×C211C2×D412yes—
32C23×C211#4114yes—
33D4×C211—28no—
34C2×C4×C211—22no—
35C2×C4×C211—24no—
36C2×C4×C211—44no—
37C2×C4×C211—82no—
38C2×C4×C211—82no—
39C2×C4×C211—84no—
40C2×C4×C211C22⋊C412yes—
41C22×C211—22no—
42C22×C211—42no—
43C22×C211—44no—
44C22×C211—41no—
45C22×C211—42no—
46C22×C211—82no—
47C22×C211C2×C22⋊C411yescharacteristic
48C22×C211#11712yes—
49C22×C211#12314yes—
50C4×C211—22no—
51C4×C211—44no—
52C4×C211—84no—
53C2×C211—21no—
54C2×C211—24no—
55C2×C211—22no—
56C2×C211—42no—
57C2×C211#38111yescharacteristic
58C211#182811yescharacteristic, direct product factor, Sylow
59#1828C21111yesmaximal, characteristic, direct product factor, Sylow
60#518C2×C21111yescharacteristic
61C2×#99C2×C21112yes—
62#342C2×C21114yescomplemented
63C22×D4C22×C21111yescharacteristic
64C4×D4—24no—
65#117C4×C21112yescomplemented
66C2×C22⋊C4C4×C21112yescomplemented
67C2×C22⋊C4C22×C21114yes—
68C2×C22⋊C4C22×C21112yes—
69#99—24no—
70C24C2×C4×C21111yescharacteristic
71C24C23×C21111yescharacteristic
72C2×D4—24no—
73C2×D4D4×C21114yes—
74C22×C4—22no—
75C22×C4—22no—
76C22×C4—24no—
77C22×C4C2×C4×C21111yescharacteristic
78C4⋊C4—22no—
79C22⋊C4—22no—
80C22⋊C4—22no—
81C22⋊C4—24no—
82C22⋊C4—24no—
83C22⋊C4C2×C4×C21114yes—
84C42—22no—
85C23—22no—
86C23—81no—
87C23—81no—
88C23C22⋊C4×C21112yes—
89C23C22×C4×C21111yescharacteristic
90C23C2×D4×C21112yes—
91C23#41×C21114yes—
92D4—28no—
93C2×C4—22no—
94C2×C4—24no—
95C2×C4—44no—
96C2×C4—82no—
97C2×C4—82no—
98C2×C4—84no—
99C2×C4C22⋊C4×C21112yes—
100C22—22no—
101C22—42no—
102C22—44no—
103C22—41no—
104C22—42no—
105C22—82no—
106C22C2×C22⋊C4×C21111yescharacteristic
107C22#117×C21112yes—
108C22#123×C21114yes—
109C4—22no—
110C4—44no—
111C4—84no—
112C2—21no—
113C2—24no—
114C2—22no—
115C2—42no—
116C2#381×C21111yescharacteristic
subgroupG/H
center, socleC2×C211#381
commutatorC23C22×C4×C211
Frattini, cosocleC24C23×C211
prime radicalC22×D4×C211C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C211 ◁ C24×C211 ◁ G

Complements

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

NH ≅ G/Ntype
3. #342×C211C2semidirect
6. #117×C211C4semidirect
7. C2×C22⋊C4×C211C4semidirect
58. C211#1828direct (N × H)
59. #1828C211direct (N × H)
62. #342C2×C211semidirect
65. #117C4×C211semidirect
66. C2×C22⋊C4C4×C211semidirect

Maximal subgroups

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

subgroupindex
#518×C2112
C2×#99×C2112
#342×C2112
#1828211