Finite Group Databasebeta

← #16835404

Subgroups — #16835404

Order 3712.

296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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×#11745215C212yesmaximal
2#14272040C214yesmaximal, complemented
3#14271637C211yesmaximal, characteristic
4C22×D116C2211yescharacteristic
5C2×C22⋊#1181C2214yes—
6C29×#117C411yescharacteristic, complemented
7#11745288C411yescharacteristic, complemented
8#11745255—22no—
9C22⋊C4×D29C412yescomplemented
10C22⋊C4×D29C2212yes—
11C4×D116—22no—
12#11745215—22no—
13#11745215—22no—
14C23×D29C2×C411yescharacteristic
15C23×D29C2311yescharacteristic
16C22×#1181—24no—
17C22×C4×C29C2×C411yescharacteristic
18C2×D116—24no—
19C2×D116D412yes—
20C2×D116D412yes—
21C2×C4×D29—22no—
22C2×C4×D29—22no—
23C22⋊#1181—24no—
24C22⋊#1181—24no—
25C4⋊C4×C29—21no—
26C22⋊C4×C29C2×C412yes—
27C42×C29—21no—
28C22⋊Dic29C2×C412yes—
29#90781—22no—
30#90781—22no—
31C4⋊Dic29—21no—
32C4×Dic29—21no—
33C23×C29C22×C411yescharacteristic
34C22×D29—22no—
35C22×D29—81no—
36C22×D29—81no—
37C22×D29C22⋊C412yes—
38C22×D29C2×D412yes—
39C22×D29#4114yes—
40C2×#1181—44no—
41C2×#1181—84no—
42C2×C4×C29—22no—
43C2×C4×C29—22no—
44C2×C4×C29C22⋊C411yescharacteristic
45C2×C4×C29C22⋊C411yescharacteristic
46C2×Dic29—22no—
47D116—24no—
48D116—24no—
49C4×D29—82no—
50C4×D29—82no—
51#1828—291nomaximal, Sylow
52C22×C29—41no—
53C22×C29C2×C22⋊C411yescharacteristic
54C22×C29#11712yes—
55C2×D29—22no—
56C2×D29—42no—
57C2×D29—44no—
58C2×D29—42no—
59C2×D29—82no—
60C2×D29#12314yes—
61#1181—84no—
62C4×C29—21no—
63C4×C29—21no—
64C4×C29—42no—
65Dic29—42no—
66#518—291no—
67C2×#99—292no—
68#342—294no—
69C2×C29—21no—
70C2×C29—22no—
71C2×C29#38111yescharacteristic
72D29—24no—
73D29—42no—
74C22×D4—291no—
75C4×D4—582no—
76C4×D4—582no—
77#117—291no—
78#117#118111yescharacteristic, complemented
79C2×C22⋊C4—292no—
80C2×C22⋊C4—292no—
81C2×C22⋊C4—294no—
82#99—582no—
83#99—582no—
84C29#182811yescharacteristic, complemented, Sylow
85C24—291no—
86C24—291no—
87C2×D4—292no—
88C2×D4—292no—
89C2×D4—584no—
90C22×C4—582no—
91C22×C4—582no—
92C22×C4—584no—
93C22×C4C2×#118111yescharacteristic
94C4⋊C4—21no—
95C4⋊C4—581no—
96C22⋊C4—292no—
97C22⋊C4—582no—
98C22⋊C4—582no—
99C22⋊C4—584no—
100C22⋊C4—584no—
101C22⋊C4C2×#118112yes—
102C42—21no—
103C42—581no—
104C23—294no—
105C23—292no—
106C23—292no—
107C23—582no—
108C23—2321no—
109C23—2321no—
110C23C22×#118111yescharacteristic
111D4—584no—
112D4—584no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—582no—
116C2×C4—1164no—
117C2×C4—2322no—
118C2×C4—2322no—
119C2×C4—2324no—
120C2×C4C22⋊#118111yescharacteristic
121C2×C4C22⋊#118111yescharacteristic
122C22—41no—
123C22—294no—
124C22—582no—
125C22—1162no—
126C22—1164no—
127C22—1162no—
128C22—2322no—
129C22#1174534512yes—
130C22C2×C22⋊#118111yescharacteristic
131C4—21no—
132C4—21no—
133C4—42no—
134C4—1162no—
135C4—2324no—
136C2—21no—
137C2—22no—
138C2—584no—
139C2—1162no—
140C2#1427210611yescharacteristic
subgroupG/H
centerC2#14272106
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC29×#117C4
socleC2×C29#381
prime radicalC22×D116C22
cosocleC23×D29C23
hypercenter#117#1181
hypocenterC29#1828
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C23 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #14272040C2semidirect
6. C29×#117C4semidirect
7. #11745288C4semidirect
9. C22⋊C4×D29C4semidirect
78. #117#1181semidirect
84. C29#1828semidirect

Maximal subgroups

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

subgroupindex
C2×#117452152
#142720402
#142716372
#182829