Finite Group Databasebeta

← #16835793

Subgroups — #16835793

Order 3712.

262 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 54 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#14272149C212yesmaximal, complemented
2#14272072C214yesmaximal, complemented
3#14271732C211yesmaximal, characteristic
4C2×#90805C2211yescharacteristic
5C22×D116C411yescharacteristic
6D29⋊M16—22no—
7C29×#117C411yescharacteristic
8#11745257—22no—
9#11745244—22no—
10#11745237C2212yes—
11#11745236C412yes—
12#11745229—22no—
13#11745221C2214yescomplemented
14C23×D29—21no—
15C22×C4×C29C2×C411yescharacteristic
16C2×C22⋊D29D412yes—
17#90805—42no—
18C2×D116—21no—
19C2×D116—24no—
20C2×D116—42no—
21C2×D116C2×C412yes—
22C2×D116C2×C411yescharacteristic
23C2×C4×D29D412yes—
24C2×Dic58C2311yescharacteristic
25#90800—24no—
26#90796—42no—
27D29⋊C8—42no—
28C4⋊C4×C29—21no—
29C22⋊C4×C29—21no—
30C42×C29C2×C412yes—
31#90781—24no—
32C23×C29C22⋊C411yescharacteristic
33C22×D29—22no—
34C22×D29—42no—
35C22×D29—82no—
36C22×D29C22⋊C412yes—
37C2×C4×C29—22no—
38C2×C4×C29—22no—
39C2×C4×C29C22⋊C411yescharacteristic
40C2×C4×C29C22×C411yescharacteristic
41C22⋊D29—42no—
42C2×Dic29C2×D412yes—
43D116—41no—
44D116—42no—
45D116—42no—
46D116—84no—
47C4×D29—22no—
48C4×D29—22no—
49Dic58—41no—
50#6599—44no—
51#2134—291nomaximal, Sylow
52C22×C29—21no—
53C22×C29—41no—
54C22×C29C2×C22⋊C411yescharacteristic
55C2×D29—22no—
56C2×D29—42no—
57C2×D29—44no—
58C2×D29—42no—
59C2×D29—84no—
60C4×C29—21no—
61C4×C29—42no—
62C4×C29#9912yes—
63Dic29—22no—
64#535—291no—
65#413—292no—
66#355—294no—
67C2×C29—21no—
68C2×C29—41no—
69C2×C29C2×#9911yescharacteristic
70D29—42no—
71D29—82no—
72C2×#41—291no—
73C22×D4—291no—
74C2×M16—582no—
75#127—292no—
76#124—292no—
77#121—582no—
78#120—582no—
79#117#118111yescharacteristic
80#101—294no—
81#100—582no—
82C29#213411yescharacteristic, complemented, Sylow
83C24—581no—
84#41—1162no—
85C2×Q8—291no—
86C2×D4—292no—
87C2×D4—291no—
88C2×D4—292no—
89C2×D4—584no—
90C2×D4—581no—
91C2×D4—1162no—
92C22×C4—292no—
93C22×C4C2×#118111yescharacteristic
94M16—584no—
95M16—1162no—
96C2×C8—1162no—
97C4⋊C4—21no—
98C22⋊C4—21no—
99C22⋊C4—584no—
100C42C2×#118112yes—
101C23—292no—
102C23—582no—
103C23—1162no—
104C23—2322no—
105C23C22⋊#118111yescharacteristic
106Q8—1161no—
107D4—1161no—
108D4—1162no—
109D4—1162no—
110D4—1162no—
111D4—2324no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—292no—
115C2×C4—582no—
116C2×C4—582no—
117C2×C4C22⋊#118111yescharacteristic
118C2×C4C22×#118111yescharacteristic
119C8—1164no—
120C22—21no—
121C22—41no—
122C22—582no—
123C22—1162no—
124C22—1164no—
125C22—1162no—
126C22—2324no—
127C22C2×C22⋊#118111yescharacteristic
128C4—21no—
129C4—42no—
130C4—582no—
131C4#1174521512yes—
132C2—21no—
133C2—41no—
134C2—1162no—
135C2—2322no—
136C2C2×#1174521511yescharacteristic
subgroupG/H
centerC2C2×#11745215
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#117C4
socleC2×C29C2×#99
prime radical#14271732C2
cosocleC2×Dic58C23
hypercenter#117#1181
hypocenterC29#2134
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #14272149C2semidirect
2. #14272072C2semidirect
13. #11745221C22semidirect
82. C29#2134semidirect

Maximal subgroups

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

subgroupindex
#142721492
#142720722
#142717322
#213429