Finite Group Databasebeta

← #16835403

Subgroups — #16835403

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×#11745227C212yesmaximal
2#14272040C214yesmaximal, complemented
3#14271636C211yesmaximal, characteristic
4C22×C22⋊D29C2211yescharacteristic
5C2×C22⋊#1181C2214yes—
6C2×C22⋊C4×C29C411yescharacteristic, complemented
7C2×C22⋊Dic29C411yescharacteristic, complemented
8C4×C22⋊D29—22no—
9#11745243—22no—
10C22⋊C4×D29C2212yes—
11#11745239C412yescomplemented
12#11745227—22no—
13#11745227—22no—
14C24×C29C2×C411yescharacteristic
15C23×D29C2311yescharacteristic
16C22×#1181—24no—
17C22×C4×C29—21no—
18C2×C22⋊D29—24no—
19C2×C22⋊D29D412yes—
20C2×C22⋊D29D412yes—
21C22×Dic29—21no—
22C22×Dic29C2×C411yescharacteristic
23C2×C4×D29—22no—
24C22⋊#1181—24no—
25C22⋊#1181—24no—
26C22⋊C4×C29—21no—
27C22⋊C4×C29C2×C412yes—
28C22⋊Dic29—21no—
29C22⋊Dic29C2×C412yes—
30#90781—22no—
31#90779—22no—
32C4×Dic29—22no—
33C23×C29—22no—
34C23×C29—81no—
35C23×C29C22⋊C411yescharacteristic
36C23×C29C22⋊C411yescharacteristic
37C23×C29C22×C411yescharacteristic
38C22×D29—81no—
39C22×D29C2×D412yes—
40C22×D29#4114yes—
41C2×#1181—44no—
42C2×#1181—84no—
43C2×C4×C29—22no—
44C2×C4×C29—81no—
45C22⋊D29—24no—
46C22⋊D29—24no—
47C2×Dic29—22no—
48C2×Dic29—22no—
49C2×Dic29—81no—
50C2×Dic29C22⋊C412yes—
51C4×D29—82no—
52#1828—291nomaximal, Sylow
53C22×C29—21no—
54C22×C29—21no—
55C22×C29—41no—
56C22×C29—41no—
57C22×C29—41no—
58C22×C29—82no—
59C22×C29C2×C22⋊C411yescharacteristic
60C22×C29#11712yes—
61C2×D29—42no—
62C2×D29—44no—
63C2×D29#12314yes—
64#1181—84no—
65C4×C29—42no—
66Dic29—22no—
67Dic29—42no—
68#518—291no—
69C2×#99—292no—
70#342—294no—
71C2×C29—21no—
72C2×C29—22no—
73C2×C29—41no—
74C2×C29—41no—
75C2×C29#38111yescharacteristic
76D29—24no—
77C22×D4—291no—
78C4×D4—582no—
79C4×D4—582no—
80#117—292no—
81C2×C22⋊C4—291no—
82C2×C22⋊C4—292no—
83C2×C22⋊C4—294no—
84C2×C22⋊C4#118111yescharacteristic, complemented
85#99—582no—
86#99—582no—
87C29#182811yescharacteristic, complemented, Sylow
88C24—291no—
89C24C2×#118111yescharacteristic
90C2×D4—292no—
91C2×D4—292no—
92C2×D4—584no—
93C22×C4—21no—
94C22×C4—291no—
95C22×C4—582no—
96C22×C4—581no—
97C22×C4—584no—
98C4⋊C4—582no—
99C22⋊C4—21no—
100C22⋊C4—292no—
101C22⋊C4—582no—
102C22⋊C4—581no—
103C22⋊C4—584no—
104C22⋊C4—584no—
105C22⋊C4C2×#118112yes—
106C42—582no—
107C23—22no—
108C23—81no—
109C23—294no—
110C23—292no—
111C23—2321no—
112C23C22⋊#118111yescharacteristic
113C23C22⋊#118111yescharacteristic
114C23C22×#118111yescharacteristic
115D4—584no—
116D4—584no—
117C2×C4—22no—
118C2×C4—81no—
119C2×C4—292no—
120C2×C4—582no—
121C2×C4—582no—
122C2×C4—1164no—
123C2×C4—2322no—
124C2×C4—2321no—
125C2×C4—2324no—
126C22—21no—
127C22—21no—
128C22—41no—
129C22—41no—
130C22—41no—
131C22—82no—
132C22—294no—
133C22—1162no—
134C22—1164no—
135C22#1174534512yes—
136C22C2×C22⋊#118111yescharacteristic
137C4—42no—
138C4—582no—
139C4—1162no—
140C4—2324no—
141C2—21no—
142C2—22no—
143C2—41no—
144C2—41no—
145C2—584no—
146C2#1427210611yescharacteristic
subgroupG/H
centerC2#14272106
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C22⋊C4×C29C4
socleC2×C29#381
prime radicalC22×C22⋊D29C22
cosocleC23×D29C23
hypercenterC2×C22⋊C4#1181
hypocenterC29#1828
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14272040C2semidirect
6. C2×C22⋊C4×C29C4semidirect
7. C2×C22⋊Dic29C4semidirect
11. #11745239C4semidirect
84. C2×C22⋊C4#1181semidirect
87. C29#1828semidirect

Maximal subgroups

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

subgroupindex
C2×#117452272
#142720402
#142716362
#182829