Finite Group Databasebeta

← #16835795

Subgroups — #16835795

Order 3712.

230 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 52 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#14272150C212yesmaximal
2#14272074C212yesmaximal, complemented
3#14272073C212yesmaximal, complemented
4#14271733C211yesmaximal, characteristic
5C2×Q8×D29C411yescharacteristic
6C2×#90807C2211yescharacteristic
7C2×#90800—22no—
8C29×#124C411yescharacteristic
9#11745306C2211yescharacteristic
10#11745298C411yescharacteristic
11#11745245—22no—
12#11745240—22no—
13#11745234C411yescharacteristic
14#11745231C2211yescharacteristic
15#11745229—22no—
16#11745221C2214yes—
17C2×Q8×C29C2×C411yescharacteristic
18C2×D4×C29C2×C411yescharacteristic
19C2×C22⋊D29D412yes—
20C22×Dic29D412yes—
21Q8×D29—42no—
22#90807—42no—
23C2×C4×D29—21no—
24C2×C4×D29C2×C411yescharacteristic
25C2×Dic58—21no—
26C2×Dic58C2×C411yescharacteristic
27C2×Dic58C2311yescharacteristic
28#90800—24no—
29#90800—42no—
30C2×#6599—42no—
31C22⋊C4×C29—22no—
32C42×C29C2×C411yescharacteristic
33C22⋊Dic29—22no—
34#90781—21no—
35C4⋊Dic29—22no—
36#90779—21no—
37#90779—22no—
38C4×Dic29C2×C411yescharacteristic
39C23×C29C22⋊C412yes—
40C22×D29C22⋊C411yescharacteristic
41Q8×C29—41no—
42D4×C29—41no—
43C2×C4×C29—21no—
44C2×C4×C29—21no—
45C2×C4×C29C22×C411yescharacteristic
46C22⋊D29—42no—
47C2×Dic29—22no—
48C2×Dic29—22no—
49C2×Dic29—21no—
50C2×Dic29—21no—
51C2×Dic29C22⋊C411yescharacteristic
52C2×Dic29C2×D412yes—
53C4×D29—22no—
54C4×D29—42no—
55Dic58—41no—
56Dic58—42no—
57Dic58—41no—
58#6599—44no—
59#2135—291nomaximal, Sylow
60C22×C29—22no—
61C22×C29—42no—
62C22×C29C2×C22⋊C411yescharacteristic
63C2×D29—21no—
64C2×D29—41no—
65C4×C29—21no—
66C4×C29—41no—
67C4×C29—41no—
68Dic29—22no—
69Dic29—41no—
70Dic29—41no—
71Dic29#9912yes—
72#536—291no—
73#413—292no—
74#356—292no—
75#356—292no—
76C2×C29—21no—
77C2×C29—42no—
78C2×C29C2×#9911yescharacteristic
79D29—41no—
80C2×#41—291no—
81C22×Q8—291no—
82C2×M16—582no—
83C4⋊Q8—291no—
84C4⋊Q8—291no—
85#124—291no—
86#124#118111yescharacteristic
87#123—582no—
88C22⋊Q8—582no—
89#117—291no—
90#101—294no—
91#100—582no—
92C29#213511yescharacteristic, complemented, Sylow
93#41—1162no—
94C2×Q8—291no—
95C2×Q8—291no—
96C2×Q8—581no—
97C2×Q8—1162no—
98C2×Q8C2×#118111yescharacteristic
99C2×D4—292no—
100C2×D4C2×#118111yescharacteristic
101C22×C4—292no—
102C22×C4—291no—
103C22×C4—581no—
104M16—584no—
105M16—1162no—
106C2×C8—1162no—
107C4⋊C4—581no—
108C4⋊C4—582no—
109C4⋊C4—582no—
110C22⋊C4—22no—
111C22⋊C4—581no—
112C22⋊C4—582no—
113C42—291no—
114C42C2×#118111yescharacteristic
115C23—291no—
116C23C22⋊#118112yes—
117Q8—41no—
118Q8—1161no—
119Q8—1161no—
120Q8—1162no—
121D4—41no—
122D4—1162no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—291no—
126C2×C4—292no—
127C2×C4—582no—
128C2×C4—582no—
129C2×C4—582no—
130C2×C4—581no—
131C2×C4—581no—
132C2×C4—1162no—
133C2×C4C22×#118111yescharacteristic
134C8—1164no—
135C22—22no—
136C22—42no—
137C22—581no—
138C22—1161no—
139C22C2×C22⋊#118111yescharacteristic
140C4—21no—
141C4—41no—
142C4—41no—
143C4—292no—
144C4—582no—
145C4—1161no—
146C4—1161no—
147C2—21no—
148C2—42no—
149C2—1161no—
150C2D29⋊#9911yescharacteristic
subgroupG/H
centerC2D29⋊#99
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#124C4
socleC2×C29C2×#99
prime radicalC2×#90807C22
cosocleC2×Dic58C23
hypercenter#124#1181
hypocenterC29#2135
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #14272074C2semidirect
3. #14272073C2semidirect
92. C29#2135semidirect

Maximal subgroups

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

subgroupindex
#142721502
#142720742
#142720732
#142717332
#213529