Finite Group Databasebeta

← #16820660

Subgroups — #16820660

Order 3712.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#14271789C211yesmaximal, characteristic
2#14271024C211yesmaximal, characteristic
3#14271024C212yesmaximal
4#14270929C212yesmaximal
5C29×#342C211yesmaximal, characteristic
6C23×Dic29C2211yescharacteristic
7C2×C22⋊C4×C29C2212yes—
8C2×C22⋊C4×C29C2211yescharacteristic
9C2×C22⋊Dic29C2211yescharacteristic
10C2×C22⋊Dic29C2212yes—
11#11745286—22no—
12#11745240—24no—
13#11745179—22no—
14#11745179—24no—
15C24×C29C2311yescharacteristic
16C22×C4×C29—22no—
17C22×C4×C29D412yes—
18C22×Dic29—21no—
19C22×Dic29—22no—
20C22×Dic29—22no—
21C22×Dic29—21no—
22C22×Dic29—21no—
23C22×Dic29D414yes—
24C22×Dic29Q812yescomplemented
25C2×Dic58—22no—
26C22⋊C4×C29—22no—
27C22⋊C4×C29—22no—
28C22⋊C4×C29—22no—
29C22⋊Dic29—22no—
30C22⋊Dic29—22no—
31C22⋊Dic29—22no—
32C4⋊Dic29—22no—
33#90779—24no—
34C23×C29—42no—
35C23×C29C2×D411yescharacteristic
36C23×C29C2×D412yes—
37C23×C29C2×Q811yescharacteristic
38C23×C29#4112yes—
39C23×C29#4111yescharacteristic
40C2×C4×C29—22no—
41C2×C4×C29—42no—
42C2×C4×C29—44no—
43C2×C4×C29—42no—
44C2×Dic29—24no—
45C2×Dic29—24no—
46C2×Dic29—22no—
47C2×Dic29—41no—
48C2×Dic29—41no—
49C2×Dic29—42no—
50C2×Dic29—44no—
51C2×Dic29—42no—
52C2×Dic29—41no—
53Dic58—82no—
54#2030—291nomaximal, Sylow
55C22×C29—22no—
56C22×C29—24no—
57C22×C29—41no—
58C22×C29—42no—
59C22×C29—41no—
60C22×C29#12011yescharacteristic
61C22×C29C22⋊Q812yes—
62C22×C29C22⋊Q811yescharacteristic
63C22×C29#12411yescharacteristic
64C22×C29#12412yes—
65C4×C29—42no—
66C4×C29—82no—
67Dic29—42no—
68Dic29—44no—
69Dic29—81no—
70#543—291no—
71#381—292no—
72#381—291no—
73#342—292no—
74#342D2911yescharacteristic
75C2×C29—21no—
76C2×C29—22no—
77C2×C29—22no—
78C2×C29—21no—
79C2×C29#39311yescharacteristic
80C2×C29#45812yes—
81C23×C4—291no—
82C22⋊Q8—584no—
83C22⋊Q8—582no—
84C2×C22⋊C4—292no—
85C2×C22⋊C4—291no—
86C2×C22⋊C4C2×D2912yes—
87C2×C22⋊C4C2×D2911yescharacteristic
88#95—584no—
89#95—582no—
90C29#203011yescharacteristic, complemented, Sylow
91C24C22×D2911yescharacteristic
92C2×Q8—582no—
93C22×C4—22no—
94C22×C4—292no—
95C22×C4—294no—
96C22×C4—581no—
97C22×C4—582no—
98C22×C4—582no—
99C22×C4—581no—
100C22×C4—581no—
101C22×C4D11612yes—
102C4⋊C4—584no—
103C4⋊C4—582no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—22no—
107C22⋊C4—582no—
108C22⋊C4—582no—
109C22⋊C4—582no—
110C23—42no—
111C23C2×D11611yescharacteristic
112C23#9080512yes—
113C23D4×D2912yes—
114C23#9080711yescharacteristic
115C23Q8×D2911yescharacteristic
116Q8—2322no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—44no—
120C2×C4—42no—
121C2×C4—584no—
122C2×C4—584no—
123C2×C4—582no—
124C2×C4—1161no—
125C2×C4—1161no—
126C2×C4—1162no—
127C2×C4—1164no—
128C2×C4—1162no—
129C2×C4—1161no—
130C22—22no—
131C22—24no—
132C22—42no—
133C22—41no—
134C22—41no—
135C22#1174523711yescharacteristic
136C22#1174524411yescharacteristic
137C22#1174524712yes—
138C22#1174525812yes—
139C22#1174525911yescharacteristic
140C4—42no—
141C4—82no—
142C4—1162no—
143C4—1164no—
144C4—2321no—
145C2—22no—
146C2—21no—
147C2—22no—
148C2—21no—
149C2#1427107611yescharacteristic
150C2#1427135412yes—
subgroupG/H
centerC22#11745244
commutator, prime radical, cosocleC24×C29C23
FrattiniC24C22×D29
FittingC29×#342C2
socleC22×C29#120
hypercenter#342D29
hypocenterC29#2030
LCSG ▷ C24×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
24. C22×Dic29Q8semidirect
90. C29#2030semidirect

Maximal subgroups

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

subgroupindex
#142717892
#142710242
#142709292
C29×#3422
#203029