Finite Group Databasebeta

← #16820659

Subgroups — #16820659

Order 3712.

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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#14271026C212yesmaximal
3#14270930C211yesmaximal, characteristic
4#14270929C212yesmaximal
5C29×#381C211yesmaximal, characteristic
6C23×C4×C29C2211yescharacteristic
7C2×C22⋊C4×C29C2211yescharacteristic
8C2×C22⋊C4×C29C2211yescharacteristic
9C2×C22⋊Dic29C2212yes—
10C2×C22⋊Dic29C2212yes—
11#11745286—22no—
12#11745240—24no—
13C29×#95—22no—
14#11745179—24no—
15C24×C29C2311yescharacteristic
16C22×C4×C29—22no—
17C22×C4×C29—21no—
18C22×C4×C29—21no—
19C22×C4×C29—22no—
20C22×C4×C29—21no—
21C22×C4×C29D412yes—
22C22×C4×C29Q812yescomplemented
23C22×Dic29—22no—
24C22×Dic29D414yes—
25C2×Dic58—22no—
26C22⋊C4×C29—22no—
27C22⋊C4×C29—22no—
28C22⋊Dic29—22no—
29C22⋊Dic29—22no—
30C22⋊Dic29—22no—
31C22⋊Dic29—22no—
32C4⋊Dic29—22no—
33#90779—24no—
34C23×C29—42no—
35C23×C29C2×D412yes—
36C23×C29C2×D411yescharacteristic
37C23×C29C2×Q811yescharacteristic
38C23×C29#4111yescharacteristic
39C23×C29#4112yes—
40C2×C4×C29—22no—
41C2×C4×C29—22no—
42C2×C4×C29—24no—
43C2×C4×C29—41no—
44C2×C4×C29—41no—
45C2×C4×C29—42no—
46C2×C4×C29—42no—
47C2×C4×C29—42no—
48C2×C4×C29—41no—
49C2×Dic29—24no—
50C2×Dic29—44no—
51C2×Dic29—44no—
52C2×Dic29—42no—
53Dic58—82no—
54#2030—291nomaximal, Sylow
55C22×C29—24no—
56C22×C29—22no—
57C22×C29—41no—
58C22×C29—41no—
59C22×C29—42no—
60C22×C29#12011yescharacteristic
61C22×C29C22⋊Q811yescharacteristic
62C22×C29C22⋊Q812yes—
63C22×C29#12411yescharacteristic
64C22×C29#12412yes—
65C4×C29—42no—
66C4×C29—42no—
67C4×C29—81no—
68Dic29—44no—
69Dic29—82no—
70#543—291no—
71#381—292no—
72#381D2911yescharacteristic
73#342—292no—
74#342—291no—
75C2×C29—22no—
76C2×C29—21no—
77C2×C29—21no—
78C2×C29—22no—
79C2×C29#39311yescharacteristic
80C2×C29#45812yes—
81C23×C4C2×D2911yescharacteristic
82C22⋊Q8—584no—
83C22⋊Q8—582no—
84C2×C22⋊C4—292no—
85C2×C22⋊C4—292no—
86C2×C22⋊C4C2×D2911yescharacteristic
87C2×C22⋊C4C2×D2911yescharacteristic
88#95—22no—
89#95—584no—
90C29#203011yescharacteristic, complemented, Sylow
91C24C22×D2911yescharacteristic
92C2×Q8—582no—
93C22×C4—21no—
94C22×C4—22no—
95C22×C4—22no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—294no—
99C22×C4—582no—
100C22×C4Dic5812yescomplemented
101C22×C4C22⋊D2912yes—
102C4⋊C4—584no—
103C4⋊C4—582no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—582no—
107C22⋊C4—582no—
108C22⋊C4—582no—
109C22⋊C4—582no—
110C23—42no—
111C23C2×Dic5811yescharacteristic
112C23#9080511yescharacteristic
113C23D4×D2912yes—
114C23#9080712yes—
115C23C2×C22⋊D2911yescharacteristic
116Q8—2322no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—24no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—42no—
124C2×C4—42no—
125C2×C4—41no—
126C2×C4—584no—
127C2×C4—1164no—
128C2×C4—1164no—
129C2×C4—1162no—
130C22—22no—
131C22—24no—
132C22—41no—
133C22—41no—
134C22—42no—
135C22#1174524012yes—
136C22#1174524712yes—
137C22#1174528611yescharacteristic
138C22#1174529811yescharacteristic
139C22#1174529911yescharacteristic
140C4—42no—
141C4—42no—
142C4—81no—
143C4—1164no—
144C4—2322no—
145C2—21no—
146C2—22no—
147C2—21no—
148C2—22no—
149C2#1427107511yescharacteristic
150C2#1427135212yes—
subgroupG/H
centerC22#11745299
commutator, prime radical, cosocleC24×C29C23
FrattiniC24C22×D29
FittingC29×#381C2
socleC22×C29#120
hypercenter#381D29
hypocenterC29#2030
LCSG ▷ C24×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
22. C22×C4×C29Q8semidirect
90. C29#2030semidirect
100. C22×C4Dic58semidirect

Maximal subgroups

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

subgroupindex
#142717892
#142710262
#142709302
#142709292
C29×#3812
#203029