Finite Group Databasebeta

← #16818500

Subgroups — #16818500

Order 3712.

210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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#14271491C212yesmaximal
2#14271093C211yesmaximal, characteristic
3#14270900C212yesmaximal
4#14270889C211yesmaximal, characteristic
5C29×#544C211yesmaximal, characteristic
6C29×C4⋊Q8—22no—
7C29×#125—22no—
8C29×C22⋊Q8—21no—
9C29×C22⋊Q8C2212yes—
10C29×#117—21no—
11C2×C4⋊C4×C29C2211yescharacteristic
12C2×C4⋊Dic29C2211yescharacteristic
13C2×#90779—21no—
14#11745183—22no—
15#11745179—21no—
16#11745179C2211yescharacteristic
17C22⋊#6597C2212yes—
18#11745156—22no—
19C2×Q8×C29—21no—
20C2×Q8×C29D412yes—
21C22×C4×C29D411yescharacteristic
22C22×C4×C29D411yescharacteristic
23C22×C4×C29C2311yescharacteristic
24C22×Dic29—21no—
25C22×Dic29—21no—
26C4⋊C4×C29—21no—
27C4⋊C4×C29—21no—
28C4⋊C4×C29—21no—
29C4⋊C4×C29—22no—
30C4⋊C4×C29—22no—
31C4⋊C4×C29—22no—
32C4⋊C4×C29D412yes—
33C22⋊C4×C29—22no—
34C42×C29—22no—
35C4⋊Dic29—22no—
36#90779—42no—
37C2×#6597—22no—
38C23×C29C2×D411yescharacteristic
39Q8×C29—42no—
40Q8×C29—81no—
41C2×C4×C29—21no—
42C2×C4×C29—21no—
43C2×C4×C29—22no—
44C2×C4×C29—22no—
45C2×C4×C29—21no—
46C2×C4×C29—41no—
47C2×C4×C29—41no—
48C2×C4×C29SD1612yes—
49C2×C4×C29C2×D412yes—
50C2×Dic29—22no—
51C2×Dic29—41no—
52C2×Dic29—41no—
53C2×Dic29—41no—
54C2×Dic29—41no—
55C2×Dic29—41no—
56#6597—42no—
57#1611—291nomaximal, Sylow
58C22×C29—21no—
59C22×C29—21no—
60C22×C29#12011yescharacteristic
61C22×C29C2×SD1611yescharacteristic
62C22×C29#13711yescharacteristic
63C4×C29—22no—
64C4×C29—22no—
65C4×C29—42no—
66C4×C29—41no—
67C4×C29—42no—
68Dic29—42no—
69Dic29—81no—
70#544D2911yescharacteristic
71#483—292no—
72#398—291no—
73#328—292no—
74#324—291no—
75C2×C29—21no—
76C2×C29—21no—
77C2×C29#44811yescharacteristic
78C2×C29#45611yescharacteristic
79C2×C29#45811yescharacteristic
80C4⋊Q8—22no—
81#125—22no—
82C22⋊Q8—21no—
83C22⋊Q8C2×D2912yes—
84#117—21no—
85C2×C4⋊C4—291no—
86C2×C4⋊C4—581no—
87C2×C4⋊C4C2×D2911yescharacteristic
88#106—582no—
89#103—582no—
90C22⋊C8—292no—
91#95—291no—
92#95—581no—
93C29#161111yescharacteristic, complemented, Sylow
94C2×Q8—21no—
95C2×Q8C22⋊D2912yes—
96C22×C4—581no—
97C22×C4—581no—
98C22×C4C22⋊D2911yescharacteristic
99C22×C4C22⋊D2911yescharacteristic
100C22×C4C22×D2911yescharacteristic
101C2×C8—582no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—582no—
109C4⋊C4—1162no—
110C4⋊C4C22⋊D2912yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×C22⋊D2911yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—582no—
124C2×C4—1161no—
125C2×C4—1161no—
126C2×C4—1161no—
127C2×C4—1161no—
128C2×C4—1161no—
129C2×C4#9078412yes—
130C2×C4C2×C22⋊D2912yes—
131C8—1162no—
132C22—21no—
133C22—21no—
134C22C2×#9078411yescharacteristic
135C22#1174530411yescharacteristic
136C22#1174531511yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—42no—
142C4—1162no—
143C4—2321no—
144C2—21no—
145C2—21no—
146C2#1427130211yescharacteristic
147C2#1427134611yescharacteristic
148C2#1427135311yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#544C2
socleC22×C29#120
prime radicalC23×C29C2×D4
hypercenter#544D29
hypocenterC29#1611
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
93. C29#1611semidirect

Maximal subgroups

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

subgroupindex
#142714912
#142710932
#142709002
#142708892
C29×#5442
#161129