Finite Group Databasebeta

← #16818534

Subgroups — #16818534

Order 3712.

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

normal subgroups only

This group has 202 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#14271496C212yesmaximal
2#14271102C211yesmaximal, 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
13#11745183—22no—
14#11745179—21no—
15#11745179—21no—
16#11745179C2211yescharacteristic
17C22⋊#6597C2212yes—
18#11745155—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—
36C2×#6597—22no—
37C23×C29C2×D411yescharacteristic
38Q8×C29—42no—
39Q8×C29—81no—
40C2×C4×C29—21no—
41C2×C4×C29—21no—
42C2×C4×C29—22no—
43C2×C4×C29—22no—
44C2×C4×C29—21no—
45C2×C4×C29—41no—
46C2×C4×C29—41no—
47C2×C4×C29Q1612yes—
48C2×C4×C29C2×D412yes—
49C2×Dic29—41no—
50C2×Dic29—41no—
51C2×Dic29—42no—
52C2×Dic29—41no—
53C2×Dic29—41no—
54#6597—42no—
55#1617—291nomaximal, Sylow
56C22×C29—21no—
57C22×C29—21no—
58C22×C29#12011yescharacteristic
59C22×C29C2×Q1611yescharacteristic
60C22×C29#13711yescharacteristic
61C4×C29—22no—
62C4×C29—22no—
63C4×C29—42no—
64C4×C29—41no—
65C4×C29—42no—
66Dic29—81no—
67Dic29—81no—
68#544D2911yescharacteristic
69#484—292no—
70#400—291no—
71#328—292no—
72#324—291no—
73C2×C29—21no—
74C2×C29—21no—
75C2×C29#45111yescharacteristic
76C2×C29#45411yescharacteristic
77C2×C29#45811yescharacteristic
78C4⋊Q8—22no—
79#125—22no—
80C22⋊Q8—21no—
81C22⋊Q8C2×D2912yes—
82#117—21no—
83C2×C4⋊C4—291no—
84C2×C4⋊C4C2×D2911yescharacteristic
85#107—582no—
86#103—582no—
87C22⋊C8—292no—
88#95—291no—
89#95—581no—
90#95—581no—
91C29#161711yescharacteristic, complemented, Sylow
92C2×Q8—21no—
93C2×Q8C22⋊D2912yes—
94C22×C4—581no—
95C22×C4—581no—
96C22×C4C22⋊D2911yescharacteristic
97C22×C4C22⋊D2911yescharacteristic
98C22×C4C22×D2911yescharacteristic
99C2×C8—582no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—582no—
107C4⋊C4C22⋊D2912yes—
108C22⋊C4—22no—
109C42—22no—
110C23C2×C22⋊D2911yescharacteristic
111Q8—42no—
112Q8—81no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—21no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—1161no—
121C2×C4—1161no—
122C2×C4—1162no—
123C2×C4—1161no—
124C2×C4—1161no—
125C2×C4#9078512yes—
126C2×C4C2×C22⋊D2912yes—
127C8—1162no—
128C22—21no—
129C22—21no—
130C22#1174530411yescharacteristic
131C22C2×#9078511yescharacteristic
132C22#1174531511yescharacteristic
133C4—22no—
134C4—22no—
135C4—42no—
136C4—41no—
137C4—42no—
138C4—2321no—
139C4—2321no—
140C2—21no—
141C2—21no—
142C2#1427131911yescharacteristic
143C2#1427133611yescharacteristic
144C2#1427135311yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#544C2
socleC22×C29#120
prime radicalC23×C29C2×D4
hypercenter#544D29
hypocenterC29#1617
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
91. C29#1617semidirect

Maximal subgroups

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

subgroupindex
#142714962
#142711022
#142709002
#142708892
C29×#5442
#161729