Finite Group Databasebeta

← #16818822

Subgroups — #16818822

Order 3712.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C29⋊#564C211yesmaximal, characteristic
2#14271573C211yesmaximal, characteristic
3#14271572C211yesmaximal, characteristic
4#14271532C211yesmaximal, characteristic
5#14270904C211yesmaximal, characteristic
6#14270904C211yesmaximal, characteristic
7C29×#330C211yesmaximal, characteristic
8C29×#125C2211yescharacteristic
9#11745252—21no—
10#11745252—21no—
11#11745251—21no—
12#11745251—21no—
13#11745251—21no—
14#11745251—21no—
15#11745232C2211yescharacteristic
16#11745232C2211yescharacteristic
17#11745231C2211yescharacteristic
18C29×#97C2211yescharacteristic
19C29×#97C2211yescharacteristic
20#11745166—21no—
21#11745165—21no—
22#11745164—21no—
23#11745164—21no—
24#11745156—21no—
25#11745155—21no—
26#11745151C2211yescharacteristic
27C2×Dic58—21no—
28C2×C8×C29—21no—
29C2×C8×C29—21no—
30C4⋊C4×C29—21no—
31C4⋊C4×C29—21no—
32C4⋊C4×C29D411yescharacteristic
33C4⋊C4×C29D411yescharacteristic
34C42×C29C2311yescharacteristic
35C4⋊Dic29—21no—
36C4⋊Dic29—21no—
37C4⋊Dic29—21no—
38C4⋊Dic29—21no—
39C4⋊Dic29D411yescharacteristic
40C4⋊Dic29D411yescharacteristic
41C4⋊Dic29D411yescharacteristic
42C4⋊Dic29D411yescharacteristic
43#90779—21no—
44#90779—21no—
45#90779—21no—
46#90779—21no—
47#90779—21no—
48#90779—21no—
49#90779—21no—
50#90779—21no—
51C4×Dic29—21no—
52C4×Dic29—21no—
53C2×#6597—21no—
54C2×C4×C29—21no—
55C2×C4×C29—21no—
56C2×C4×C29C2×D411yescharacteristic
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D411yescharacteristic
59C2×Dic29—21no—
60C2×Dic29—21no—
61C2×Dic29—21no—
62C2×Dic29—21no—
63C2×Dic29—41no—
64Dic58—42no—
65C8×C29—22no—
66C8×C29—41no—
67#6597—22no—
68#1663—291nomaximal, Sylow
69C22×C29#12011yescharacteristic
70C4×C29—21no—
71C4×C29—21no—
72C4×C29—21no—
73C4×C29—41no—
74C4×C29—41no—
75Dic29—41no—
76Dic29—41no—
77Dic29—41no—
78Dic29—41no—
79Dic29—81no—
80#564—291no—
81#501—291no—
82#501—291no—
83#491—291no—
84#330—291no—
85#330—291no—
86#330D2911yescharacteristic
87C2×C29#45411yescharacteristic
88C2×C29#45611yescharacteristic
89C2×C29#45611yescharacteristic
90C4⋊Q8—291no—
91#125—291no—
92#125—291no—
93#125—581no—
94#125—581no—
95#125—581no—
96#125—581no—
97#125—581no—
98#125—581no—
99#125C2×D2911yescharacteristic
100#107—581no—
101#107—581no—
102#106—581no—
103#106—581no—
104#103—581no—
105#103—581no—
106#97—291no—
107#97C2×D2911yescharacteristic
108#97C2×D2911yescharacteristic
109C29#166311yescharacteristic, complemented, Sylow
110C2×Q8—581no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—581no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—291no—
117C4⋊C4—291no—
118C4⋊C4—291no—
119C4⋊C4—291no—
120C4⋊C4—581no—
121C4⋊C4—581no—
122C4⋊C4—581no—
123C4⋊C4—581no—
124C4⋊C4—581no—
125C4⋊C4—581no—
126C4⋊C4—581no—
127C4⋊C4—581no—
128C4⋊C4—581no—
129C4⋊C4—581no—
130C4⋊C4—581no—
131C4⋊C4—581no—
132C4⋊C4D11611yescharacteristic
133C4⋊C4D11611yescharacteristic
134C42—581no—
135C42—581no—
136C42C22×D2911yescharacteristic
137Q8—1162no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—581no—
141C2×C4—581no—
142C2×C4—581no—
143C2×C4—581no—
144C2×C4—1161no—
145C2×C4C2×D11611yescharacteristic
146C2×C4D4×D2911yescharacteristic
147C2×C4D4×D2911yescharacteristic
148C8—22no—
149C8—41no—
150C8—582no—
151C22#1174524411yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—1161no—
158C4—1161no—
159C4—1161no—
160C4—1161no—
161C4—2321no—
162C2#1427133711yescharacteristic
163C2#1427134711yescharacteristic
164C2#1427134811yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#330C2
socle, prime radicalC22×C29#120
hypercenter#330D29
hypocenterC29#1663
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
109. C29#1663semidirect

Maximal subgroups

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

subgroupindex
C29⋊#5642
#142715732
#142715722
#142715322
#142709042
C29×#3302
#166329