Finite Group Databasebeta

← #16818805

Subgroups — #16818805

Order 3712.

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

normal subgroups only

This group has 196 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
1#14271917C211yesmaximal, characteristic
2#14271573C211yesmaximal, characteristic, complemented
3#14271572C211yesmaximal, characteristic, complemented
4#14271557C211yesmaximal, characteristic
5#14270904C211yesmaximal, characteristic, complemented
6#14270902C211yesmaximal, characteristic
7C29×#330C211yesmaximal, characteristic, complemented
8C29×#125C2211yescharacteristic
9C2×Dic116—21no—
10C2×#90773—21no—
11#11745260—21no—
12#11745260—21no—
13#11745259—21no—
14#11745258—21no—
15#11745256—21no—
16#11745250—21no—
17#11745237C2211yescharacteristic
18#11745232C2211yescharacteristic
19#11745231C2211yescharacteristic
20C29×#97C2211yescharacteristic
21C29×#97C2211yescharacteristic
22#11745166—21no—
23#11745165—21no—
24#11745156—21no—
25#11745155—21no—
26#11745151C2211yescharacteristic
27C2×D116D411yescharacteristic
28C2×C4×D29—21no—
29C2×Dic58—21no—
30C2×Dic58—21no—
31C2×Dic58D411yescharacteristic
32C2×C8×C29—21no—
33C2×C8×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29—21no—
36C4⋊C4×C29D411yescharacteristic
37C4⋊C4×C29D411yescharacteristic
38C42×C29C2311yescharacteristic
39#90781—21no—
40#90781—21no—
41#90781—21no—
42#90781—21no—
43#90781—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29—21no—
46C4⋊Dic29—21no—
47C4⋊Dic29D411yescharacteristic
48C4⋊Dic29D411yescharacteristic
49#90779—21no—
50#90779—21no—
51#90779—21no—
52C4×Dic29—21no—
53C2×#6597—21no—
54Dic116—42no—
55#90773—42no—
56C22×D29—21no—
57C2×C4×C29—21no—
58C2×C4×C29—21no—
59C2×C4×C29C2×D411yescharacteristic
60C2×C4×C29C2×D411yescharacteristic
61C2×C4×C29C2×D411yescharacteristic
62C2×Dic29—21no—
63C2×Dic29—21no—
64C2×Dic29—21no—
65C2×Dic29—41no—
66D116—41no—
67C4×D29—81no—
68Dic58—41no—
69Dic58—41no—
70Dic58—41no—
71Dic58—81no—
72C8×C29—22no—
73C8×C29—22no—
74#6597—22no—
75#1660—291nomaximal, Sylow
76C22×C29#12011yescharacteristic
77C2×D29—41no—
78C2×D29—41no—
79C2×D29—41no—
80C4×C29—21no—
81C4×C29—21no—
82C4×C29—21no—
83C4×C29—41no—
84C4×C29—41no—
85Dic29—41no—
86Dic29—41no—
87Dic29—41no—
88Dic29—81no—
89#563—291no—
90#501—291no—
91#501—291no—
92#497—291no—
93#330—291no—
94#330D2911yescharacteristic, complemented
95#329—291no—
96C2×C29#45311yescharacteristic
97C2×C29#45611yescharacteristic
98C2×C29#45611yescharacteristic
99D29—81no—
100C2×Q16—581no—
101C2×SD16—581no—
102C4⋊Q8—291no—
103C4⋊Q8—581no—
104#126—581no—
105#126—581no—
106#125—291no—
107#125C2×D2911yescharacteristic
108#124—291no—
109#123—581no—
110C22⋊Q8—581no—
111C22⋊Q8—581no—
112#107—581no—
113#107—581no—
114#106—581no—
115#106—581no—
116#97—291no—
117#97C2×D2911yescharacteristic
118#97C2×D2911yescharacteristic
119C29#166011yescharacteristic, complemented, Sylow
120C2×Q8—291no—
121C2×Q8—581no—
122C2×Q8—581no—
123C2×D4—291no—
124C22×C4—581no—
125Q16—1162no—
126SD16—1162no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—581no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—291no—
133C4⋊C4—291no—
134C4⋊C4—581no—
135C4⋊C4—581no—
136C4⋊C4—581no—
137C4⋊C4—581no—
138C4⋊C4—581no—
139C4⋊C4—581no—
140C4⋊C4D11611yescharacteristic
141C4⋊C4D11611yescharacteristic
142C22⋊C4—581no—
143C22⋊C4—581no—
144C22⋊C4—581no—
145C22⋊C4—581no—
146C22⋊C4—581no—
147C42—581no—
148C42C22×D2911yescharacteristic
149C23—581no—
150Q8—1161no—
151Q8—1161no—
152Q8—1161no—
153Q8—2321no—
154D4—1161no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—581no—
158C2×C4—581no—
159C2×C4—581no—
160C2×C4—1161no—
161C2×C4—2321no—
162C2×C4C2×D11611yescharacteristic
163C2×C4D4×D2911yescharacteristic
164C2×C4D4×D2911yescharacteristic
165C8—22no—
166C8—22no—
167C8—582no—
168C22—1161no—
169C22—1161no—
170C22—1161no—
171C22#1174524411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—1161no—
178C4—1161no—
179C4—1161no—
180C4—2321no—
181C2—2321no—
182C2#1427133211yescharacteristic
183C2#1427134711yescharacteristic
184C2#1427134811yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#330C2
socleC22×C29#120
prime radicalC2×D116D4
hypercenter#330D29
hypocenterC29#1660
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #14271573C2semidirect
3. #14271572C2semidirect
5. #14270904C2semidirect
7. C29×#330C2semidirect
94. #330D29semidirect
119. C29#1660semidirect

Maximal subgroups

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

subgroupindex
#142719172
#142715732
#142715722
#142715572
#142709042
#142709022
C29×#3302
#166029