Finite Group Databasebeta

← #16818017

Subgroups — #16818017

Order 3712.

242 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 81 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#14271220C211yesmaximal, characteristic, complemented
2C4×C4⋊Dic29C211yesmaximal, characteristic, complemented
3#14270900C212yesmaximal, complemented
4#14270897C212yesmaximal
5C29×#529C211yesmaximal, characteristic
6C29×#126—21no—
7C29×#125C411yescharacteristic, complemented
8C29×#124C411yescharacteristic, complemented
9C29×#123—21no—
10C29×C22⋊Q8C2211yescharacteristic
11C29×#121C2211yescharacteristic
12C4×Q8×C29C411yescharacteristic, complemented
13C4×D4×C29—21no—
14C4×D4×C29C411yescharacteristic, complemented
15C29×#117—21no—
16C2×C42×C29C2211yescharacteristic
17C2×C4⋊Dic29—21no—
18C2×C4×Dic29—21no—
19#11745179C2212yes—
20C22⋊#6597C2212yes—
21C4⋊#6597—21no—
22#11745151—21no—
23C2×Q8×C29C2×C411yescharacteristic
24C2×D4×C29—21no—
25C2×D4×C29C2×C411yescharacteristic
26C22×C4×C29—21no—
27C22×C4×C29D411yescharacteristic
28C22×C4×C29D411yescharacteristic
29C22×C4×C29C2311yescharacteristic
30C22×Dic29—22no—
31C4⋊C4×C29—21no—
32C4⋊C4×C29—21no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29C2×C411yescharacteristic
36C4⋊C4×C29C2×C411yescharacteristic
37C22⋊C4×C29—21no—
38C22⋊C4×C29—21no—
39C22⋊C4×C29—21no—
40C22⋊C4×C29—21no—
41C22⋊C4×C29—21no—
42C42×C29—21no—
43C42×C29C2×C411yescharacteristic
44C42×C29C2×C411yescharacteristic
45C42×C29D411yescharacteristic
46C42×C29D411yescharacteristic
47C4⋊Dic29—24no—
48C4×Dic29—42no—
49C2×#6597—22no—
50C23×C29—21no—
51C23×C29C2×D411yescharacteristic
52Q8×C29—41no—
53D4×C29—41no—
54D4×C29—41no—
55D4×C29—41no—
56C2×C4×C29—21no—
57C2×C4×C29—21no—
58C2×C4×C29—22no—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—21no—
62C2×C4×C29—41no—
63C2×C4×C29—42no—
64C2×C4×C29C22⋊C411yescharacteristic
65C2×C4×C29C22⋊C411yescharacteristic
66C2×C4×C29C22⋊C411yescharacteristic
67C2×C4×C29C22⋊C411yescharacteristic
68C2×C4×C29C22×C411yescharacteristic
69C2×C4×C29C2×D411yescharacteristic
70C2×Dic29—24no—
71C2×Dic29—42no—
72C2×Dic29—42no—
73#6597—42no—
74#1509—291nomaximal, Sylow
75C22×C29—21no—
76C22×C29—21no—
77C22×C29—41no—
78C22×C29—41no—
79C22×C29—41no—
80C22×C29C2×C22⋊C411yescharacteristic
81C22×C29AGL(1,ℤ/8)11yescharacteristic
82C22×C29#13711yescharacteristic
83C4×C29—21no—
84C4×C29—21no—
85C4×C29—21no—
86C4×C29—21no—
87C4×C29—21no—
88C4×C29—41no—
89C4×C29—41no—
90C4×C29—41no—
91C4×C29#10412yes—
92Dic29—44no—
93#529D2911yescharacteristic
94#432—291no—
95C4×C4⋊C4—291no—
96#328—292no—
97#327—292no—
98C2×C29—21no—
99C2×C29—21no—
100C2×C29—81no—
101C2×C29#41011yescharacteristic
102C2×C29#41711yescharacteristic
103C2×C29C2×#10411yescharacteristic
104#126—21no—
105#125Dic2911yescharacteristic, complemented
106#124Dic2911yescharacteristic, complemented
107#123—21no—
108C22⋊Q8C2×D2911yescharacteristic
109#121C2×D2911yescharacteristic
110C4×Q8Dic2911yescharacteristic, complemented
111C4×D4—21no—
112C4×D4Dic2911yescharacteristic, complemented
113#117—21no—
114C2×C4⋊C4—581no—
115C2×C42—581no—
116C2×C42C2×D2911yescharacteristic
117C4⋊C8—581no—
118C22⋊C8—292no—
119#97—581no—
120#95—292no—
121C29#150911yescharacteristic, complemented, Sylow
122C2×Q8C2×Dic2911yescharacteristic
123C2×D4—21no—
124C2×D4C2×Dic2911yescharacteristic
125C22×C4—21no—
126C22×C4—582no—
127C22×C4C22⋊D2911yescharacteristic
128C22×C4C22⋊D2911yescharacteristic
129C22×C4C22×D2911yescharacteristic
130C2×C8—582no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—584no—
136C4⋊C4C2×Dic2911yescharacteristic
137C4⋊C4C2×Dic2911yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C22⋊C4—21no—
143C42—21no—
144C42—1162no—
145C42C2×Dic2911yescharacteristic
146C42C2×Dic2911yescharacteristic
147C42C22⋊D2911yescharacteristic
148C42C22⋊D2911yescharacteristic
149C23—21no—
150C23C2×C22⋊D2911yescharacteristic
151Q8—41no—
152D4—41no—
153D4—41no—
154D4—41no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—584no—
164C2×C4—1162no—
165C2×C4—1162no—
166C2×C4C22⋊Dic2911yescharacteristic
167C2×C4C22⋊Dic2911yescharacteristic
168C2×C4C22⋊Dic2911yescharacteristic
169C2×C4C22⋊Dic2911yescharacteristic
170C2×C4C22×Dic2911yescharacteristic
171C2×C4C2×C22⋊D2911yescharacteristic
172C8—1162no—
173C22—21no—
174C22—21no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22#1174531111yescharacteristic
179C22#1174531311yescharacteristic
180C22C2×C22⋊Dic2911yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—41no—
189C4—1164no—
190C4#1174518512yes—
191C2—21no—
192C2—21no—
193C2—81no—
194C2#1427113711yescharacteristic
195C2#1427116411yescharacteristic
196C2C2×#1174518511yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#529C2
socleC22×C29C2×C22⋊C4
prime radicalC29×#121C22
cosocleC22×C4×C29C23
hypercenter#529D29
hypocenterC29#1509
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #14271220C2semidirect
2. C4×C4⋊Dic29C2semidirect
3. #14270900C2semidirect
7. C29×#125C4semidirect
8. C29×#124C4semidirect
12. C4×Q8×C29C4semidirect
14. C4×D4×C29C4semidirect
105. #125Dic29semidirect
106. #124Dic29semidirect
110. C4×Q8Dic29semidirect
112. C4×D4Dic29semidirect
121. C29#1509semidirect

Maximal subgroups

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

subgroupindex
#142712202
C4×C4⋊Dic292
#142709002
#142708972
C29×#5292
#150929