Finite Group Databasebeta

← #16820623

Subgroups — #16820623

Order 3712.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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#14271725C211yesmaximal, characteristic
2C2×#11745291C212yesmaximal, complemented
3C2×#11745154C212yesmaximal, complemented
4#14270930C211yesmaximal, characteristic, complemented
5C29×#381C211yesmaximal, characteristic, complemented
6C23×C4×C29C2211yescharacteristic
7C22×C22⋊D29C2212yes—
8C2×C22⋊C4×C29C2211yescharacteristic
9C2×C22⋊C4×C29C2211yescharacteristic
10C2×C22⋊Dic29C2212yes—
11#11745292—22no—
12#11745291—24no—
13#11745291—24no—
14C2×#90781—22no—
15C2×#90779—22no—
16#11745248—22no—
17#11745244—22no—
18C29×#95—22no—
19#11745154—24no—
20C24×C29C2311yescharacteristic
21C23×D29D412yes—
22C22×C4×C29—22no—
23C22×C4×C29—22no—
24C22×C4×C29—21no—
25C22×C4×C29—21no—
26C22×C4×C29—21no—
27C22×C4×C29D412yes—
28C22×C4×C29D412yescomplemented
29C2×C22⋊D29—22no—
30C2×C22⋊D29—22no—
31C2×C22⋊D29—22no—
32C2×C22⋊D29—22no—
33C2×C22⋊D29—22no—
34C2×C22⋊D29—22no—
35C22×Dic29—22no—
36C22×Dic29D412yes—
37C2×D116—22no—
38C22⋊C4×C29—22no—
39C22⋊C4×C29—22no—
40C22⋊Dic29—22no—
41C22⋊Dic29D414yescomplemented
42#90781—28no—
43#90781—24no—
44C4⋊Dic29—22no—
45#90779—28no—
46C23×C29—42no—
47C23×C29C2×D411yescharacteristic
48C23×C29C2×D412yes—
49C23×C29C2×D412yes—
50C23×C29C2×D411yescharacteristic
51C23×C29#4111yescharacteristic
52C22×D29—22no—
53C22×D29—22no—
54C22×D29—22no—
55C22×D29—44no—
56C2×C4×C29—24no—
57C2×C4×C29—22no—
58C2×C4×C29—22no—
59C2×C4×C29—41no—
60C2×C4×C29—42no—
61C2×C4×C29—41no—
62C2×C4×C29—42no—
63C2×C4×C29—42no—
64C2×C4×C29—41no—
65C22⋊D29—42no—
66C22⋊D29—42no—
67C22⋊D29—42no—
68C22⋊D29—42no—
69C2×Dic29—22no—
70C2×Dic29—24no—
71C2×Dic29—22no—
72C2×Dic29—22no—
73C2×Dic29—44no—
74D116—82no—
75#2022—291nomaximal, Sylow
76C22×C29—24no—
77C22×C29—22no—
78C22×C29—41no—
79C22×C29—42no—
80C22×C29—41no—
81C22×C29#12011yescharacteristic
82C22×C29#12012yes—
83C22×C29#12111yescharacteristic
84C22×C29#12112yes—
85C22×C29#12711yescharacteristic
86C2×D29—44no—
87C2×D29—42no—
88C2×D29—44no—
89C2×D29—82no—
90C4×C29—42no—
91C4×C29—42no—
92C4×C29—81no—
93Dic29—44no—
94Dic29—42no—
95#534—291no—
96C2×#123—292no—
97C2×#99—292no—
98#381D2911yescharacteristic, complemented
99#342—291no—
100C2×C29—22no—
101C2×C29—21no—
102C2×C29—22no—
103C2×C29—21no—
104C2×C29#39211yescharacteristic
105C2×C29#45812yes—
106D29—82no—
107C22×D4—292no—
108C23×C4C2×D2911yescharacteristic
109#123—582no—
110#123—584no—
111#123—584no—
112#121—582no—
113#120—582no—
114C2×C4⋊C4—582no—
115C2×C22⋊C4—292no—
116C2×C22⋊C4—582no—
117C2×C22⋊C4C2×D2911yescharacteristic
118C2×C22⋊C4C2×D2911yescharacteristic
119#99—584no—
120#95—22no—
121C29#202211yescharacteristic, complemented, Sylow
122C24—292no—
123C24C22×D2911yescharacteristic
124C2×D4—582no—
125C2×D4—582no—
126C2×D4—582no—
127C2×D4—582no—
128C2×D4—582no—
129C2×D4—582no—
130C2×D4—582no—
131C22×C4—21no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—292no—
137C22×C4—582no—
138C22×C4D11612yescomplemented
139C22×C4C22⋊D2912yes—
140C4⋊C4—588no—
141C4⋊C4—582no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—294no—
145C22⋊C4—588no—
146C22⋊C4—584no—
147C22⋊C4—582no—
148C23—42no—
149C23—582no—
150C23—582no—
151C23—582no—
152C23—1164no—
153C23C2×D11611yescharacteristic
154C23#9080511yescharacteristic
155C23D4×D2912yes—
156C23D4×D2912yes—
157C23C2×C22⋊D2911yescharacteristic
158D4—1162no—
159D4—1162no—
160D4—1162no—
161D4—1162no—
162D4—2322no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—24no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—582no—
173C2×C4—584no—
174C2×C4—582no—
175C2×C4—582no—
176C2×C4—1164no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—1164no—
183C22—1162no—
184C22—1164no—
185C22—2322no—
186C22#1174524412yes—
187C22#1174524612yes—
188C22#1174529211yescharacteristic
189C22#1174529911yescharacteristic
190C22#1174530211yescharacteristic
191C4—42no—
192C4—42no—
193C4—81no—
194C4—1164no—
195C4—1162no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—2322no—
201C2#1427107211yescharacteristic
202C2#1427135212yes—
subgroupG/H
centerC22#11745299
commutator, cosocleC24×C29C23
FrattiniC24C22×D29
FittingC29×#381C2
socleC22×C29#120
prime radical#14271725C2
hypercenter#381D29
hypocenterC29#2022
LCSG ▷ C24×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#11745291C2semidirect
3. C2×#11745154C2semidirect
4. #14270930C2semidirect
5. C29×#381C2semidirect
28. C22×C4×C29D4semidirect
41. C22⋊Dic29D4semidirect
98. #381D29semidirect
121. C29#2022semidirect
138. C22×C4D116semidirect

Maximal subgroups

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

subgroupindex
#142717252
C2×#117452912
C2×#117451542
#142709302
C29×#3812
#202229