Finite Group Databasebeta

← #16821872

Subgroups — #16821872

Order 3712.

1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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
1C23×C4×D29C211yesmaximal, characteristic
2C2×#11745239C212yesmaximal, complemented
3#14271026C211yesmaximal, characteristic, complemented
4#14271022C214yesmaximal, complemented
5#14271018C212yesmaximal
6#14271010C214yesmaximal, complemented
7C29×#381C211yesmaximal, characteristic, complemented
8C24×D29C2211yescharacteristic
9C23×C4×C29C2211yescharacteristic
10C23×Dic29C2211yescharacteristic
11C22×C4×D29—28no—
12C22×C4×D29C418yescomplemented
13C22×C4×D29C2212yes—
14C22×C4×D29C2212yes—
15C2×C22⋊C4×C29C2212yes—
16C2×C22⋊Dic29C2212yes—
17C2×#90781C2218yes—
18C2×#90779C2214yescomplemented
19C2×C4×Dic29C2214yescomplemented
20#11745239—28no—
21C29×#95C2214yescomplemented
22#11745179C2214yescomplemented
23C24×C29C2311yescharacteristic
24C23×D29—24no—
25C23×D29—28no—
26C23×D29C2×C414yes—
27C23×D29C2312yes—
28C22×C4×C29—24no—
29C22×C4×C29C2×C414yes—
30C22×C4×C29C2314yes—
31C22×C4×C29C2312yes—
32C22×Dic29C2×C414yes—
33C22×Dic29D418yes—
34C22×Dic29C2314yes—
35C22×Dic29C2311yescharacteristic
36C22×Dic29C2311yescharacteristic
37C2×C4×D29—232no—
38C2×C4×D29—28no—
39C2×C4×D29—28no—
40C2×C4×D29C2×C418yes—
41C2×C4×D29C2×C418yes—
42C22⋊C4×C29—24no—
43C22⋊Dic29—24no—
44#90781—216no—
45#90779—28no—
46C4×Dic29—28no—
47C23×C29—24no—
48C23×C29C22×C412yes—
49C23×C29C2×D414yes—
50C23×C29C2411yescharacteristic
51C22×D29—232no—
52C22×D29—28no—
53C22×D29—24no—
54C22×D29—24no—
55C22×D29—216no—
56C22×D29C22×C414yes—
57C22×D29#4118yes—
58C2×C4×C29—28no—
59C2×C4×C29—24no—
60C2×C4×C29—24no—
61C2×C4×C29—28no—
62C2×C4×C29C22×C414yes—
63C2×Dic29—24no—
64C2×Dic29—28no—
65C2×Dic29C22⋊C4116yescomplemented
66C2×Dic29C22×C412yes—
67C2×Dic29C22×C412yes—
68C2×Dic29C2×D414yes—
69C2×Dic29C2×D414yes—
70C4×D29—216no—
71C4×D29—216no—
72#2280—291nomaximal, Sylow
73C22×C29—24no—
74C22×C29—28no—
75C22×C29C2×C22⋊C414yes—
76C22×C29C23×C411yescharacteristic
77C22×C29C22×D412yes—
78C22×C29C2×#4114yes—
79C2×D29—232no—
80C2×D29—24no—
81C2×D29—24no—
82C2×D29—216no—
83C2×D29#11718yescomplemented
84C4×C29—24no—
85C4×C29—44no—
86Dic29—44no—
87Dic29C2×C22⋊C414yes—
88Dic29C2×C22⋊C414yes—
89C24×C4—291no—
90C2×#117—292no—
91#381—291no—
92#381D2911yescharacteristic, complemented
93#380—294no—
94#379—292no—
95C4×C22⋊C4—294no—
96C2×C29—24no—
97C2×C29C22×C22⋊C411yescharacteristic
98C2×C29C2×#11712yes—
99C2×C29#52514yes—
100D29—28no—
101C25—291no—
102C23×C4—291no—
103C23×C4—298no—
104C23×C4—292no—
105C23×C4—292no—
106C23×C4—588no—
107C23×C4C2×D2911yescharacteristic
108#117—588no—
109C2×C4⋊C4—294no—
110C2×C22⋊C4—292no—
111C2×C22⋊C4—298no—
112C2×C22⋊C4C2×D2912yes—
113C2×C42—294no—
114#95—294no—
115#95C2×D2914yescomplemented
116C29#228011yescharacteristic, complemented, Sylow
117C24—292no—
118C24—294no—
119C24—588no—
120C24—584no—
121C24C22×D2911yescharacteristic
122C22×C4—24no—
123C22×C4—294no—
124C22×C4—298no—
125C22×C4—291no—
126C22×C4—291no—
127C22×C4—298no—
128C22×C4—298no—
129C22×C4—294no—
130C22×C4—588no—
131C22×C4—588no—
132C22×C4—5832no—
133C22×C4C4×D2914yes—
134C22×C4C22×D2914yes—
135C22×C4C22×D2912yes—
136C4⋊C4—588no—
137C22⋊C4—24no—
138C22⋊C4—5816no—
139C22⋊C4—584no—
140C42—588no—
141C23—24no—
142C23—294no—
143C23—298no—
144C23—5816no—
145C23—5832no—
146C23—584no—
147C23—584no—
148C23—588no—
149C23C2×C4×D2912yes—
150C23D4×D2914yes—
151C23C23×D2911yescharacteristic
152C2×C4—24no—
153C2×C4—28no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—292no—
157C2×C4—292no—
158C2×C4—294no—
159C2×C4—294no—
160C2×C4—2916no—
161C2×C4—5816no—
162C2×C4—5816no—
163C2×C4—584no—
164C2×C4—588no—
165C2×C4C2×C4×D2914yes—
166C22—24no—
167C22—28no—
168C22—298no—
169C22—5832no—
170C22—584no—
171C22—584no—
172C22—5816no—
173C22C22⋊C4×D2914yes—
174C22C22×C4×D2911yescharacteristic
175C22C2×D4×D2912yes—
176C22#41×D2914yes—
177C4—24no—
178C4—44no—
179C4—294no—
180C4—294no—
181C4—1164no—
182C2—24no—
183C2—588no—
184C2C2×C22⋊C4×D2911yescharacteristic
185C2#117×D2912yes—
186C2#1427167114yes—
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#381C2
socle, cosocleC23×C29C24
prime radicalC24×D29C22
hypercenter#381D29
hypocenterC29#2280
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#11745239C2semidirect
3. #14271026C2semidirect
4. #14271022C2semidirect
6. #14271010C2semidirect
7. C29×#381C2semidirect
12. C22×C4×D29C4semidirect
18. C2×#90779C22semidirect
19. C2×C4×Dic29C22semidirect
21. C29×#95C22semidirect
22. #11745179C22semidirect
65. C2×Dic29C22⋊C4semidirect
83. C2×D29#117semidirect
92. #381D29semidirect
115. #95C2×D29semidirect
116. C29#2280semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D292
C2×#117452392
#142710262
#142710222
#142710182
#142710102
C29×#3812
#228029