Finite Group Databasebeta

← #16829425

Subgroups — #16829425

Order 3712.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#14271674C211yesmaximal, characteristic
2C2×#11745288C211yesmaximal, characteristic, complemented
3#14271505C214yesmaximal, complemented
4#14271488C214yesmaximal, complemented
5#14271205C212yesmaximal, complemented
6#14271165C212yesmaximal, complemented
7C29×#407C211yesmaximal, characteristic, complemented
8C23×C4×C29C2211yescharacteristic
9C2×#90805C2211yescharacteristic
10C2×M16×C29C2212yes—
11#11745315—21no—
12C2×C22⋊Dic29—21no—
13#11745292C2212yes—
14#11745291—21no—
15C4×C22⋊D29—22no—
16#11745288—22no—
17#11745288C2214yes—
18#11745288C2211yescharacteristic
19C2×C4⋊Dic29C2212yes—
20#11745286C2212yes—
21C2×C4×Dic29—21no—
22C29×C22⋊C8C2214yes—
23#11745169C2214yescomplemented
24#11745166C2214yescomplemented
25#11745165C2214yescomplemented
26#11745164C2214yescomplemented
27C24×C29D411yescharacteristic
28C22×C4×C29—24no—
29C22×C4×C29D411yescharacteristic
30C22×C4×C29D412yes—
31C22×C4×C29C2312yes—
32C22×C4×C29C2311yescharacteristic
33C2×C22⋊D29—22no—
34C2×C22⋊D29—21no—
35C22×Dic29—22no—
36#90805—24no—
37C2×D116C2311yescharacteristic
38C2×C4×D29—21no—
39C2×Dic58C2311yescharacteristic
40M16×C29—24no—
41C2×C8×C29C2314yes—
42C22⋊Dic29—22no—
43C22⋊Dic29—24no—
44C22⋊Dic29—21no—
45#90781—22no—
46C4⋊Dic29—22no—
47C4⋊Dic29C2312yes—
48C4⋊Dic29C2314yes—
49#90779—22no—
50C4×Dic29—24no—
51C4×Dic29—21no—
52C23×C29—22no—
53C23×C29—42no—
54C23×C29C2×D412yes—
55C23×C29C2×D411yescharacteristic
56C22×D29—21no—
57C2×C4×C29—22no—
58C2×C4×C29—24no—
59C2×C4×C29—24no—
60C2×C4×C29C2×D412yes—
61C2×C4×C29C2×D411yescharacteristic
62C2×C4×C29#4114yes—
63C2×C4×C29C2411yescharacteristic
64C22⋊D29—44no—
65C22⋊D29—42no—
66C2×Dic29—24no—
67C2×Dic29—22no—
68C2×Dic29—21no—
69C2×Dic29—44no—
70D116—22no—
71C4×D29—42no—
72Dic58—22no—
73C8×C29—24no—
74#3093—291nomaximal, Sylow
75C22×C29—22no—
76C22×C29—22no—
77C22×C29—22no—
78C22×C29—22no—
79C22×C29—44no—
80C22×C29#12312yes—
81C22×C29C22×D411yescharacteristic
82C2×D29—41no—
83C2×D29—42no—
84C4×C29—22no—
85C4×C29#12312yes—
86C4×C29C2×#4112yes—
87Dic29—41no—
88Dic29—44no—
89Dic29—42no—
90#525—291no—
91C2×#117—291no—
92#485—294no—
93#482—294no—
94#428—292no—
95#417—292no—
96#407D2911yescharacteristic, complemented
97C2×C29—22no—
98C2×C29—42no—
99C2×C29C2×#12311yescharacteristic
100C2×C29#57512yes—
101D29—81no—
102C2×#41—291no—
103C23×C4C2×D2911yescharacteristic
104C2×M16C2×D2912yes—
105#123—581no—
106C22⋊Q8—292no—
107#121—292no—
108#120—581no—
109C4×D4—582no—
110#117—294no—
111#117—291no—
112#117—582no—
113C2×C4⋊C4—292no—
114C2×C22⋊C4—581no—
115C2×C42—581no—
116#107—294no—
117#106—294no—
118#103—294no—
119#102—294no—
120C22⋊C8C2×D2914yes—
121C29#309311yescharacteristic, complemented, Sylow
122C24D11611yescharacteristic
123#41—584no—
124C2×Q8—291no—
125C2×D4—291no—
126C2×D4—582no—
127C2×D4—581no—
128C22×C4—24no—
129C22×C4—582no—
130C22×C4—581no—
131C22×C4D11611yescharacteristic
132C22×C4D11612yes—
133C22×C4C22×D2912yes—
134C22×C4C22×D2911yescharacteristic
135M16—24no—
136C2×C8C22×D2914yes—
137C4⋊C4—294no—
138C4⋊C4—292no—
139C4⋊C4—582no—
140C4⋊C4—582no—
141C22⋊C4—584no—
142C22⋊C4—581no—
143C22⋊C4—582no—
144C22⋊C4—582no—
145C42—584no—
146C42—581no—
147C23—22no—
148C23—42no—
149C23—581no—
150C23C2×D11612yes—
151C23C2×D11611yescharacteristic
152Q8—582no—
153D4—582no—
154D4—1164no—
155D4—1162no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—584no—
160C2×C4—582no—
161C2×C4—581no—
162C2×C4—1164no—
163C2×C4—1162no—
164C2×C4C2×D11612yes—
165C2×C4C2×D11611yescharacteristic
166C2×C4#9080714yes—
167C2×C4C23×D2911yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—1161no—
175C22—1162no—
176C22#1174524812yes—
177C22C22×D11611yescharacteristic
178C4—22no—
179C4—1161no—
180C4—1164no—
181C4—1162no—
182C4#1174524812yes—
183C4C2×#9080712yes—
184C2—22no—
185C2—42no—
186C2—2321no—
187C2C2×#1174524811yescharacteristic
188C2#1427196312yes—
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#407C2
socleC22×C29C22×D4
prime radical#14271674C2
hypercenter#407D29
hypocenterC29#3093
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#11745288C2semidirect
3. #14271505C2semidirect
4. #14271488C2semidirect
5. #14271205C2semidirect
6. #14271165C2semidirect
7. C29×#407C2semidirect
23. #11745169C22semidirect
24. #11745166C22semidirect
25. #11745165C22semidirect
26. #11745164C22semidirect
96. #407D29semidirect
121. C29#3093semidirect

Maximal subgroups

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

subgroupindex
#142716742
C2×#117452882
#142715052
#142714882
#142712052
#142711652
C29×#4072
#309329