Finite Group Databasebeta

← #16834774

Subgroups — #16834774

Order 3712.

214 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 58 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#14272183C211yesmaximal, characteristic, complemented
2#14272179C211yesmaximal, characteristic, complemented
3#14272009C212yesmaximal, complemented
4#14272006C212yesmaximal
5C2×#11745241C211yesmaximal, characteristic
6C2×C22⋊C4×C29C411yescharacteristic
7C2×C22⋊Dic29C411yescharacteristic
8C2×C22⋊Dic29C2211yescharacteristic
9C2×C4⋊Dic29C411yescharacteristic
10C2×#90779C411yescharacteristic
11C2×#90779C2211yescharacteristic
12C2×C4×Dic29C2211yescharacteristic
13#11745241—21no—
14#11745241—21no—
15#11745241—21no—
16#11745241—21no—
17C22⋊#6599C2212yes—
18C22⋊#6599C2212yes—
19#11745220—21no—
20#11745218—21no—
21C4⋊#6599—21no—
22C4×#6599—21no—
23C24×C29C2×C411yescharacteristic
24C22×C4×C29C2×C411yescharacteristic
25C22×C4×C29C2×C411yescharacteristic
26C22×Dic29C2×C411yescharacteristic
27C22×Dic29C2×C411yescharacteristic
28C22×Dic29C2×C411yescharacteristic
29C22×Dic29C2311yescharacteristic
30C2×#6599—22no—
31C2×#6599—22no—
32C22⋊C4×C29—21no—
33C22⋊C4×C29—21no—
34C22⋊Dic29—21no—
35C22⋊Dic29—21no—
36C22⋊Dic29—21no—
37C22⋊Dic29—21no—
38C4⋊Dic29—21no—
39C4⋊Dic29—21no—
40#90779—21no—
41#90779—21no—
42#90779—21no—
43#90779—21no—
44C4×Dic29D411yescharacteristic
45C4×Dic29D411yescharacteristic
46C4×Dic29D411yescharacteristic
47C4×Dic29D411yescharacteristic
48C23×C29—21no—
49C23×C29—22no—
50C23×C29—41no—
51C23×C29—41no—
52C23×C29C22×C411yescharacteristic
53C2×C4×C29—22no—
54C2×C4×C29—21no—
55C2×C4×C29—41no—
56C2×C4×C29C22⋊C411yescharacteristic
57C2×C4×C29C22⋊C411yescharacteristic
58C2×Dic29—21no—
59C2×Dic29—21no—
60C2×Dic29—22no—
61C2×Dic29—41no—
62C2×Dic29—41no—
63C2×Dic29—41no—
64C2×Dic29C22⋊C411yescharacteristic
65C2×Dic29C22⋊C411yescharacteristic
66C2×Dic29C2×D411yescharacteristic
67C2×Dic29C2×D411yescharacteristic
68#6599—42no—
69#6599—42no—
70#1473—291nomaximal, Sylow
71C22×C29—21no—
72C22×C29—21no—
73C22×C29—41no—
74C22×C29—41no—
75C22×C29—41no—
76C22×C29—82no—
77C22×C29C2×C22⋊C411yescharacteristic
78C22×C29#13112yes—
79C4×C29—21no—
80C4×C29—21no—
81C4×C29—41no—
82Dic29—21no—
83Dic29—21no—
84Dic29—21no—
85Dic29—21no—
86Dic29—41no—
87Dic29—41no—
88C2×#126—291no—
89#432—291no—
90#431—291no—
91#324—292no—
92#323—292no—
93C2×C29—22no—
94C2×C29—81no—
95C2×C29#40811yescharacteristic
96C2×C29#41011yescharacteristic
97C2×C29#41311yescharacteristic
98#126—581no—
99#126—581no—
100#126—581no—
101#126—581no—
102C2×C4⋊C4—291no—
103C2×C4⋊C4—291no—
104C2×C4⋊C4—291no—
105C2×C22⋊C4—291no—
106C2×C22⋊C4—291no—
107C2×C22⋊C4#118111yescharacteristic
108C2×C42—291no—
109C4⋊C8—581no—
110C4⋊C8—581no—
111C22⋊C8—292no—
112C22⋊C8—292no—
113#97—581no—
114C4×C8—581no—
115C29#147311yescharacteristic, complemented, Sylow
116C24C2×#118111yescharacteristic
117C22×C4—291no—
118C22×C4—291no—
119C22×C4—291no—
120C22×C4—291no—
121C22×C4C2×#118111yescharacteristic
122C22×C4C2×#118111yescharacteristic
123C2×C8—582no—
124C2×C8—582no—
125C4⋊C4—581no—
126C4⋊C4—581no—
127C4⋊C4—581no—
128C4⋊C4—581no—
129C4⋊C4—581no—
130C4⋊C4—581no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—581no—
134C22⋊C4—581no—
135C22⋊C4—581no—
136C22⋊C4—581no—
137C42—291no—
138C42—291no—
139C42—291no—
140C42—291no—
141C23—21no—
142C23—22no—
143C23—41no—
144C23—41no—
145C23C22×#118111yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—291no—
150C2×C4—291no—
151C2×C4—291no—
152C2×C4—291no—
153C2×C4—582no—
154C2×C4—581no—
155C2×C4—581no—
156C2×C4—1161no—
157C2×C4—1161no—
158C2×C4—1161no—
159C2×C4C22⋊#118111yescharacteristic
160C2×C4C22⋊#118111yescharacteristic
161C8—1162no—
162C8—1162no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—82no—
169C22#1174534612yes—
170C22C2×C22⋊#118111yescharacteristic
171C4—21no—
172C4—21no—
173C4—41no—
174C4—581no—
175C4—581no—
176C4—581no—
177C4—581no—
178C4—1161no—
179C4—1161no—
180C2—22no—
181C2—81no—
182C2#1427213611yescharacteristic
183C2#1427214311yescharacteristic
184C2#1427214911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C22⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC24×C29C2×C4
cosocleC22×Dic29C23
hypercenterC2×C22⋊C4#1181
hypocenterC29#1473
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14272183C2semidirect
2. #14272179C2semidirect
3. #14272009C2semidirect
115. C29#1473semidirect

Maximal subgroups

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

subgroupindex
#142721832
#142721792
#142720092
#142720062
C2×#117452412
#147329