Finite Group Databasebeta

← #16835400

Subgroups — #16835400

Order 3712.

306 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 68 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#14272134C211yesmaximal, characteristic
2C4×C22⋊#1181C211yesmaximal, characteristic
3#14272033C212yesmaximal, complemented
4#14272033C212yesmaximal, complemented
5#117×D29C211yesmaximal, characteristic
6C22×C4×D29C2211yescharacteristic
7C2×C22⋊#1181—21no—
8C2×C4×#1181C2212yes—
9C2×#90796C2212yes—
10C29×#117C411yescharacteristic, complemented
11#11745288C411yescharacteristic, complemented
12#11745254C2211yescharacteristic
13#11745254C2211yescharacteristic
14C4⋊C4×D29C411yescharacteristic, complemented
15C4⋊C4×D29C411yescharacteristic, complemented
16C22⋊C4×D29—21no—
17#11745239—21no—
18#11745234—21no—
19C42×D29—21no—
20C22⋊#6599—21no—
21(C2×#1181)⋊C4—21no—
22#11745219—21no—
23C23×D29D411yescharacteristic
24C22×#1181—22no—
25C22×C4×C29C2×C411yescharacteristic
26C22×Dic29D411yescharacteristic
27C2×C4×D29—24no—
28C2×C4×D29—21no—
29C2×C4×D29—21no—
30C2×C4×D29C2×C411yescharacteristic
31C2×C4×D29D411yescharacteristic
32C2×C4×D29D411yescharacteristic
33C2×C4×D29C2311yescharacteristic
34C22⋊#1181—24no—
35C2×#6599—22no—
36C4×#1181—24no—
37#90796—24no—
38C4⋊C4×C29C2×C411yescharacteristic
39C4⋊C4×C29C2×C411yescharacteristic
40C22⋊C4×C29—21no—
41C42×C29—21no—
42C22⋊Dic29—21no—
43#90781—21no—
44#90781—21no—
45C4⋊Dic29C2×C411yescharacteristic
46C4⋊Dic29C2×C411yescharacteristic
47#90779—21no—
48#90779—21no—
49C4×Dic29—21no—
50C4×Dic29—21no—
51C4×Dic29—21no—
52C23×C29C22⋊C411yescharacteristic
53C22×D29—22no—
54C22×D29—22no—
55C22×D29—41no—
56C22×D29C22⋊C411yescharacteristic
57C22×D29C2×D411yescharacteristic
58C2×#1181—24no—
59C2×#1181—42no—
60C2×#1181—42no—
61C2×C4×C29—22no—
62C2×C4×C29—21no—
63C2×C4×C29—21no—
64C2×C4×C29C22⋊C411yescharacteristic
65C2×C4×C29C22×C411yescharacteristic
66C2×Dic29—22no—
67C2×Dic29—21no—
68C2×Dic29—21no—
69C2×Dic29C22⋊C411yescharacteristic
70C2×Dic29C2×D411yescharacteristic
71C4×D29—22no—
72C4×D29—22no—
73C4×D29—22no—
74C4×D29—42no—
75C4×D29—42no—
76C4×D29#4114yes—
77#6599—42no—
78#1826—291nomaximal, Sylow
79C22×C29—21no—
80C22×C29—21no—
81C22×C29—21no—
82C22×C29C2×C22⋊C411yescharacteristic
83C2×D29—21no—
84C2×D29—21no—
85C2×D29—21no—
86C2×D29—21no—
87C2×D29—44no—
88C2×D29#10412yes—
89C2×D29#12312yes—
90#1181—44no—
91C4×C29—21no—
92C4×C29—41no—
93C4×C29—41no—
94C4×C29#11712yes—
95Dic29—21no—
96Dic29—41no—
97Dic29—41no—
98Dic29#12312yes—
99C2×#117—291no—
100#407—291no—
101C4×C22⋊C4—291no—
102#339—292no—
103#339—292no—
104C2×C29—41no—
105C2×C29#38111yescharacteristic
106C2×C29C2×#10411yescharacteristic
107C2×C29#42111yescharacteristic
108D29—22no—
109D29—22no—
110C23×C4—291no—
111C2×M16—292no—
112#117—291no—
113#117—291no—
114#117—291no—
115#117—581no—
116#117—581no—
117#117#118111yescharacteristic, complemented
118C2×C4⋊C4—291no—
119C2×C4⋊C4—291no—
120C2×C22⋊C4—581no—
121C2×C22⋊C4—581no—
122C2×C42—292no—
123C2×C42—581no—
124C22⋊C8—581no—
125C22⋊C8—581no—
126#95—581no—
127C29#182611yescharacteristic, complemented, Sylow
128C24—291no—
129C22×C4—291no—
130C22×C4—291no—
131C22×C4—291no—
132C22×C4—291no—
133C22×C4—291no—
134C22×C4—584no—
135C22×C4—581no—
136C22×C4—581no—
137C22×C4—582no—
138C22×C4C2×#118111yescharacteristic
139M16—584no—
140C2×C8—582no—
141C4⋊C4—291no—
142C4⋊C4—291no—
143C4⋊C4—581no—
144C4⋊C4—581no—
145C4⋊C4C2×#118111yescharacteristic
146C4⋊C4C2×#118111yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—581no—
149C22⋊C4—581no—
150C22⋊C4—584no—
151C22⋊C4—581no—
152C42—21no—
153C42—581no—
154C42—581no—
155C42—584no—
156C42—581no—
157C23—291no—
158C23—291no—
159C23—582no—
160C23—582no—
161C23—1161no—
162C23C22⋊#118111yescharacteristic
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—291no—
167C2×C4—294no—
168C2×C4—291no—
169C2×C4—582no—
170C2×C4—582no—
171C2×C4—582no—
172C2×C4—582no—
173C2×C4—584no—
174C2×C4—581no—
175C2×C4—581no—
176C2×C4—1162no—
177C2×C4—1162no—
178C2×C4—1162no—
179C2×C4—1162no—
180C2×C4C22⋊#118111yescharacteristic
181C2×C4C22×#118111yescharacteristic
182C8—1162no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—292no—
187C22—292no—
188C22—581no—
189C22—581no—
190C22—581no—
191C22—581no—
192C22—1164no—
193C22C2×C22⋊#118111yescharacteristic
194C4—21no—
195C4—41no—
196C4—41no—
197C4—292no—
198C4—581no—
199C4—1164no—
200C4—1161no—
201C4—1161no—
202C4#1174534512yes—
203C2—41no—
204C2—582no—
205C2—582no—
206C2#1427210611yescharacteristic
207C2D29⋊#10411yescharacteristic
208C2#1427216011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#117C4
socleC22×C29C2×C22⋊C4
prime radicalC23×D29D4
cosocleC2×C4×D29C23
hypercenter#117#1181
hypocenterC29#1826
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #14272033C2semidirect
4. #14272033C2semidirect
10. C29×#117C4semidirect
11. #11745288C4semidirect
14. C4⋊C4×D29C4semidirect
15. C4⋊C4×D29C4semidirect
117. #117#1181semidirect
127. C29#1826semidirect

Maximal subgroups

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

subgroupindex
#142721342
C4×C22⋊#11812
#142720332
#117×D292
#182629