Finite Group Databasebeta

← #16834771

Subgroups — #16834771

Order 3712.

270 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 64 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#14272133C211yesmaximal, characteristic
2C2×C22⋊#6599C211yesmaximal, characteristic
3#14272009C212yesmaximal, complemented
4#14272008C212yesmaximal, complemented
5C2×#11745240C211yesmaximal, characteristic
6C23×Dic29C2211yescharacteristic
7C22×Dic58C411yescharacteristic
8C2×#90800—21no—
9C22×#6599—21no—
10C2×C22⋊C4×C29C411yescharacteristic
11C2×C22⋊Dic29C411yescharacteristic
12C2×C4⋊Dic29C2211yescharacteristic
13C2×#90779C411yescharacteristic
14C2×#90779C2211yescharacteristic
15#11745240—21no—
16#11745240—21no—
17#11745240—21no—
18#11745240—21no—
19C22⋊#6599—21no—
20C22⋊#6599—21no—
21C22⋊#6599C2212yes—
22C22⋊#6599C2212yes—
23C24×C29C2×C411yescharacteristic
24C22×C4×C29C2×C411yescharacteristic
25C22×C4×C29C2×C411yescharacteristic
26C22×Dic29—42no—
27C22×Dic29C2×C411yescharacteristic
28C22×Dic29C2×C411yescharacteristic
29C22×Dic29C2×C411yescharacteristic
30C22×Dic29D411yescharacteristic
31C22×Dic29D411yescharacteristic
32C22×Dic29D411yescharacteristic
33C22×Dic29D411yescharacteristic
34C22×Dic29C2311yescharacteristic
35C2×Dic58—21no—
36C2×Dic58—21no—
37C2×Dic58—42no—
38#90800—42no—
39C2×#6599—22no—
40C2×#6599—22no—
41C2×#6599—42no—
42C22⋊C4×C29—21no—
43C22⋊C4×C29—21no—
44C22⋊Dic29—21no—
45C22⋊Dic29—21no—
46C4⋊Dic29—21no—
47C4⋊Dic29—21no—
48#90779—21no—
49#90779—21no—
50#90779—21no—
51#90779—21no—
52C23×C29—22no—
53C23×C29—22no—
54C23×C29—41no—
55C23×C29C22⋊C411yescharacteristic
56C23×C29C22⋊C411yescharacteristic
57C23×C29C22×C411yescharacteristic
58C2×C4×C29—21no—
59C2×C4×C29—21no—
60C2×C4×C29—22no—
61C2×C4×C29—41no—
62C2×Dic29—22no—
63C2×Dic29—22no—
64C2×Dic29—22no—
65C2×Dic29—21no—
66C2×Dic29—21no—
67C2×Dic29—22no—
68C2×Dic29—41no—
69C2×Dic29—41no—
70C2×Dic29—41no—
71C2×Dic29—41no—
72C2×Dic29C22⋊C411yescharacteristic
73C2×Dic29C22⋊C411yescharacteristic
74C2×Dic29C2×D411yescharacteristic
75C2×Dic29C2×D411yescharacteristic
76Dic58—42no—
77Dic58—42no—
78#6599—42no—
79#6599—42no—
80#1472—291nomaximal, Sylow
81C22×C29—21no—
82C22×C29—21no—
83C22×C29—21no—
84C22×C29—21no—
85C22×C29—21no—
86C22×C29—21no—
87C22×C29—21no—
88C22×C29—44no—
89C22×C29#10112yes—
90C22×C29C2×C22⋊C411yescharacteristic
91C22×C29#13112yes—
92C4×C29—41no—
93C4×C29—41no—
94Dic29—21no—
95Dic29—21no—
96Dic29—21no—
97Dic29—41no—
98Dic29—41no—
99Dic29#9912yes—
100C2×C22⋊Q8—291no—
101#407—291no—
102C2×C22⋊C8—291no—
103#324—292no—
104#324—292no—
105C2×C29—22no—
106C2×C29—22no—
107C2×C29—41no—
108C2×C29#40811yescharacteristic
109C2×C29C2×#9911yescharacteristic
110C2×C29C2×#10111yescharacteristic
111C22×Q8—291no—
112C23×C4—291no—
113C2×M16—581no—
114C22×C8—581no—
115C22⋊Q8—581no—
116C22⋊Q8—581no—
117C22⋊Q8—581no—
118C22⋊Q8—581no—
119C2×C4⋊C4—291no—
120C2×C4⋊C4—291no—
121C2×C4⋊C4—291no—
122C2×C22⋊C4—291no—
123C2×C22⋊C4#118111yescharacteristic
124C22⋊C8—292no—
125C22⋊C8—292no—
126C22⋊C8—581no—
127C22⋊C8—581no—
128C29#147211yescharacteristic, complemented, Sylow
129C24C2×#118111yescharacteristic
130C2×Q8—581no—
131C2×Q8—581no—
132C2×Q8—1162no—
133C22×C4—291no—
134C22×C4—291no—
135C22×C4—291no—
136C22×C4—291no—
137C22×C4—291no—
138C22×C4—291no—
139C22×C4—291no—
140C22×C4—291no—
141C22×C4—1162no—
142C22×C4C2×#118111yescharacteristic
143C22×C4C2×#118111yescharacteristic
144M16—1162no—
145C2×C8—582no—
146C2×C8—582no—
147C2×C8—1162no—
148C4⋊C4—581no—
149C4⋊C4—581no—
150C4⋊C4—581no—
151C4⋊C4—581no—
152C4⋊C4—581no—
153C4⋊C4—581no—
154C22⋊C4—21no—
155C22⋊C4—21no—
156C22⋊C4—581no—
157C22⋊C4—581no—
158C23—22no—
159C23—22no—
160C23—41no—
161C23C22⋊#118111yescharacteristic
162C23C22⋊#118111yescharacteristic
163C23C22×#118111yescharacteristic
164Q8—1162no—
165Q8—1162no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—291no—
171C2×C4—291no—
172C2×C4—291no—
173C2×C4—291no—
174C2×C4—582no—
175C2×C4—582no—
176C2×C4—582no—
177C2×C4—582no—
178C2×C4—581no—
179C2×C4—581no—
180C2×C4—1161no—
181C2×C4—1161no—
182C2×C4—1161no—
183C2×C4—1161no—
184C8—1162no—
185C8—1162no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—44no—
194C22#1174522112yes—
195C22#1174534612yes—
196C22C2×C22⋊#118111yescharacteristic
197C4—41no—
198C4—41no—
199C4—292no—
200C4—581no—
201C4—581no—
202C4—581no—
203C4—1161no—
204C4—1161no—
205C2—22no—
206C2—22no—
207C2—41no—
208C2#1427213611yescharacteristic
209C2D29⋊#9911yescharacteristic
210C2C2×#1174522111yescharacteristic
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#1472
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #14272009C2semidirect
4. #14272008C2semidirect
128. C29#1472semidirect

Maximal subgroups

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

subgroupindex
#142721332
C2×C22⋊#65992
#142720092
#142720082
C2×#117452402
#147229