Finite Group Databasebeta

← #16820559

Subgroups — #16820559

Order 3712.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#14271963C211yesmaximal, characteristic, complemented
2#14271674C212yesmaximal, complemented
3#14271179C212yesmaximal, complemented
4#14270920C211yesmaximal, characteristic, complemented
5C29×#407C211yesmaximal, characteristic, complemented
6C23×C4×C29C2211yescharacteristic
7C2×#90805C2212yes—
8C2×M16×C29C2211yescharacteristic
9C2×M16×C29C2211yescharacteristic
10#11745315—22no—
11#11745292—22no—
12#11745291—22no—
13C4×C22⋊D29—24no—
14#11745288C2212yes—
15#11745286—22no—
16#11745271—22no—
17#11745270—22no—
18#11745266—22no—
19C29×C22⋊C8—22no—
20#11745173—24no—
21C24×C29D411yescharacteristic
22C22×C4×C29—22no—
23C22×C4×C29—22no—
24C22×C4×C29—21no—
25C22×C4×C29—21no—
26C22×C4×C29D411yescharacteristic
27C22×C4×C29C2311yescharacteristic
28C2×C22⋊D29—24no—
29C2×C22⋊D29—22no—
30#90805—22no—
31#90805—22no—
32#90805—22no—
33#90805—22no—
34C2×D116D412yescomplemented
35C2×C4×D29—22no—
36C2×Dic58D412yescomplemented
37M16×C29—22no—
38M16×C29—22no—
39C2×C8×C29—21no—
40C2×C8×C29D412yescomplemented
41C22⋊Dic29—24no—
42C22⋊Dic29—22no—
43#90781—24no—
44C4⋊Dic29—22no—
45#90779—24no—
46C4×Dic29D414yescomplemented
47Dic116—22no—
48D232—22no—
49#90773—24no—
50C23×C29—22no—
51C23×C29—21no—
52C23×C29—42no—
53C23×C29C2×D411yescharacteristic
54C22×D29—22no—
55C2×C4×C29—22no—
56C2×C4×C29—21no—
57C2×C4×C29—41no—
58C2×C4×C29—42no—
59C2×C4×C29—41no—
60C2×C4×C29C2×D412yes—
61C2×C4×C29C2×D412yes—
62C2×C4×C29C2×D411yescharacteristic
63C2×C4×C29#4111yescharacteristic
64C22⋊D29—48no—
65C22⋊D29—42no—
66C22⋊D29—42no—
67C2×Dic29—24no—
68C2×Dic29—22no—
69D116—22no—
70D116—22no—
71C4×D29—42no—
72C4×D29—42no—
73Dic58—22no—
74Dic58—22no—
75C8×C29—22no—
76C8×C29—41no—
77#2010—291nomaximal, Sylow
78C22×C29—24no—
79C22×C29—22no—
80C22×C29—41no—
81C22×C29—42no—
82C22×C29—41no—
83C22×C29—41no—
84C22×C29#12012yes—
85C22×C29#12111yescharacteristic
86C2×D29—44no—
87C2×D29—42no—
88C4×C29—41no—
89C4×C29#12011yescharacteristic
90C4×C29#12112yes—
91C4×C29#12711yescharacteristic
92Dic29—44no—
93Dic29—42no—
94#575—291no—
95#525—292no—
96#421—292no—
97#407D2911yescharacteristic, complemented
98H(3,ℤ/4)—291no—
99C2×C29—22no—
100C2×C29—21no—
101C2×C29—42no—
102C2×C29#39211yescharacteristic
103D29—82no—
104C2×#41—292no—
105C23×C4C2×D2911yescharacteristic
106#137—582no—
107AGL(1,ℤ/8)—582no—
108#135—582no—
109C2×M16C2×D2911yescharacteristic
110C2×M16C2×D2911yescharacteristic
111#123—582no—
112C22⋊Q8—582no—
113#121—582no—
114#120—582no—
115C4×D4—584no—
116#117—292no—
117#104—584no—
118C22⋊C8—22no—
119C29#201011yescharacteristic, complemented, Sylow
120C24D11611yescharacteristic
121#41—582no—
122#41—582no—
123#41—582no—
124#41—582no—
125C2×Q8—292no—
126C2×D4—292no—
127C2×D4—584no—
128C2×D4—582no—
129C22×C4—21no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—21no—
133C22×C4—582no—
134C22×C4D11611yescharacteristic
135C22×C4C22×D2911yescharacteristic
136Q16—582no—
137SD16—584no—
138D8—582no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D2912yescomplemented
143C4⋊C4—584no—
144C4⋊C4—582no—
145C22⋊C4—584no—
146C22⋊C4—584no—
147C22⋊C4—582no—
148C42—294no—
149C23—21no—
150C23—22no—
151C23—42no—
152C23—582no—
153C23C2×D11611yescharacteristic
154Q8—582no—
155Q8—582no—
156D4—582no—
157D4—582no—
158D4—1168no—
159D4—1162no—
160D4—1162no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—584no—
167C2×C4—582no—
168C2×C4—1162no—
169C2×C4—1162no—
170C2×C4#9080511yescharacteristic
171C2×C4D4×D2912yes—
172C2×C4D4×D2912yes—
173C2×C4C2×C22⋊D2911yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—1164no—
183C22—1162no—
184C22#1174524412yes—
185C22#1174529211yescharacteristic
186C4—41no—
187C4—1164no—
188C4—1162no—
189C4#1174524612yes—
190C4#1174529911yescharacteristic
191C4#1174530211yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—2322no—
196C2#1427107211yescharacteristic
subgroupG/H
centerC4#11745302
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#407C2
socleC2×C29#392
hypercenter#407D29
hypocenterC29#2010
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #14271963C2semidirect
2. #14271674C2semidirect
3. #14271179C2semidirect
4. #14270920C2semidirect
5. C29×#407C2semidirect
34. C2×D116D4semidirect
36. C2×Dic58D4semidirect
40. C2×C8×C29D4semidirect
46. C4×Dic29D4semidirect
97. #407D29semidirect
119. C29#2010semidirect
142. C2×C8C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142719632
#142716742
#142711792
#142709202
C29×#4072
#201029