Finite Group Databasebeta

← #16820019

Subgroups — #16820019

Order 3712.

344 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 89 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#14271727C211yesmaximal, characteristic
2#14271169C212yesmaximal, complemented
3#14271137C211yesmaximal, characteristic, complemented
4#14270920C212yesmaximal, complemented
5C29×#568C211yesmaximal, characteristic, complemented
6C2×#41×C29C2211yescharacteristic
7C22×D116C2211yescharacteristic
8C29×#131—24no—
9C2×M16×C29—22no—
10C2×M16×C29C2212yes—
11#11745309C412yescomplemented
12#11745302C412yescomplemented
13#11745299—22no—
14#11745292—22no—
15#11745288C2212yes—
16#11745288C2211yescharacteristic
17#11745182—22no—
18#11745169—24no—
19C23×D29—21no—
20#41×C29—22no—
21#41×C29—22no—
22C2×Q8×C29C2×C411yescharacteristic
23C2×D4×C29C2×C411yescharacteristic
24C2×D4×C29D412yes—
25C22×C4×C29D412yes—
26C22×C4×C29C2311yescharacteristic
27C2×C22⋊D29—24no—
28C2×D116—22no—
29C2×D116—22no—
30C2×D116—21no—
31C2×D116C2×C412yes—
32M16×C29—24no—
33M16×C29—22no—
34M16×C29—22no—
35C2×C8×C29—24no—
36C2×C8×C29D414yescomplemented
37C22⋊Dic29—21no—
38C22⋊Dic29—22no—
39#90781—24no—
40C4⋊Dic29—21no—
41C4⋊Dic29—22no—
42C4×Dic29—22no—
43C4×Dic29C2×C412yes—
44C23×C29C22⋊C412yes—
45C23×C29C2×D411yescharacteristic
46C22×D29—22no—
47C22×D29—42no—
48C22×D29—82no—
49Q8×C29—22no—
50D4×C29—24no—
51D4×C29—22no—
52C2×C4×C29—22no—
53C2×C4×C29—22no—
54C2×C4×C29C22⋊C412yes—
55C2×C4×C29C22×C411yescharacteristic
56C2×C4×C29C2×D412yes—
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29#4112yes—
59C22⋊D29—84no—
60C2×Dic29—22no—
61C2×Dic29—42no—
62D116—24no—
63D116—41no—
64D116—41no—
65C8×C29—24no—
66#1910—291nomaximal, Sylow
67C22×C29—22no—
68C22×C29—41no—
69C22×C29—42no—
70C22×C29C2×C22⋊C411yescharacteristic
71C22×C29#12112yes—
72C2×D29—44no—
73C2×D29—42no—
74C2×D29—84no—
75C4×C29—22no—
76C4×C29C4×D412yes—
77C4×C29#12011yescharacteristic
78C4×C29#12311yescharacteristic
79Dic29—42no—
80Dic29—82no—
81#568D2911yescharacteristic, complemented
82#535—291no—
83#418—292no—
84#410—291no—
85H(3,ℤ/4)—292no—
86C2×C29—21no—
87C2×C29—22no—
88C2×C29—42no—
89C2×C29#38611yescharacteristic
90D29—82no—
91C2×#41C2×D2911yescharacteristic
92C22×D4—291no—
93#131—24no—
94C2×M16—22no—
95C2×M16C2×D2912yes—
96#127—292no—
97#124—292no—
98#121—582no—
99#120—582no—
100#117—291no—
101#117—292no—
102#102—584no—
103#99—582no—
104C29#191011yescharacteristic, complemented, Sylow
105C24—581no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D2911yescharacteristic
109C2×D4—292no—
110C2×D4—584no—
111C2×D4—582no—
112C2×D4—582no—
113C2×D4—581no—
114C2×D4C4×D2911yescharacteristic
115C2×D4D11612yes—
116C22×C4C22⋊D2912yes—
117C22×C4C22×D2911yescharacteristic
118M16—24no—
119M16—22no—
120M16—22no—
121C2×C8—24no—
122C2×C8C22⋊D2914yescomplemented
123C4⋊C4—581no—
124C4⋊C4—582no—
125C22⋊C4—581no—
126C22⋊C4—584no—
127C22⋊C4—582no—
128C42—292no—
129C42—582no—
130C23—582no—
131C23—1162no—
132C23—2322no—
133C23#9078112yes—
134C23C2×D11611yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—584no—
139D4—1161no—
140D4—1161no—
141D4—2324no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—582no—
145C2×C4—1162no—
146C2×C4#9078112yes—
147C2×C4C2×C4×D2911yescharacteristic
148C2×C4#9080512yes—
149C2×C4C2×C22⋊D2912yes—
150C2×C4C2×C22⋊D2911yescharacteristic
151C8—24no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—1164no—
156C22—1162no—
157C22—2324no—
158C22C2×#9078111yescharacteristic
159C22#1174529212yes—
160C4—22no—
161C4—1162no—
162C4—2322no—
163C4C4×C22⋊D2912yes—
164C4#1174529111yescharacteristic
165C4#1174531511yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—2322no—
170C2#1427104211yescharacteristic
subgroupG/H
centerC2#14271042
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#568C2
socleC2×C29#386
prime radical#14271727C2
cosocleC22×C4×C29C23
hypercenter#568D29
hypocenterC29#1910
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #14271169C2semidirect
3. #14271137C2semidirect
4. #14270920C2semidirect
5. C29×#568C2semidirect
11. #11745309C4semidirect
12. #11745302C4semidirect
36. C2×C8×C29D4semidirect
81. #568D29semidirect
104. C29#1910semidirect
122. C2×C8C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142717272
#142711692
#142711372
#142709202
C29×#5682
#191029