Finite Group Databasebeta

← #16818603

Subgroups — #16818603

Order 3712.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271887C211yesmaximal, characteristic, complemented
2#14271511C211yesmaximal, characteristic, complemented
3#14271364C211yesmaximal, characteristic, complemented
4#14271359C211yesmaximal, characteristic
5#14270893C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×#332C211yesmaximal, characteristic, complemented
8C29×C4⋊Q8C2211yescharacteristic
9#11745309—21no—
10Q8×Dic29—21no—
11C2×D232—21no—
12C2×#90773—21no—
13#11745260—22no—
14#11745259—21no—
15#11745254—21no—
16#11745236C2211yescharacteristic
17C4×D116C2211yescharacteristic
18C4×Dic58C2211yescharacteristic
19C29×C4⋊C8C2211yescharacteristic
20C29×C4⋊C8C2211yescharacteristic
21#11745169—21no—
22#11745169—21no—
23#11745157—22no—
24C4×#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×D116—21no—
27C2×D116—21no—
28C2×D116—21no—
29C2×D116D411yescharacteristic
30C2×C4×D29—21no—
31C2×Dic58D411yescharacteristic
32C2×C8×C29—21no—
33C2×C8×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29D412yes—
36C42×C29C2311yescharacteristic
37#90781—22no—
38#90781—22no—
39#90781—21no—
40C4⋊Dic29—22no—
41C4⋊Dic29D411yescharacteristic
42C4⋊Dic29D411yescharacteristic
43#90779—21no—
44C4×Dic29—22no—
45C4×Dic29—21no—
46C2×#6597—21no—
47D232—42no—
48#90773—42no—
49C22×D29—21no—
50C22×D29—41no—
51Q8×C29—41no—
52Q8×C29—41no—
53C2×C4×C29—22no—
54C2×C4×C29C2×D411yescharacteristic
55C2×C4×C29C2×D411yescharacteristic
56C2×C4×C29C2×D411yescharacteristic
57C2×Dic29—21no—
58C2×Dic29—21no—
59C2×Dic29—21no—
60D116—21no—
61D116—21no—
62D116—42no—
63D116—41no—
64D116—41no—
65D116—41no—
66D116—41no—
67C4×D29—41no—
68C4×D29—41no—
69Dic58—21no—
70Dic58—21no—
71C8×C29—41no—
72C8×C29—41no—
73#6597—41no—
74#1628—291nomaximal, Sylow
75C22×C29#12011yescharacteristic
76C2×D29—41no—
77C2×D29—41no—
78C2×D29—41no—
79C2×D29—81no—
80C2×D29—81no—
81C2×D29—81no—
82C4×C29—21no—
83C4×C29—42no—
84C4×C29#13511yescharacteristic
85C4×C29#13511yescharacteristic
86C4×C29AGL(1,ℤ/8)11yescharacteristic
87C4×C29AGL(1,ℤ/8)11yescharacteristic
88Dic29—41no—
89Dic29—41no—
90Dic29—41no—
91#556—291no—
92#486—291no—
93#460—291no—
94#459—291no—
95#332D2911yescharacteristic, complemented
96Q8⋊C8—291no—
97D4⋊C8—291no—
98C2×C29#44911yescharacteristic
99C2×C29#44911yescharacteristic
100C2×C29#45411yescharacteristic
101D29—81no—
102D29—161no—
103C2×SD16—581no—
104C2×D8—581no—
105C4⋊Q8C2×D2911yescharacteristic
106#127—291no—
107#126—582no—
108#124—581no—
109C22⋊Q8—581no—
110C4×Q8—291no—
111C4×Q8—581no—
112C4×D4—291no—
113#117—581no—
114C4⋊C8C2×D2911yescharacteristic
115C4⋊C8C2×D2911yescharacteristic
116#102—581no—
117#102—581no—
118#102—582no—
119C4×C8—291no—
120C29#162811yescharacteristic, complemented, Sylow
121C2×Q8—21no—
122C2×Q8—291no—
123C2×D4—291no—
124C2×D4—581no—
125C2×D4—581no—
126C2×D4—581no—
127C22×C4—581no—
128SD16—1162no—
129D8—1162no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—581no—
133C4⋊C4—21no—
134C4⋊C4—291no—
135C4⋊C4—291no—
136C4⋊C4—582no—
137C4⋊C4—581no—
138C4⋊C4D11612yes—
139C22⋊C4—582no—
140C22⋊C4—582no—
141C22⋊C4—581no—
142C42—582no—
143C42—581no—
144C42C22×D2911yescharacteristic
145C23—581no—
146C23—1161no—
147Q8—41no—
148Q8—41no—
149Q8—581no—
150Q8—581no—
151D4—581no—
152D4—581no—
153D4—1162no—
154D4—1161no—
155D4—1161no—
156D4—1161no—
157D4—1161no—
158C2×C4—22no—
159C2×C4—581no—
160C2×C4—581no—
161C2×C4—581no—
162C2×C4—1161no—
163C2×C4—1161no—
164C2×C4C2×D11611yescharacteristic
165C2×C4D4×D2911yescharacteristic
166C2×C4D4×D2911yescharacteristic
167C8—41no—
168C8—41no—
169C8—1161no—
170C22—1161no—
171C22—1161no—
172C22—1161no—
173C22—2321no—
174C22—2321no—
175C22—2321no—
176C22#1174524411yescharacteristic
177C4—21no—
178C4—42no—
179C4—1161no—
180C4—1161no—
181C4—1161no—
182C4#1174527311yescharacteristic
183C4#1174527611yescharacteristic
184C4#1174527811yescharacteristic
185C4#1174528111yescharacteristic
186C2—4641no—
187C2—2321no—
188C2#1427130911yescharacteristic
189C2#1427131111yescharacteristic
190C2#1427133811yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#332C2
socleC22×C29#120
prime radical#14271359C2
hypercenter#332D29
hypocenterC29#1628
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #14271887C2semidirect
2. #14271511C2semidirect
3. #14271364C2semidirect
5. #14270893C2semidirect
6. #14270890C2semidirect
7. C29×#332C2semidirect
95. #332D29semidirect
120. C29#1628semidirect

Maximal subgroups

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

subgroupindex
#142718872
#142715112
#142713642
#142713592
#142708932
#142708902
C29×#3322
#162829