Finite Group Databasebeta

← #16818599

Subgroups — #16818599

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#14271360C211yesmaximal, characteristic, complemented
3#14271355C211yesmaximal, characteristic
4#14270909C211yesmaximal, characteristic, complemented
5#14270895C211yesmaximal, characteristic, complemented
6#14270892C211yesmaximal, characteristic, complemented
7C29×#486C211yesmaximal, characteristic, complemented
8C29×C4⋊Q8C2211yescharacteristic
9C29×#127C2211yescharacteristic
10#11745309—21no—
11Q8×Dic29—21no—
12C2×#90783—21no—
13C2×#90782—21no—
14#11745260—22no—
15#11745259—21no—
16#11745254—21no—
17C4×D116C2211yescharacteristic
18C4×Dic58C2211yescharacteristic
19C29×#102—22no—
20C4×C8×C29C2211yescharacteristic
21#11745180—21no—
22#11745180—21no—
23C4⋊#6597C2211yescharacteristic
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×D4×C29—21no—
27C2×D4×C29—21no—
28C2×D4×C29—21no—
29C2×D116D411yescharacteristic
30C2×C4×D29—21no—
31C2×Dic58D411yescharacteristic
32C2×C8×C29—21no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29D412yes—
35C42×C29C2311yescharacteristic
36#90783—42no—
37#90782—42no—
38#90781—22no—
39#90781—22no—
40#90781—21no—
41C4⋊Dic29—22no—
42C4⋊Dic29D411yescharacteristic
43C4⋊Dic29D411yescharacteristic
44#90779—21no—
45C4×Dic29—22no—
46C4×Dic29—21no—
47C2×#6597—21no—
48C2×#6597—21no—
49C23×C29—41no—
50C22×D29—21no—
51Q8×C29—41no—
52Q8×C29—41no—
53D4×C29—42no—
54D4×C29—41no—
55D4×C29—41no—
56D4×C29—41no—
57D4×C29—41no—
58C2×C4×C29—22no—
59C2×C4×C29C2×D411yescharacteristic
60C2×C4×C29C2×D411yescharacteristic
61C2×C4×C29C2×D411yescharacteristic
62C2×Dic29—21no—
63C2×Dic29—21no—
64C2×Dic29—21no—
65D116—21no—
66D116—21no—
67C4×D29—41no—
68C4×D29—41no—
69Dic58—21no—
70Dic58—21no—
71C8×C29—41no—
72#6597—41no—
73#6597—41no—
74#1628—291nomaximal, Sylow
75C22×C29—81no—
76C22×C29—81no—
77C22×C29—81no—
78C22×C29#12011yescharacteristic
79C2×D29—41no—
80C2×D29—41no—
81C2×D29—41no—
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#486D2911yescharacteristic, complemented
93#460—291no—
94#459—291no—
95#332—291no—
96Q8⋊C8—291no—
97D4⋊C8—291no—
98C2×C29—161no—
99C2×C29#44911yescharacteristic
100C2×C29#44911yescharacteristic
101C2×C29#45411yescharacteristic
102D29—81no—
103C2×SD16—581no—
104C2×D8—581no—
105C4⋊Q8C2×D2911yescharacteristic
106#127C2×D2911yescharacteristic
107#126—582no—
108#124—581no—
109C22⋊Q8—581no—
110C4×Q8—291no—
111C4×Q8—581no—
112C4×D4—291no—
113#117—581no—
114C4⋊C8—291no—
115C4⋊C8—291no—
116#102—22no—
117#102—581no—
118#102—581no—
119C4×C8C2×D2911yescharacteristic
120C29#162811yescharacteristic, complemented, Sylow
121C2×Q8—21no—
122C2×Q8—291no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—291no—
127C22×C4—581no—
128SD16—1162no—
129D8—1162no—
130C2×C8—21no—
131C2×C8—581no—
132C2×C8—581no—
133C4⋊C4—21no—
134C4⋊C4—291no—
135C4⋊C4—291no—
136C4⋊C4—582no—
137C4⋊C4—581no—
138C4⋊C4C22⋊D2912yes—
139C22⋊C4—582no—
140C22⋊C4—582no—
141C22⋊C4—581no—
142C42—582no—
143C42—581no—
144C42C22×D2911yescharacteristic
145C23—41no—
146C23—581no—
147Q8—41no—
148Q8—41no—
149Q8—581no—
150Q8—581no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—581no—
157D4—581no—
158C2×C4—22no—
159C2×C4—581no—
160C2×C4—581no—
161C2×C4—581no—
162C2×C4—1161no—
163C2×C4—1161no—
164C2×C4D4×D2911yescharacteristic
165C2×C4D4×D2911yescharacteristic
166C2×C4C2×C22⋊D2911yescharacteristic
167C8—41no—
168C8—1161no—
169C8—1161no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—1161no—
174C22—1161no—
175C22—1161no—
176C22#1174529911yescharacteristic
177C4—21no—
178C4—42no—
179C4—1161no—
180C4—1161no—
181C4—1161no—
182C4#1174527311yescharacteristic
183C4#1174527411yescharacteristic
184C4#1174527611yescharacteristic
185C4#1174527811yescharacteristic
186C2—161no—
187C2—2321no—
188C2#1427130511yescharacteristic
189C2#1427130711yescharacteristic
190C2#1427133511yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#486C2
socleC22×C29#120
prime radical#14271355C2
hypercenter#486D29
hypocenterC29#1628
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14271887C2semidirect
2. #14271360C2semidirect
4. #14270909C2semidirect
5. #14270895C2semidirect
6. #14270892C2semidirect
7. C29×#486C2semidirect
92. #486D29semidirect
120. C29#1628semidirect

Maximal subgroups

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

subgroupindex
#142718872
#142713602
#142713552
#142709092
#142708952
#142708922
C29×#4862
#162829