Finite Group Databasebeta

← #16818645

Subgroups — #16818645

Order 3712.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#14271817C211yesmaximal, characteristic
2#14271514C211yesmaximal, characteristic, complemented
3#14271454C211yesmaximal, characteristic, complemented
4#14271453C211yesmaximal, characteristic, complemented
5#14270908C211yesmaximal, characteristic, complemented
6#14270892C211yesmaximal, characteristic, complemented
7C29×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#90807—21no—
9C4×D4×C29C2211yescharacteristic
10#11745292—21no—
11C2×C4⋊Dic29—21no—
12#11745259—21no—
13#11745248—22no—
14C4×D116C2211yescharacteristic
15#11745231C2211yescharacteristic
16#11745231C2211yescharacteristic
17C29×C4⋊C8C2211yescharacteristic
18C4×C8×C29C2211yescharacteristic
19#11745180—21no—
20#11745169—21no—
21#11745165—21no—
22#11745164—22no—
23#11745156—21no—
24C4⋊#6597C2211yescharacteristic
25C2×D4×C29D411yescharacteristic
26C22×C4×C29—21no—
27C2×C22⋊D29—22no—
28C22×Dic29—22no—
29#90807—42no—
30#90807—42no—
31C2×D116D411yescharacteristic
32C2×C4×D29—21no—
33C2×Dic58—21no—
34C2×Dic58—21no—
35C2×C8×C29—21no—
36C2×C8×C29—21no—
37C4⋊C4×C29D411yescharacteristic
38C22⋊C4×C29—21no—
39C42×C29C2311yescharacteristic
40#90781—22no—
41#90781—21no—
42C4⋊Dic29—22no—
43C4⋊Dic29—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29—21no—
46C4⋊Dic29D411yescharacteristic
47C4⋊Dic29D412yes—
48C2×#6597—21no—
49C23×C29—21no—
50C22×D29—21no—
51D4×C29—21no—
52D4×C29SD1612yes—
53C2×C4×C29—21no—
54C2×C4×C29—41no—
55C2×C4×C29—41no—
56C2×C4×C29C2×D411yescharacteristic
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D411yescharacteristic
59C22⋊D29—44no—
60C2×Dic29—22no—
61C2×Dic29—21no—
62C2×Dic29—44no—
63C2×Dic29—41no—
64D116—21no—
65D116—21no—
66C4×D29—41no—
67C4×D29—41no—
68Dic58—41no—
69Dic58—41no—
70Dic58—42no—
71C8×C29—41no—
72C8×C29—41no—
73#6597—41no—
74#1635—291nomaximal, Sylow
75C22×C29—22no—
76C22×C29—41no—
77C22×C29—41no—
78C22×C29#12011yescharacteristic
79C2×D29—41no—
80C2×D29—41no—
81C2×D29—41no—
82C4×C29—21no—
83C4×C29—41no—
84C4×C29C2×SD1611yescharacteristic
85C4×C29#13511yescharacteristic
86C4×C29AGL(1,ℤ/8)11yescharacteristic
87C4×C29#13711yescharacteristic
88Dic29—42no—
89Dic29—41no—
90Dic29—81no—
91#547—291no—
92#487—291no—
93#476—291no—
94#476—291no—
95#332—291no—
96D4⋊C8—291no—
97D4⋊C8D2911yescharacteristic, complemented
98C2×C29—42no—
99C2×C29#45011yescharacteristic
100C2×C29#45211yescharacteristic
101C2×C29#45411yescharacteristic
102D29—81no—
103C2×#41—581no—
104C4⋊Q8—291no—
105C4⋊Q8—291no—
106#123—582no—
107C22⋊Q8—581no—
108#121—581no—
109C4×D4—291no—
110C4×D4C2×D2911yescharacteristic
111C2×C4⋊C4—581no—
112#106—581no—
113#106—581no—
114C4⋊C8—291no—
115C4⋊C8C2×D2911yescharacteristic
116#103—582no—
117#102—581no—
118#102—581no—
119C4×C8C2×D2911yescharacteristic
120C29#163511yescharacteristic, complemented, Sylow
121#41—1162no—
122#41—1162no—
123C2×Q8—581no—
124C2×Q8—581no—
125C2×D4—291no—
126C2×D4—582no—
127C2×D4D11611yescharacteristic
128C22×C4—21no—
129C22×C4—582no—
130C22×C4—581no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—581no—
134C4⋊C4—292no—
135C4⋊C4—291no—
136C4⋊C4—582no—
137C4⋊C4—581no—
138C4⋊C4—581no—
139C4⋊C4—581no—
140C4⋊C4D11611yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—582no—
143C22⋊C4—581no—
144C42C22×D2911yescharacteristic
145C23—21no—
146C23—581no—
147Q8—1162no—
148Q8—1161no—
149Q8—1161no—
150D4—21no—
151D4—581no—
152D4—581no—
153D4—1164no—
154D4#9077312yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—581no—
159C2×C4—582no—
160C2×C4—1164no—
161C2×C4—1161no—
162C2×C4—1161no—
163C2×C4—1161no—
164C2×C4C2×D11611yescharacteristic
165C2×C4D4×D2911yescharacteristic
166C2×C4D4×D2911yescharacteristic
167C8—41no—
168C8—41no—
169C8—1161no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—1161no—
174C22—1161no—
175C22—1161no—
176C22#1174524411yescharacteristic
177C4—21no—
178C4—41no—
179C4—1161no—
180C4—1162no—
181C4—2321no—
182C4C2×#9077311yescharacteristic
183C4#1174527011yescharacteristic
184C4#1174527411yescharacteristic
185C4#1174527711yescharacteristic
186C2—42no—
187C2—2321no—
188C2#1427131611yescharacteristic
189C2#1427132611yescharacteristic
190C2#1427133711yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×D4⋊C8C2
socleC22×C29#120
prime radical#14271817C2
hypercenterD4⋊C8D29
hypocenterC29#1635
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14271514C2semidirect
3. #14271454C2semidirect
4. #14271453C2semidirect
5. #14270908C2semidirect
6. #14270892C2semidirect
7. C29×D4⋊C8C2semidirect
97. D4⋊C8D29semidirect
120. C29#1635semidirect

Maximal subgroups

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

subgroupindex
#142718172
#142715142
#142714542
#142714532
#142709082
#142708922
C29×D4⋊C82
#163529