Finite Group Databasebeta

← #16818605

Subgroups — #16818605

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#14271886C211yesmaximal, characteristic, complemented
2#14271510C211yesmaximal, characteristic, complemented
3#14271363C211yesmaximal, characteristic, complemented
4#14271359C211yesmaximal, characteristic
5#14270910C211yesmaximal, characteristic, complemented
6#14270892C211yesmaximal, characteristic, complemented
7C29×Q8⋊C8C211yesmaximal, characteristic, complemented
8C4×Q8×C29C2211yescharacteristic
9#11745308—21no—
10C2×#90784—21no—
11C2×D232—21no—
12#11745260—22no—
13#11745254—21no—
14#11745237—21no—
15#11745236C2211yescharacteristic
16C4×D116C2211yescharacteristic
17#11745231C2211yescharacteristic
18C4×Dic58—21no—
19C29×C4⋊C8C2211yescharacteristic
20C4×C8×C29C2211yescharacteristic
21#11745169—22no—
22#11745169—21no—
23#11745157—21no—
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29D411yescharacteristic
26C2×D116—21no—
27C2×D116—21no—
28C2×D116—21no—
29C2×D116D411yescharacteristic
30C2×C4×D29—21no—
31C2×Dic58—21no—
32C2×C8×C29—21no—
33C2×C8×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29D411yescharacteristic
36C42×C29—21no—
37C42×C29C2311yescharacteristic
38#90784—42no—
39#90781—22no—
40#90781—22no—
41#90781—21no—
42C4⋊Dic29—21no—
43C4⋊Dic29D411yescharacteristic
44C4⋊Dic29D412yes—
45#90779—22no—
46C4×Dic29—22no—
47C2×#6597—21no—
48D232—42no—
49C22×D29—21no—
50C22×D29—41no—
51Q8×C29—21no—
52Q8×C29—21no—
53C2×C4×C29—21no—
54C2×C4×C29—21no—
55C2×C4×C29C2×D411yescharacteristic
56C2×C4×C29C2×D411yescharacteristic
57C2×C4×C29C2×D411yescharacteristic
58C2×Dic29—21no—
59C2×Dic29—22no—
60D116—21no—
61D116—21no—
62D116—42no—
63D116—41no—
64D116—41no—
65D116—41no—
66D116—41no—
67C4×D29—41no—
68C4×D29—41no—
69Dic58—41no—
70Dic58—41no—
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—41no—
84C4×C29—41no—
85C4×C29#13511yescharacteristic
86C4×C29#13511yescharacteristic
87C4×C29AGL(1,ℤ/8)11yescharacteristic
88C4×C29AGL(1,ℤ/8)11yescharacteristic
89Dic29—42no—
90Dic29—41no—
91#556—291no—
92#486—291no—
93#460—291no—
94#459—291no—
95#332—291no—
96Q8⋊C8D2911yescharacteristic, complemented
97D4⋊C8—291no—
98C2×C29#44911yescharacteristic
99C2×C29#44911yescharacteristic
100C2×C29#45411yescharacteristic
101D29—81no—
102D29—161no—
103C2×SD16—581no—
104C2×D8—581no—
105C4⋊Q8—291no—
106#127—291no—
107#126—582no—
108#124—581no—
109C22⋊Q8—581no—
110C4×Q8—581no—
111C4×Q8C2×D2911yescharacteristic
112C4×D4—291no—
113#117—581no—
114C4⋊C8—291no—
115C4⋊C8C2×D2911yescharacteristic
116#102—581no—
117#102—582no—
118#102—581no—
119C4×C8C2×D2911yescharacteristic
120C29#162811yescharacteristic, complemented, Sylow
121C2×Q8—581no—
122C2×Q8D11611yescharacteristic
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—292no—
136C4⋊C4—582no—
137C4⋊C4—581no—
138C4⋊C4D11611yescharacteristic
139C22⋊C4—582no—
140C22⋊C4—582no—
141C22⋊C4—581no—
142C42—21no—
143C42—582no—
144C42C22×D2911yescharacteristic
145C23—581no—
146C23—1161no—
147Q8—21no—
148Q8—21no—
149Q8—1161no—
150Q8—1161no—
151D4—581no—
152D4—581no—
153D4—1162no—
154D4—1161no—
155D4—1161no—
156D4—1161no—
157D4—1161no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—581no—
161C2×C4—582no—
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—41no—
179C4—41no—
180C4—1161no—
181C4—1162no—
182C4#1174526611yescharacteristic
183C4#1174527011yescharacteristic
184C4#1174527611yescharacteristic
185C4#1174528111yescharacteristic
186C2—4641no—
187C2—2321no—
188C2#1427131011yescharacteristic
189C2#1427131111yescharacteristic
190C2#1427133711yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×Q8⋊C8C2
socleC22×C29#120
prime radical#14271359C2
hypercenterQ8⋊C8D29
hypocenterC29#1628
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #14271886C2semidirect
2. #14271510C2semidirect
3. #14271363C2semidirect
5. #14270910C2semidirect
6. #14270892C2semidirect
7. C29×Q8⋊C8C2semidirect
96. Q8⋊C8D29semidirect
120. C29#1628semidirect

Maximal subgroups

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

subgroupindex
#142718862
#142715102
#142713632
#142713592
#142709102
#142708922
C29×Q8⋊C82
#162829