Finite Group Databasebeta

← #16818591

Subgroups — #16818591

Order 3712.

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

normal subgroups only

This group has 210 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#14271892C211yesmaximal, characteristic, complemented
2#14271510C211yesmaximal, characteristic
3#14271364C211yesmaximal, characteristic
4#14271363C211yesmaximal, characteristic
5#14270910C211yesmaximal, characteristic, complemented
6#14270895C211yesmaximal, characteristic, complemented
7C29×Q8⋊C8C211yesmaximal, characteristic, complemented
8C4×Q8×C29C2211yescharacteristic
9Q8×Dic29—21no—
10C2×#90784—21no—
11C2×#90773—21no—
12#11745252—21no—
13#11745252—22no—
14#11745236C2211yescharacteristic
15#11745231—21no—
16#11745231C2211yescharacteristic
17C4×Dic58—21no—
18C4×Dic58C2211yescharacteristic
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×Dic58—21no—
30C2×Dic58D411yescharacteristic
31C2×C8×C29—21no—
32C2×C8×C29—21no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29D411yescharacteristic
35C42×C29—21no—
36C42×C29C2311yescharacteristic
37#90784—42no—
38C4⋊Dic29—22no—
39C4⋊Dic29—22no—
40C4⋊Dic29—21no—
41C4⋊Dic29D411yescharacteristic
42C4⋊Dic29D412yes—
43#90779—22no—
44#90779—21no—
45C4×Dic29—22no—
46C4×Dic29—21no—
47C2×#6597—21no—
48#90773—42no—
49C22×D29—41no—
50Q8×C29—21no—
51Q8×C29SD1612yescomplemented
52C2×C4×C29—21no—
53C2×C4×C29—21no—
54C2×C4×C29C2×D411yescharacteristic
55C2×C4×C29C2×D411yescharacteristic
56C2×C4×C29C2×D411yescharacteristic
57C2×Dic29—21no—
58C2×Dic29—21no—
59C2×Dic29—22no—
60D116—42no—
61D116—41no—
62D116—41no—
63D116—41no—
64D116—41no—
65Dic58—21no—
66Dic58—21no—
67Dic58—41no—
68Dic58—41no—
69C8×C29—41no—
70C8×C29—41no—
71#6597—41no—
72#1626—291nomaximal, Sylow
73C22×C29#12011yescharacteristic
74C2×D29—81no—
75C2×D29—81no—
76C2×D29—81no—
77C4×C29—22no—
78C4×C29—21no—
79C4×C29—41no—
80C4×C29C2×SD1611yescharacteristic
81C4×C29#13511yescharacteristic
82C4×C29AGL(1,ℤ/8)11yescharacteristic
83C4×C29#13711yescharacteristic
84Dic29—41no—
85Dic29—42no—
86Dic29—41no—
87#557—291no—
88#486—291no—
89#460—291no—
90#460—291no—
91#332—291no—
92Q8⋊C8—291no—
93Q8⋊C8D2911yescharacteristic, complemented
94C2×C29#44811yescharacteristic
95C2×C29#44911yescharacteristic
96C2×C29#45411yescharacteristic
97D29—161no—
98C2×SD16—581no—
99C2×SD16—581no—
100C4⋊Q8—291no—
101C4⋊Q8—581no—
102#127—291no—
103#125—582no—
104#125—581no—
105C4×Q8—291no—
106C4×Q8—581no—
107C4×Q8—581no—
108C4×Q8C2×D2911yescharacteristic
109C4⋊C8—291no—
110C4⋊C8C2×D2911yescharacteristic
111#102—581no—
112#102—582no—
113#102—581no—
114C4×C8C2×D2911yescharacteristic
115C29#162611yescharacteristic, complemented, Sylow
116C2×Q8—291no—
117C2×Q8—581no—
118C2×Q8D11611yescharacteristic
119C2×D4—581no—
120C2×D4—581no—
121C2×D4—581no—
122SD16—1162no—
123SD16—1162no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—581no—
127C4⋊C4—21no—
128C4⋊C4—291no—
129C4⋊C4—292no—
130C4⋊C4—582no—
131C4⋊C4—582no—
132C4⋊C4—582no—
133C4⋊C4—581no—
134C4⋊C4—581no—
135C4⋊C4D11611yescharacteristic
136C42—21no—
137C42—582no—
138C42—581no—
139C42C22×D2911yescharacteristic
140C23—1161no—
141Q8—21no—
142Q8—581no—
143Q8—581no—
144Q8—1161no—
145Q8—1161no—
146Q8#9077312yescomplemented
147D4—1162no—
148D4—1161no—
149D4—1161no—
150D4—1161no—
151D4—1161no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—581no—
155C2×C4—582no—
156C2×C4—581no—
157C2×C4C2×D11611yescharacteristic
158C2×C4D4×D2911yescharacteristic
159C2×C4D4×D2911yescharacteristic
160C8—41no—
161C8—41no—
162C8—1161no—
163C22—2321no—
164C22—2321no—
165C22—2321no—
166C22#1174524411yescharacteristic
167C4—22no—
168C4—21no—
169C4—41no—
170C4—1161no—
171C4—1162no—
172C4—1161no—
173C4C2×#9077311yescharacteristic
174C4#1174527111yescharacteristic
175C4#1174527611yescharacteristic
176C4#1174528111yescharacteristic
177C2—4641no—
178C2#1427130411yescharacteristic
179C2#1427131111yescharacteristic
180C2#1427133711yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×Q8⋊C8C2
socleC22×C29#120
prime radical#11745236C22
hypercenterQ8⋊C8D29
hypocenterC29#1626
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. #14271892C2semidirect
5. #14270910C2semidirect
6. #14270895C2semidirect
7. C29×Q8⋊C8C2semidirect
51. Q8×C29SD16semidirect
93. Q8⋊C8D29semidirect
115. C29#1626semidirect
146. Q8#90773semidirect

Maximal subgroups

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

subgroupindex
#142718922
#142715102
#142713642
#142713632
#142709102
#142708952
C29×Q8⋊C82
#162629