Finite Group Databasebeta

← #16818640

Subgroups — #16818640

Order 3712.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#14271816C211yesmaximal, characteristic
2#14271450C211yesmaximal, characteristic, complemented
3#14271450C211yesmaximal, characteristic, complemented
4#14270909C211yesmaximal, characteristic, complemented
5#14270892C211yesmaximal, characteristic, complemented
6#14270892C211yesmaximal, characteristic, complemented
7C29×#487C211yesmaximal, characteristic, complemented
8C2×#90809—21no—
9C29×C4⋊Q8C2211yescharacteristic
10C29×C4⋊Q8C2211yescharacteristic
11#11745308—21no—
12#11745257—21no—
13#11745256—22no—
14C4⋊C4×D29—21no—
15C4×D116C2211yescharacteristic
16C4×D116C2211yescharacteristic
17C29×#103—22no—
18C4×C8×C29C2211yescharacteristic
19#11745157—21no—
20#11745157—21no—
21#11745156—21no—
22#11745156—21no—
23C4⋊#6597C2211yescharacteristic
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×Q8×C29—21no—
27#90809—42no—
28#90809—42no—
29C2×D116—22no—
30C2×D116D411yescharacteristic
31C2×D116D411yescharacteristic
32C2×C4×D29—22no—
33C2×C4×D29—21no—
34C2×C4×D29—21no—
35C2×C8×C29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29D412yes—
40C42×C29C2311yescharacteristic
41#90781—22no—
42#90781—21no—
43#90781—21no—
44C4⋊Dic29D411yescharacteristic
45C4⋊Dic29D411yescharacteristic
46#90779—22no—
47C2×#6597—21no—
48C2×#6597—21no—
49C22×D29—21no—
50C22×D29—21no—
51Q8×C29—42no—
52Q8×C29—41no—
53Q8×C29—41no—
54C2×C4×C29—22no—
55C2×C4×C29—41no—
56C2×C4×C29C2×D411yescharacteristic
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D411yescharacteristic
59C2×Dic29—21no—
60C2×Dic29—21no—
61D116—21no—
62D116—21no—
63D116—21no—
64D116—44no—
65D116SD1612yes—
66C4×D29—44no—
67C4×D29—41no—
68C4×D29—41no—
69C4×D29—41no—
70C4×D29—41no—
71C8×C29—41no—
72#6597—41no—
73#6597—41no—
74#1635—291nomaximal, Sylow
75C22×C29#12011yescharacteristic
76C2×D29—22no—
77C2×D29—41no—
78C2×D29—41no—
79C2×D29—41no—
80C2×D29—41no—
81C2×D29—41no—
82C4×C29—21no—
83C4×C29—42no—
84C4×C29—81no—
85C4×C29C2×SD1611yescharacteristic
86C4×C29#13511yescharacteristic
87C4×C29AGL(1,ℤ/8)11yescharacteristic
88C4×C29#13711yescharacteristic
89Dic29—41no—
90Dic29—41no—
91#547—291no—
92#487D2911yescharacteristic, complemented
93#476—291no—
94#476—291no—
95#332—291no—
96D4⋊C8—291no—
97D4⋊C8—291no—
98C2×C29#45011yescharacteristic
99C2×C29#45211yescharacteristic
100C2×C29#45411yescharacteristic
101D29—42no—
102D29—81no—
103C2×#41—581no—
104C4⋊Q8C2×D2911yescharacteristic
105C4⋊Q8C2×D2911yescharacteristic
106#123—582no—
107C22⋊Q8—581no—
108#121—581no—
109C4×D4—291no—
110C4×D4—291no—
111C2×C4⋊C4—581no—
112#106—581no—
113#106—581no—
114C4⋊C8—291no—
115C4⋊C8—291no—
116#103—22no—
117#102—581no—
118#102—581no—
119C4×C8C2×D2911yescharacteristic
120C29#163511yescharacteristic, complemented, Sylow
121#41—1162no—
122#41—1162no—
123C2×Q8—21no—
124C2×Q8—21no—
125C2×D4—291no—
126C2×D4—291no—
127C2×D4—582no—
128C22×C4—582no—
129C22×C4—581no—
130C22×C4—581no—
131C2×C8—21no—
132C2×C8—581no—
133C2×C8—581no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—291no—
138C4⋊C4—291no—
139C4⋊C4—582no—
140C4⋊C4C22⋊D2912yes—
141C22⋊C4—582no—
142C22⋊C4—581no—
143C22⋊C4—581no—
144C42C22×D2911yescharacteristic
145C23—581no—
146C23—581no—
147Q8—42no—
148Q8—41no—
149Q8—41no—
150D4—292no—
151D4—581no—
152D4—581no—
153D4—581no—
154D4—1164no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—581no—
158C2×C4—581no—
159C2×C4—1164no—
160C2×C4—1161no—
161C2×C4—1161no—
162C2×C4—1161no—
163C2×C4—1161no—
164C2×C4D4×D2911yescharacteristic
165C2×C4D4×D2911yescharacteristic
166C2×C4C2×C22⋊D2911yescharacteristic
167C8—41no—
168C8—1161no—
169C8—1161no—
170C22—582no—
171C22—1161no—
172C22—1161no—
173C22—1161no—
174C22—1161no—
175C22—1161no—
176C22#1174529911yescharacteristic
177C4—21no—
178C4—42no—
179C4—81no—
180C4—1161no—
181C4—1161no—
182C4SD16×D2911yescharacteristic
183C4#1174527611yescharacteristic
184C4#1174528011yescharacteristic
185C4#1174528111yescharacteristic
186C2—1162no—
187C2—2321no—
188C2#1427131211yescharacteristic
189C2#1427132411yescharacteristic
190C2#1427133511yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#487C2
socleC22×C29#120
prime radical#14271816C2
hypercenter#487D29
hypocenterC29#1635
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #14271450C2semidirect
3. #14271450C2semidirect
4. #14270909C2semidirect
5. #14270892C2semidirect
6. #14270892C2semidirect
7. C29×#487C2semidirect
92. #487D29semidirect
120. C29#1635semidirect

Maximal subgroups

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

subgroupindex
#142718162
#142714502
#142709092
#142708922
C29×#4872
#163529