Finite Group Databasebeta

← #16818446

Subgroups — #16818446

Order 3712.

308 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 308 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#14271725C211yesmaximal, characteristic
2#14271304C212yesmaximal, complemented
3#14271075C211yesmaximal, characteristic, complemented
4#14270898C212yesmaximal, complemented
5C29×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D29—21no—
7C22×Dic58C2211yescharacteristic, complemented
8C2×C22⋊C4×C29C2211yescharacteristic
9C2×C22⋊Dic29—21no—
10#11745292—21no—
11#11745292C2212yes—
12C2×#90773—22no—
13#11745248—22no—
14#11745244—22no—
15C29×C22⋊C8C2212yescomplemented
16#11745179—21no—
17#11745179C2211yescharacteristic, complemented
18#11745164—22no—
19C24×C29D411yescharacteristic
20C23×D29—21no—
21C22×C4×C29D411yescharacteristic
22C22×C4×C29C2311yescharacteristic
23C2×C22⋊D29—22no—
24C2×C22⋊D29—22no—
25C2×C22⋊D29—42no—
26C2×C22⋊D29—42no—
27C22×Dic29—21no—
28C22×Dic29—21no—
29C22×Dic29—21no—
30C2×D116—21no—
31C2×D116D412yes—
32C2×Dic58—22no—
33C2×Dic58—42no—
34C2×C8×C29—22no—
35C22⋊C4×C29—22no—
36C22⋊Dic29—42no—
37#90781—22no—
38#90781—22no—
39C4⋊Dic29—21no—
40C4⋊Dic29D412yes—
41#90773—44no—
42C23×C29—21no—
43C23×C29—21no—
44C23×C29—41no—
45C23×C29—41no—
46C23×C29SD1612yescomplemented
47C23×C29C2×D411yescharacteristic
48C22×D29—22no—
49C22×D29—42no—
50C22×D29—81no—
51C22×D29—81no—
52C2×C4×C29—21no—
53C2×C4×C29—41no—
54C2×C4×C29—41no—
55C2×C4×C29C2×D412yes—
56C22⋊D29—44no—
57C22⋊D29—42no—
58C22⋊D29—42no—
59C2×Dic29—22no—
60C2×Dic29—22no—
61C2×Dic29—41no—
62C2×Dic29—42no—
63C2×Dic29—41no—
64C2×Dic29—41no—
65C2×Dic29—41no—
66C2×Dic29—41no—
67D116—42no—
68D116—81no—
69Dic58—24no—
70Dic58—42no—
71C8×C29—42no—
72#1601—291nomaximal, Sylow
73C22×C29—21no—
74C22×C29—21no—
75C22×C29—22no—
76C22×C29—42no—
77C22×C29—41no—
78C22×C29—41no—
79C22×C29—81no—
80C22×C29#12011yescharacteristic
81C22×C29C2×SD1611yescharacteristic
82C22×C29AGL(1,ℤ/8)11yescharacteristic
83C2×D29—42no—
84C2×D29—42no—
85C2×D29—42no—
86C2×D29—84no—
87C4×C29—22no—
88C4×C29—41no—
89Dic29—42no—
90Dic29—42no—
91Dic29—81no—
92#534—291no—
93#448—292no—
94#393—291no—
95#327—292no—
96#323D2911yescharacteristic, complemented
97C2×C29—21no—
98C2×C29—21no—
99C2×C29—42no—
100C2×C29#45011yescharacteristic
101C2×C29#45511yescharacteristic
102C2×C29B(4,𝔽2)11yescharacteristic
103D29—82no—
104C22×Q8—291no—
105C22×D4—581no—
106C2×SD16—582no—
107#123—582no—
108#121—292no—
109#121—581no—
110#120—582no—
111C2×C22⋊C4—581no—
112C2×C22⋊C4C2×D2911yescharacteristic
113#103—582no—
114C22⋊C8C2×D2912yescomplemented
115#95—291no—
116#95—581no—
117C29#160111yescharacteristic, complemented, Sylow
118C24—581no—
119C24D11611yescharacteristic
120C2×Q8—582no—
121C2×Q8—1162no—
122C2×D4—292no—
123C2×D4—581no—
124C2×D4—582no—
125C2×D4—582no—
126C2×D4—1162no—
127C2×D4—1162no—
128C22×C4—581no—
129C22×C4—581no—
130C22×C4—581no—
131C22×C4D11611yescharacteristic
132C22×C4C22×D2911yescharacteristic
133SD16—1164no—
134C2×C8—22no—
135C4⋊C4—292no—
136C4⋊C4—581no—
137C22⋊C4—22no—
138C22⋊C4—582no—
139C22⋊C4—582no—
140C22⋊C4—1162no—
141C23—21no—
142C23—21no—
143C23—41no—
144C23—41no—
145C23—582no—
146C23—1162no—
147C23—2321no—
148C23—2321no—
149C23#9077312yescomplemented
150C23C2×D11611yescharacteristic
151Q8—584no—
152Q8—1162no—
153D4—1162no—
154D4—1164no—
155D4—1162no—
156D4—1162no—
157D4—2321no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—582no—
162C2×C4—582no—
163C2×C4—1162no—
164C2×C4—1161no—
165C2×C4—1161no—
166C2×C4—1161no—
167C2×C4—1161no—
168C2×C4—1161no—
169C2×C4D4×D2912yes—
170C8—42no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—81no—
178C22—1162no—
179C22—1162no—
180C22—1162no—
181C22—2324no—
182C22#1174524411yescharacteristic
183C22C2×#9077311yescharacteristic
184C22#1174527011yescharacteristic
185C4—22no—
186C4—41no—
187C4—1162no—
188C4—1162no—
189C4—2321no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—2322no—
194C2#1427131611yescharacteristic
195C2#1427134311yescharacteristic
196C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#323C2
socleC22×C29#120
prime radical#14271725C2
hypercenter#323D29
hypocenterC29#1601
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14271304C2semidirect
3. #14271075C2semidirect
4. #14270898C2semidirect
5. C29×#323C2semidirect
7. C22×Dic58C22semidirect
15. C29×C22⋊C8C22semidirect
17. #11745179C22semidirect
46. C23×C29SD16semidirect
96. #323D29semidirect
114. C22⋊C8C2×D29semidirect
117. C29#1601semidirect
149. C23#90773semidirect

Maximal subgroups

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

subgroupindex
#142717252
#142713042
#142710752
#142708982
C29×#3232
#160129