Finite Group Databasebeta

← #16818443

Subgroups — #16818443

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#14271302C212yesmaximal, complemented
3#14270896C212yesmaximal, complemented
4#14270887C211yesmaximal, characteristic, complemented
5C29×#393C211yesmaximal, characteristic, complemented
6C22×Q8×C29C2211yescharacteristic, complemented
7C22×C22⋊D29—21no—
8C2×C22⋊C4×C29—21no—
9C2×C22⋊C4×C29C2211yescharacteristic
10C2×#90784—22no—
11#11745292—21no—
12#11745292C2212yes—
13#11745248—22no—
14#11745244—22no—
15C29×#95—21no—
16C29×#95C2211yescharacteristic, complemented
17#11745183—22no—
18C22⋊#6597C2212yescomplemented
19C24×C29D411yescharacteristic
20C23×D29—21no—
21C2×Q8×C29—22no—
22C2×Q8×C29—42no—
23C22×C4×C29—21no—
24C22×C4×C29—21no—
25C22×C4×C29D411yescharacteristic
26C22×C4×C29C2311yescharacteristic
27C2×C22⋊D29—22no—
28C2×C22⋊D29—22no—
29C2×C22⋊D29—42no—
30C2×C22⋊D29—42no—
31C22×Dic29—21no—
32C2×D116—21no—
33C2×D116D412yes—
34C22⋊C4×C29—22no—
35C22⋊C4×C29—42no—
36#90784—44no—
37#90781—22no—
38#90781—22no—
39C4⋊Dic29—21no—
40C4⋊Dic29D412yes—
41C2×#6597—22no—
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—
52Q8×C29—24no—
53Q8×C29—42no—
54C2×C4×C29—22no—
55C2×C4×C29—21no—
56C2×C4×C29—41no—
57C2×C4×C29—41no—
58C2×C4×C29—41no—
59C2×C4×C29—41no—
60C2×C4×C29—41no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29C2×D412yes—
64C22⋊D29—44no—
65C22⋊D29—42no—
66C22⋊D29—42no—
67C2×Dic29—22no—
68C2×Dic29—42no—
69D116—42no—
70D116—81no—
71#6597—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—
89C4×C29—42no—
90C4×C29—81no—
91Dic29—42no—
92#534—291no—
93#448—292no—
94#393D2911yescharacteristic, complemented
95#327—292no—
96#323—291no—
97C2×C29—21no—
98C2×C29—21no—
99C2×C29—42no—
100C2×C29#45011yescharacteristic
101C2×C29#45511yescharacteristic
102C2×C29B(4,𝔽2)11yescharacteristic
103D29—82no—
104C22×Q8C2×D2911yescharacteristic, complemented
105C22×D4—581no—
106C2×SD16—582no—
107#123—582no—
108#121—292no—
109#121—581no—
110#120—582no—
111C2×C22⋊C4—21no—
112C2×C22⋊C4C2×D2911yescharacteristic
113#103—582no—
114C22⋊C8—292no—
115#95—21no—
116#95C2×D2911yescharacteristic, complemented
117C29#160111yescharacteristic, complemented, Sylow
118C24—581no—
119C24C22⋊D2911yescharacteristic
120C2×Q8—22no—
121C2×Q8—42no—
122C2×D4—292no—
123C2×D4—581no—
124C2×D4—582no—
125C2×D4—582no—
126C2×D4—1162no—
127C2×D4—1162no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—581no—
131C22×C4C22⋊D2911yescharacteristic
132C22×C4C22×D2911yescharacteristic
133SD16—1164no—
134C2×C8—582no—
135C4⋊C4—292no—
136C4⋊C4—581no—
137C22⋊C4—22no—
138C22⋊C4—42no—
139C22⋊C4—582no—
140C22⋊C4—582no—
141C23—21no—
142C23—21no—
143C23—41no—
144C23—41no—
145C23—582no—
146C23—1162no—
147C23—2321no—
148C23—2321no—
149C23#9078412yescomplemented
150C23C2×C22⋊D2911yescharacteristic
151Q8—24no—
152Q8—42no—
153D4—1162no—
154D4—1164no—
155D4—1162no—
156D4—1162no—
157D4—2321no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—582no—
168C2×C4—1162no—
169C2×C4D4×D2912yes—
170C8—1162no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—81no—
178C22—1162no—
179C22—1162no—
180C22—1162no—
181C22—2324no—
182C22#1174529911yescharacteristic
183C22C2×#9078411yescharacteristic
184C22#1174531111yescharacteristic
185C4—22no—
186C4—41no—
187C4—42no—
188C4—81no—
189C4—1162no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—2322no—
194C2#1427131311yescharacteristic
195C2#1427134011yescharacteristic
196C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#393C2
socleC22×C29#120
prime radical#14271725C2
hypercenter#393D29
hypocenterC29#1601
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #14271302C2semidirect
3. #14270896C2semidirect
4. #14270887C2semidirect
5. C29×#393C2semidirect
6. C22×Q8×C29C22semidirect
16. C29×#95C22semidirect
18. C22⋊#6597C22semidirect
46. C23×C29SD16semidirect
94. #393D29semidirect
104. C22×Q8C2×D29semidirect
116. #95C2×D29semidirect
117. C29#1601semidirect
149. C23#90784semidirect

Maximal subgroups

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

subgroupindex
#142717252
#142713022
#142708962
#142708872
C29×#3932
#160129