Finite Group Databasebeta

← #16818412

Subgroups — #16818412

Order 3712.

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

normal subgroups only

This group has 368 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, complemented
2#14271299C212yesmaximal, complemented
3#14271072C211yesmaximal, characteristic, complemented
4#14270898C212yesmaximal, complemented
5C29×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D29—21no—
7C22×C22⋊D29—21no—
8C22×D116C2211yescharacteristic, complemented
9C2×C22⋊C4×C29C2211yescharacteristic
10#11745292—21no—
11#11745292C2212yes—
12C2×#90781—21no—
13C2×D232—22no—
14#11745248—22no—
15#11745244—22no—
16C29×C22⋊C8C2212yescomplemented
17#11745179C2211yescharacteristic, complemented
18#11745169—22no—
19C24×C29D411yescharacteristic
20C23×D29—21no—
21C23×D29—21no—
22C22×C4×C29D411yescharacteristic
23C22×C4×C29C2311yescharacteristic
24C2×C22⋊D29—22no—
25C2×C22⋊D29—22no—
26C2×C22⋊D29—42no—
27C2×C22⋊D29—42no—
28C2×C22⋊D29—42no—
29C2×C22⋊D29—42no—
30C2×C22⋊D29—42no—
31C22×Dic29—21no—
32C22×Dic29—21no—
33C2×D116—22no—
34C2×D116—21no—
35C2×D116—42no—
36C2×D116D412yescomplemented
37C2×C8×C29—22no—
38C22⋊C4×C29—22no—
39#90781—22no—
40#90781—22no—
41#90781—42no—
42C4⋊Dic29—21no—
43C4⋊Dic29D412yescomplemented
44D232—44no—
45C23×C29—21no—
46C23×C29—21no—
47C23×C29—41no—
48C23×C29—41no—
49C23×C29D812yescomplemented
50C23×C29C2×D411yescharacteristic
51C22×D29—22no—
52C22×D29—22no—
53C22×D29—41no—
54C22×D29—41no—
55C22×D29—41no—
56C22×D29—42no—
57C22×D29—41no—
58C22×D29—41no—
59C22×D29—41no—
60C22×D29—81no—
61C22×D29—81no—
62C2×C4×C29—21no—
63C2×C4×C29—41no—
64C2×C4×C29—41no—
65C2×C4×C29C2×D412yes—
66C22⋊D29—44no—
67C22⋊D29—48no—
68C22⋊D29—42no—
69C22⋊D29—42no—
70C2×Dic29—22no—
71C2×Dic29—22no—
72C2×Dic29—41no—
73C2×Dic29—42no—
74C2×Dic29—41no—
75D116—24no—
76D116—42no—
77D116—42no—
78D116—81no—
79C8×C29—42no—
80#1595—291nomaximal, Sylow
81C22×C29—21no—
82C22×C29—21no—
83C22×C29—22no—
84C22×C29—42no—
85C22×C29—41no—
86C22×C29—41no—
87C22×C29—81no—
88C22×C29#12011yescharacteristic
89C22×C29C2×D811yescharacteristic
90C22×C29AGL(1,ℤ/8)11yescharacteristic
91C2×D29—42no—
92C2×D29—42no—
93C2×D29—42no—
94C2×D29—42no—
95C2×D29—42no—
96C2×D29—42no—
97C2×D29—81no—
98C2×D29—81no—
99C2×D29—84no—
100C2×D29—81no—
101C2×D29—81no—
102C4×C29—22no—
103C4×C29—41no—
104Dic29—42no—
105Dic29—42no—
106#534—291no—
107#447—292no—
108#392—291no—
109#327—292no—
110#323D2911yescharacteristic, complemented
111C2×C29—21no—
112C2×C29—21no—
113C2×C29—42no—
114C2×C29#44711yescharacteristic
115C2×C29#45311yescharacteristic
116C2×C29B(4,𝔽2)11yescharacteristic
117D29—82no—
118D29—82no—
119C22×D4—291no—
120C22×D4—581no—
121C22×D4—581no—
122C2×D8—582no—
123#123—582no—
124#121—292no—
125#121—581no—
126#120—582no—
127C2×C22⋊C4—581no—
128C2×C22⋊C4C2×D2911yescharacteristic
129#102—582no—
130C22⋊C8C2×D2912yescomplemented
131#95—291no—
132C29#159511yescharacteristic, complemented, Sylow
133C24—581no—
134C24—581no—
135C24D11611yescharacteristic
136C2×D4—292no—
137C2×D4—581no—
138C2×D4—582no—
139C2×D4—582no—
140C2×D4—582no—
141C2×D4—1162no—
142C2×D4—1162no—
143C2×D4—1162no—
144C2×D4—1162no—
145C2×D4—1162no—
146C2×D4—1162no—
147C22×C4—581no—
148C22×C4—581no—
149C22×C4D11611yescharacteristic
150C22×C4C22×D2911yescharacteristic
151D8—1164no—
152C2×C8—22no—
153C4⋊C4—292no—
154C4⋊C4—581no—
155C22⋊C4—22no—
156C22⋊C4—582no—
157C22⋊C4—582no—
158C22⋊C4—1162no—
159C23—21no—
160C23—21no—
161C23—41no—
162C23—41no—
163C23—582no—
164C23—582no—
165C23—1161no—
166C23—1161no—
167C23—1161no—
168C23—1162no—
169C23—1161no—
170C23—1161no—
171C23—1161no—
172C23—2321no—
173C23—2321no—
174C23D23212yescomplemented
175C23C2×D11611yescharacteristic
176D4—584no—
177D4—1162no—
178D4—1162no—
179D4—1164no—
180D4—1168no—
181D4—1162no—
182D4—1162no—
183D4—2321no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—582no—
188C2×C4—582no—
189C2×C4—1161no—
190C2×C4—1162no—
191C2×C4—1161no—
192C2×C4D4×D2912yes—
193C8—42no—
194C22—21no—
195C22—21no—
196C22—22no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22—81no—
201C22—1162no—
202C22—1162no—
203C22—1162no—
204C22—1162no—
205C22—1162no—
206C22—1162no—
207C22—2321no—
208C22—2321no—
209C22—2324no—
210C22—2321no—
211C22—2321no—
212C22#1174524411yescharacteristic
213C22C2×D23211yescharacteristic
214C22#1174527011yescharacteristic
215C4—22no—
216C4—41no—
217C4—1162no—
218C4—1162no—
219C2—21no—
220C2—21no—
221C2—42no—
222C2—2322no—
223C2—2322no—
224C2#1427129911yescharacteristic
225C2#1427133311yescharacteristic
226C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#323C2
socleC22×C29#120
hypercenter#323D29
hypocenterC29#1595
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
1. #14271725C2semidirect
2. #14271299C2semidirect
3. #14271072C2semidirect
4. #14270898C2semidirect
5. C29×#323C2semidirect
8. C22×D116C22semidirect
16. C29×C22⋊C8C22semidirect
17. #11745179C22semidirect
36. C2×D116D4semidirect
43. C4⋊Dic29D4semidirect
49. C23×C29D8semidirect
110. #323D29semidirect
130. C22⋊C8C2×D29semidirect
132. C29#1595semidirect
174. C23D232semidirect

Maximal subgroups

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

subgroupindex
#142717252
#142712992
#142710722
#142708982
C29×#3232
#159529