Finite Group Databasebeta

← #16818410

Subgroups — #16818410

Order 3712.

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

normal subgroups only

This group has 368 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#14271296C212yesmaximal, complemented
2#14271072C211yesmaximal, characteristic, complemented
3#14270897C212yesmaximal, complemented
4#14270887C211yesmaximal, characteristic, complemented
5C29×#534C211yesmaximal, characteristic, complemented
6C22×D4×C29—21no—
7C22×C22⋊D29—21no—
8C22×D116C2211yescharacteristic, complemented
9C29×#123—22no—
10C29×#121—21no—
11C29×#121C2212yes—
12C29×#120—22no—
13C2×C22⋊C4×C29C2211yescharacteristic
14C2×#90782—22no—
15C2×#90781—21no—
16#11745179C2211yescharacteristic, complemented
17C22⋊#6597C2212yescomplemented
18#11745157—22no—
19C24×C29—21no—
20C24×C29D411yescharacteristic
21C23×D29—21no—
22C2×D4×C29—22no—
23C2×D4×C29—22no—
24C2×D4×C29—21no—
25C2×D4×C29—42no—
26C2×D4×C29—42no—
27C2×D4×C29D412yescomplemented
28C22×C4×C29—21no—
29C22×C4×C29D411yescharacteristic
30C22×C4×C29C2311yescharacteristic
31C2×C22⋊D29—42no—
32C2×C22⋊D29—42no—
33C2×C22⋊D29—42no—
34C22×Dic29—21no—
35C2×D116—22no—
36C2×D116—42no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29D412yescomplemented
39C22⋊C4×C29—22no—
40C22⋊C4×C29—22no—
41C22⋊C4×C29—22no—
42#90782—44no—
43#90781—42no—
44C2×#6597—22no—
45C23×C29—21no—
46C23×C29—21no—
47C23×C29—22no—
48C23×C29—41no—
49C23×C29—41no—
50C23×C29—42no—
51C23×C29—81no—
52C23×C29—81no—
53C23×C29D812yescomplemented
54C23×C29C2×D411yescharacteristic
55C22×D29—22no—
56C22×D29—41no—
57C22×D29—41no—
58C22×D29—41no—
59C22×D29—41no—
60C22×D29—41no—
61C22×D29—41no—
62D4×C29—42no—
63D4×C29—44no—
64D4×C29—42no—
65D4×C29—42no—
66D4×C29—81no—
67C2×C4×C29—21no—
68C2×C4×C29—22no—
69C2×C4×C29—41no—
70C2×C4×C29—42no—
71C2×C4×C29—41no—
72C2×C4×C29C2×D412yes—
73C22⋊D29—48no—
74C2×Dic29—22no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77D116—24no—
78D116—42no—
79#6597—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—42no—
88C22×C29—42no—
89C22×C29—42no—
90C22×C29—81no—
91C22×C29—84no—
92C22×C29#12011yescharacteristic
93C22×C29C2×D811yescharacteristic
94C22×C29AGL(1,ℤ/8)11yescharacteristic
95C2×D29—42no—
96C2×D29—42no—
97C2×D29—42no—
98C2×D29—81no—
99C2×D29—81no—
100C2×D29—81no—
101C2×D29—81no—
102C4×C29—22no—
103C4×C29—42no—
104C4×C29—41no—
105Dic29—42no—
106#534D2911yescharacteristic, complemented
107#447—292no—
108#392—291no—
109#327—292no—
110#323—291no—
111C2×C29—21no—
112C2×C29—21no—
113C2×C29—42no—
114C2×C29—82no—
115C2×C29#44711yescharacteristic
116C2×C29#45311yescharacteristic
117C2×C29B(4,𝔽2)11yescharacteristic
118D29—82no—
119C22×D4—21no—
120C22×D4—291no—
121C22×D4—581no—
122C2×D8—582no—
123#123—22no—
124#121—21no—
125#121C2×D2912yes—
126#120—22no—
127C2×C22⋊C4—581no—
128C2×C22⋊C4C2×D2911yescharacteristic
129#102—582no—
130C22⋊C8—292no—
131#95—291no—
132C29#159511yescharacteristic, complemented, Sylow
133C24—21no—
134C24—581no—
135C24C22⋊D2911yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—21no—
139C2×D4—42no—
140C2×D4—42no—
141C2×D4—582no—
142C2×D4—1162no—
143C2×D4—1162no—
144C2×D4—1162no—
145C2×D4—1162no—
146C2×D4C22⋊D2912yescomplemented
147C22×C4—21no—
148C22×C4—581no—
149C22×C4C22⋊D2911yescharacteristic
150C22×C4C22×D2911yescharacteristic
151D8—1164no—
152C2×C8—582no—
153C4⋊C4—21no—
154C4⋊C4C22⋊D2912yescomplemented
155C22⋊C4—22no—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—1162no—
159C23—21no—
160C23—21no—
161C23—22no—
162C23—41no—
163C23—41no—
164C23—42no—
165C23—81no—
166C23—81no—
167C23—582no—
168C23—1161no—
169C23—1161no—
170C23—1161no—
171C23—1161no—
172C23—1161no—
173C23—1161no—
174C23#9078212yescomplemented
175C23C2×C22⋊D2911yescharacteristic
176D4—42no—
177D4—44no—
178D4—42no—
179D4—42no—
180D4—81no—
181D4—584no—
182D4—1162no—
183D4—1168no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—42no—
188C2×C4—41no—
189C2×C4—582no—
190C2×C4—1161no—
191C2×C4—1161no—
192C2×C4C2×C22⋊D2912yes—
193C8—1162no—
194C22—21no—
195C22—21no—
196C22—22no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—81no—
204C22—84no—
205C22—1162no—
206C22—1162no—
207C22—1162no—
208C22—2321no—
209C22—2321no—
210C22—2321no—
211C22—2321no—
212C22C2×#9078211yescharacteristic
213C22#1174529411yescharacteristic
214C22#1174531511yescharacteristic
215C4—22no—
216C4—42no—
217C4—41no—
218C4—1162no—
219C2—21no—
220C2—21no—
221C2—42no—
222C2—82no—
223C2—2322no—
224C2#1427129711yescharacteristic
225C2#1427133111yescharacteristic
226C2#1427135011yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#534C2
socleC22×C29#120
hypercenter#534D29
hypocenterC29#1595
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #14271296C2semidirect
2. #14271072C2semidirect
3. #14270897C2semidirect
4. #14270887C2semidirect
5. C29×#534C2semidirect
8. C22×D116C22semidirect
16. #11745179C22semidirect
17. C22⋊#6597C22semidirect
27. C2×D4×C29D4semidirect
38. C4⋊C4×C29D4semidirect
53. C23×C29D8semidirect
106. #534D29semidirect
132. C29#1595semidirect
146. C2×D4C22⋊D29semidirect
154. C4⋊C4C22⋊D29semidirect
174. C23#90782semidirect

Maximal subgroups

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

subgroupindex
#142712962
#142710722
#142708972
#142708872
C29×#5342
#159529