Finite Group Databasebeta

← #16819445

Subgroups — #16819445

Order 3712.

620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#11745359C211yesmaximal, characteristic
2C2×#11745153C212yesmaximal, complemented
3#14271162C212yesmaximal, complemented
4C2×#11745181C211yesmaximal, characteristic, complemented
5C29×#390C211yesmaximal, characteristic, complemented
6C22×D4×C29C2211yescharacteristic
7C22×C22⋊D29—22no—
8#11745359—22no—
9#11745359—24no—
10#11745359C414yescomplemented
11C2×#90807—22no—
12C2×D4×D29—22no—
13C2×#90805C2212yes—
14C2×C4⋊C4×C29C2211yescharacteristic, complemented
15C2×C22⋊C4×C29—22no—
16C2×C42×C29C2211yescharacteristic, complemented
17C2×#90777C2212yescomplemented
18#11745181—22no—
19#11745158—22no—
20#11745157—22no—
21#11745153—24no—
22C24×C29D412yes—
23C23×D29—22no—
24C2×D4×C29—22no—
25C2×D4×C29—22no—
26C2×D4×C29C2×C412yes—
27C2×D4×C29D412yes—
28C22×C4×C29—21no—
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C2×C22⋊D29—24no—
32C2×C22⋊D29—28no—
33C2×C22⋊D29—28no—
34C2×C22⋊D29—22no—
35C22×Dic29—22no—
36#90807—28no—
37#90807—28no—
38D4×D29—28no—
39D4×D29—28no—
40#90805—22no—
41#90805—22no—
42#90805C2×C414yes—
43#90805D414yes—
44C2×D116D412yes—
45C2×C4×D29—22no—
46C2×Dic58D412yes—
47C4⋊C4×C29—22no—
48C22⋊C4×C29—44no—
49C42×C29—22no—
50#90777—22no—
51#90777—22no—
52C2×#6597—22no—
53C23×C29—22no—
54C23×C29—22no—
55C23×C29—42no—
56C23×C29—42no—
57C23×C29C22⋊C414yes—
58C23×C29C2×D411yescharacteristic
59C22×D29—22no—
60C22×D29—28no—
61C22×D29—82no—
62C22×D29—82no—
63D4×C29—24no—
64D4×C29—24no—
65C2×C4×C29—22no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29—42no—
69C2×C4×C29—41no—
70C2×C4×C29C22×C411yescharacteristic
71C2×C4×C29C2×D411yescharacteristic
72C2×C4×C29C2×D412yes—
73C2×C4×C29C2×D412yes—
74C22⋊D29—216no—
75C22⋊D29—24no—
76C22⋊D29—24no—
77C2×Dic29—28no—
78C2×Dic29—22no—
79D116—22no—
80D116C22⋊C414yescomplemented
81C4×D29—24no—
82C4×D29—24no—
83Dic58—22no—
84Dic58C22⋊C414yescomplemented
85#6597—42no—
86#1792—291nomaximal, Sylow
87C22×C29—21no—
88C22×C29—21no—
89C22×C29—24no—
90C22×C29—44no—
91C22×C29—42no—
92C22×C29—42no—
93C22×C29—82no—
94C22×C29C2×C22⋊C411yescharacteristic
95C22×C29#12011yescharacteristic
96C22×C29#12011yescharacteristic
97C2×D29—24no—
98C2×D29—42no—
99C2×D29—42no—
100C2×D29—88no—
101C4×C29—42no—
102C4×C29—81no—
103C4×C29C2×C22⋊C412yes—
104C4×C29#12012yes—
105Dic29—24no—
106C2×H(5,𝔽2)—291no—
107C2×#104—292no—
108#417—292no—
109C2×#100—291no—
110#390D2911yescharacteristic, complemented
111C2×C29—21no—
112C2×C29—21no—
113C2×C29—44no—
114C2×C29#37911yescharacteristic
115C2×C29#45311yescharacteristic
116C2×C29#45511yescharacteristic
117D29—44no—
118H(5,𝔽2)—294no—
119H(5,𝔽2)—584no—
120H(5,𝔽2)—582no—
121C2×#41—292no—
122C2×#41—582no—
123C22×D4—582no—
124C22×D4—582no—
125C22×D4C2×D2911yescharacteristic
126C2×M16—292no—
127C2×C4⋊C4C2×D2911yescharacteristic, complemented
128C2×C22⋊C4—22no—
129C2×C42C2×D2911yescharacteristic, complemented
130#104—584no—
131#103—582no—
132#102—582no—
133#100—582no—
134C29#179211yescharacteristic, complemented, Sylow
135C24—582no—
136C24C22⋊D2912yes—
137#41—294no—
138#41—294no—
139#41—588no—
140#41—588no—
141#41—582no—
142#41—582no—
143C2×Q8—292no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—292no—
147C2×D4—588no—
148C2×D4—588no—
149C2×D4—584no—
150C2×D4—588no—
151C2×D4—588no—
152C2×D4—582no—
153C2×D4C4×D2912yes—
154C2×D4D11612yes—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—582no—
158C22×C4—582no—
159C22×C4C22×D2911yescharacteristic
160M16—582no—
161M16—582no—
162C2×C8—582no—
163C4⋊C4—22no—
164C22⋊C4—44no—
165C42—22no—
166C23—22no—
167C23—22no—
168C23—42no—
169C23—42no—
170C23—588no—
171C23—582no—
172C23—2322no—
173C23—2322no—
174C23#9078114yes—
175C23C2×C22⋊D2911yescharacteristic
176Q8—294no—
177Q8—582no—
178D4—24no—
179D4—24no—
180D4—294no—
181D4—5816no—
182D4—584no—
183D4—584no—
184D4—582no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4—588no—
191C2×C4—582no—
192C2×C4—584no—
193C2×C4—584no—
194C2×C4C2×C4×D2911yescharacteristic
195C2×C4C2×D11611yescharacteristic
196C2×C4D4×D2912yes—
197C2×C4D4×D2912yes—
198C8—1162no—
199C22—21no—
200C22—21no—
201C22—24no—
202C22—44no—
203C22—42no—
204C22—42no—
205C22—82no—
206C22—584no—
207C22—1162no—
208C22—1162no—
209C22—2328no—
210C22C2×#9078111yescharacteristic
211C22#1174529911yescharacteristic
212C22#1174529911yescharacteristic
213C4—42no—
214C4—81no—
215C4—584no—
216C4C22⋊C4×D2912yes—
217C4#1174524412yes—
218C2—21no—
219C2—21no—
220C2—44no—
221C2—1164no—
222C2#1427101811yescharacteristic
223C2#1427133011yescharacteristic
224C2#1427134011yescharacteristic
subgroupG/H
centerC22#11745299
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#390C2
socleC22×C29#120
prime radicalC2×#11745359C2
cosocleC22×C4×C29C23
hypercenter#390D29
hypocenterC29#1792
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#11745153C2semidirect
3. #14271162C2semidirect
4. C2×#11745181C2semidirect
5. C29×#390C2semidirect
10. #11745359C4semidirect
14. C2×C4⋊C4×C29C22semidirect
16. C2×C42×C29C22semidirect
17. C2×#90777C22semidirect
80. D116C22⋊C4semidirect
84. Dic58C22⋊C4semidirect
110. #390D29semidirect
127. C2×C4⋊C4C2×D29semidirect
129. C2×C42C2×D29semidirect
134. C29#1792semidirect

Maximal subgroups

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

subgroupindex
C2×#117453592
C2×#117451532
#142711622
C2×#117451812
C29×#3902
#179229