Finite Group Databasebeta

← #16819442

Subgroups — #16819442

Order 3712.

548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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#14271999C211yesmaximal, characteristic
2#14271147C211yesmaximal, characteristic, complemented
3#14271145C212yesmaximal, complemented
4#14271129C212yesmaximal, complemented
5C29×#408C211yesmaximal, characteristic, complemented
6C2×#41×C29C2211yescharacteristic
7#11745365—22no—
8#11745364—22no—
9#41×D29—24no—
10#11745362—21no—
11#11745359—21no—
12#11745359C414yes—
13C2×#90805—22no—
14C2×#90805C2212yes—
15C2×M16×C29C2211yescharacteristic, complemented
16C22×C8×C29C2211yescharacteristic, complemented
17C2×#90777C2212yescomplemented
18C29×C22⋊C8—22no—
19#11745184—21no—
20#11745181—21no—
21#11745172—22no—
22#11745171—22no—
23#11745168—24no—
24#41×C29—22no—
25#41×C29—22no—
26C2×Q8×C29D411yescharacteristic
27C2×D4×C29C2×C412yes—
28C2×D4×C29D411yescharacteristic
29C22×C4×C29D412yes—
30C22×C4×C29C2311yescharacteristic
31C2×C22⋊D29—24no—
32C2×C22⋊D29C2×C414yes—
33#90809—24no—
34Q8×D29—24no—
35#90807—24no—
36#90807—28no—
37D4×D29—24no—
38D4×D29—28no—
39#90805—24no—
40#90805—24no—
41#90805—24no—
42#90805—22no—
43#90805—22no—
44#90805—22no—
45#90805—22no—
46C2×D116—22no—
47C2×D116D412yes—
48C2×C4×D29—24no—
49C2×C4×D29D414yes—
50C2×Dic58—22no—
51C2×Dic58D412yes—
52M16×C29—22no—
53C2×C8×C29—22no—
54C2×C8×C29—21no—
55C2×C8×C29—21no—
56#90777—22no—
57#90777—22no—
58C2×#6597—22no—
59C23×C29C22⋊C412yes—
60C23×C29C22×C411yescharacteristic
61C22×D29—24no—
62C22×D29C22⋊C414yes—
63Q8×C29—22no—
64D4×C29—24no—
65D4×C29—22no—
66C2×C4×C29—22no—
67C2×C4×C29—22no—
68C2×C4×C29C22⋊C412yes—
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29C2×D412yes—
71C2×C4×C29C2×D412yes—
72C2×C4×C29C2×D411yescharacteristic
73C22⋊D29—28no—
74C22⋊D29—24no—
75C22⋊D29—24no—
76C2×Dic29—24no—
77C2×Dic29C22⋊C414yes—
78D116—24no—
79D116—22no—
80D116—22no—
81C4×D29—28no—
82C4×D29—24no—
83C4×D29—24no—
84Dic58—24no—
85Dic58—22no—
86Dic58—22no—
87C8×C29—41no—
88C8×C29—41no—
89#6597—42no—
90#1791—291nomaximal, Sylow
91C22×C29—22no—
92C22×C29—41no—
93C22×C29—42no—
94C22×C29C2×C22⋊C411yescharacteristic
95C22×C29C2×C22⋊C412yes—
96C2×D29—24no—
97C2×D29—44no—
98C2×D29—84no—
99C4×C29—22no—
100C4×C29#12011yescharacteristic
101C4×C29#12011yescharacteristic
102C4×C29#12012yes—
103Dic29—24no—
104#585—291no—
105#413—291no—
106#413—292no—
107#408—292no—
108#408D2911yescharacteristic, complemented
109C2×C29—22no—
110C2×C29—21no—
111C2×C29—42no—
112C2×C29#37911yescharacteristic
113D29—44no—
1142−1+4—582no—
1152−1+4—581no—
116H(5,𝔽2)—294no—
117H(5,𝔽2)—582no—
118H(5,𝔽2)—581no—
119C2×#41—292no—
120C2×#41—584no—
121C2×#41—582no—
122C2×#41C2×D2911yescharacteristic
123C2×M16—292no—
124C2×M16C2×D2911yescharacteristic, complemented
125C22×C8C2×D2911yescharacteristic, complemented
126#101—582no—
127#101—581no—
128#100—582no—
129#100—581no—
130C22⋊C8—22no—
131C22⋊C8—584no—
132C29#179111yescharacteristic, complemented, Sylow
133#41—22no—
134#41—22no—
135#41—584no—
136#41—584no—
137#41—588no—
138#41—584no—
139#41—584no—
140#41—584no—
141#41—582no—
142#41—582no—
143#41—582no—
144#41—582no—
145C2×Q8—292no—
146C2×Q8—582no—
147C2×Q8—584no—
148C2×Q8D11611yescharacteristic
149C2×D4—294no—
150C2×D4—292no—
151C2×D4—582no—
152C2×D4—588no—
153C2×D4—584no—
154C2×D4—584no—
155C2×D4C4×D2912yes—
156C2×D4D11611yescharacteristic
157C22×C4—294no—
158C22×C4—584no—
159C22×C4C22⋊D2912yes—
160C22×C4C22×D2911yescharacteristic
161M16—22no—
162M16—582no—
163M16—582no—
164C2×C8—22no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—582no—
168C23—294no—
169C23—584no—
170C23#9078112yes—
171C23C2×C4×D2911yescharacteristic
172Q8—22no—
173Q8—584no—
174Q8—582no—
175Q8—582no—
176D4—24no—
177D4—22no—
178D4—584no—
179D4—588no—
180D4—584no—
181D4—584no—
182D4—582no—
183D4—582no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—294no—
187C2×C4—588no—
188C2×C4—584no—
189C2×C4—584no—
190C2×C4—584no—
191C2×C4#9078112yes—
192C2×C4C2×D11611yescharacteristic
193C2×C4D4×D2912yes—
194C2×C4D4×D2912yes—
195C2×C4C2×C22⋊D2911yescharacteristic
196C8—41no—
197C8—41no—
198C8—1162no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—584no—
203C22—1164no—
204C22—2324no—
205C22C22⋊C4×D2912yes—
206C22C2×#9078111yescharacteristic
207C4—22no—
208C4—584no—
209C4#1174524412yes—
210C4#1174529911yescharacteristic
211C4#1174529911yescharacteristic
212C2—21no—
213C2—22no—
214C2—42no—
215C2—1164no—
216C2#1427101811yescharacteristic
subgroupG/H
centerC4#11745299
commutatorC23×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#408C2
socleC2×C29#379
prime radical#14271999C2
cosocleC22×C4×C29C23
hypercenter#408D29
hypocenterC29#1791
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #14271147C2semidirect
3. #14271145C2semidirect
4. #14271129C2semidirect
5. C29×#408C2semidirect
15. C2×M16×C29C22semidirect
16. C22×C8×C29C22semidirect
17. C2×#90777C22semidirect
108. #408D29semidirect
124. C2×M16C2×D29semidirect
125. C22×C8C2×D29semidirect
132. C29#1791semidirect

Maximal subgroups

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

subgroupindex
#142719992
#142711472
#142711452
#142711292
C29×#4082
#179129