Finite Group Databasebeta

← #16819455

Subgroups — #16819455

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#14271179C212yesmaximal, complemented
3#14271160C212yesmaximal, complemented
4#14271137C211yesmaximal, characteristic, complemented
5C29×#408C211yesmaximal, characteristic, complemented
6C2×#41×C29C2211yescharacteristic
7#11745365—22no—
8#11745364—22no—
9#41×D29—24no—
10#11745362C412yescomplemented
11#11745359—22no—
12#11745359C412yescomplemented
13C2×#90805—22no—
14C2×#90805C2212yes—
15C2×M16×C29C2211yescharacteristic, complemented
16C22×C8×C29C2211yescharacteristic, complemented
17#11745288C2212yescomplemented
18C29×C22⋊C8—22no—
19#11745182—22no—
20#11745173—24no—
21#11745169—22no—
22#11745164—22no—
23#41×C29—22no—
24#41×C29—22no—
25C2×Q8×C29C2×C411yescharacteristic
26C2×D4×C29C2×C411yescharacteristic
27C2×D4×C29D412yes—
28C22×C4×C29D412yes—
29C22×C4×C29C2311yescharacteristic
30C2×C22⋊D29—24no—
31C2×C22⋊D29—22no—
32#90809—24no—
33Q8×D29—24no—
34#90807—28no—
35#90807—24no—
36D4×D29—28no—
37D4×D29—24no—
38#90805—24no—
39#90805—24no—
40#90805—24no—
41#90805—22no—
42#90805—22no—
43#90805C2×C414yes—
44#90805D414yes—
45C2×D116—22no—
46C2×D116D412yes—
47C2×C4×D29—24no—
48C2×C4×D29—22no—
49C2×Dic58—22no—
50C2×Dic58D412yes—
51M16×C29—22no—
52C2×C8×C29—22no—
53C2×C8×C29—21no—
54C2×C8×C29—21no—
55C22⋊Dic29—22no—
56C4⋊Dic29—22no—
57C4×Dic29—22no—
58C23×C29C22⋊C412yes—
59C23×C29C2×D411yescharacteristic
60C22×D29—24no—
61C22×D29—22no—
62Q8×C29—22no—
63D4×C29—24no—
64D4×C29—22no—
65C2×C4×C29—22no—
66C2×C4×C29—22no—
67C2×C4×C29C22⋊C412yes—
68C2×C4×C29C22×C411yescharacteristic
69C2×C4×C29C2×D412yes—
70C2×C4×C29C2×D412yes—
71C2×C4×C29C2×D411yescharacteristic
72C22⋊D29—28no—
73C22⋊D29—24no—
74C22⋊D29—24no—
75C2×Dic29—24no—
76C2×Dic29—22no—
77C2×Dic29—42no—
78D116—24no—
79D116—22no—
80D116C22⋊C414yes—
81C4×D29—28no—
82C4×D29—24no—
83C4×D29—24no—
84Dic58—24no—
85Dic58—22no—
86Dic58C22⋊C414yes—
87C8×C29—41no—
88C8×C29—41no—
89#1794—291nomaximal, Sylow
90C22×C29—22no—
91C22×C29—41no—
92C22×C29—42no—
93C22×C29C2×C22⋊C411yescharacteristic
94C22×C29#12012yes—
95C2×D29—24no—
96C2×D29—82no—
97C2×D29—84no—
98C4×C29—22no—
99C4×C29C2×C22⋊C412yes—
100C4×C29#12011yescharacteristic
101C4×C29#12011yescharacteristic
102Dic29—24no—
103Dic29—82no—
104#585—291no—
105#421—292no—
106#416—292no—
107#410—291no—
108#408D2911yescharacteristic, complemented
109C2×C29—22no—
110C2×C29—21no—
111C2×C29—42no—
112C2×C29#37911yescharacteristic
113D29—44no—
1142−1+4—292no—
1152−1+4—582no—
116H(5,𝔽2)—292no—
117H(5,𝔽2)—582no—
118H(5,𝔽2)—582no—
119C2×#41—292no—
120C2×#41—584no—
121C2×#41—582no—
122C2×#41C2×D2911yescharacteristic
123C2×M16C2×D2911yescharacteristic, complemented
124C22×C8C2×D2911yescharacteristic, complemented
125#117—292no—
126#104—584no—
127#103—582no—
128#102—582no—
129#99—582no—
130C22⋊C8—22no—
131C29#179411yescharacteristic, complemented, Sylow
132#41—22no—
133#41—22no—
134#41—294no—
135#41—294no—
136#41—584no—
137#41—584no—
138#41—584no—
139#41—588no—
140#41—584no—
141#41—584no—
142#41—582no—
143#41—582no—
144C2×Q8—292no—
145C2×Q8—582no—
146C2×Q8—584no—
147C2×Q8C4×D2911yescharacteristic
148C2×D4—292no—
149C2×D4—582no—
150C2×D4—584no—
151C2×D4—588no—
152C2×D4—584no—
153C2×D4—582no—
154C2×D4C4×D2911yescharacteristic
155C2×D4D11612yes—
156C22×C4—584no—
157C22×C4—582no—
158C22×C4C22⋊D2912yes—
159C22×C4C22×D2911yescharacteristic
160M16—22no—
161C2×C8—22no—
162C2×C8—21no—
163C2×C8—21no—
164C4⋊C4—582no—
165C22⋊C4—582no—
166C42—582no—
167C23—584no—
168C23—582no—
169C23#9078112yes—
170C23C2×D11611yescharacteristic
171Q8—22no—
172Q8—294no—
173Q8—584no—
174Q8—582no—
175D4—24no—
176D4—22no—
177D4—294no—
178D4—584no—
179D4—588no—
180D4—584no—
181D4—584no—
182D4—582no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—588no—
186C2×C4—584no—
187C2×C4—582no—
188C2×C4—584no—
189C2×C4—584no—
190C2×C4—1162no—
191C2×C4#9078112yes—
192C2×C4C2×C4×D2911yescharacteristic
193C2×C4D4×D2912yes—
194C2×C4D4×D2912yes—
195C2×C4C2×C22⋊D2911yescharacteristic
196C8—41no—
197C8—41no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—584no—
202C22—2322no—
203C22—2324no—
204C22#1174524412yes—
205C22C2×#9078111yescharacteristic
206C4—22no—
207C4—584no—
208C4—2322no—
209C4C22⋊C4×D2912yes—
210C4#1174529911yescharacteristic
211C4#1174529911yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—1164no—
216C2#1427101811yescharacteristic
subgroupG/H
centerC4#11745299
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#408C2
socleC2×C29#379
prime radical#14271999C2
cosocleC22×C4×C29C23
hypercenter#408D29
hypocenterC29#1794
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #14271179C2semidirect
3. #14271160C2semidirect
4. #14271137C2semidirect
5. C29×#408C2semidirect
10. #11745362C4semidirect
12. #11745359C4semidirect
15. C2×M16×C29C22semidirect
16. C22×C8×C29C22semidirect
17. #11745288C22semidirect
108. #408D29semidirect
123. C2×M16C2×D29semidirect
124. C22×C8C2×D29semidirect
131. C29#1794semidirect

Maximal subgroups

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

subgroupindex
#142719992
#142711792
#142711602
#142711372
C29×#4082
#179429