Finite Group Databasebeta

← #17994559

Subgroups — #17994559

Order 4736.

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#14558369C211yesmaximal, characteristic
2#14557549C212yesmaximal, complemented
3#14557530C212yesmaximal, complemented
4#14557507C211yesmaximal, characteristic, complemented
5C37×#408C211yesmaximal, characteristic, complemented
6#11924584C412yescomplemented
7#11924583—22no—
8#11924582—22no—
9#11924581—22no—
10#11924581C412yescomplemented
11C2×#10596962—22no—
12C2×#10596962C2212yes—
13#41×D37—24no—
14#11924495C2212yescomplemented
15#11924462—24no—
16#11924461—22no—
17#11924458—22no—
18#11924451—22no—
19C2×#41×C37C2211yescharacteristic
20C2×M16×C37C2211yescharacteristic, complemented
21C22×C8×C37C2211yescharacteristic, complemented
22C22⋊C8×C37—22no—
23#41×C37—22no—
24#41×C37—22no—
25C2×Q8×C37C2×C411yescharacteristic
26C2×D4×C37C2×C411yescharacteristic
27C2×D4×C37D412yes—
28C22×C4×C37D412yes—
29C22×C4×C37C2311yescharacteristic
30C2×C22⋊D37—24no—
31C2×C22⋊D37—22no—
32#10596966—24no—
33Q8×D37—24no—
34#10596964—28no—
35#10596964—24no—
36D4×D37—28no—
37D4×D37—24no—
38#10596962—24no—
39#10596962—24no—
40#10596962—24no—
41#10596962—22no—
42#10596962—22no—
43#10596962C2×C414yes—
44#10596962D414yes—
45C2×D148—22no—
46C2×D148D412yes—
47C2×C4×D37—24no—
48C2×C4×D37—22no—
49C2×Dic74—22no—
50C2×Dic74D412yes—
51M16×C37—22no—
52C2×C8×C37—21no—
53C2×C8×C37—21no—
54C2×C8×C37—22no—
55C22⋊Dic37—22no—
56C4⋊Dic37—22no—
57C4×Dic37—22no—
58C23×C37C22⋊C412yes—
59C23×C37C2×D411yescharacteristic
60C22×D37—24no—
61C22×D37—22no—
62Q8×C37—22no—
63D4×C37—24no—
64D4×C37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—22no—
67C2×C4×C37C22⋊C412yes—
68C2×C4×C37C22×C411yescharacteristic
69C2×C4×C37C2×D412yes—
70C2×C4×C37C2×D412yes—
71C2×C4×C37C2×D411yescharacteristic
72C22⋊D37—28no—
73C22⋊D37—24no—
74C22⋊D37—24no—
75C2×Dic37—24no—
76C2×Dic37—22no—
77C2×Dic37—42no—
78D148—24no—
79D148—22no—
80D148C22⋊C414yes—
81C4×D37—28no—
82C4×D37—24no—
83C4×D37—24no—
84Dic74—24no—
85Dic74—22no—
86Dic74C22⋊C414yes—
87C8×C37—41no—
88C8×C37—41no—
89C22×C37—22no—
90C22×C37—41no—
91C22×C37—42no—
92C22×C37C2×C22⋊C411yescharacteristic
93C22×C37#12012yes—
94C2×D37—24no—
95C2×D37—82no—
96C2×D37—84no—
97C4×C37—22no—
98C4×C37C2×C22⋊C412yes—
99C4×C37#12011yescharacteristic
100C4×C37#12011yescharacteristic
101Dic37—24no—
102Dic37—82no—
103#1794—371nomaximal, Sylow
104C2×C37—22no—
105C2×C37—21no—
106C2×C37—42no—
107C2×C37#37911yescharacteristic
108D37—44no—
109#585—371no—
110#421—372no—
111#416—372no—
112#410—371no—
113#408D3711yescharacteristic, complemented
114C37#179411yescharacteristic, complemented, Sylow
1152−1+4—372no—
1162−1+4—742no—
117H(5,𝔽2)—372no—
118H(5,𝔽2)—742no—
119H(5,𝔽2)—742no—
120C2×#41—372no—
121C2×#41—744no—
122C2×#41—742no—
123C2×#41C2×D3711yescharacteristic
124C2×M16C2×D3711yescharacteristic, complemented
125C22×C8C2×D3711yescharacteristic, complemented
126#117—372no—
127#104—744no—
128#103—742no—
129#102—742no—
130#99—742no—
131C22⋊C8—22no—
132#41—22no—
133#41—22no—
134#41—374no—
135#41—374no—
136#41—744no—
137#41—744no—
138#41—744no—
139#41—748no—
140#41—744no—
141#41—744no—
142#41—742no—
143#41—742no—
144C2×Q8—372no—
145C2×Q8—742no—
146C2×Q8—744no—
147C2×Q8C4×D3711yescharacteristic
148C2×D4—372no—
149C2×D4—742no—
150C2×D4—744no—
151C2×D4—748no—
152C2×D4—744no—
153C2×D4—742no—
154C2×D4C4×D3711yescharacteristic
155C2×D4D14812yes—
156C22×C4—744no—
157C22×C4—742no—
158C22×C4C22⋊D3712yes—
159C22×C4C22×D3711yescharacteristic
160M16—22no—
161C2×C8—22no—
162C2×C8—21no—
163C2×C8—21no—
164C4⋊C4—742no—
165C22⋊C4—742no—
166C42—742no—
167C23—744no—
168C23—742no—
169C23#1059693812yes—
170C23C2×D14811yescharacteristic
171Q8—22no—
172Q8—374no—
173Q8—744no—
174Q8—742no—
175D4—24no—
176D4—22no—
177D4—374no—
178D4—744no—
179D4—748no—
180D4—744no—
181D4—744no—
182D4—742no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—748no—
186C2×C4—744no—
187C2×C4—742no—
188C2×C4—744no—
189C2×C4—744no—
190C2×C4—1482no—
191C2×C4#1059693812yes—
192C2×C4C2×C4×D3711yescharacteristic
193C2×C4D4×D3712yes—
194C2×C4D4×D3712yes—
195C2×C4C2×C22⋊D3711yescharacteristic
196C8—41no—
197C8—41no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—2962no—
202C22—2964no—
203C22—744no—
204C22C2×#1059693811yescharacteristic
205C22#1192450612yes—
206C4—22no—
207C4—2962no—
208C4—744no—
209C4C22⋊C4×D3712yes—
210C4#1192450411yescharacteristic
211C4#1192450411yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—1484no—
216C2#1455738811yescharacteristic
subgroupG/H
centerC4#11924504
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#408C2
socleC2×C37#379
prime radical#14558369C2
cosocleC22×C4×C37C23
hypercenter#408D37
hypocenterC37#1794
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #14557549C2semidirect
3. #14557530C2semidirect
4. #14557507C2semidirect
5. C37×#408C2semidirect
6. #11924584C4semidirect
10. #11924581C4semidirect
14. #11924495C22semidirect
20. C2×M16×C37C22semidirect
21. C22×C8×C37C22semidirect
113. #408D37semidirect
114. C37#1794semidirect
124. C2×M16C2×D37semidirect
125. C22×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583692
#145575492
#145575302
#145575072
C37×#4082
#179437