Finite Group Databasebeta

← #17994546

Subgroups — #17994546

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#14557517C211yesmaximal, characteristic, complemented
3#14557515C212yesmaximal, complemented
4#14557499C212yesmaximal, complemented
5C37×#408C211yesmaximal, characteristic, complemented
6#11924584—21no—
7#11924583—22no—
8#11924582—22no—
9#11924581—21no—
10#11924581C414yes—
11C2×#10596962—22no—
12C2×#10596962C2212yes—
13#41×D37—24no—
14C2×#10596934C2212yescomplemented
15#11924455—21no—
16#11924454—22no—
17#11924453—21no—
18#11924452—22no—
19#11924448—24no—
20C2×#41×C37C2211yescharacteristic
21C2×M16×C37C2211yescharacteristic, complemented
22C22×C8×C37C2211yescharacteristic, complemented
23C22⋊C8×C37—22no—
24#41×C37—22no—
25#41×C37—22no—
26C2×Q8×C37D411yescharacteristic
27C2×D4×C37C2×C412yes—
28C2×D4×C37D411yescharacteristic
29C22×C4×C37D412yes—
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—24no—
32C2×C22⋊D37C2×C414yes—
33#10596966—24no—
34Q8×D37—24no—
35#10596964—24no—
36#10596964—28no—
37D4×D37—24no—
38D4×D37—28no—
39#10596962—24no—
40#10596962—24no—
41#10596962—24no—
42#10596962—22no—
43#10596962—22no—
44#10596962—22no—
45#10596962—22no—
46C2×D148—22no—
47C2×D148D412yes—
48C2×C4×D37—24no—
49C2×C4×D37D414yes—
50C2×Dic74—22no—
51C2×Dic74D412yes—
52M16×C37—22no—
53C2×C8×C37—21no—
54C2×C8×C37—21no—
55C2×C8×C37—22no—
56#10596934—22no—
57#10596934—22no—
58C2×#64436—22no—
59C23×C37C22⋊C412yes—
60C23×C37C22×C411yescharacteristic
61C22×D37—24no—
62C22×D37C22⋊C414yes—
63Q8×C37—22no—
64D4×C37—24no—
65D4×C37—22no—
66C2×C4×C37—22no—
67C2×C4×C37—22no—
68C2×C4×C37C22⋊C412yes—
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D412yes—
71C2×C4×C37C2×D412yes—
72C2×C4×C37C2×D411yescharacteristic
73C22⋊D37—28no—
74C22⋊D37—24no—
75C22⋊D37—24no—
76C2×Dic37—24no—
77C2×Dic37C22⋊C414yes—
78D148—24no—
79D148—22no—
80D148—22no—
81C4×D37—28no—
82C4×D37—24no—
83C4×D37—24no—
84Dic74—24no—
85Dic74—22no—
86Dic74—22no—
87C8×C37—41no—
88C8×C37—41no—
89#64436—42no—
90C22×C37—22no—
91C22×C37—41no—
92C22×C37—42no—
93C22×C37C2×C22⋊C412yes—
94C22×C37C2×C22⋊C411yescharacteristic
95C2×D37—24no—
96C2×D37—44no—
97C2×D37—84no—
98C4×C37—22no—
99C4×C37#12011yescharacteristic
100C4×C37#12011yescharacteristic
101C4×C37#12012yes—
102Dic37—24no—
103#1791—371nomaximal, Sylow
104C2×C37—22no—
105C2×C37—21no—
106C2×C37—42no—
107C2×C37#37911yescharacteristic
108D37—44no—
109#585—371no—
110#413—371no—
111#413—372no—
112#408—372no—
113#408D3711yescharacteristic, complemented
114C37#179111yescharacteristic, complemented, Sylow
1152−1+4—742no—
1162−1+4—741no—
117H(5,𝔽2)—374no—
118H(5,𝔽2)—742no—
119H(5,𝔽2)—741no—
120C2×#41—372no—
121C2×#41—744no—
122C2×#41—742no—
123C2×#41C2×D3711yescharacteristic
124C2×M16—372no—
125C2×M16C2×D3711yescharacteristic, complemented
126C22×C8C2×D3711yescharacteristic, complemented
127#101—742no—
128#101—741no—
129#100—742no—
130#100—741no—
131C22⋊C8—22no—
132C22⋊C8—744no—
133#41—22no—
134#41—22no—
135#41—744no—
136#41—744no—
137#41—748no—
138#41—744no—
139#41—744no—
140#41—744no—
141#41—742no—
142#41—742no—
143#41—742no—
144#41—742no—
145C2×Q8—372no—
146C2×Q8—742no—
147C2×Q8—744no—
148C2×Q8D14811yescharacteristic
149C2×D4—374no—
150C2×D4—372no—
151C2×D4—742no—
152C2×D4—748no—
153C2×D4—744no—
154C2×D4—744no—
155C2×D4C4×D3712yes—
156C2×D4D14811yescharacteristic
157C22×C4—374no—
158C22×C4—744no—
159C22×C4C22⋊D3712yes—
160C22×C4C22×D3711yescharacteristic
161M16—22no—
162M16—742no—
163M16—742no—
164C2×C8—22no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—742no—
168C23—374no—
169C23—744no—
170C23#1059693812yes—
171C23C2×C4×D3711yescharacteristic
172Q8—22no—
173Q8—744no—
174Q8—742no—
175Q8—742no—
176D4—24no—
177D4—22no—
178D4—744no—
179D4—748no—
180D4—744no—
181D4—744no—
182D4—742no—
183D4—742no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—374no—
187C2×C4—748no—
188C2×C4—744no—
189C2×C4—744no—
190C2×C4—744no—
191C2×C4#1059693812yes—
192C2×C4C2×D14811yescharacteristic
193C2×C4D4×D3712yes—
194C2×C4D4×D3712yes—
195C2×C4C2×C22⋊D3711yescharacteristic
196C8—41no—
197C8—41no—
198C8—1482no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—2964no—
203C22—744no—
204C22—1484no—
205C22C22⋊C4×D3712yes—
206C22C2×#1059693811yescharacteristic
207C4—22no—
208C4—744no—
209C4#1192450411yescharacteristic
210C4#1192450411yescharacteristic
211C4#1192450612yes—
212C2—21no—
213C2—22no—
214C2—42no—
215C2—1484no—
216C2#1455738811yescharacteristic
subgroupG/H
centerC4#11924504
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#408C2
socleC2×C37#379
prime radical#14558369C2
cosocleC22×C4×C37C23
hypercenter#408D37
hypocenterC37#1791
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #14557517C2semidirect
3. #14557515C2semidirect
4. #14557499C2semidirect
5. C37×#408C2semidirect
14. C2×#10596934C22semidirect
21. C2×M16×C37C22semidirect
22. C22×C8×C37C22semidirect
113. #408D37semidirect
114. C37#1791semidirect
125. C2×M16C2×D37semidirect
126. C22×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583692
#145575172
#145575152
#145574992
C37×#4082
#179137