Finite Group Databasebeta

← #18004888

Subgroups — #18004888

Order 4736.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#14558138C211yesmaximal, characteristic
2#14558010C211yesmaximal, characteristic, complemented
3#14557858C212yesmaximal, complemented
4#14557841C212yesmaximal, complemented
5#14557734C212yesmaximal, complemented
6#14557674C212yesmaximal, complemented
7#14557635C212yesmaximal, complemented
8C4×#10596930C212yesmaximal, complemented
9C37×#433C211yesmaximal, characteristic, complemented
10C22×Dic74C2211yescharacteristic
11C2×#10596930C2212yes—
12C2×#10596930C2212yes—
13#11924533C2211yescharacteristic
14#11924528C2211yescharacteristic
15#11924521—22no—
16#11924510C2212yes—
17#11924509—22no—
18C4×Dic74C2212yes—
19C4×Dic74C2212yes—
20#11924501—22no—
21C4×D148C2212yes—
22#11924495C2211yescharacteristic
23#11924492—22no—
24#11924470C2212yes—
25#11924468C2212yes—
26#11924461C2212yes—
27#11924461C2212yes—
28#11924458C2212yes—
29#11924458C2212yes—
30#117×C37C2211yescharacteristic
31C4⋊C8×C37C2212yes—
32C22⋊C8×C37C2212yes—
33#97×C37C2211yescharacteristic
34C4×C8×C37C2211yescharacteristic
35C22×C4×C37C2311yescharacteristic
36C2×C22⋊D37—22no—
37C22×Dic37—21no—
38C2×D148—22no—
39C2×D148C2312yes—
40C2×C4×D37—22no—
41C2×Dic74—21no—
42C2×Dic74—24no—
43C2×Dic74C2312yes—
44C2×C8×C37C2312yes—
45C2×C8×C37C2312yes—
46C4⋊C4×C37D412yes—
47C22⋊C4×C37D412yes—
48C42×C37C2311yescharacteristic
49C42×C37C2311yescharacteristic
50C22⋊Dic37—21no—
51#10596938—22no—
52#10596938—22no—
53C4⋊Dic37C2312yes—
54C4⋊Dic37C2312yes—
55#10596936—22no—
56#10596936—22no—
57#10596936—22no—
58C4×Dic37—22no—
59C4×Dic37—22no—
60C4×Dic37—21no—
61#10596930—24no—
62#10596930—24no—
63C23×C37C2×D411yescharacteristic
64C22×D37—22no—
65C2×C4×C37—22no—
66C2×C4×C37C2×D412yes—
67C2×C4×C37C2×D412yes—
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37C2411yescharacteristic
70C22⋊D37—82no—
71C2×Dic37—24no—
72C2×Dic37—22no—
73C2×Dic37—22no—
74C2×Dic37—22no—
75D148—22no—
76D148—22no—
77D148—82no—
78C4×D37—82no—
79Dic74—24no—
80Dic74—22no—
81Dic74#4114yes—
82C8×C37—22no—
83C8×C37—22no—
84C22×C37—21no—
85C22×C37—22no—
86C22×C37C22×D411yescharacteristic
87C2×D37—42no—
88C2×D37—42no—
89C2×D37—42no—
90C4×C37—21no—
91C4×C37—22no—
92C4×C37—22no—
93C4×C37C2×#4112yes—
94Dic37—24no—
95Dic37—42no—
96Dic37—42no—
97#3126—371nomaximal, Sylow
98C2×C37—41no—
99C2×C37#52511yescharacteristic
100C2×C37#57712yes—
101D37—82no—
102#540—371no—
103#519—371no—
104#482—372no—
105#479—372no—
106#460—372no—
107#448—372no—
108#440—372no—
109C4×SD16—372no—
110#433D3711yescharacteristic, complemented
111C37#312611yescharacteristic, complemented, Sylow
112C22×Q8—371no—
113C2×SD16—372no—
114C2×SD16—372no—
115#127—371no—
116#125—371no—
117#123—742no—
118#121—372no—
119#121—742no—
120C4×Q8—372no—
121C4×Q8—372no—
122C4×Q8—742no—
123C4×D4—372no—
124#117—371no—
125#117—742no—
126#117C2×D3711yescharacteristic
127#107—372no—
128#106—372no—
129C4⋊C8C2×D3712yes—
130#103—372no—
131#103—372no—
132#102—372no—
133#102—372no—
134C22⋊C8C2×D3712yes—
135#97C2×D3711yescharacteristic
136C4×C8C2×D3711yescharacteristic
137C2×Q8—372no—
138C2×Q8—744no—
139C2×Q8—741no—
140C2×D4—372no—
141C2×D4—742no—
142C2×D4—742no—
143C22×C4—742no—
144C22×C4—741no—
145C22×C4C22×D3711yescharacteristic
146SD16—744no—
147SD16—744no—
148C2×C8C22×D3712yes—
149C2×C8C22×D3712yes—
150C4⋊C4—372no—
151C4⋊C4—372no—
152C4⋊C4—742no—
153C4⋊C4—742no—
154C4⋊C4—742no—
155C4⋊C4D14812yes—
156C22⋊C4—741no—
157C22⋊C4—742no—
158C22⋊C4—742no—
159C22⋊C4D14812yes—
160C42—741no—
161C42—742no—
162C42—742no—
163C42C22×D3711yescharacteristic
164C42C22×D3711yescharacteristic
165C23—742no—
166C23C2×D14811yescharacteristic
167Q8—374no—
168Q8—744no—
169Q8—742no—
170D4—2962no—
171D4—2962no—
172D4—742no—
173D4—742no—
174C2×C4—22no—
175C2×C4—2962no—
176C2×C4—744no—
177C2×C4—742no—
178C2×C4—742no—
179C2×C4—742no—
180C2×C4C2×D14812yes—
181C2×C4C2×D14812yes—
182C2×C4C2×D14811yescharacteristic
183C2×C4C23×D3711yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—1482no—
189C22—1482no—
190C22—1482no—
191C22C22×D14811yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—744no—
196C4—1482no—
197C4—1482no—
198C4#41×D3712yes—
199C2—41no—
200C2—2962no—
201C2#1455804511yescharacteristic
202C2#1455834512yes—
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#433C2
socleC22×C37C22×D4
prime radical#14558138C2
hypercenter#433D37
hypocenterC37#3126
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #14558010C2semidirect
3. #14557858C2semidirect
4. #14557841C2semidirect
5. #14557734C2semidirect
6. #14557674C2semidirect
7. #14557635C2semidirect
8. C4×#10596930C2semidirect
9. C37×#433C2semidirect
110. #433D37semidirect
111. C37#3126semidirect

Maximal subgroups

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

subgroupindex
#145581382
#145580102
#145578582
#145578412
#145577342
#145576742
#145576352
C4×#105969302
C37×#4332
#312637