Finite Group Databasebeta

← #18004882

Subgroups — #18004882

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#14558010C211yesmaximal, characteristic, complemented
2#14557854C212yesmaximal, complemented
3#14557837C212yesmaximal, complemented
4#14557730C212yesmaximal, complemented
5#14557671C212yesmaximal, complemented
6#14557633C212yesmaximal, complemented
7C4×#10596940C212yesmaximal, complemented
8#14557594C211yesmaximal, characteristic, complemented
9C37×#540C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11C2×#10596940C2212yes—
12C2×#10596940C2212yes—
13C4×Dic74C2212yes—
14C4×Dic74C2212yes—
15#11924501—22no—
16#11924495C2211yescharacteristic
17#11924492—22no—
18#11924469C2212yes—
19#11924467C2212yes—
20C4⋊#64436C2212yes—
21#11924459C2212yes—
22#11924459C2212yes—
23#11924457C2212yes—
24#11924457C2212yes—
25C22⋊#64436C2212yes—
26#11924447C2211yescharacteristic
27C4×#64436C2211yescharacteristic
28#127×C37C2211yescharacteristic
29#125×C37C2211yescharacteristic
30#123×C37—22no—
31#121×C37—22no—
32#121×C37C2212yes—
33C4×D4×C37C2212yes—
34#117×C37C2211yescharacteristic
35C2×D4×C37—22no—
36C2×D4×C37—22no—
37C2×D4×C37C2312yes—
38C22×C4×C37—22no—
39C22×C4×C37C2311yescharacteristic
40C22×Dic37—21no—
41C2×Dic74—21no—
42C2×Dic74—24no—
43C2×Dic74C2312yes—
44C4⋊C4×C37—22no—
45C4⋊C4×C37D412yes—
46C4⋊C4×C37C2312yes—
47C22⋊C4×C37—22no—
48C22⋊C4×C37—22no—
49C22⋊C4×C37D412yes—
50C42×C37C2311yescharacteristic
51C42×C37C2311yescharacteristic
52C22⋊Dic37—21no—
53#10596940—24no—
54#10596940—24no—
55C4⋊Dic37C2312yes—
56#10596936—22no—
57#10596936—22no—
58C4×Dic37—22no—
59C4×Dic37—22no—
60C4×Dic37—21no—
61C2×#64436C2312yes—
62C2×#64436C2312yes—
63C23×C37—22no—
64C23×C37C2×D411yescharacteristic
65D4×C37—22no—
66D4×C37—22no—
67D4×C37—82no—
68D4×C37—82no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37—82no—
72C2×C4×C37C2×D412yes—
73C2×C4×C37C2×D412yes—
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2411yescharacteristic
76C2×Dic37—24no—
77C2×Dic37—22no—
78C2×Dic37—22no—
79Dic74—24no—
80Dic74—22no—
81Dic74#4114yes—
82#64436—22no—
83#64436—22no—
84C22×C37—21no—
85C22×C37—22no—
86C22×C37—42no—
87C22×C37—42no—
88C22×C37—42no—
89C22×C37C22×D411yescharacteristic
90C4×C37—21no—
91C4×C37—22no—
92C4×C37—22no—
93C4×C37—42no—
94C4×C37C2×#4112yes—
95Dic37—24no—
96Dic37—42no—
97#3126—371nomaximal, Sylow
98C2×C37—41no—
99C2×C37—82no—
100C2×C37#52511yescharacteristic
101C2×C37#57712yes—
102#540D3711yescharacteristic
103#519—371no—
104#482—372no—
105#479—372no—
106#460—372no—
107#448—372no—
108#440—372no—
109C4×SD16—372no—
110#433—371no—
111C37#312611yescharacteristic, complemented, Sylow
112C22×Q8—371no—
113C2×SD16—372no—
114C2×SD16—372no—
115#127C2×D3711yescharacteristic
116#125C2×D3711yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D3712yes—
120C4×Q8—372no—
121C4×Q8—372no—
122C4×Q8—742no—
123C4×D4C2×D3712yes—
124#117—371no—
125#117—742no—
126#117C2×D3711yescharacteristic
127#107—372no—
128#106—372no—
129C4⋊C8—372no—
130#103—372no—
131#103—372no—
132#102—372no—
133#102—372no—
134C22⋊C8—372no—
135#97—371no—
136C4×C8—371no—
137C2×Q8—372no—
138C2×Q8—744no—
139C2×Q8—741no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D3712yes—
143C22×C4—22no—
144C22×C4—741no—
145C22×C4C22×D3711yescharacteristic
146SD16—744no—
147SD16—744no—
148C2×C8—372no—
149C2×C8—372no—
150C4⋊C4—22no—
151C4⋊C4—372no—
152C4⋊C4—742no—
153C4⋊C4—742no—
154C4⋊C4C22⋊D3712yes—
155C4⋊C4C22×D3712yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—741no—
159C22⋊C4C22⋊D3712yes—
160C42—741no—
161C42—742no—
162C42—742no—
163C42C22×D3711yescharacteristic
164C42C22×D3711yescharacteristic
165C23—22no—
166C23C2×C22⋊D3711yescharacteristic
167Q8—374no—
168Q8—744no—
169Q8—742no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—744no—
178C2×C4—742no—
179C2×C4—742no—
180C2×C4C2×C22⋊D3712yes—
181C2×C4C2×C22⋊D3712yes—
182C2×C4C2×C22⋊D3711yescharacteristic
183C2×C4C23×D3711yescharacteristic
184C8—742no—
185C8—742no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D3711yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—744no—
197C4—1482no—
198C4#41×D3712yes—
199C2—41no—
200C2—82no—
201C2#1455804011yescharacteristic
202C2#1455834412yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC37×#540C2
socleC22×C37C22×D4
hypercenter#540D37
hypocenterC37#3126
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #14558010C2semidirect
2. #14557854C2semidirect
3. #14557837C2semidirect
4. #14557730C2semidirect
5. #14557671C2semidirect
6. #14557633C2semidirect
7. C4×#10596940C2semidirect
8. #14557594C2semidirect
111. C37#3126semidirect

Maximal subgroups

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

subgroupindex
#145580102
#145578542
#145578372
#145577302
#145576712
#145576332
C4×#105969402
#145575942
C37×#5402
#312637