Finite Group Databasebeta

← #18004414

Subgroups — #18004414

Order 4736.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C4×#10596962C211yesmaximal, characteristic
2#14557837C214yesmaximal, complemented
3#14557830C214yesmaximal, complemented
4#14557573C212yesmaximal, complemented
5#14557557C211yesmaximal, characteristic, complemented
6#14557532C212yesmaximal
7C2×#125×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C2×#10596934C2212yes—
10C4×Dic74C2212yes—
11C4×D148C2212yes—
12C4×C22⋊D37—22no—
13#11924495C2211yescharacteristic
14#11924493—21no—
15C42×D37—21no—
16#11924469C2214yes—
17#11924467C2214yes—
18C4⋊#64436C2214yes—
19#11924459C2214yes—
20#11924456C2214yes—
21#125×C37—21no—
22#125×C37—21no—
23#125×C37C2214yes—
24C2×C4⋊C4×C37—22no—
25C2×C4⋊C4×C37C2212yes—
26C2×C42×C37C2211yescharacteristic
27C22×C4×C37—22no—
28C22×C4×C37D412yes—
29C22×C4×C37C2311yescharacteristic
30C2×C22⋊D37—21no—
31#10596962—22no—
32#10596962Q814yes—
33C2×D148C2311yescharacteristic
34C2×C4×D37—21no—
35C2×C4×D37—22no—
36C2×Dic74C2311yescharacteristic
37C4⋊C4×C37—24no—
38C4⋊C4×C37—24no—
39C4⋊C4×C37—22no—
40C4⋊C4×C37C2314yes—
41C42×C37D411yescharacteristic
42C42×C37D411yescharacteristic
43C42×C37C2312yes—
44C22⋊Dic37—21no—
45#10596938—22no—
46C4⋊Dic37C2312yes—
47#10596936—22no—
48C4×Dic37—21no—
49C4×Dic37—22no—
50#10596934—24no—
51C2×#64436C2314yes—
52C23×C37C2×D411yescharacteristic
53C22×D37—21no—
54C2×C4×C37—24no—
55C2×C4×C37—42no—
56C2×C4×C37—44no—
57C2×C4×C37C2×D412yes—
58C2×C4×C37C2×D412yes—
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×Q812yes—
61C2×C4×C37#4112yes—
62C2×C4×C37C2411yescharacteristic
63C22⋊D37—24no—
64C2×Dic37—21no—
65C2×Dic37—22no—
66D148—21no—
67D148C2×Q812yes—
68C4×D37—24no—
69C4×D37—44no—
70Dic74—21no—
71Dic74C2×Q812yes—
72#64436—24no—
73C22×C37—22no—
74C22×C37C22⋊Q812yes—
75C22×C37C22×D411yescharacteristic
76C2×D37—22no—
77C2×D37—42no—
78C4×C37—22no—
79C4×C37—22no—
80C4×C37—44no—
81C4×C37C22⋊Q812yes—
82C4×C37C22×Q811yescharacteristic
83C4×C37C2×#4111yescharacteristic
84Dic37—22no—
85Dic37—42no—
86#3080—371nomaximal, Sylow
87C2×C37—22no—
88C2×C37C2×C22⋊Q811yescharacteristic
89C2×C37#57512yes—
90D37—42no—
91C2×#125D3711yescharacteristic, complemented
92C4×#41—371no—
93#479—374no—
94#478—374no—
95#428—372no—
96#423—371no—
97#417—372no—
98C37#308011yescharacteristic, complemented, Sylow
99C2×#41—371no—
100C2×M16—372no—
101#125—21no—
102#125—21no—
103#125C2×D3714yes—
104C4×Q8—372no—
105C4×D4—372no—
106C4×D4—742no—
107#117—371no—
108#117—741no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4C2×D3712yes—
111C2×C42—741no—
112C2×C42C2×D3711yescharacteristic
113#107—374no—
114#106—374no—
115C4⋊C8—374no—
116#103—374no—
117#102—374no—
118#41—374no—
119#41—742no—
120C2×Q8—371no—
121C2×D4—371no—
122C2×D4—741no—
123C22×C4—22no—
124C22×C4—741no—
125C22×C4—742no—
126C22×C4C22⋊D3712yes—
127C22×C4C22×D3711yescharacteristic
128M16—744no—
129C2×C8—374no—
130C4⋊C4—24no—
131C4⋊C4—24no—
132C4⋊C4—22no—
133C4⋊C4—372no—
134C4⋊C4—742no—
135C4⋊C4C22×D3714yes—
136C22⋊C4—741no—
137C22⋊C4—742no—
138C42—741no—
139C42—742no—
140C42C22⋊D3711yescharacteristic
141C42C22⋊D3711yescharacteristic
142C42C22×D3712yes—
143C23—741no—
144C23C2×C22⋊D3711yescharacteristic
145Q8—372no—
146Q8—741no—
147D4—372no—
148D4—744no—
149D4—741no—
150C2×C4—24no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—741no—
154C2×C4—744no—
155C2×C4—742no—
156C2×C4—1484no—
157C2×C4Q8×D3712yes—
158C2×C4#1059696612yes—
159C2×C4C2×C22⋊D3712yes—
160C2×C4C2×C22⋊D3712yes—
161C2×C4C2×C22⋊D3711yescharacteristic
162C2×C4C23×D3711yescharacteristic
163C8—744no—
164C22—22no—
165C22—742no—
166C22—1482no—
167C22#1192451212yes—
168C22C22×C22⋊D3711yescharacteristic
169C4—22no—
170C4—22no—
171C4—44no—
172C4—742no—
173C4—1482no—
174C4#1192451212yes—
175C4C2×Q8×D3711yescharacteristic
176C4C2×#1059696611yescharacteristic
177C2—22no—
178C2—1482no—
179C2C2×#1192451211yescharacteristic
180C2#1455833112yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#125×C37C2
socleC22×C37C22×D4
prime radicalC2×#10596962C22
hypercenterC2×#125D37
hypocenterC37#3080
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #14557837C2semidirect
3. #14557830C2semidirect
4. #14557573C2semidirect
5. #14557557C2semidirect
7. C2×#125×C37C2semidirect
91. C2×#125D37semidirect
98. C37#3080semidirect

Maximal subgroups

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

subgroupindex
C4×#105969622
#145578372
#145578302
#145575732
#145575572
#145575322
C2×#125×C372
#308037