Finite Group Databasebeta

← #17996572

Subgroups — #17996572

Order 4736.

206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 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#14558350C211yesmaximal, characteristic
2#14557974C211yesmaximal, characteristic, complemented
3C2×#11924482C211yesmaximal, characteristic, complemented
4#14557348C211yesmaximal, characteristic, complemented
5#14557339C211yesmaximal, characteristic, complemented
6#14557317C211yesmaximal, characteristic, complemented
7C37×#473C211yesmaximal, characteristic, complemented
8#11924583—21no—
9#11924569—21no—
10#11924569—22no—
11#11924558—21no—
12#11924558C2211yescharacteristic
13C2×Dic148—21no—
14C2×Dic148C2211yescharacteristic
15#11924482—22no—
16#11924482—21no—
17#11924479—21no—
18#11924476C2211yescharacteristic
19C2×#10596925C2211yescharacteristic
20#137×C37—21no—
21C2×Q16×C37C2211yescharacteristic
22#131×C37C2211yescharacteristic
23#108×C37C2211yescharacteristic
24#101×C37—21no—
25#41×C37D411yescharacteristic
26C2×Q8×C37—21no—
27Q8×D37—41no—
28#10596964—42no—
29#10596964—41no—
30#10596962—22no—
31#10596962—21no—
32C2×Dic74—22no—
33C2×Dic74—21no—
34Q16×C37—21no—
35Q16×C37—21no—
36Q16×C37—41no—
37SD16×C37—41no—
38M16×C37—21no—
39M16×C37—21no—
40M16×C37D411yescharacteristic
41C2×C8×C37—21no—
42C2×C8×C37C2311yescharacteristic
43Dic148—22no—
44Dic148—21no—
45Dic148D411yescharacteristic
46Dic148D412yes—
47D296D411yescharacteristic
48#10596930—22no—
49#10596930—21no—
50#10596925—21no—
51#10596925—21no—
52Q8×C37—41no—
53Q8×C37—41no—
54Q8×C37D811yescharacteristic
55D4×C37—21no—
56D4×C37D811yescharacteristic
57C2×C4×C37—21no—
58C2×C4×C37—41no—
59C2×C4×C37C2×D411yescharacteristic
60C22⋊D37—42no—
61C22⋊D37—41no—
62C2×Dic37—42no—
63C2×Dic37—41no—
64D148—21no—
65C4×D37—42no—
66C4×D37—41no—
67Dic74—22no—
68Dic74—21no—
69Dic74—42no—
70Dic74—41no—
71C8×C37—21no—
72C8×C37—41no—
73C8×C37C2×D411yescharacteristic
74C8×C37C2×D411yescharacteristic
75C22×C37—21no—
76C22×C37AGL(1,ℤ/8)11yescharacteristic
77C2×D37—41no—
78C4×C37—21no—
79C4×C37—81no—
80C4×C37#12011yescharacteristic
81C4×C37C2×D811yescharacteristic
82Dic37—41no—
83Dic37—42no—
84#2195—371nomaximal, Sylow
85C2×C37—21no—
86C2×C37—41no—
87C2×C37#44711yescharacteristic
88D37—81no—
89#578—371no—
90#510—371no—
91C2×Q32—371no—
92#473D3711yescharacteristic, complemented
93#362—371no—
94#359—371no—
95#350—371no—
96C37#219511yescharacteristic, complemented, Sylow
972−1+4—741no—
98#137—21no—
99#137—742no—
100#137—741no—
101#135—371no—
102#135—741no—
103C2×Q16—371no—
104C2×Q16—741no—
105C2×Q16C2×D3711yescharacteristic
106#131C2×D3711yescharacteristic
107Q32—742no—
108Q32—741no—
109SD32—741no—
110M32—371no—
111C2×C16—371no—
112#108C2×D3711yescharacteristic
113#101—21no—
114#41—742no—
115#41—741no—
116#41—1482no—
117#41—1481no—
118#41C22⋊D3711yescharacteristic
119C2×Q8—21no—
120C2×Q8—742no—
121C2×Q8—741no—
122C2×Q8—1481no—
123Q16—21no—
124Q16—21no—
125Q16—41no—
126Q16—372no—
127Q16—371no—
128Q16—742no—
129Q16—741no—
130SD16—41no—
131SD16—742no—
132SD16—741no—
133D8—371no—
134M16—21no—
135M16—21no—
136M16C22⋊D3711yescharacteristic
137C2×C8—21no—
138C2×C8C22×D3711yescharacteristic
139C16—741no—
140C16—741no—
141Q8—41no—
142Q8—41no—
143Q8—742no—
144Q8—741no—
145Q8—1482no—
146Q8—1481no—
147Q8#1059693911yescharacteristic
148D4—21no—
149D4—741no—
150D4—1482no—
151D4—1481no—
152D4#1059693911yescharacteristic
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—1482no—
156C2×C4—1482no—
157C2×C4—1481no—
158C2×C4—1481no—
159C2×C4C2×C22⋊D3711yescharacteristic
160C8—21no—
161C8—41no—
162C8D4×D3711yescharacteristic
163C8D4×D3711yescharacteristic
164C22—21no—
165C22—1481no—
166C22#1192456111yescharacteristic
167C4—21no—
168C4—81no—
169C4—1482no—
170C4—1481no—
171C4#1192450411yescharacteristic
172C4C2×#1059693911yescharacteristic
173C2—21no—
174C2—41no—
175C2—2961no—
176C2#1455766611yescharacteristic
subgroupG/H
centerC2#14557666
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#473C2
socleC2×C37#447
prime radical#14558350C2
hypercenter#473D37
hypocenterC37#2195
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #473

Complements

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

NH ≅ G/Ntype
2. #14557974C2semidirect
3. C2×#11924482C2semidirect
4. #14557348C2semidirect
5. #14557339C2semidirect
6. #14557317C2semidirect
7. C37×#473C2semidirect
92. #473D37semidirect
96. C37#2195semidirect

Maximal subgroups

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

subgroupindex
#145583502
#145579742
C2×#119244822
#145573482
#145573392
#145573172
C37×#4732
#219537