Finite Group Databasebeta

← #17996571

Subgroups — #17996571

Order 4736.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#14558347C211yesmaximal, characteristic
2C2×#11924482C211yesmaximal, characteristic, complemented
3#14557805C211yesmaximal, characteristic, complemented
4#14557350C211yesmaximal, characteristic, complemented
5#14557340C211yesmaximal, characteristic, complemented
6#14557318C211yesmaximal, characteristic, complemented
7C37×#510C211yesmaximal, characteristic, complemented
8#11924583—21no—
9#11924567—21no—
10#11924566—21no—
11#11924565—22no—
12#11924555—21no—
13C2×Dic148C2211yescharacteristic
14Q16×D37—21no—
15#11924542C2211yescharacteristic
16#11924482—22no—
17C2×#10596925C2211yescharacteristic
18#11924472C2211yescharacteristic
19#11924455—21no—
20#135×C37C2211yescharacteristic
21C2×Q16×C37C2211yescharacteristic
22Q32×C37—21no—
23SD32×C37—21no—
24M32×C37C2211yescharacteristic
25#41×C37—21no—
26C2×Q8×C37—21no—
27Q8×D37—22no—
28#10596964—22no—
29#10596964—42no—
30#10596962—41no—
31#10596962D411yescharacteristic
32C2×Dic74—21no—
33C2×Dic74—41no—
34Q16×C37—21no—
35Q16×C37—21no—
36Q16×C37D411yescharacteristic
37SD16×C37—21no—
38D8×C37D411yescharacteristic
39C2×C8×C37C2311yescharacteristic
40#10596942—22no—
41#10596942—41no—
42#10596941—41no—
43#10596940—22no—
44#10596934—21no—
45#10596934D411yescharacteristic
46Dic148—21no—
47Dic148D412yes—
48#10596929—21no—
49C8×D37—21no—
50C16×C37—21no—
51#10596925—21no—
52Q8×C37—21no—
53Q8×C37—41no—
54Q8×C37—41no—
55D4×C37—21no—
56D4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37C2×D411yescharacteristic
60C22⋊D37—21no—
61C22⋊D37—42no—
62C2×Dic37—42no—
63C2×Dic37—41no—
64D148D811yescharacteristic
65C4×D37—21no—
66C4×D37—42no—
67Dic74—22no—
68Dic74—42no—
69Dic74—41no—
70Dic74D811yescharacteristic
71C8×C37C2×D411yescharacteristic
72C8×C37C2×D411yescharacteristic
73#64436—21no—
74#64436—41no—
75C22×C37—41no—
76C22×C37AGL(1,ℤ/8)11yescharacteristic
77C2×D37—21no—
78C4×C37—41no—
79C4×C37—81no—
80C4×C37#12011yescharacteristic
81C4×C37C2×D811yescharacteristic
82Dic37—21no—
83Dic37—42no—
84#2195—371nomaximal, Sylow
85C2×C37—21no—
86C2×C37—81no—
87C2×C37#44711yescharacteristic
88D37—41no—
89#578—371no—
90#510D3711yescharacteristic, complemented
91C2×Q32—371no—
92#473—371no—
93#362—371no—
94#359—371no—
95#350—371no—
96C37#219511yescharacteristic, complemented, Sylow
972−1+4—741no—
98#137—741no—
99#137—742no—
100#137—741no—
101#135—741no—
102#135C2×D3711yescharacteristic
103C2×Q16—371no—
104C2×Q16—741no—
105C2×Q16C2×D3711yescharacteristic
106#131—371no—
107Q32—21no—
108Q32—742no—
109SD32—21no—
110M32C2×D3711yescharacteristic
111C2×C16—371no—
112#108—371no—
113#101—741no—
114#41—21no—
115#41—371no—
116#41—742no—
117#41—1481no—
118#41—1482no—
119C2×Q8—21no—
120C2×Q8—742no—
121C2×Q8—741no—
122C2×Q8—1481no—
123Q16—21no—
124Q16—21no—
125Q16—372no—
126Q16—742no—
127Q16—741no—
128Q16—1481no—
129Q16C22⋊D3711yescharacteristic
130SD16—21no—
131SD16—742no—
132SD16—1481no—
133D8C22⋊D3711yescharacteristic
134M16—371no—
135M16—741no—
136M16—741no—
137C2×C8—741no—
138C2×C8C22×D3711yescharacteristic
139C16—21no—
140C16—741no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—371no—
145Q8—742no—
146Q8—1482no—
147Q8—1481no—
148D4—21no—
149D4—41no—
150D4—371no—
151D4—741no—
152D4—1482no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—741no—
156C2×C4—1482no—
157C2×C4—1482no—
158C2×C4—1481no—
159C2×C4D4×D3711yescharacteristic
160C8—741no—
161C8—1481no—
162C8D4×D3711yescharacteristic
163C8C2×C22⋊D3711yescharacteristic
164C22—41no—
165C22—741no—
166C22#1192456011yescharacteristic
167C4—41no—
168C4—81no—
169C4—741no—
170C4—1482no—
171C4#1192450411yescharacteristic
172C4D8×D3711yescharacteristic
173C2—21no—
174C2—81no—
175C2—1481no—
176C2#1455766511yescharacteristic
subgroupG/H
centerC2#14557665
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#510C2
socleC2×C37#447
prime radical#14558347C2
hypercenter#510D37
hypocenterC37#2195
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C2×#11924482C2semidirect
3. #14557805C2semidirect
4. #14557350C2semidirect
5. #14557340C2semidirect
6. #14557318C2semidirect
7. C37×#510C2semidirect
90. #510D37semidirect
96. C37#2195semidirect

Maximal subgroups

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

subgroupindex
#145583472
C2×#119244822
#145578052
#145573502
#145573402
#145573182
C37×#5102
#219537