Finite Group Databasebeta

← #17996564

Subgroups — #17996564

Order 4736.

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

normal subgroups only

This group has 216 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#14558335C211yesmaximal, characteristic
2C2×#11924479C211yesmaximal, characteristic, complemented
3#14557805C211yesmaximal, characteristic, complemented
4#14557347C211yesmaximal, characteristic, complemented
5#14557340C211yesmaximal, characteristic, complemented
6#14557318C211yesmaximal, characteristic, complemented
7C37×#510C211yesmaximal, characteristic, complemented
8#11924582—21no—
9#11924567—21no—
10#11924563—22no—
11#11924561—21no—
12#11924559—21no—
13C2×D296C2211yescharacteristic
14D8×D37—21no—
15#11924542C2211yescharacteristic
16#11924479—22no—
17C2×#10596925C2211yescharacteristic, complemented
18#11924472C2211yescharacteristic, complemented
19#11924455—21no—
20#135×C37C2211yescharacteristic
21C2×Q16×C37C2211yescharacteristic, complemented
22Q32×C37—21no—
23SD32×C37—21no—
24M32×C37C2211yescharacteristic, complemented
25#41×C37—21no—
26C2×Q8×C37—21no—
27#10596966—22no—
28D4×D37—22no—
29D4×D37—42no—
30#10596962—41no—
31#10596962D411yescharacteristic
32C2×D148—21no—
33C2×D148—41no—
34Q16×C37—21no—
35Q16×C37—21no—
36Q16×C37D411yescharacteristic
37SD16×C37—21no—
38D8×C37D411yescharacteristic
39C2×C8×C37C2311yescharacteristic
40#10596942—41no—
41#10596941—22no—
42#10596941—41no—
43#10596939—22no—
44#10596934—21no—
45#10596934D411yescharacteristic
46D296—21no—
47D296D412yes—
48#10596929—21no—
49C8×D37—21no—
50C16×C37—21no—
51#10596925—21no—
52C22×D37—42no—
53C22×D37—41no—
54Q8×C37—21no—
55Q8×C37—41no—
56Q8×C37—41no—
57D4×C37—21no—
58D4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37C2×D411yescharacteristic
62C22⋊D37—21no—
63C22⋊D37—42no—
64D148—22no—
65D148—42no—
66D148—41no—
67D148D811yescharacteristic
68C4×D37—21no—
69C4×D37—42no—
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—
78C2×D37—42no—
79C2×D37—162no—
80C2×D37—161no—
81C4×C37—41no—
82C4×C37—81no—
83C4×C37#12011yescharacteristic
84C4×C37C2×D811yescharacteristic
85Dic37—21no—
86#2194—371nomaximal, Sylow
87C2×C37—21no—
88C2×C37—81no—
89C2×C37#44711yescharacteristic
90D37—41no—
91D37—82no—
92#576—371no—
93#510D3711yescharacteristic, complemented
94C2×SD32—371no—
95#473—371no—
96#361—371no—
97#359—371no—
98#350—371no—
99C37#219411yescharacteristic, complemented, Sylow
100H(5,𝔽2)—741no—
101#137—741no—
102AGL(1,ℤ/8)—741no—
103AGL(1,ℤ/8)—742no—
104#135—741no—
105#135C2×D3711yescharacteristic
106C2×Q16C2×D3711yescharacteristic, complemented
107C2×D8—371no—
108C2×D8—741no—
109#131—371no—
110Q32—21no—
111SD32—21no—
112SD32—742no—
113M32C2×D3711yescharacteristic, complemented
114C2×C16—371no—
115#108—371no—
116#101—741no—
117#41—21no—
118#41—371no—
119#41—742no—
120#41—1481no—
121C2×Q8—21no—
122C2×D4—742no—
123C2×D4—741no—
124C2×D4—1481no—
125C2×D4—1482no—
126Q16—21no—
127Q16—21no—
128Q16—1481no—
129Q16C22⋊D3711yescharacteristic
130SD16—21no—
131SD16—742no—
132SD16—1481no—
133D8—372no—
134D8—742no—
135D8—741no—
136D8C22⋊D3711yescharacteristic
137M16—371no—
138M16—741no—
139M16—741no—
140C2×C8—741no—
141C2×C8C22×D3711yescharacteristic
142C16—21no—
143C16—741no—
144C23—1482no—
145C23—1481no—
146Q8—21no—
147Q8—41no—
148Q8—41no—
149Q8—371no—
150D4—21no—
151D4—41no—
152D4—371no—
153D4—741no—
154D4—742no—
155D4—1482no—
156D4—1482no—
157D4—1481no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—741no—
161C2×C4—1482no—
162C2×C4D4×D3711yescharacteristic
163C8—741no—
164C8—1481no—
165C8D4×D3711yescharacteristic
166C8C2×C22⋊D3711yescharacteristic
167C22—41no—
168C22—741no—
169C22—5921no—
170C22—5922no—
171C22—1482no—
172C22#1192456011yescharacteristic
173C4—41no—
174C4—81no—
175C4—741no—
176C4#1192450411yescharacteristic
177C4D8×D3711yescharacteristic
178C2—21no—
179C2—81no—
180C2—2962no—
181C2—1481no—
182C2#1455766511yescharacteristic
subgroupG/H
centerC2#14557665
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#510C2
socleC2×C37#447
prime radical#14558335C2
hypercenter#510D37
hypocenterC37#2194
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×#11924479C2semidirect
3. #14557805C2semidirect
4. #14557347C2semidirect
5. #14557340C2semidirect
6. #14557318C2semidirect
7. C37×#510C2semidirect
17. C2×#10596925C22semidirect
18. #11924472C22semidirect
21. C2×Q16×C37C22semidirect
24. M32×C37C22semidirect
93. #510D37semidirect
99. C37#2194semidirect
106. C2×Q16C2×D37semidirect
113. M32C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583352
C2×#119244792
#145578052
#145573472
#145573402
#145573182
C37×#5102
#219437