Finite Group Databasebeta

← #17996569

Subgroups — #17996569

Order 4736.

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

normal subgroups only

This group has 216 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#14558338C211yesmaximal, characteristic
2#14557976C211yesmaximal, characteristic, complemented
3C2×#11924481C211yesmaximal, characteristic, complemented
4#14557808C211yesmaximal, characteristic, complemented
5#14557347C211yesmaximal, characteristic, complemented
6#14557341C211yesmaximal, characteristic, complemented
7C37×#350C211yesmaximal, characteristic, complemented
8#11924582—21no—
9#11924566—21no—
10#11924564—21no—
11#11924564—22no—
12#11924558—21no—
13#11924558C2211yescharacteristic
14C2×Dic148C2211yescharacteristic, complemented
15C2×D296—21no—
16C2×D296C2211yescharacteristic
17Dic296—21no—
18#11924481—22no—
19#11924481—21no—
20#11924472C2211yescharacteristic, complemented
21#11924454—21no—
22#131×C37C2211yescharacteristic
23M32×C37C2211yescharacteristic, complemented
24C2×C16×C37C2211yescharacteristic, complemented
25#41×C37D411yescharacteristic
26#10596966—41no—
27D4×D37—42no—
28D4×D37—41no—
29#10596962—22no—
30#10596962—21no—
31C2×D148—22no—
32C2×D148—21no—
33C2×Dic74—21no—
34M16×C37—21no—
35M16×C37D411yescharacteristic
36C2×C8×C37—21no—
37C2×C8×C37C2311yescharacteristic
38#10596942—41no—
39#10596940—41no—
40#10596934—21no—
41Dic148—21no—
42Dic148—21no—
43Dic148D411yescharacteristic
44D296—22no—
45D296—21no—
46D296D411yescharacteristic
47D296D412yes—
48#10596930—22no—
49#10596930—21no—
50C16×C37—21no—
51C16×C37—21no—
52C22×D37—42no—
53C22×D37—41no—
54Q8×C37D811yescharacteristic
55D4×C37—21no—
56D4×C37D811yescharacteristic
57C2×C4×C37—21no—
58C2×C4×C37C2×D411yescharacteristic
59C22⋊D37—42no—
60C22⋊D37—41no—
61C2×Dic37—41no—
62D148—22no—
63D148—21no—
64D148—42no—
65D148—41no—
66C4×D37—42no—
67C4×D37—41no—
68Dic74—21no—
69Dic74—41no—
70Dic74—41no—
71C8×C37—21no—
72C8×C37C2×D411yescharacteristic
73C8×C37C2×D411yescharacteristic
74#64436—41no—
75C22×C37—21no—
76C22×C37AGL(1,ℤ/8)11yescharacteristic
77C2×D37—42no—
78C2×D37—41no—
79C2×D37—161no—
80C2×D37—162no—
81C4×C37—21no—
82C4×C37#12011yescharacteristic
83C4×C37C2×D811yescharacteristic
84Dic37—41no—
85Dic37—81no—
86#2194—371nomaximal, Sylow
87C2×C37—21no—
88C2×C37—41no—
89C2×C37#44711yescharacteristic
90D37—82no—
91D37—81no—
92#576—371no—
93#510—371no—
94C2×SD32—371no—
95#473—371no—
96#361—371no—
97#359—371no—
98#350D3711yescharacteristic, complemented
99C37#219411yescharacteristic, complemented, Sylow
100H(5,𝔽2)—741no—
101#137—741no—
102AGL(1,ℤ/8)—742no—
103AGL(1,ℤ/8)—741no—
104#135—371no—
105#135—741no—
106C2×Q16—371no—
107C2×D8—371no—
108C2×D8—741no—
109#131C2×D3711yescharacteristic
110Q32—741no—
111SD32—742no—
112SD32—741no—
113M32C2×D3711yescharacteristic, complemented
114C2×C16C2×D3711yescharacteristic, complemented
115#108—371no—
116#101—741no—
117#41—742no—
118#41—741no—
119#41—1481no—
120#41D14811yescharacteristic
121C2×Q8—741no—
122C2×D4—742no—
123C2×D4—741no—
124C2×D4—1482no—
125C2×D4—1481no—
126Q16—371no—
127Q16—741no—
128Q16—741no—
129Q16—1481no—
130SD16—742no—
131SD16—741no—
132SD16—1481no—
133D8—372no—
134D8—371no—
135D8—742no—
136D8—741no—
137M16—21no—
138M16—741no—
139M16D14811yescharacteristic
140C2×C8—21no—
141C2×C8C22×D3711yescharacteristic
142C16—21no—
143C16—21no—
144C23—1482no—
145C23—1481no—
146Q8—741no—
147Q8—1481no—
148Q8—1481no—
149Q8D29611yescharacteristic
150D4—21no—
151D4—742no—
152D4—741no—
153D4—1482no—
154D4—1482no—
155D4—1481no—
156D4—1481no—
157D4D29611yescharacteristic
158C2×C4—21no—
159C2×C4—1482no—
160C2×C4—1481no—
161C2×C4—1481no—
162C2×C4C2×D14811yescharacteristic
163C8—21no—
164C8—1481no—
165C8D4×D3711yescharacteristic
166C8D4×D3711yescharacteristic
167C22—21no—
168C22—5921no—
169C22—5922no—
170C22—1482no—
171C22—1481no—
172C22#1192456411yescharacteristic
173C4—21no—
174C4—2961no—
175C4—1481no—
176C4#1192450611yescharacteristic
177C4C2×D29611yescharacteristic
178C2—21no—
179C2—41no—
180C2—2962no—
181C2—2961no—
182C2#1455766911yescharacteristic
subgroupG/H
centerC2#14557669
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#350C2
socleC2×C37#447
prime radical#14558338C2
hypercenter#350D37
hypocenterC37#2194
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #350

Complements

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

NH ≅ G/Ntype
2. #14557976C2semidirect
3. C2×#11924481C2semidirect
4. #14557808C2semidirect
5. #14557347C2semidirect
6. #14557341C2semidirect
7. C37×#350C2semidirect
14. C2×Dic148C22semidirect
20. #11924472C22semidirect
23. M32×C37C22semidirect
24. C2×C16×C37C22semidirect
98. #350D37semidirect
99. C37#2194semidirect
113. M32C2×D37semidirect
114. C2×C16C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583382
#145579762
C2×#119244812
#145578082
#145573472
#145573412
C37×#3502
#219437