Finite Group Databasebeta

← #17996568

Subgroups — #17996568

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
2#14557973C211yesmaximal, characteristic, complemented
3C2×#11924481C211yesmaximal, characteristic, complemented
4#14557809C211yesmaximal, characteristic, complemented
5#14557345C211yesmaximal, characteristic, complemented
6#14557316C211yesmaximal, characteristic, complemented
7C37×#359C211yesmaximal, characteristic, complemented
8#11924582—21no—
9#11924569—21no—
10#11924563—22no—
11#11924561—21no—
12#11924559—21no—
13C2×Dic148C2211yescharacteristic, complemented
14C2×D296C2211yescharacteristic
15D8×D37—21no—
16#11924542C2211yescharacteristic
17#11924482—21no—
18#11924481—22no—
19#11924480—21no—
20#11924476C2211yescharacteristic, complemented
21#11924454—21no—
22#135×C37C2211yescharacteristic
23C2×C16×C37C2211yescharacteristic, complemented
24#108×C37C2211yescharacteristic, complemented
25#41×C37—21no—
26#10596966—22no—
27D4×D37—22no—
28D4×D37—42no—
29#10596962—41no—
30#10596962D411yescharacteristic
31C2×D148—21no—
32C2×D148—41no—
33C2×Dic74—21no—
34Q16×C37D411yescharacteristic
35SD16×C37—21no—
36D8×C37D411yescharacteristic
37M16×C37—21no—
38C2×C8×C37C2311yescharacteristic
39#10596941—22no—
40#10596939—22no—
41#10596934D411yescharacteristic
42Dic148—21no—
43Dic148—21no—
44Dic148—41no—
45D296—21no—
46D296D412yes—
47#10596930—41no—
48#10596929—21no—
49C8×D37—21no—
50C16×C37—21no—
51#10596925—21no—
52C22×D37—42no—
53C22×D37—41no—
54Q8×C37—21no—
55D4×C37—21no—
56D4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37C2×D411yescharacteristic
59C22⋊D37—21no—
60C22⋊D37—42no—
61C2×Dic37—41no—
62D148—22no—
63D148—42no—
64D148—41no—
65D148D811yescharacteristic
66C4×D37—21no—
67C4×D37—42no—
68Dic74—41no—
69Dic74—41no—
70Dic74D811yescharacteristic
71C8×C37—41no—
72C8×C37C2×D411yescharacteristic
73C8×C37C2×D411yescharacteristic
74#64436—21no—
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#12011yescharacteristic
83C4×C37C2×D811yescharacteristic
84Dic37—21no—
85Dic37—81no—
86#2194—371nomaximal, Sylow
87C2×C37—21no—
88C2×C37—81no—
89C2×C37#44711yescharacteristic
90D37—41no—
91D37—82no—
92#576—371no—
93#510—371no—
94C2×SD32—371no—
95#473—371no—
96#361—371no—
97#359D3711yescharacteristic, complemented
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×Q16—371no—
107C2×D8—371no—
108C2×D8—741no—
109#131—371no—
110Q32—741no—
111SD32—742no—
112SD32—741no—
113M32—371no—
114C2×C16C2×D3711yescharacteristic, complemented
115#108C2×D3711yescharacteristic, complemented
116#101—741no—
117#41—21no—
118#41—371no—
119#41—742no—
120#41—1481no—
121C2×Q8—741no—
122C2×D4—742no—
123C2×D4—741no—
124C2×D4—1481no—
125C2×D4—1482no—
126Q16—741no—
127Q16—741no—
128Q16—1481no—
129Q16D14811yescharacteristic
130SD16—21no—
131SD16—742no—
132SD16—1481no—
133D8—372no—
134D8—742no—
135D8—741no—
136D8D14811yescharacteristic
137M16—21no—
138M16—371no—
139M16—741no—
140C2×C8—741no—
141C2×C8C22×D3711yescharacteristic
142C16—21no—
143C16—741no—
144C23—1482no—
145C23—1481no—
146Q8—21no—
147Q8—371no—
148Q8—1481no—
149Q8—1481no—
150D4—21no—
151D4—41no—
152D4—371no—
153D4—741no—
154D4—742no—
155D4—1482no—
156D4—1482no—
157D4—1481no—
158C2×C4—41no—
159C2×C4—741no—
160C2×C4—1482no—
161C2×C4—1481no—
162C2×C4D4×D3711yescharacteristic
163C8—41no—
164C8—741no—
165C8C2×D14811yescharacteristic
166C8D4×D3711yescharacteristic
167C22—41no—
168C22—741no—
169C22—5921no—
170C22—5922no—
171C22—1482no—
172C22#1192456311yescharacteristic
173C4—41no—
174C4—2961no—
175C4—741no—
176C4#1192450611yescharacteristic
177C4D8×D3711yescharacteristic
178C2—21no—
179C2—81no—
180C2—2962no—
181C2—1481no—
182C2#1455766811yescharacteristic
subgroupG/H
centerC2#14557668
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#359C2
socleC2×C37#447
prime radical#14558335C2
hypercenter#359D37
hypocenterC37#2194
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #359

Complements

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

NH ≅ G/Ntype
2. #14557973C2semidirect
3. C2×#11924481C2semidirect
4. #14557809C2semidirect
5. #14557345C2semidirect
6. #14557316C2semidirect
7. C37×#359C2semidirect
13. C2×Dic148C22semidirect
20. #11924476C22semidirect
23. C2×C16×C37C22semidirect
24. #108×C37C22semidirect
97. #359D37semidirect
99. C37#2194semidirect
114. C2×C16C2×D37semidirect
115. #108C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583352
#145579732
C2×#119244812
#145578092
#145573452
#145573162
C37×#3592
#219437