Finite Group Databasebeta

← #17996558

Subgroups — #17996558

Order 4736.

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

normal subgroups only

This group has 210 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, complemented
2#14557969C211yesmaximal, characteristic, complemented
3C2×#11924480C211yesmaximal, characteristic, complemented
4#14557348C211yesmaximal, characteristic, complemented
5#14557339C211yesmaximal, characteristic, complemented
6#14557317C211yesmaximal, characteristic, complemented
7C37×#472C211yesmaximal, characteristic, complemented
8#11924583—21no—
9#11924569—21no—
10#11924569—22no—
11#11924558—21no—
12#11924558C2211yescharacteristic
13C2×Dic148—21no—
14C2×Dic148C2211yescharacteristic
15#11924480—22no—
16#11924480—21no—
17#11924477—21no—
18#11924476C2211yescharacteristic
19C2×#10596925C2211yescharacteristic
20AGL(1,ℤ/8)×C37—21no—
21C2×D8×C37C2211yescharacteristic
22#131×C37C2211yescharacteristic
23#108×C37C2211yescharacteristic
24#100×C37—21no—
25#41×C37D411yescharacteristic
26C2×D4×C37—21no—
27Q8×D37—41no—
28#10596964—42no—
29#10596964—41no—
30#10596962—22no—
31#10596962—21no—
32C2×Dic74—22no—
33C2×Dic74—21no—
34SD16×C37—41no—
35D8×C37—21no—
36D8×C37—21no—
37D8×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—
52C23×C37—41no—
53Q8×C37D811yescharacteristic
54D4×C37—21no—
55D4×C37—41no—
56D4×C37—41no—
57D4×C37D811yescharacteristic
58C2×C4×C37—21no—
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×C37—81no—
77C22×C37—161no—
78C22×C37AGL(1,ℤ/8)11yescharacteristic
79C2×D37—41no—
80C4×C37—21no—
81C4×C37#12011yescharacteristic
82C4×C37C2×D811yescharacteristic
83Dic37—41no—
84Dic37—42no—
85#2193—371nomaximal, Sylow
86C2×C37—21no—
87C2×C37—41no—
88C2×C37—161no—
89C2×C37#44711yescharacteristic
90D37—81no—
91#578—371no—
92#509—371no—
93C2×SD32—371no—
94#472D3711yescharacteristic, complemented
95#362—371no—
96#359—371no—
97#350—371no—
98C37#219311yescharacteristic, complemented, Sylow
992−1+4—741no—
100#137—742no—
101#137—741no—
102AGL(1,ℤ/8)—21no—
103#135—371no—
104#135—741no—
105C2×Q16—371no—
106C2×Q16—741no—
107C2×D8C2×D3711yescharacteristic
108#131C2×D3711yescharacteristic
109SD32—742no—
110SD32—741no—
111D16—741no—
112M32—371no—
113C2×C16—371no—
114#108C2×D3711yescharacteristic
115#100—21no—
116#41—742no—
117#41—741no—
118#41—1482no—
119#41—1481no—
120#41C22⋊D3711yescharacteristic
121C2×Q8—742no—
122C2×Q8—741no—
123C2×Q8—1481no—
124C2×D4—21no—
125Q16—372no—
126Q16—371no—
127Q16—742no—
128Q16—741no—
129SD16—41no—
130SD16—742no—
131SD16—741no—
132D8—21no—
133D8—21no—
134D8—41no—
135D8—371no—
136M16—21no—
137M16—21no—
138M16C22⋊D3711yescharacteristic
139C2×C8—21no—
140C2×C8C22×D3711yescharacteristic
141C16—741no—
142C16—741no—
143C23—41no—
144Q8—742no—
145Q8—741no—
146Q8—1482no—
147Q8—1481no—
148Q8#1059693911yescharacteristic
149D4—21no—
150D4—41no—
151D4—41no—
152D4—741no—
153D4—1482no—
154D4—1481no—
155D4#1059693911yescharacteristic
156C2×C4—21no—
157C2×C4—1482no—
158C2×C4—1482no—
159C2×C4—1481no—
160C2×C4—1481no—
161C2×C4C2×C22⋊D3711yescharacteristic
162C8—21no—
163C8—41no—
164C8D4×D3711yescharacteristic
165C8D4×D3711yescharacteristic
166C22—21no—
167C22—81no—
168C22—161no—
169C22—1481no—
170C22#1192456111yescharacteristic
171C4—21no—
172C4—1482no—
173C4—1481no—
174C4#1192450411yescharacteristic
175C4C2×#1059693911yescharacteristic
176C2—21no—
177C2—41no—
178C2—161no—
179C2—2961no—
180C2#1455766611yescharacteristic
subgroupG/H
centerC2#14557666
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#472C2
socleC2×C37#447
hypercenter#472D37
hypocenterC37#2193
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #14558350C2semidirect
2. #14557969C2semidirect
3. C2×#11924480C2semidirect
4. #14557348C2semidirect
5. #14557339C2semidirect
6. #14557317C2semidirect
7. C37×#472C2semidirect
94. #472D37semidirect
98. C37#2193semidirect

Maximal subgroups

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

subgroupindex
#145583502
#145579692
C2×#119244802
#145573482
#145573392
#145573172
C37×#4722
#219337