Finite Group Databasebeta

← #17996559

Subgroups — #17996559

Order 4736.

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

normal subgroups only

This group has 210 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#14558346C211yesmaximal, characteristic, complemented
2#14557969C211yesmaximal, characteristic, complemented
3#14557800C211yesmaximal, characteristic, complemented
4#14557349C211yesmaximal, characteristic, complemented
5#14557341C211yesmaximal, characteristic, complemented
6#14557316C211yesmaximal, characteristic, complemented
7C2×SD32×C37C211yesmaximal, characteristic, complemented
8#11924584—21no—
9#11924568—22no—
10#11924567—21no—
11#11924562—21no—
12#11924559—21no—
13#11924558C2211yescharacteristic
14Q16×D37—21no—
15#11924542C2211yescharacteristic
16#11924480—21no—
17#11924477—21no—
18#11924476C2211yescharacteristic
19#11924472C2211yescharacteristic
20#11924453—21no—
21C2×Q16×C37C2211yescharacteristic
22C2×D8×C37C2211yescharacteristic
23SD32×C37—22no—
24C2×C16×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×D4×C37—21no—
27#10596966—22no—
28#10596966—41no—
29Q8×D37—22no—
30Q8×D37—41no—
31#10596962—21no—
32#10596962—42no—
33#10596962D411yescharacteristic
34Q16×C37—21no—
35Q16×C37D412yes—
36D8×C37—21no—
37D8×C37—21no—
38C2×C8×C37C2311yescharacteristic
39#10596942—22no—
40#10596941—22no—
41#10596940—41no—
42#10596939—41no—
43#10596934—21no—
44#10596934D411yescharacteristic
45Dic148D411yescharacteristic
46D296D411yescharacteristic
47#10596930—21no—
48#10596929—21no—
49C8×D37—21no—
50C16×C37—21no—
51#10596925—21no—
52C23×C37—41no—
53Q8×C37—22no—
54Q8×C37—41no—
55D4×C37—41no—
56D4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37C2×D411yescharacteristic
59C22⋊D37—21no—
60C22⋊D37—41no—
61D148—21no—
62D148—42no—
63D148D811yescharacteristic
64C4×D37—21no—
65C4×D37—42no—
66C4×D37—42no—
67C4×D37—41no—
68Dic74—21no—
69Dic74—42no—
70Dic74D811yescharacteristic
71C8×C37C2×D411yescharacteristic
72C8×C37C2×D411yescharacteristic
73#64436—21no—
74#64436—41no—
75C22×C37—81no—
76C22×C37—161no—
77C22×C37AGL(1,ℤ/8)11yescharacteristic
78C2×D37—21no—
79C2×D37—41no—
80C4×C37—42no—
81C4×C37#12011yescharacteristic
82C4×C37C2×D811yescharacteristic
83Dic37—21no—
84Dic37—41no—
85#2193—371nomaximal, Sylow
86C2×C37—21no—
87C2×C37—161no—
88C2×C37#44711yescharacteristic
89D37—41no—
90D37—81no—
91#578—371no—
92#509—371no—
93C2×SD32D3711yescharacteristic, complemented
94#472—371no—
95#362—371no—
96#359—371no—
97#350—371no—
98C37#219311yescharacteristic, complemented, Sylow
992−1+4—741no—
100#137—741no—
101#137—742no—
102AGL(1,ℤ/8)—741no—
103#135—371no—
104#135—741no—
105C2×Q16—741no—
106C2×Q16C2×D3711yescharacteristic
107C2×D8C2×D3711yescharacteristic
108#131—371no—
109SD32—22no—
110SD32—741no—
111D16—741no—
112M32—371no—
113C2×C16C2×D3711yescharacteristic
114#108—371no—
115#100—741no—
116#41—371no—
117#41—742no—
118#41—741no—
119#41—1482no—
120#41—1481no—
121C2×Q8—21no—
122C2×Q8—742no—
123C2×Q8—1481no—
124C2×D4—21no—
125Q16—21no—
126Q16—371no—
127Q16—742no—
128Q16C22⋊D3712yes—
129SD16—742no—
130SD16—741no—
131SD16—1481no—
132D8—21no—
133D8—21no—
134D8—371no—
135D8—1481no—
136M16—371no—
137M16—741no—
138M16—741no—
139C2×C8—741no—
140C2×C8C22×D3711yescharacteristic
141C16—21no—
142C16—741no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—371no—
147Q8—741no—
148Q8—1482no—
149D4—41no—
150D4—41no—
151D4—371no—
152D4—741no—
153D4—741no—
154D4—1482no—
155D4—1481no—
156C2×C4—41no—
157C2×C4—741no—
158C2×C4—1482no—
159C2×C4—1482no—
160C2×C4—1481no—
161C2×C4D4×D3711yescharacteristic
162C8—741no—
163C8—1481no—
164C8D4×D3711yescharacteristic
165C8C2×C22⋊D3711yescharacteristic
166C22—81no—
167C22—161no—
168C22—741no—
169C22—1481no—
170C22#1192456011yescharacteristic
171C4—42no—
172C4—741no—
173C4—1481no—
174C4#1192450411yescharacteristic
175C4D8×D3711yescharacteristic
176C2—21no—
177C2—161no—
178C2—2961no—
179C2—1481no—
180C2#1455766511yescharacteristic
subgroupG/H
centerC2#14557665
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC2×SD32×C37C2
socleC2×C37#447
hypercenterC2×SD32D37
hypocenterC37#2193
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #14558346C2semidirect
2. #14557969C2semidirect
3. #14557800C2semidirect
4. #14557349C2semidirect
5. #14557341C2semidirect
6. #14557316C2semidirect
7. C2×SD32×C37C2semidirect
93. C2×SD32D37semidirect
98. C37#2193semidirect

Maximal subgroups

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

subgroupindex
#145583462
#145579692
#145578002
#145573492
#145573412
#145573162
C2×SD32×C372
#219337