Finite Group Databasebeta

← #17996563

Subgroups — #17996563

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#14557971C211yesmaximal, characteristic, complemented
3C2×#11924479C211yesmaximal, characteristic, complemented
4#14557804C211yesmaximal, characteristic, complemented
5#14557339C211yesmaximal, characteristic, complemented
6#14557318C211yesmaximal, characteristic, complemented
7C37×#362C211yesmaximal, characteristic, complemented
8#11924584—21no—
9#11924568—22no—
10#11924567—21no—
11#11924564—21no—
12#11924559—21no—
13#11924558C2211yescharacteristic
14Q16×D37—21no—
15C2×D296C2211yescharacteristic
16#11924542C2211yescharacteristic
17#11924481—21no—
18#11924479—22no—
19D592—21no—
20C2×#10596925C2211yescharacteristic
21#11924452—21no—
22C2×Q16×C37C2211yescharacteristic
23M32×C37C2211yescharacteristic
24#108×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26#10596966—22no—
27#10596966—41no—
28Q8×D37—22no—
29Q8×D37—41no—
30#10596962—21no—
31#10596962—42no—
32#10596962D411yescharacteristic
33C2×D148—21no—
34Q16×C37—21no—
35Q16×C37D412yes—
36M16×C37—21no—
37C2×C8×C37C2311yescharacteristic
38#10596942—22no—
39#10596941—22no—
40#10596934D411yescharacteristic
41Dic148D411yescharacteristic
42D296—21no—
43D296—21no—
44D296—41no—
45D296D411yescharacteristic
46#10596930—21no—
47#10596930—41no—
48#10596929—21no—
49C8×D37—21no—
50C16×C37—21no—
51#10596925—21no—
52C22×D37—41no—
53Q8×C37—22no—
54Q8×C37—41no—
55C2×C4×C37—41no—
56C2×C4×C37C2×D411yescharacteristic
57C22⋊D37—21no—
58C22⋊D37—41no—
59D148—21no—
60D148—42no—
61D148—41no—
62D148—41no—
63D148D811yescharacteristic
64C4×D37—21no—
65C4×D37—42no—
66C4×D37—42no—
67C4×D37—41no—
68Dic74—21no—
69Dic74—42no—
70Dic74D811yescharacteristic
71C8×C37—41no—
72C8×C37C2×D411yescharacteristic
73C8×C37C2×D411yescharacteristic
74#64436—21no—
75C22×C37AGL(1,ℤ/8)11yescharacteristic
76C2×D37—21no—
77C2×D37—41no—
78C2×D37—81no—
79C2×D37—161no—
80C4×C37—42no—
81C4×C37#12011yescharacteristic
82C4×C37C2×D811yescharacteristic
83Dic37—21no—
84Dic37—41no—
85#2193—371nomaximal, Sylow
86C2×C37—21no—
87C2×C37#44711yescharacteristic
88D37—41no—
89D37—81no—
90D37—161no—
91#578—371no—
92#509—371no—
93C2×SD32—371no—
94#472—371no—
95#362D3711yescharacteristic, complemented
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×D8—371no—
108#131—371no—
109SD32—741no—
110SD32—742no—
111D16—741no—
112M32C2×D3711yescharacteristic
113C2×C16—371no—
114#108C2×D3711yescharacteristic
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—741no—
125Q16—21no—
126Q16—371no—
127Q16—742no—
128Q16D14812yes—
129SD16—742no—
130SD16—741no—
131SD16—1481no—
132D8—371no—
133D8—741no—
134D8—741no—
135D8—1481no—
136M16—21no—
137M16—371no—
138M16—741no—
139C2×C8—741no—
140C2×C8C22×D3711yescharacteristic
141C16—21no—
142C16—741no—
143C23—1481no—
144Q8—22no—
145Q8—41no—
146Q8—371no—
147Q8—741no—
148Q8—1482no—
149D4—371no—
150D4—741no—
151D4—741no—
152D4—1482no—
153D4—1481no—
154D4—1481no—
155D4—1481no—
156C2×C4—41no—
157C2×C4—741no—
158C2×C4—1482no—
159C2×C4—1482no—
160C2×C4—1481no—
161C2×C4D4×D3711yescharacteristic
162C8—41no—
163C8—741no—
164C8C2×D14811yescharacteristic
165C8D4×D3711yescharacteristic
166C22—2961no—
167C22—741no—
168C22—5921no—
169C22—1481no—
170C22#1192456311yescharacteristic
171C4—42no—
172C4—741no—
173C4—1481no—
174C4#1192450611yescharacteristic
175C4D8×D3711yescharacteristic
176C2—21no—
177C2—2961no—
178C2—5921no—
179C2—1481no—
180C2#1455766811yescharacteristic
subgroupG/H
centerC2#14557668
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#362C2
socleC2×C37#447
hypercenter#362D37
hypocenterC37#2193
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
1. #14558346C2semidirect
2. #14557971C2semidirect
3. C2×#11924479C2semidirect
4. #14557804C2semidirect
5. #14557339C2semidirect
6. #14557318C2semidirect
7. C37×#362C2semidirect
95. #362D37semidirect
98. C37#2193semidirect

Maximal subgroups

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

subgroupindex
#145583462
#145579712
C2×#119244792
#145578042
#145573392
#145573182
C37×#3622
#219337