Finite Group Databasebeta

← #17996549

Subgroups — #17996549

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#14558333C211yesmaximal, characteristic
2#14557976C212yesmaximal, complemented
3#14557791C211yesmaximal, characteristic, complemented
4#14557344C212yesmaximal, complemented
5C37×#349C211yesmaximal, characteristic, complemented
6C2×#10596962—21no—
7#11924569—22no—
8#11924564—22no—
9#11924558—21no—
10#11924558C2212yes—
11C2×Dic148C2211yescharacteristic, complemented
12#11924515—21no—
13Dic296—22no—
14#11924481—22no—
15#11924468C2211yescharacteristic, complemented
16#11924461—21no—
17C2×M16×C37C2211yescharacteristic
18M32×C37C2212yescomplemented
19C22×C4×C37D411yescharacteristic
20C2×C22⋊D37—41no—
21#10596962—22no—
22#10596962—22no—
23#10596962—41no—
24#10596962—41no—
25C2×D148—21no—
26C2×C4×D37—41no—
27C2×Dic74—21no—
28C2×Dic74—21no—
29M16×C37—22no—
30C2×C8×C37D411yescharacteristic
31C2×C8×C37C2311yescharacteristic
32C22⋊Dic37—41no—
33C4⋊Dic37—21no—
34#10596936—41no—
35Dic148—21no—
36Dic148—22no—
37Dic148D412yes—
38D296—21no—
39D296D412yes—
40#10596930—22no—
41#10596930—22no—
42C16×C37—22no—
43C23×C37D811yescharacteristic
44C22×D37—41no—
45C2×C4×C37—21no—
46C2×C4×C37—21no—
47C2×C4×C37D811yescharacteristic
48C2×C4×C37C2×D411yescharacteristic
49C22⋊D37—42no—
50C22⋊D37—42no—
51C2×Dic37—41no—
52C2×Dic37—41no—
53C2×Dic37—41no—
54D148—22no—
55D148—41no—
56C4×D37—42no—
57C4×D37—42no—
58Dic74—22no—
59Dic74—41no—
60Dic74—41no—
61Dic74—41no—
62C8×C37—21no—
63C8×C37C2×D412yes—
64C22×C37—21no—
65C22×C37—41no—
66C22×C37C2×D811yescharacteristic
67C2×D37—42no—
68C2×D37—82no—
69C4×C37—21no—
70C4×C37#12011yescharacteristic
71C4×C37AGL(1,ℤ/8)11yescharacteristic
72Dic37—42no—
73Dic37—81no—
74Dic37—81no—
75#2191—371nomaximal, Sylow
76C2×C37—21no—
77C2×C37—41no—
78C2×C37#44711yescharacteristic
79D37—82no—
80#575—371no—
81#510—372no—
82#470—371no—
83#360—372no—
84#349D3711yescharacteristic, complemented
85C37#219111yescharacteristic, complemented, Sylow
86C2×#41—741no—
87#137—742no—
88AGL(1,ℤ/8)—742no—
89#135—372no—
90#135—741no—
91C2×Q16—371no—
92C2×M16C2×D3711yescharacteristic
93C22⋊Q8—741no—
94Q32—742no—
95SD32—742no—
96M32C2×D3712yescomplemented
97#106—371no—
98#103—741no—
99#41—742no—
100#41—742no—
101#41—1481no—
102#41—1481no—
103C2×Q8—741no—
104C2×Q8—741no—
105C2×D4—741no—
106C2×D4—1481no—
107C22×C4—1481no—
108C22×C4D14811yescharacteristic
109Q16—372no—
110Q16—741no—
111Q16—742no—
112SD16—742no—
113SD16—742no—
114D8—372no—
115D8—741no—
116M16—22no—
117C2×C8D14811yescharacteristic
118C2×C8C22×D3711yescharacteristic
119C4⋊C4—741no—
120C4⋊C4—1481no—
121C22⋊C4—1481no—
122C16—22no—
123C23—1481no—
124C23D29611yescharacteristic
125Q8—742no—
126Q8—1481no—
127Q8—1481no—
128Q8—1481no—
129D4—742no—
130D4—1481no—
131D4—1482no—
132D4—1482no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—1482no—
136C2×C4—1481no—
137C2×C4—1481no—
138C2×C4—1481no—
139C2×C4—1482no—
140C2×C4D29611yescharacteristic
141C2×C4C2×D14811yescharacteristic
142C8—21no—
143C8D4×D3712yes—
144C22—21no—
145C22—41no—
146C22—2962no—
147C22—1482no—
148C22C2×D29611yescharacteristic
149C4—21no—
150C4—2961no—
151C4—2961no—
152C4—1482no—
153C4#1192450611yescharacteristic
154C4#1192456411yescharacteristic
155C2—21no—
156C2—41no—
157C2—2962no—
158C2#1455766911yescharacteristic
subgroupG/H
centerC2#14557669
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#349C2
socleC2×C37#447
prime radical#14558333C2
hypercenter#349D37
hypocenterC37#2191
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #14557976C2semidirect
3. #14557791C2semidirect
4. #14557344C2semidirect
5. C37×#349C2semidirect
11. C2×Dic148C22semidirect
15. #11924468C22semidirect
18. M32×C37C22semidirect
84. #349D37semidirect
85. C37#2191semidirect
96. M32C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583332
#145579762
#145577912
#145573442
C37×#3492
#219137