Finite Group Databasebeta

← #17996546

Subgroups — #17996546

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#14557974C212yesmaximal, complemented
3#14557342C212yesmaximal, complemented
4#14557315C211yesmaximal, characteristic, complemented
5C37×#470C211yesmaximal, characteristic, complemented
6C2×#10596962—21no—
7#11924569—22no—
8#11924564—22no—
9#11924558—21no—
10#11924558C2212yes—
11#11924482—22no—
12#11924479—22no—
13#11924476C2212yescomplemented
14C2×Q16×C37C2211yescharacteristic, complemented
15C2×M16×C37C2211yescharacteristic
16C22⋊Q8×C37—21no—
17#106×C37C2211yescharacteristic, complemented
18#103×C37—21no—
19C2×Q8×C37—21no—
20C22×C4×C37D411yescharacteristic
21C2×C22⋊D37—41no—
22#10596962—22no—
23#10596962—22no—
24#10596962—41no—
25#10596962—41no—
26C2×D148—21no—
27C2×C4×D37—41no—
28C2×Dic74—21no—
29Q16×C37—22no—
30M16×C37—22no—
31C2×C8×C37D411yescharacteristic
32C2×C8×C37C2311yescharacteristic
33C4⋊C4×C37—21no—
34C4⋊C4×C37—41no—
35C22⋊C4×C37—41no—
36Dic148—21no—
37Dic148D412yes—
38D296—21no—
39D296D412yes—
40#10596930—22no—
41#10596930—22no—
42#10596925—22no—
43C23×C37D811yescharacteristic
44C22×D37—41no—
45Q8×C37—41no—
46Q8×C37—41no—
47C2×C4×C37—21no—
48C2×C4×C37—21no—
49C2×C4×C37—41no—
50C2×C4×C37—41no—
51C2×C4×C37D811yescharacteristic
52C2×C4×C37C2×D411yescharacteristic
53C22⋊D37—42no—
54C22⋊D37—42no—
55C2×Dic37—41no—
56D148—22no—
57D148—41no—
58C4×D37—42no—
59C4×D37—42no—
60Dic74—22no—
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—81no—
71C4×C37—81no—
72C4×C37#12011yescharacteristic
73C4×C37AGL(1,ℤ/8)11yescharacteristic
74Dic37—42no—
75#2191—371nomaximal, Sylow
76C2×C37—21no—
77C2×C37—41no—
78C2×C37#44711yescharacteristic
79D37—82no—
80#575—371no—
81#510—372no—
82#470D3711yescharacteristic, complemented
83#360—372no—
84#349—371no—
85C37#219111yescharacteristic, complemented, Sylow
86C2×#41—741no—
87#137—742no—
88AGL(1,ℤ/8)—742no—
89#135—372no—
90#135—741no—
91C2×Q16C2×D3711yescharacteristic, complemented
92C2×M16C2×D3711yescharacteristic
93C22⋊Q8—21no—
94Q32—742no—
95SD32—742no—
96M32—372no—
97#106C2×D3711yescharacteristic, complemented
98#103—21no—
99#41—742no—
100#41—742no—
101#41—1481no—
102#41—1481no—
103C2×Q8—21no—
104C2×Q8—741no—
105C2×D4—741no—
106C2×D4—1481no—
107C22×C4—1481no—
108C22×C4C22⋊D3711yescharacteristic
109Q16—22no—
110Q16—372no—
111Q16—741no—
112SD16—742no—
113SD16—742no—
114D8—372no—
115D8—741no—
116M16—22no—
117C2×C8C22⋊D3711yescharacteristic
118C2×C8C22×D3711yescharacteristic
119C4⋊C4—21no—
120C4⋊C4—41no—
121C22⋊C4—41no—
122C16—742no—
123C23—1481no—
124C23#1059693911yescharacteristic
125Q8—41no—
126Q8—41no—
127Q8—742no—
128Q8—1481no—
129D4—742no—
130D4—1481no—
131D4—1482no—
132D4—1482no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—1482no—
138C2×C4—1481no—
139C2×C4—1482no—
140C2×C4#1059693911yescharacteristic
141C2×C4C2×C22⋊D3711yescharacteristic
142C8—21no—
143C8D4×D3712yes—
144C22—21no—
145C22—41no—
146C22—2962no—
147C22—1482no—
148C22C2×#1059693911yescharacteristic
149C4—21no—
150C4—81no—
151C4—81no—
152C4—1482no—
153C4#1192450411yescharacteristic
154C4#1192456111yescharacteristic
155C2—21no—
156C2—41no—
157C2—2962no—
158C2#1455766611yescharacteristic
subgroupG/H
centerC2#14557666
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#470C2
socleC2×C37#447
prime radical#14558333C2
hypercenter#470D37
hypocenterC37#2191
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #14557974C2semidirect
3. #14557342C2semidirect
4. #14557315C2semidirect
5. C37×#470C2semidirect
13. #11924476C22semidirect
14. C2×Q16×C37C22semidirect
17. #106×C37C22semidirect
82. #470D37semidirect
85. C37#2191semidirect
91. C2×Q16C2×D37semidirect
97. #106C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583332
#145579742
#145573422
#145573152
C37×#4702
#219137