Finite Group Databasebeta

← #17996542

Subgroups — #17996542

Order 4736.

226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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#14557968C212yesmaximal, complemented
2#14557786C211yesmaximal, characteristic, complemented
3#14557343C212yesmaximal, complemented
4#14557315C211yesmaximal, characteristic, complemented
5C37×#575C211yesmaximal, characteristic, complemented
6C2×D296C2211yescharacteristic, complemented
7#11924510—21no—
8#11924479—22no—
9#11924477—22no—
10#11924476C2212yescomplemented
11#11924468C2211yescharacteristic, complemented
12#11924458—21no—
13C2×#41×C37—21no—
14#137×C37—22no—
15AGL(1,ℤ/8)×C37—22no—
16#135×C37—21no—
17#135×C37C2212yes—
18C2×M16×C37C2211yescharacteristic
19#41×C37—22no—
20#41×C37—22no—
21#41×C37—41no—
22#41×C37—41no—
23C2×Q8×C37—21no—
24C2×D4×C37—21no—
25C2×D4×C37—41no—
26C22×C4×C37—41no—
27C22×C4×C37D411yescharacteristic
28C2×C22⋊D37—41no—
29C2×D148—21no—
30Q16×C37—21no—
31Q16×C37D412yescomplemented
32SD16×C37—22no—
33SD16×C37—22no—
34D8×C37—21no—
35D8×C37D412yescomplemented
36M16×C37—22no—
37C2×C8×C37D411yescharacteristic
38C2×C8×C37C2311yescharacteristic
39#10596938—41no—
40C4⋊Dic37—21no—
41D296—22no—
42#10596925—22no—
43C23×C37—41no—
44C23×C37D811yescharacteristic
45C22×D37—41no—
46Q8×C37—22no—
47Q8×C37—41no—
48D4×C37—22no—
49D4×C37—41no—
50D4×C37—42no—
51D4×C37—42no—
52C2×C4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37—42no—
55C2×C4×C37—41no—
56C2×C4×C37—42no—
57C2×C4×C37D811yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C22⋊D37—82no—
60C2×Dic37—41no—
61D148—41no—
62D148—41no—
63C8×C37—21no—
64C8×C37C2×D412yes—
65C22×C37—21no—
66C22×C37—41no—
67C22×C37—42no—
68C22×C37—82no—
69C22×C37C2×D811yescharacteristic
70C2×D37—81no—
71C2×D37—81no—
72C2×D37—81no—
73C4×C37—21no—
74C4×C37—42no—
75C4×C37#12011yescharacteristic
76C4×C37AGL(1,ℤ/8)11yescharacteristic
77Dic37—81no—
78#2190—371nomaximal, Sylow
79C2×C37—21no—
80C2×C37—41no—
81C2×C37—82no—
82C2×C37#44711yescharacteristic
83D37—161no—
84#575D3711yescharacteristic, complemented
85#509—372no—
86#469—371no—
87#360—372no—
88#349—371no—
89C37#219011yescharacteristic, complemented, Sylow
90C2×#41—21no—
91#137—22no—
92AGL(1,ℤ/8)—22no—
93#135—21no—
94#135C2×D3712yes—
95C2×D8—371no—
96C2×M16C2×D3711yescharacteristic
97#121—741no—
98SD32—742no—
99D16—742no—
100M32—372no—
101#106—371no—
102#102—741no—
103#41—22no—
104#41—22no—
105#41—41no—
106#41—41no—
107C2×Q8—21no—
108C2×D4—21no—
109C2×D4—41no—
110C2×D4—741no—
111C2×D4—1481no—
112C22×C4—41no—
113C22×C4C22⋊D3711yescharacteristic
114Q16—21no—
115Q16C22⋊D3712yescomplemented
116SD16—22no—
117SD16—22no—
118D8—21no—
119D8—742no—
120D8C22⋊D3712yescomplemented
121M16—22no—
122C2×C8C22⋊D3711yescharacteristic
123C2×C8C22×D3711yescharacteristic
124C4⋊C4—741no—
125C22⋊C4—1481no—
126C16—742no—
127C23—41no—
128C23—1481no—
129C23#1059693911yescharacteristic
130Q8—22no—
131Q8—41no—
132D4—22no—
133D4—41no—
134D4—42no—
135D4—42no—
136D4—2962no—
137D4—1481no—
138D4—1481no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—42no—
144C2×C4—1481no—
145C2×C4#1059693911yescharacteristic
146C2×C4C2×C22⋊D3711yescharacteristic
147C8—21no—
148C8C2×C22⋊D3712yes—
149C22—21no—
150C22—41no—
151C22—42no—
152C22—82no—
153C22—2961no—
154C22—2961no—
155C22—2961no—
156C22C2×#1059693911yescharacteristic
157C4—21no—
158C4—42no—
159C4—2961no—
160C4#1192450511yescharacteristic
161C4#1192456211yescharacteristic
162C2—21no—
163C2—41no—
164C2—82no—
165C2—5921no—
166C2#1455766711yescharacteristic
subgroupG/H
centerC2#14557667
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#575C2
socleC2×C37#447
hypercenter#575D37
hypocenterC37#2190
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14557968C2semidirect
2. #14557786C2semidirect
3. #14557343C2semidirect
4. #14557315C2semidirect
5. C37×#575C2semidirect
6. C2×D296C22semidirect
10. #11924476C22semidirect
11. #11924468C22semidirect
31. Q16×C37D4semidirect
35. D8×C37D4semidirect
84. #575D37semidirect
89. C37#2190semidirect
115. Q16C22⋊D37semidirect
120. D8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145579682
#145577862
#145573432
#145573152
C37×#5752
#219037