Finite Group Databasebeta

← #17996594

Subgroups — #17996594

Order 4736.

246 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 41 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#14558269C211yesmaximal, characteristic, complemented
2#14557724C212yesmaximal, complemented
3#14557700C211yesmaximal, characteristic
4#14557322C212yesmaximal, complemented
5C37×#353C211yesmaximal, characteristic, complemented
6#11924581C2211yescharacteristic
7#11924562—21no—
8#11924523—22no—
9#11924520—22no—
10#11924517—21no—
11#11924517C2212yes—
12C4×Dic74—21no—
13D4×Dic37—22no—
14#11924464—21no—
15#11924453C2211yescharacteristic
16#11924450—22no—
17#127×C37C2211yescharacteristic
18#99×C37C2212yes—
19C2×D4×C37—22no—
20C2×D4×C37D411yescharacteristic
21C2×D4×C37C2311yescharacteristic
22C2×C22⋊D37—22no—
23C22×Dic37—21no—
24C22×Dic37D412yes—
25#10596964—41no—
26D4×D37—41no—
27#10596962—21no—
28C2×Dic74—21no—
29C22⋊C4×C37—22no—
30C42×C37D411yescharacteristic
31C22⋊Dic37—22no—
32C22⋊Dic37—21no—
33C22⋊Dic37—22no—
34C22⋊Dic37D412yes—
35#10596940—41no—
36#10596939—41no—
37#10596938—42no—
38C4⋊Dic37—21no—
39C4⋊Dic37—42no—
40#10596936—22no—
41C4×Dic37—22no—
42#10596934—21no—
43C23×C37—21no—
44C23×C37C2×D412yes—
45C22×D37—22no—
46D4×C37—41no—
47D4×C37—41no—
48D4×C37—44no—
49C2×C4×C37—21no—
50C2×C4×C37—42no—
51C2×C4×C37C2×D411yescharacteristic
52C22⋊D37—42no—
53C22⋊D37—41no—
54C2×Dic37—22no—
55C2×Dic37—22no—
56C2×Dic37—22no—
57C2×Dic37—42no—
58C2×Dic37—81no—
59D148—21no—
60C4×D37—41no—
61Dic74—21no—
62Dic74—42no—
63#64436—41no—
64C22×C37—22no—
65C22×C37—42no—
66C22×C37—42no—
67C22×C37—41no—
68C22×C37#12011yescharacteristic
69C2×D37—41no—
70C2×D37—82no—
71C4×C37—22no—
72C4×C37—21no—
73C4×C37—82no—
74Dic37—42no—
75Dic37—41no—
76Dic37—42no—
77#2198—371nomaximal, Sylow
78C2×C37—21no—
79C2×C37—42no—
80C2×C37—81no—
81C2×C37B(4,𝔽2)11yescharacteristic
82D37—81no—
83#559—371no—
84#458—372no—
85#453—371no—
86#353D3711yescharacteristic, complemented
87#352—372no—
88C37#219811yescharacteristic, complemented, Sylow
89H(5,𝔽2)—371no—
90AGL(1,ℤ/8)—741no—
91#127C2×D3711yescharacteristic
92#124—742no—
93#123—372no—
94#123—742no—
95#123—741no—
96C4×Q8—741no—
97C4×D4—742no—
98#104—741no—
99#100—371no—
100#99—742no—
101#99C2×D3712yes—
102#41—741no—
103#41—1481no—
104C2×Q8—741no—
105C2×D4—22no—
106C2×D4—742no—
107C2×D4—1481no—
108C2×D4D14811yescharacteristic
109C2×D4C22×D3711yescharacteristic
110C22×C4—372no—
111C22×C4—741no—
112SD16—1481no—
113D8—1481no—
114M16—741no—
115C4⋊C4—741no—
116C4⋊C4—742no—
117C4⋊C4—1482no—
118C22⋊C4—22no—
119C22⋊C4—372no—
120C22⋊C4—742no—
121C22⋊C4—741no—
122C22⋊C4—742no—
123C22⋊C4—1482no—
124C42—742no—
125C42D14811yescharacteristic
126C23—21no—
127C23—742no—
128C23D4×D3712yes—
129Q8—741no—
130Q8—1482no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—741no—
135D4—1482no—
136D4—1481no—
137C2×C4—21no—
138C2×C4—42no—
139C2×C4—2961no—
140C2×C4—742no—
141C2×C4—742no—
142C2×C4—742no—
143C2×C4—1481no—
144C2×C4—1482no—
145C2×C4C2×D14811yescharacteristic
146C8—1481no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—2962no—
152C22—1481no—
153C22#1192450611yescharacteristic
154C4—22no—
155C4—21no—
156C4—82no—
157C4—1482no—
158C4—1482no—
159C4—1481no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—2961no—
164C2#1455772111yescharacteristic
subgroupG/H
centerC2#14557721
commutator, cosocleC2×D4×C37C23
FrattiniC2×D4C22×D37
FittingC37×#353C2
socleC2×C37B(4,𝔽2)
prime radical#14557700C2
hypercenter#353D37
hypocenterC37#2198
LCSG ▷ C2×D4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
1. #14558269C2semidirect
2. #14557724C2semidirect
4. #14557322C2semidirect
5. C37×#353C2semidirect
86. #353D37semidirect
88. C37#2198semidirect

Maximal subgroups

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

subgroupindex
#145582692
#145577242
#145577002
#145573222
C37×#3532
#219837