Finite Group Databasebeta

← #17996596

Subgroups — #17996596

Order 4736.

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

normal subgroups only

This group has 270 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#14558275C211yesmaximal, characteristic, complemented
2#14557720C212yesmaximal, complemented
3#14557328C211yesmaximal, characteristic, complemented
4#14557321C212yesmaximal, complemented
5C37×#455C211yesmaximal, characteristic, complemented
6#11924525—21no—
7#11924524—21no—
8#11924522—22no—
9#11924506—22no—
10#11924504—22no—
11#11924504C2212yes—
12#11924451—22no—
13#11924451C2212yes—
14H(5,𝔽2)×C37C2211yescharacteristic
15#137×C37—21no—
16#124×C37C2211yescharacteristic
17#104×C37—21no—
18#100×C37C2211yescharacteristic
19C23×D37D412yescomplemented
20#41×C37—21no—
21#41×C37—41no—
22C2×Q8×C37D411yescharacteristic, complemented
23C2×D4×C37—22no—
24C2×D4×C37—41no—
25C2×D4×C37C2311yescharacteristic
26C2×C22⋊D37—22no—
27C2×C22⋊D37—42no—
28C2×D148—21no—
29C2×D148—21no—
30C2×Dic74—21no—
31Q16×C37—41no—
32SD16×C37—41no—
33M16×C37—21no—
34C22⋊C4×C37—22no—
35C42×C37D411yescharacteristic, complemented
36C22⋊Dic37—22no—
37C22⋊Dic37D412yescomplemented
38#10596938—22no—
39#10596938—22no—
40#10596938—22no—
41#10596938—42no—
42C4×Dic37—21no—
43C23×C37—22no—
44C23×C37C2×D412yes—
45C22×D37—22no—
46C22×D37—42no—
47C22×D37—82no—
48Q8×C37—21no—
49Q8×C37—41no—
50D4×C37—21no—
51D4×C37—41no—
52D4×C37—42no—
53D4×C37—41no—
54C2×C4×C37—22no—
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37C2×D411yescharacteristic
59C22⋊D37—82no—
60C22⋊D37—84no—
61C2×Dic37—22no—
62C2×Dic37—42no—
63D148—81no—
64D148—81no—
65Dic74—81no—
66C8×C37—41no—
67C22×C37—22no—
68C22×C37—42no—
69C22×C37—41no—
70C22×C37—82no—
71C22×C37#12011yescharacteristic
72C2×D37—42no—
73C2×D37—42no—
74C2×D37—44no—
75C2×D37—42no—
76C2×D37—82no—
77C4×C37—21no—
78C4×C37—41no—
79C4×C37—41no—
80C4×C37—41no—
81Dic37—42no—
82Dic37—82no—
83#2199—371nomaximal, Sylow
84C2×C37—21no—
85C2×C37—42no—
86C2×C37—81no—
87C2×C37B(4,𝔽2)11yescharacteristic
88D37—82no—
89H(3,𝔽4)—371no—
90B(4,𝔽2)—372no—
91#455D3711yescharacteristic, complemented
92#354—371no—
93AΣL(1,𝔽16)—372no—
94C37#219911yescharacteristic, complemented, Sylow
95H(5,𝔽2)C2×D3711yescharacteristic
96#137—21no—
97#124—742no—
98#124—741no—
99#124—741no—
100#124C2×D3711yescharacteristic
101#120—372no—
102#120—742no—
103#120—742no—
104#104—21no—
105#100C2×D3711yescharacteristic
106#99—372no—
107#99—742no—
108C24—372no—
109#41—21no—
110#41—41no—
111C2×Q8—741no—
112C2×Q8C22⋊D3711yescharacteristic, complemented
113C2×D4—22no—
114C2×D4—41no—
115C2×D4—741no—
116C2×D4—741no—
117C2×D4—742no—
118C2×D4—1482no—
119C2×D4C22×D3711yescharacteristic
120Q16—41no—
121SD16—41no—
122M16—21no—
123C22⋊C4—22no—
124C22⋊C4—372no—
125C22⋊C4—742no—
126C22⋊C4—742no—
127C22⋊C4—742no—
128C22⋊C4—742no—
129C22⋊C4—1482no—
130C42—741no—
131C42C22⋊D3711yescharacteristic, complemented
132C23—22no—
133C23—2962no—
134C23—742no—
135C23—1482no—
136C23D4×D3712yes—
137Q8—21no—
138Q8—41no—
139Q8—2961no—
140D4—21no—
141D4—41no—
142D4—42no—
143D4—41no—
144D4—2961no—
145D4—2961no—
146D4—2964no—
147D4—2962no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—742no—
153C2×C4—1482no—
154C2×C4C2×C22⋊D3711yescharacteristic
155C8—41no—
156C22—22no—
157C22—42no—
158C22—41no—
159C22—82no—
160C22—2962no—
161C22—1482no—
162C22—1482no—
163C22—1484no—
164C22—1482no—
165C22#1192450411yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—41no—
170C4—2962no—
171C4—1482no—
172C2—21no—
173C2—42no—
174C2—81no—
175C2—2962no—
176C2#1455771911yescharacteristic
subgroupG/H
centerC2#14557719
commutator, cosocleC2×D4×C37C23
FrattiniC2×D4C22×D37
FittingC37×#455C2
socleC2×C37B(4,𝔽2)
hypercenter#455D37
hypocenterC37#2199
LCSG ▷ C2×D4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #14558275C2semidirect
2. #14557720C2semidirect
3. #14557328C2semidirect
4. #14557321C2semidirect
5. C37×#455C2semidirect
19. C23×D37D4semidirect
22. C2×Q8×C37D4semidirect
35. C42×C37D4semidirect
37. C22⋊Dic37D4semidirect
91. #455D37semidirect
94. C37#2199semidirect
112. C2×Q8C22⋊D37semidirect
131. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145582752
#145577202
#145573282
#145573212
C37×#4552
#219937