Finite Group Databasebeta

← #17993884

Subgroups — #17993884

Order 4736.

262 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 45 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#14557920C212yesmaximal, complemented
3#14557273C211yesmaximal, characteristic, complemented
4#14557272C212yesmaximal, complemented
5C37×#496C211yesmaximal, characteristic, complemented
6C2×#10596940—22no—
7C2×#10596939—22no—
8#11924525—21no—
9#11924524C2212yes—
10#11924522—22no—
11#11924506—22no—
12#11924504—21no—
13#11924447C2212yescomplemented
14C2×SD16×C37—21no—
15C2×D8×C37—21no—
16#127×C37C2211yescharacteristic, complemented
17#124×C37C2211yescharacteristic
18#97×C37C2211yescharacteristic, complemented
19C23×D37—21no—
20C2×Q8×C37D411yescharacteristic
21C2×D4×C37—22no—
22C2×D4×C37—21no—
23C2×D4×C37D411yescharacteristic
24C2×C22⋊D37—22no—
25C2×D148—21no—
26C2×D148D412yes—
27C2×Dic74D412yes—
28SD16×C37—42no—
29D8×C37—42no—
30C2×C8×C37—21no—
31C22⋊C4×C37—22no—
32C42×C37C2311yescharacteristic
33C22⋊Dic37—21no—
34#10596940—44no—
35#10596939—44no—
36#10596938—22no—
37#10596938—22no—
38#10596938—22no—
39C4×Dic37—21no—
40C2×#64436—22no—
41C23×C37—21no—
42C23×C37—41no—
43C22×D37—22no—
44C22×D37—82no—
45C22×D37—81no—
46Q8×C37—41no—
47D4×C37—41no—
48D4×C37—42no—
49D4×C37—42no—
50D4×C37—41no—
51D4×C37—41no—
52C2×C4×C37—21no—
53C2×C4×C37C2×D412yes—
54C2×C4×C37C2×D411yescharacteristic
55C22⋊D37—82no—
56C2×Dic37—22no—
57D148—42no—
58D148—81no—
59Dic74—42no—
60C8×C37—22no—
61#64436—24no—
62C22×C37—42no—
63C22×C37—41no—
64C22×C37—82no—
65C22×C37—81no—
66C22×C37#12011yescharacteristic
67C2×D37—42no—
68C2×D37—42no—
69C2×D37—42no—
70C2×D37—84no—
71C4×C37—22no—
72C4×C37—21no—
73C4×C37—41no—
74Dic37—42no—
75#1655—371nomaximal, Sylow
76C2×C37—81no—
77C2×C37—161no—
78C2×C37#45312yes—
79C2×C37#45311yescharacteristic
80D37—82no—
81H(3,𝔽4)—371no—
82#496—372no—
83#496D3711yescharacteristic, complemented
84#329—371no—
85#329—372no—
86C37#165511yescharacteristic, complemented, Sylow
87C2×SD16—21no—
88C2×SD16—742no—
89C2×D8—21no—
90C2×D8—742no—
91#127C2×D3711yescharacteristic, complemented
92#124—372no—
93#124—742no—
94#124—741no—
95#124C2×D3711yescharacteristic
96#120—742no—
97#120—741no—
98#97—372no—
99#97C2×D3711yescharacteristic, complemented
100C24—741no—
101C2×Q8—372no—
102C2×Q8C22⋊D3711yescharacteristic
103C2×D4—22no—
104C2×D4—21no—
105C2×D4—372no—
106C2×D4—741no—
107C2×D4—742no—
108C2×D4C22⋊D3711yescharacteristic
109SD16—42no—
110SD16—1484no—
111D8—42no—
112D8—1484no—
113C2×C8—21no—
114C2×C8—742no—
115C22⋊C4—22no—
116C22⋊C4—742no—
117C22⋊C4—741no—
118C22⋊C4—742no—
119C22⋊C4—742no—
120C42—741no—
121C42C22×D3711yescharacteristic
122C23—21no—
123C23—41no—
124C23—2962no—
125C23—2961no—
126C23—742no—
127Q8—41no—
128Q8—1482no—
129D4—41no—
130D4—41no—
131D4—42no—
132D4—41no—
133D4—42no—
134D4—2961no—
135D4—2962no—
136D4—1482no—
137C2×C4—21no—
138C2×C4—742no—
139C2×C4D4×D3712yes—
140C2×C4C2×C22⋊D3711yescharacteristic
141C8—22no—
142C8—744no—
143C22—42no—
144C22—41no—
145C22—82no—
146C22—81no—
147C22—2964no—
148C22—1482no—
149C22—1482no—
150C22—1482no—
151C22#1192450411yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—1482no—
156C2—81no—
157C2—161no—
158C2—2962no—
159C2#1455769912yes—
160C2#1455770011yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#496C2
socleC22×C37#120
hypercenter#496D37
hypocenterC37#1655
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14558275C2semidirect
2. #14557920C2semidirect
3. #14557273C2semidirect
4. #14557272C2semidirect
5. C37×#496C2semidirect
13. #11924447C22semidirect
16. #127×C37C22semidirect
18. #97×C37C22semidirect
83. #496D37semidirect
86. C37#1655semidirect
91. #127C2×D37semidirect
99. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582752
#145579202
#145572732
#145572722
C37×#4962
#165537