Finite Group Databasebeta

← #17993886

Subgroups — #17993886

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#14557923C211yesmaximal, characteristic, complemented
3#14557922C212yesmaximal, complemented
4#14557272C212yesmaximal, complemented
5C37×#329C211yesmaximal, characteristic, complemented
6C2×#10596930—22no—
7C2×#10596941—21no—
8C2×D296—22no—
9C2×#10596939—21no—
10#11924533C2211yescharacteristic, complemented
11#11924525—21no—
12#11924524C2212yes—
13#11924522—22no—
14#11924506—22no—
15#11924504—21no—
16#11924447C2211yescharacteristic, complemented
17#124×C37C2211yescharacteristic
18#97×C37C2212yescomplemented
19C23×D37—21no—
20C2×Q8×C37D411yescharacteristic
21C2×D4×C37D411yescharacteristic
22C2×C22⋊D37—22no—
23C2×D148—21no—
24C2×D148—22no—
25C2×D148—21no—
26C2×D148D412yes—
27C2×Dic74D412yes—
28C2×C8×C37—22no—
29C22⋊C4×C37—22no—
30C42×C37C2311yescharacteristic
31C22⋊Dic37—21no—
32#10596941—42no—
33#10596939—42no—
34#10596938—22no—
35#10596938—22no—
36#10596938—22no—
37C4×Dic37—21no—
38C2×#64436—21no—
39D296—44no—
40#10596930—44no—
41C23×C37—21no—
42C22×D37—22no—
43C22×D37—41no—
44C22×D37—82no—
45C22×D37—81no—
46Q8×C37—41no—
47D4×C37—41no—
48C2×C4×C37—21no—
49C2×C4×C37C2×D411yescharacteristic
50C2×C4×C37C2×D412yes—
51C22⋊D37—82no—
52C2×Dic37—22no—
53D148—42no—
54D148—42no—
55D148—42no—
56D148—41no—
57D148—41no—
58D148—81no—
59Dic74—42no—
60C8×C37—24no—
61#64436—22no—
62C22×C37—42no—
63C22×C37—41no—
64C22×C37#12011yescharacteristic
65C2×D37—42no—
66C2×D37—42no—
67C2×D37—42no—
68C2×D37—84no—
69C2×D37—82no—
70C2×D37—81no—
71C4×C37—21no—
72C4×C37—22no—
73C4×C37—41no—
74Dic37—42no—
75#1655—371nomaximal, Sylow
76C2×C37—81no—
77C2×C37#45312yes—
78C2×C37#45311yescharacteristic
79D37—82no—
80D37—161no—
81H(3,𝔽4)—371no—
82#496—371no—
83#496—372no—
84#329—372no—
85#329D3711yescharacteristic, complemented
86C37#165511yescharacteristic, complemented, Sylow
87C2×SD16—742no—
88C2×SD16—741no—
89C2×D8—742no—
90C2×D8—741no—
91#127—371no—
92#124—372no—
93#124—742no—
94#124—741no—
95#124C2×D3711yescharacteristic
96#120—742no—
97#120—741no—
98#97—371no—
99#97C2×D3712yescomplemented
100C24—741no—
101C2×Q8—372no—
102C2×Q8D14811yescharacteristic
103C2×D4—372no—
104C2×D4—741no—
105C2×D4—742no—
106C2×D4—741no—
107C2×D4—742no—
108C2×D4D14811yescharacteristic
109SD16—1484no—
110SD16—1482no—
111D8—1484no—
112D8—1482no—
113C2×C8—22no—
114C2×C8—741no—
115C22⋊C4—22no—
116C22⋊C4—742no—
117C22⋊C4—741no—
118C22⋊C4—742no—
119C22⋊C4—742no—
120C42—741no—
121C42C22×D3711yescharacteristic
122C23—21no—
123C23—2962no—
124C23—2961no—
125C23—742no—
126C23—1481no—
127Q8—41no—
128Q8—1482no—
129D4—41no—
130D4—2961no—
131D4—2962no—
132D4—1482no—
133D4—1481no—
134D4—1482no—
135D4—1481no—
136D4—1482no—
137C2×C4—21no—
138C2×C4—742no—
139C2×C4C2×D14811yescharacteristic
140C2×C4D4×D3712yes—
141C8—24no—
142C8—742no—
143C22—42no—
144C22—41no—
145C22—2964no—
146C22—2962no—
147C22—2961no—
148C22—1482no—
149C22—1482no—
150C22—1482no—
151C22#1192450611yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—1482no—
156C2—81no—
157C2—2962no—
158C2—5921no—
159C2#1455770212yes—
160C2#1455770311yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#329C2
socleC22×C37#120
hypercenter#329D37
hypocenterC37#1655
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #14558275C2semidirect
2. #14557923C2semidirect
3. #14557922C2semidirect
4. #14557272C2semidirect
5. C37×#329C2semidirect
10. #11924533C22semidirect
16. #11924447C22semidirect
18. #97×C37C22semidirect
85. #329D37semidirect
86. C37#1655semidirect
99. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582752
#145579232
#145579222
#145572722
C37×#3292
#165537