Finite Group Databasebeta

← #17993902

Subgroups — #17993902

Order 4736.

228 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 49 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#14557928C211yesmaximal, characteristic, complemented
2#14557892C212yesmaximal, complemented
3#14557273C212yesmaximal, complemented
4#14557273C211yesmaximal, characteristic, complemented
5C37×H(3,𝔽4)C211yesmaximal, characteristic
6C2×#10596942—21no—
7C2×#10596940—21no—
8#11924536C2211yescharacteristic, complemented
9#11924460—22no—
10#11924457—22no—
11#11924447C2212yescomplemented
12#11924447C2211yescharacteristic, complemented
13#124×C37—21no—
14#124×C37—22no—
15#124×C37C2212yes—
16#124×C37C2211yescharacteristic
17#120×C37—21no—
18#120×C37—22no—
19C24×C37—21no—
20C2×Q8×C37D411yescharacteristic
21C2×Q8×C37D412yes—
22C2×D4×C37—21no—
23C2×D4×C37—22no—
24C2×D4×C37D411yescharacteristic
25C2×D4×C37D412yes—
26C2×Dic74—21no—
27C22⋊C4×C37—22no—
28C22⋊C4×C37—21no—
29C22⋊C4×C37—22no—
30C22⋊C4×C37—22no—
31C22⋊C4×C37—22no—
32C42×C37—21no—
33C42×C37C2311yescharacteristic
34#10596942—42no—
35#10596940—42no—
36C4⋊Dic37—22no—
37C2×#64436—21no—
38C2×#64436—22no—
39C23×C37—21no—
40C23×C37—22no—
41C23×C37—81no—
42C23×C37—82no—
43Q8×C37—41no—
44Q8×C37—42no—
45D4×C37—41no—
46D4×C37—42no—
47D4×C37—81no—
48D4×C37—82no—
49C2×C4×C37—21no—
50C2×C4×C37—22no—
51C2×C4×C37C2×D412yes—
52C2×C4×C37C2×D411yescharacteristic
53C2×Dic37—41no—
54Dic74—41no—
55Dic74—41no—
56#64436—22no—
57#64436—42no—
58C22×C37—41no—
59C22×C37—42no—
60C22×C37—42no—
61C22×C37—42no—
62C22×C37—42no—
63C22×C37—84no—
64C22×C37#12011yescharacteristic
65C4×C37—21no—
66C4×C37—22no—
67C4×C37—41no—
68C4×C37—42no—
69Dic37—81no—
70#1659—371nomaximal, Sylow
71C2×C37—81no—
72C2×C37—82no—
73C2×C37#45311yescharacteristic
74C2×C37#45512yes—
75H(3,𝔽4)D3711yescharacteristic
76#497—371no—
77#489—372no—
78#329—371no—
79#329—372no—
80C37#165911yescharacteristic, complemented, Sylow
81C2×Q16—741no—
82C2×SD16—741no—
83C4⋊Q8—371no—
84#124—22no—
85#124—21no—
86#124C2×D3712yes—
87#124C2×D3711yescharacteristic
88#120—22no—
89#120—21no—
90#103—742no—
91#102—742no—
92#97—372no—
93#97—371no—
94C24—21no—
95C2×Q8—741no—
96C2×Q8C22⋊D3712yes—
97C2×Q8C22⋊D3711yescharacteristic
98C2×D4—21no—
99C2×D4—22no—
100C2×D4C22⋊D3712yes—
101C2×D4C22⋊D3711yescharacteristic
102Q16—1482no—
103SD16—1482no—
104C2×C8—741no—
105C2×C8—742no—
106C4⋊C4—742no—
107C22⋊C4—22no—
108C22⋊C4—21no—
109C22⋊C4—22no—
110C22⋊C4—22no—
111C22⋊C4—22no—
112C42—21no—
113C42C22×D3711yescharacteristic
114C23—21no—
115C23—22no—
116C23—81no—
117C23—82no—
118Q8—41no—
119Q8—42no—
120Q8—1481no—
121Q8—1481no—
122D4—41no—
123D4—42no—
124D4—81no—
125D4—82no—
126C2×C4—21no—
127C2×C4—22no—
128C2×C4—1481no—
129C2×C4C2×C22⋊D3712yes—
130C2×C4C2×C22⋊D3711yescharacteristic
131C8—742no—
132C8—1482no—
133C22—41no—
134C22—42no—
135C22—42no—
136C22—42no—
137C22—42no—
138C22—84no—
139C22#1192450511yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—42no—
144C4—2961no—
145C2—81no—
146C2—82no—
147C2#1455770111yescharacteristic
148C2#1455771112yes—
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
Fitting, prime radicalC37×H(3,𝔽4)C2
socleC22×C37#120
hypercenterH(3,𝔽4)D37
hypocenterC37#1659
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #14557928C2semidirect
2. #14557892C2semidirect
3. #14557273C2semidirect
4. #14557273C2semidirect
8. #11924536C22semidirect
11. #11924447C22semidirect
12. #11924447C22semidirect
80. C37#1659semidirect

Maximal subgroups

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

subgroupindex
#145579282
#145578922
#145572732
C37×H(3,𝔽4)2
#165937