Finite Group Databasebeta

← #17995757

Subgroups — #17995757

Order 4736.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#14558164C211yesmaximal, characteristic
2#14557542C212yesmaximal
3#14557302C211yesmaximal, characteristic
4#14557293C212yesmaximal
5C37×#391C211yesmaximal, characteristic
6C2×#10596934C2212yes—
7#11924535—22no—
8#11924527—22no—
9#11924515—22no—
10#11924495C2212yes—
11#11924460—22no—
12#11924460—22no—
13C22×Q8×C37C2211yescharacteristic
14C2×C4⋊C4×C37C2211yescharacteristic
15C2×C42×C37C2211yescharacteristic
16#95×C37—22no—
17C2×Q8×C37—21no—
18C2×Q8×C37—22no—
19C2×Q8×C37—22no—
20C2×Q8×C37Q812yescomplemented
21C22×C4×C37—21no—
22C22×C4×C37—21no—
23C22×C4×C37D412yes—
24C22×C4×C37C2311yescharacteristic
25C2×Dic74—22no—
26C4⋊C4×C37—22no—
27C42×C37—22no—
28C22⋊Dic37—22no—
29C4⋊Dic37—22no—
30C4⋊Dic37D412yes—
31C4⋊Dic37D412yes—
32#10596936—24no—
33C4×Dic37—22no—
34#10596934—22no—
35#10596934—22no—
36C2×#64436—22no—
37C23×C37C2×D411yescharacteristic
38Q8×C37—24no—
39Q8×C37—42no—
40C2×C4×C37—22no—
41C2×C4×C37—22no—
42C2×C4×C37—22no—
43C2×C4×C37—41no—
44C2×C4×C37—41no—
45C2×C4×C37—41no—
46C2×C4×C37—41no—
47C2×C4×C37—42no—
48C2×C4×C37C2×D412yes—
49C2×C4×C37C2×Q811yescharacteristic
50C2×C4×C37#4111yescharacteristic
51C2×C4×C37#4112yes—
52C2×Dic37—22no—
53C2×Dic37—22no—
54Dic74—82no—
55#64436—42no—
56C22×C37—21no—
57C22×C37—21no—
58C22×C37#12011yescharacteristic
59C22×C37C22⋊Q811yescharacteristic
60C22×C37#12411yescharacteristic
61C4×C37—42no—
62C4×C37—42no—
63C4×C37—42no—
64C4×C37C22⋊Q812yes—
65C4×C37#12412yes—
66Dic37—42no—
67Dic37—42no—
68#2028—371nomaximal, Sylow
69C2×C37—21no—
70C2×C37—21no—
71C2×C37#39311yescharacteristic
72C2×C37#45511yescharacteristic
73C2×C37#45611yescharacteristic
74#544—371no—
75#419—372no—
76#391D3711yescharacteristic
77#343—371no—
78#339—372no—
79C37#202811yescharacteristic, complemented, Sylow
80C22×Q8C2×D3711yescharacteristic
81C2×M16—372no—
82C4⋊Q8—742no—
83#125—742no—
84C22⋊Q8—742no—
85#117—372no—
86C2×C4⋊C4C2×D3711yescharacteristic
87C2×C42C2×D3711yescharacteristic
88#103—742no—
89#103—742no—
90#95—22no—
91C2×Q8—21no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8—742no—
95C2×Q8Dic7412yescomplemented
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D3712yes—
99C22×C4C22×D3711yescharacteristic
100M16—742no—
101M16—742no—
102C2×C8—742no—
103C4⋊C4—22no—
104C4⋊C4—372no—
105C4⋊C4—372no—
106C4⋊C4—744no—
107C4⋊C4—742no—
108C22⋊C4—742no—
109C42—22no—
110C42—742no—
111C23C2×C22⋊D3711yescharacteristic
112Q8—24no—
113Q8—42no—
114Q8—2962no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—742no—
124C2×C4—742no—
125C2×C4C2×Dic7411yescharacteristic
126C2×C4#1059696211yescharacteristic
127C2×C4D4×D3712yes—
128C2×C4#1059696412yes—
129C8—1482no—
130C22—21no—
131C22—21no—
132C22#1192450411yescharacteristic
133C22#1192451511yescharacteristic
134C22#1192452311yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—1482no—
139C4—1482no—
140C4#1192451312yes—
141C4#1192452212yes—
142C2—21no—
143C2—21no—
144C2#1455744511yescharacteristic
145C2#1455771011yescharacteristic
146C2#1455771511yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#391C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#391D37
hypocenterC37#2028
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
20. C2×Q8×C37Q8semidirect
79. C37#2028semidirect
95. C2×Q8Dic74semidirect

Maximal subgroups

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

subgroupindex
#145581642
#145575422
#145573022
#145572932
C37×#3912
#202837