Finite Group Databasebeta

← #18009696

Subgroups — #18009696

Order 4736.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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#14558519C211yesmaximal, characteristic
2#14558512C211yesmaximal, characteristic
3#14557499C211yesmaximal, characteristic
4D37⋊M16—21no—
5#11924615—21no—
6#11924597C412yescomplemented
7#11924596—21no—
8#11924595C412yes—
9#11924594—21no—
10C2×#10596962C2211yescharacteristic
11C2×#10596934C411yescharacteristic, complemented
12#11924448—21no—
13#11924448—21no—
14C22×C8×C37C411yescharacteristic, complemented
15C22×C4×C37C2×C411yescharacteristic
16C2×C22⋊D37D411yescharacteristic
17C2×C22⋊D37Q811yescharacteristic
18#10596962—41no—
19#10596962—41no—
20C2×D148C2×C411yescharacteristic
21C2×C4×D37D411yescharacteristic
22C2×C4×D37D411yescharacteristic
23C2×Dic74C2×C411yescharacteristic
24C22⋊#3866—22no—
25#10596957—22no—
26C4⋊#3866—41no—
27C4×#3866—41no—
28#10596953—41no—
29D37⋊C8—41no—
30C2×C8×C37—21no—
31C2×C8×C37—41no—
32#10596934—41no—
33C2×#64436—21no—
34C23×C37C4⋊C411yescharacteristic
35C22×D37C22⋊C411yescharacteristic
36C22×D37C4⋊C411yescharacteristic
37C2×#3866—42no—
38C2×C4×C37—21no—
39C2×C4×C37—21no—
40C2×C4×C37C4211yescharacteristic
41C2×C4×C37C22⋊C411yescharacteristic
42C22⋊D37—41no—
43C22⋊D37—41no—
44C2×Dic37C22⋊C411yescharacteristic
45C2×Dic37C4⋊C411yescharacteristic
46D148—41no—
47C4×D37—21no—
48C4×D37—21no—
49C4×D37—21no—
50C4×D37—21no—
51Dic74—41no—
52#64438—42no—
53C8×C37—41no—
54#64436—41no—
55C22×C37—21no—
56C22×C37—41no—
57C22×C37#9511yescharacteristic
58C2×D37—21no—
59C2×D37—21no—
60C2×D37—41no—
61C2×D37—41no—
62#3866—82no—
63C4×C37—21no—
64C4×C37#9911yescharacteristic
65C4×C37#9911yescharacteristic
66Dic37—21no—
67Dic37—21no—
68#1395—371nomaximal, Sylow
69C2×C37—21no—
70C2×C37—41no—
71C2×C37#34211yescharacteristic
72D37—41no—
73D37—41no—
74#413—371no—
75#410—371no—
76#408—371no—
77C37#139511yescharacteristic, complemented, Sylow
78C2×#41—371no—
79C2×M16—371no—
80C2×M16—741no—
81C22×C8#386611yescharacteristic, complemented
82#117—741no—
83#101—372no—
84#100—741no—
85#99—372no—
86#99—741no—
87C22⋊C8—741no—
88C22⋊C8—741no—
89#41—1481no—
90#41—1481no—
91C2×Q8—371no—
92C2×D4—371no—
93C2×D4—371no—
94C2×D4—371no—
95C22×C4—371no—
96C22×C4—371no—
97C22×C4C2×#386611yescharacteristic
98M16—742no—
99M16—1481no—
100M16—1481no—
101C2×C8—21no—
102C2×C8—41no—
103C2×C8—741no—
104C2×C8—1481no—
105C4⋊C4—1481no—
106C22⋊C4—742no—
107C42—1481no—
108C23—371no—
109C23—371no—
110C23C4⋊#386611yescharacteristic
111Q8—1481no—
112D4—1481no—
113D4—1481no—
114D4—1481no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—371no—
118C2×C4—371no—
119C2×C4—741no—
120C2×C4—741no—
121C2×C4—741no—
122C2×C4—741no—
123C2×C4—1482no—
124C2×C4C4×#386611yescharacteristic
125C2×C4C22⋊#386611yescharacteristic
126C8—41no—
127C8—1482no—
128C8—1481no—
129C22—21no—
130C22—41no—
131C22—741no—
132C22—741no—
133C22—1481no—
134C22—1481no—
135C22(C2×#3866)⋊C411yescharacteristic
136C4—21no—
137C4—2962no—
138C4—741no—
139C4—741no—
140C4#1192459411yescharacteristic
141C4#1192459511yescharacteristic
142C2—21no—
143C2—41no—
144C2—1481no—
145C2—1481no—
146C2#1455841111yescharacteristic
subgroupG/H
centerC4#11924595
commutatorC2×C4×C37C42
FrattiniC22×C4C2×#3866
FittingC22×C8×C37C4
socleC2×C37#342
prime radical, cosocleC2×#10596962C22
hypercenterC22×C8#3866
hypocenterC37#1395
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
6. #11924597C4semidirect
11. C2×#10596934C4semidirect
14. C22×C8×C37C4semidirect
77. C37#1395semidirect
81. C22×C8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585192
#145585122
#145574992
#139537