Finite Group Databasebeta

← #18009698

Subgroups — #18009698

Order 4736.

162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 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#14558514C211yesmaximal, characteristic
2#14558508C211yesmaximal, characteristic
3#14557516C211yesmaximal, characteristic
4C2×#10596953C411yescharacteristic, complemented
5C2×D37⋊C8C411yescharacteristic, complemented
6#11924615—21no—
7#11924595—21no—
8#11924595C412yes—
9#11924593—21no—
10#11924593—21no—
11C2×#10596966C2211yescharacteristic
12M16×D37—21no—
13#11924455C411yescharacteristic, complemented
14#11924452—21no—
15#101×C37C411yescharacteristic, complemented
16C2×Q8×C37C2×C411yescharacteristic
17#10596966—41no—
18#10596966—41no—
19C2×D148C2×C411yescharacteristic
20C2×D148D411yescharacteristic
21C2×D148Q811yescharacteristic
22C2×C4×D37C2×C411yescharacteristic
23C2×C4×D37D411yescharacteristic
24C2×C4×D37D411yescharacteristic
25C22⋊#3866—22no—
26C2×#64438—21no—
27C2×#64438—21no—
28C4⋊#3866—41no—
29C4×#3866—41no—
30#10596953—41no—
31D37⋊C8—41no—
32M16×C37—21no—
33#10596934—21no—
34#10596929—41no—
35C8×D37—41no—
36C22×D37C22⋊C411yescharacteristic
37C22×D37C4⋊C411yescharacteristic
38C22×D37C4⋊C411yescharacteristic
39C2×#3866—42no—
40Q8×C37—41no—
41C2×C4×C37C4211yescharacteristic
42C2×C4×C37C22⋊C411yescharacteristic
43C2×C4×C37C4⋊C411yescharacteristic
44C2×Dic37C22⋊C411yescharacteristic
45D148—41no—
46D148—41no—
47D148—41no—
48C4×D37—21no—
49C4×D37—21no—
50C4×D37—21no—
51C4×D37—21no—
52C4×D37—21no—
53C4×D37—21no—
54#64438—41no—
55#64438—41no—
56C8×C37—41no—
57#64436—41no—
58C22×C37#9511yescharacteristic
59C2×D37—21no—
60C2×D37—21no—
61C2×D37—21no—
62C2×D37—41no—
63C2×D37—41no—
64C2×D37—41no—
65#3866—82no—
66C4×C37—21no—
67C4×C37—21no—
68C4×C37—21no—
69Dic37#9911yescharacteristic
70Dic37#9911yescharacteristic
71#1395—371nomaximal, Sylow
72C2×C37—21no—
73C2×C37#34211yescharacteristic
74D37—41no—
75D37—41no—
76D37—41no—
77#413—371no—
78#410—371no—
79#408—371no—
80C37#139511yescharacteristic, complemented, Sylow
81C2×#41—371no—
82C2×M16—371no—
83C2×M16—741no—
84C22×C8—371no—
85#117—741no—
86#101—371no—
87#101#386611yescharacteristic, complemented
88#100—741no—
89#99—372no—
90#99—741no—
91C22⋊C8—741no—
92C22⋊C8—741no—
93#41—1481no—
94#41—1481no—
95C2×Q8C2×#386611yescharacteristic
96C2×D4—371no—
97C2×D4—371no—
98C2×D4—371no—
99C22×C4—371no—
100C22×C4—371no—
101C22×C4—371no—
102M16—21no—
103M16—741no—
104M16—1481no—
105M16—1481no—
106C2×C8—741no—
107C2×C8—741no—
108C2×C8—1481no—
109C2×C8—1481no—
110C4⋊C4—1481no—
111C22⋊C4—742no—
112C42—1481no—
113C23—371no—
114C23—371no—
115C23—371no—
116Q8—41no—
117D4—1481no—
118D4—1481no—
119D4—1481no—
120C2×C4—371no—
121C2×C4—741no—
122C2×C4—741no—
123C2×C4—741no—
124C2×C4—741no—
125C2×C4—741no—
126C2×C4—741no—
127C2×C4—1482no—
128C2×C4C4×#386611yescharacteristic
129C2×C4C4⋊#386611yescharacteristic
130C2×C4C22⋊#386611yescharacteristic
131C8—41no—
132C8—1481no—
133C8—1481no—
134C8—1481no—
135C22—741no—
136C22—741no—
137C22—741no—
138C22—1481no—
139C22—1481no—
140C22—1481no—
141C22(C2×#3866)⋊C411yescharacteristic
142C4—21no—
143C4—21no—
144C4—21no—
145C4—371no—
146C4—371no—
147C4—2962no—
148C2—21no—
149C2—1481no—
150C2—1481no—
151C2—1481no—
152C2#1455841011yescharacteristic
subgroupG/H
centerC2#14558410
commutatorC2×C4×C37C42
FrattiniC2×Q8C2×#3866
Fitting#101×C37C4
socleC2×C37#342
prime radical, cosocleC2×#10596966C22
hypercenter#101#3866
hypocenterC37#1395
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
4. C2×#10596953C4semidirect
5. C2×D37⋊C8C4semidirect
13. #11924455C4semidirect
15. #101×C37C4semidirect
80. C37#1395semidirect
87. #101#3866semidirect

Maximal subgroups

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

subgroupindex
#145585142
#145585082
#145575162
#139537