Finite Group Databasebeta

← #17993275

Subgroups — #17993275

Order 4736.

240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4⋊Q8×D37C211yesmaximal, characteristic
2#14557585C211yesmaximal, characteristic
3#14557555C211yesmaximal, characteristic
4#14557282C211yesmaximal, characteristic, complemented
5#14557281C211yesmaximal, characteristic, complemented
6#14557281C211yesmaximal, characteristic, complemented
7C37×#333C211yesmaximal, characteristic, complemented
8C2×Q8×D37C412yes—
9C2×#10596929—21no—
10#11924536C2211yescharacteristic
11#11924535—21no—
12#11924535—21no—
13#11924534C412yes—
14C4⋊C4×D37—21no—
15C4⋊C4×D37—21no—
16C42×D37C2211yescharacteristic
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21C8×Dic37—21no—
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37C2×C412yes—
26Q8×D37—44no—
27C2×C4×D37—22no—
28C2×C4×D37C2×C411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×C4×D37D411yescharacteristic
31C2×Dic74—22no—
32C2×Dic74C2×C412yes—
33C2×C8×C37—21no—
34C2×C8×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37—21no—
37C42×C37C2311yescharacteristic
38C4⋊Dic37—21no—
39C4⋊Dic37—21no—
40#10596936—22no—
41#10596936—22no—
42C4×Dic37C2×C411yescharacteristic
43C4×Dic37D411yescharacteristic
44C4×Dic37D411yescharacteristic
45C2×#64436—21no—
46C2×#64436—21no—
47#10596929—42no—
48C22×D37C22⋊C411yescharacteristic
49Q8×C37—42no—
50C2×C4×C37—22no—
51C2×C4×C37C22×C411yescharacteristic
52C2×C4×C37C2×D411yescharacteristic
53C2×C4×C37C2×D411yescharacteristic
54C2×Dic37—22no—
55C2×Dic37C22⋊C411yescharacteristic
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C22⋊C411yescharacteristic
58C4×D37—21no—
59C4×D37—21no—
60C4×D37—22no—
61C4×D37—44no—
62C4×D37SD1612yes—
63C4×D37Q1612yes—
64Dic74—44no—
65Dic74—42no—
66C8×C37—41no—
67C8×C37—41no—
68#64436—41no—
69#64436—41no—
70C22×C37C2×C22⋊C411yescharacteristic
71C2×D37—21no—
72C2×D37—21no—
73C2×D37#10312yes—
74C4×C37—21no—
75C4×C37—42no—
76C4×C37C2×SD1611yescharacteristic
77C4×C37C2×Q1611yescharacteristic
78C4×C37#13711yescharacteristic
79C4×C37#13711yescharacteristic
80Dic37—21no—
81Dic37—42no—
82Dic37#10012yes—
83Dic37#10312yes—
84#1548—371nomaximal, Sylow
85C2×C37C2×#10011yescharacteristic
86C2×C37C2×#10311yescharacteristic
87C2×C37#41911yescharacteristic
88D37—22no—
89C2×C4⋊Q8—371no—
90#431—371no—
91#423—371no—
92#333—371no—
93#333—371no—
94#333—371no—
95#333D3711yescharacteristic, complemented
96C37#154811yescharacteristic, complemented, Sylow
97C22×Q8—372no—
98C2×M16—741no—
99C4⋊Q8—372no—
100C4⋊Q8—371no—
101C4⋊Q8—741no—
102C4⋊Q8—741no—
103C4⋊Q8C2×D3711yescharacteristic
104C2×C4⋊C4—741no—
105C2×C4⋊C4—741no—
106C2×C42—371no—
107C4⋊C8—371no—
108C4⋊C8—371no—
109C4⋊C8—741no—
110C4⋊C8C2×D3711yescharacteristic
111C4⋊C8C2×D3711yescharacteristic
112C22⋊C8—741no—
113C4×C8—741no—
114C2×Q8—372no—
115C2×Q8—742no—
116C2×Q8—1484no—
117C2×Q8C4×D3712yes—
118C22×C4—371no—
119C22×C4—371no—
120C22×C4—371no—
121C22×C4—742no—
122M16—1482no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—741no—
126C2×C8—741no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—742no—
130C4⋊C4—742no—
131C4⋊C4—741no—
132C4⋊C4—741no—
133C42—371no—
134C42—371no—
135C42—371no—
136C42C22×D3711yescharacteristic
137C23—371no—
138Q8—42no—
139Q8—1482no—
140Q8—1484no—
141C2×C4—22no—
142C2×C4—371no—
143C2×C4—371no—
144C2×C4—372no—
145C2×C4—372no—
146C2×C4—371no—
147C2×C4—742no—
148C2×C4—741no—
149C2×C4—741no—
150C2×C4—742no—
151C2×C4—1484no—
152C2×C4C2×C4×D3711yescharacteristic
153C2×C4D4×D3711yescharacteristic
154C2×C4D4×D3711yescharacteristic
155C8—41no—
156C8—41no—
157C8—1481no—
158C8—1481no—
159C22—372no—
160C22—741no—
161C22—741no—
162C22C22⋊C4×D3711yescharacteristic
163C4—21no—
164C4—42no—
165C4—372no—
166C4—372no—
167C4—741no—
168C4—1482no—
169C4SD16×D3711yescharacteristic
170C4Q16×D3711yescharacteristic
171C4#1192456511yescharacteristic
172C4#1192456811yescharacteristic
173C2—742no—
174C2#100×D3711yescharacteristic
175C2#103×D3711yescharacteristic
176C2#1455754011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#333C2
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC42×C37C23
hypercenter#333D37
hypocenterC37#1548
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #14557282C2semidirect
5. #14557281C2semidirect
6. #14557281C2semidirect
7. C37×#333C2semidirect
95. #333D37semidirect
96. C37#1548semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D372
#145575852
#145575552
#145572822
#145572812
C37×#3332
#154837