Finite Group Databasebeta

← #17993671

Subgroups — #17993671

Order 4736.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558243C211yesmaximal, characteristic, complemented
2#14557906C211yesmaximal, characteristic, complemented
3#14557733C211yesmaximal, characteristic, complemented
4#14557729C211yesmaximal, characteristic
5#14557281C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596930—22no—
9C2×#10596941—21no—
10C2×D296—21no—
11#11924536C2211yescharacteristic
12#11924533C2211yescharacteristic
13#11924528—21no—
14#11924514—22no—
15#11924512—21no—
16C4×D148—21no—
17C4×D148C2211yescharacteristic
18C4⋊C4×D37—21no—
19C4⋊#64436C2211yescharacteristic
20#11924458—21no—
21#11924456—21no—
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37D411yescharacteristic
26C2×D148—21no—
27C2×D148—21no—
28C2×D148—21no—
29C2×D148D411yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37—22no—
32C2×Dic74D412yes—
33C2×C8×C37—21no—
34C2×C8×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37D411yescharacteristic
37C42×C37—21no—
38C42×C37C2311yescharacteristic
39#10596941—42no—
40#10596938—22no—
41#10596938—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37—21no—
44C4⋊Dic37D411yescharacteristic
45#10596936—22no—
46#10596936—22no—
47C2×#64436—21no—
48D296—42no—
49#10596930—44no—
50C22×D37—21no—
51C22×D37—41no—
52Q8×C37—21no—
53Q8×C37—21no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×Dic37—21no—
60C2×Dic37—22no—
61D148—21no—
62D148—42no—
63D148—41no—
64D148—41no—
65D148—41no—
66D148—41no—
67D148SD1612yescomplemented
68C4×D37—41no—
69C4×D37—41no—
70C4×D37—82no—
71Dic74—42no—
72C8×C37—22no—
73C8×C37—41no—
74#64436—41no—
75C22×C37#12011yescharacteristic
76C2×D37—22no—
77C2×D37—41no—
78C2×D37—41no—
79C2×D37—81no—
80C2×D37—81no—
81C2×D37—81no—
82C4×C37—21no—
83C4×C37—41no—
84C4×C37—41no—
85C4×C37C2×SD1611yescharacteristic
86C4×C37#13511yescharacteristic
87C4×C37AGL(1,ℤ/8)11yescharacteristic
88C4×C37#13711yescharacteristic
89Dic37—41no—
90Dic37—42no—
91#1622—371nomaximal, Sylow
92C2×C37#44811yescharacteristic
93C2×C37#44911yescharacteristic
94C2×C37#45311yescharacteristic
95D37—42no—
96D37—161no—
97#554—371no—
98#492—371no—
99#460—371no—
100#459—371no—
101#333—371no—
102Q8⋊C8D3711yescharacteristic, complemented
103D4⋊C8—371no—
104C37#162211yescharacteristic, complemented, Sylow
105C2×SD16—742no—
106C2×SD16—741no—
107C2×D8—741no—
108C4⋊Q8—371no—
109#127—371no—
110#125—741no—
111C22⋊Q8—742no—
112C22⋊Q8—741no—
113C4×Q8C2×D3711yescharacteristic
114C4×D4—371no—
115C4×D4—741no—
116C2×C4⋊C4—741no—
117C4⋊C8—371no—
118C4⋊C8C2×D3711yescharacteristic
119#102—741no—
120#102—741no—
121C4×C8C2×D3711yescharacteristic
122C2×Q8—372no—
123C2×Q8D14811yescharacteristic
124C2×D4—371no—
125C2×D4—741no—
126C2×D4—741no—
127C2×D4—741no—
128C22×C4—742no—
129C22×C4—741no—
130SD16—1484no—
131SD16—1482no—
132D8—1482no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—741no—
136C4⋊C4—21no—
137C4⋊C4—371no—
138C4⋊C4—742no—
139C4⋊C4—742no—
140C4⋊C4—741no—
141C4⋊C4—741no—
142C4⋊C4D14811yescharacteristic
143C22⋊C4—742no—
144C22⋊C4—741no—
145C42—21no—
146C42C22×D3711yescharacteristic
147C23—741no—
148C23—1481no—
149Q8—21no—
150Q8—21no—
151Q8—1482no—
152D4—372no—
153D4—741no—
154D4—1482no—
155D4—1481no—
156D4—1481no—
157D4—1481no—
158D4—1481no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—2962no—
162C2×C4—741no—
163C2×C4—742no—
164C2×C4—1481no—
165C2×C4—1481no—
166C2×C4C2×D14811yescharacteristic
167C2×C4D4×D3711yescharacteristic
168C2×C4D4×D3711yescharacteristic
169C8—22no—
170C8—41no—
171C8—1481no—
172C22—2961no—
173C22—2961no—
174C22—2961no—
175C22—742no—
176C22—1481no—
177C22—1481no—
178C22#1192450611yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—1482no—
183C4—1481no—
184C4SD16×D3711yescharacteristic
185C4#1192455811yescharacteristic
186C4#1192456411yescharacteristic
187C4#1192456811yescharacteristic
188C2—5921no—
189C2—1482no—
190C2#1455767311yescharacteristic
191C2#1455768011yescharacteristic
192C2#1455770211yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37#120
prime radical#14557729C2
hypercenterQ8⋊C8D37
hypocenterC37#1622
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #14558243C2semidirect
2. #14557906C2semidirect
3. #14557733C2semidirect
5. #14557281C2semidirect
6. #14557262C2semidirect
7. C37×Q8⋊C8C2semidirect
67. D148SD16semidirect
102. Q8⋊C8D37semidirect
104. C37#1622semidirect

Maximal subgroups

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

subgroupindex
#145582432
#145579062
#145577332
#145577292
#145572812
#145572622
C37×Q8⋊C82
#162237