Finite Group Databasebeta

← #17995664

Subgroups — #17995664

Order 4736.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#14558333C211yesmaximal, characteristic, complemented
2#14558045C212yesmaximal, complemented
3#14557551C212yesmaximal, complemented
4#14557496C211yesmaximal, characteristic, complemented
5C37×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
6C2×#10596962C2212yes—
7C22×C4×D37C2211yescharacteristic
8#11924569—22no—
9#11924564—22no—
10#11924558—22no—
11C2×#10596934C2211yescharacteristic
12#11924520—22no—
13#11924516—22no—
14#11924511—22no—
15#11924506—22no—
16C4×D148—24no—
17#11924464—24no—
18#11924448—22no—
19C2×M16×C37C2211yescharacteristic
20#117×C37C2212yes—
21C23×D37D411yescharacteristic
22C22×C4×C37C2311yescharacteristic
23C2×C22⋊D37—22no—
24C22×Dic37D411yescharacteristic
25#10596962—22no—
26#10596962—22no—
27#10596962—22no—
28#10596962—22no—
29C2×D148—24no—
30C2×D148D412yescomplemented
31C2×C4×D37—22no—
32C2×C4×D37—22no—
33C2×C4×D37—22no—
34C2×C4×D37—21no—
35C2×C4×D37—21no—
36C2×Dic74D412yescomplemented
37M16×C37—22no—
38C2×C8×C37D412yescomplemented
39C4⋊C4×C37—22no—
40C22⋊C4×C37—22no—
41C42×C37D414yescomplemented
42#10596938—24no—
43#10596938—24no—
44C4⋊Dic37—24no—
45#10596934—22no—
46C2×#64436—21no—
47Dic148—22no—
48D296—22no—
49#10596930—24no—
50C23×C37C2×D411yescharacteristic
51C22×D37—22no—
52C22×D37—21no—
53C22×D37—22no—
54C22×D37—42no—
55C2×C4×C37—24no—
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D412yes—
58C2×C4×C37C2×D412yes—
59C2×C4×C37#4111yescharacteristic
60C22⋊D37—42no—
61C22⋊D37—42no—
62C2×Dic37—22no—
63C2×Dic37—22no—
64C2×Dic37—21no—
65D148—22no—
66D148—22no—
67D148—48no—
68C4×D37—41no—
69C4×D37—42no—
70C4×D37—42no—
71C4×D37—41no—
72C4×D37—42no—
73Dic74—22no—
74Dic74—22no—
75C8×C37—22no—
76#64436—41no—
77C22×C37—41no—
78C22×C37#12012yes—
79C22×C37#12111yescharacteristic
80C2×D37—24no—
81C2×D37—22no—
82C2×D37—42no—
83C2×D37—41no—
84C2×D37—41no—
85C2×D37—44no—
86C2×D37—42no—
87C4×C37—44no—
88C4×C37#12011yescharacteristic
89C4×C37#12112yes—
90C4×C37#12711yescharacteristic
91Dic37—42no—
92Dic37—41no—
93#2010—371nomaximal, Sylow
94C2×C37—22no—
95C2×C37—21no—
96C2×C37#39211yescharacteristic
97D37—42no—
98D37—82no—
99#575—371no—
100#525—372no—
101#421—372no—
102#407—371no—
103H(3,ℤ/4)D3711yescharacteristic, complemented
104C37#201011yescharacteristic, complemented, Sylow
105C2×#41—372no—
106C23×C4—371no—
107#137—742no—
108AGL(1,ℤ/8)—742no—
109#135—742no—
110C2×M16—371no—
111C2×M16C2×D3711yescharacteristic
112#123—742no—
113C22⋊Q8—742no—
114#121—742no—
115#120—742no—
116C4×D4—744no—
117#117C2×D3712yes—
118#104—744no—
119C22⋊C8—742no—
120C24—371no—
121#41—742no—
122#41—742no—
123#41—742no—
124#41—742no—
125C2×Q8—372no—
126C2×D4—372no—
127C2×D4—744no—
128C2×D4—742no—
129C22×C4—371no—
130C22×C4—741no—
131C22×C4—742no—
132C22×C4—742no—
133C22×C4—742no—
134C22×C4—741no—
135C22×C4C22×D3711yescharacteristic
136Q16—742no—
137SD16—744no—
138D8—742no—
139M16—22no—
140M16—742no—
141C2×C8—741no—
142C2×C8D14812yescomplemented
143C4⋊C4—22no—
144C4⋊C4—744no—
145C22⋊C4—22no—
146C22⋊C4—744no—
147C22⋊C4—744no—
148C42D14814yescomplemented
149C23—742no—
150C23—741no—
151C23—742no—
152C23—1482no—
153C23D4×D3711yescharacteristic
154Q8—742no—
155Q8—742no—
156D4—742no—
157D4—742no—
158D4—1488no—
159D4—1482no—
160D4—1482no—
161C2×C4—24no—
162C2×C4—742no—
163C2×C4—742no—
164C2×C4—741no—
165C2×C4—1481no—
166C2×C4—1482no—
167C2×C4—1482no—
168C2×C4—1481no—
169C2×C4—1482no—
170C2×C4C2×D14811yescharacteristic
171C2×C4C2×D14812yes—
172C2×C4D4×D3712yes—
173C2×C4#1059696611yescharacteristic
174C8—22no—
175C8—1481no—
176C22—41no—
177C22—744no—
178C22—742no—
179C22—1484no—
180C22—1482no—
181C22—1481no—
182C22—1482no—
183C22—1481no—
184C22#1192450612yes—
185C22#1192451111yescharacteristic
186C4—44no—
187C4—1481no—
188C4—1482no—
189C4#1192450611yescharacteristic
190C4#1192451112yes—
191C4#1192453311yescharacteristic
192C2—22no—
193C2—21no—
194C2—2962no—
195C2—1482no—
196C2#1455744311yescharacteristic
subgroupG/H
centerC4#11924533
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×H(3,ℤ/4)C2
socleC2×C37#392
hypercenterH(3,ℤ/4)D37
hypocenterC37#2010
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #14558333C2semidirect
2. #14558045C2semidirect
3. #14557551C2semidirect
4. #14557496C2semidirect
5. C37×H(3,ℤ/4)C2semidirect
30. C2×D148D4semidirect
36. C2×Dic74D4semidirect
38. C2×C8×C37D4semidirect
41. C42×C37D4semidirect
103. H(3,ℤ/4)D37semidirect
104. C37#2010semidirect
142. C2×C8D148semidirect
148. C42D148semidirect

Maximal subgroups

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

subgroupindex
#145583332
#145580452
#145575512
#145574962
C37×H(3,ℤ/4)2
#201037