Finite Group Databasebeta

← #17993879

Subgroups — #17993879

Order 4736.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#14558187C211yesmaximal, characteristic
2#14557929C211yesmaximal, characteristic, complemented
3#14557735C211yesmaximal, characteristic, complemented
4#14557280C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#474C211yesmaximal, characteristic, complemented
8C2×#10596964—21no—
9C2×#10596941—21no—
10#11924536C2211yescharacteristic
11#11924520—22no—
12#11924516—21no—
13#11924510—21no—
14C4×D148C2211yescharacteristic
15C2×C4⋊Dic37—21no—
16#11924467—22no—
17C4⋊#64436C2211yescharacteristic
18#11924460—21no—
19C4×#64436C2211yescharacteristic
20C4⋊Q8×C37C2211yescharacteristic
21C4×D4×C37C2211yescharacteristic
22#107×C37—21no—
23C4⋊C8×C37C2211yescharacteristic
24#102×C37—21no—
25C2×Q8×C37—21no—
26C2×D4×C37D411yescharacteristic
27C22×C4×C37—21no—
28C2×C22⋊D37—22no—
29C22×Dic37—22no—
30#10596964—42no—
31#10596964—42no—
32C2×D148D411yescharacteristic
33C2×C4×D37—21no—
34C2×Dic74—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37D411yescharacteristic
39C22⋊C4×C37—21no—
40C42×C37C2311yescharacteristic
41#10596941—42no—
42#10596938—22no—
43#10596938—21no—
44C4⋊Dic37—22no—
45C4⋊Dic37—21no—
46C4⋊Dic37D411yescharacteristic
47C4⋊Dic37D412yes—
48C2×#64436—21no—
49C2×#64436—21no—
50C23×C37—21no—
51C22×D37—21no—
52Q8×C37—41no—
53Q8×C37—41no—
54D4×C37—21no—
55D4×C37SD1612yescomplemented
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C22⋊D37—44no—
64C2×Dic37—22no—
65C2×Dic37—21no—
66C2×Dic37—44no—
67D148—21no—
68D148—21no—
69C4×D37—41no—
70C4×D37—41no—
71Dic74—41no—
72Dic74—41no—
73C8×C37—41no—
74#64436—22no—
75#64436—41no—
76C22×C37—22no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37#12011yescharacteristic
80C2×D37—41no—
81C2×D37—41no—
82C2×D37—41no—
83C4×C37—21no—
84C4×C37—41no—
85C4×C37—81no—
86C4×C37C2×SD1611yescharacteristic
87C4×C37#13511yescharacteristic
88C4×C37AGL(1,ℤ/8)11yescharacteristic
89C4×C37AGL(1,ℤ/8)11yescharacteristic
90Dic37—42no—
91Dic37—41no—
92#1654—371nomaximal, Sylow
93C2×C37—42no—
94C2×C37#44911yescharacteristic
95C2×C37#45011yescharacteristic
96C2×C37#45611yescharacteristic
97D37—81no—
98#547—371no—
99#498—371no—
100#474D3711yescharacteristic, complemented
101#461—371no—
102#332—371no—
103D4⋊C8—371no—
104D4⋊C8—371no—
105C37#165411yescharacteristic, complemented, Sylow
106C2×#41—741no—
107C2×SD16—741no—
108C4⋊Q8—371no—
109C4⋊Q8C2×D3711yescharacteristic
110#123—742no—
111C22⋊Q8—741no—
112#121—741no—
113C4×D4—371no—
114C4×D4C2×D3711yescharacteristic
115C2×C4⋊C4—741no—
116#107—21no—
117#106—742no—
118C4⋊C8—371no—
119C4⋊C8C2×D3711yescharacteristic
120#103—741no—
121#102—21no—
122C4×C8—371no—
123#41—1482no—
124#41—1482no—
125C2×Q8—21no—
126C2×Q8—741no—
127C2×D4—371no—
128C2×D4—742no—
129C2×D4C22⋊D3711yescharacteristic
130C22×C4—21no—
131C22×C4—742no—
132C22×C4—741no—
133SD16—1482no—
134C2×C8—21no—
135C2×C8—741no—
136C2×C8—741no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—371no—
140C4⋊C4—372no—
141C4⋊C4—742no—
142C4⋊C4—741no—
143C4⋊C4C22⋊D3711yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—742no—
146C22⋊C4—741no—
147C42C22×D3711yescharacteristic
148C23—21no—
149C23—741no—
150Q8—41no—
151Q8—41no—
152Q8—1481no—
153Q8—1481no—
154D4—21no—
155D4—741no—
156D4—741no—
157D4—1484no—
158D4#1059694112yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—741no—
164C2×C4—742no—
165C2×C4—1484no—
166C2×C4—1481no—
167C2×C4—1481no—
168C2×C4D4×D3711yescharacteristic
169C2×C4D4×D3711yescharacteristic
170C2×C4C2×C22⋊D3711yescharacteristic
171C8—41no—
172C8—742no—
173C8—1481no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—1481no—
178C22—1481no—
179C22—1481no—
180C22#1192450411yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—1481no—
185C4—1482no—
186C4C2×#1059694111yescharacteristic
187C4#1192455511yescharacteristic
188C4#1192456011yescharacteristic
189C4#1192456111yescharacteristic
190C2—42no—
191C2—2961no—
192C2#1455767511yescharacteristic
193C2#1455768311yescharacteristic
194C2#1455771411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#474C2
socleC22×C37#120
prime radical#14558187C2
hypercenter#474D37
hypocenterC37#1654
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #14557929C2semidirect
3. #14557735C2semidirect
4. #14557280C2semidirect
5. D4⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×#474C2semidirect
55. D4×C37SD16semidirect
100. #474D37semidirect
105. C37#1654semidirect
158. D4#10596941semidirect

Maximal subgroups

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

subgroupindex
#145581872
#145579292
#145577352
#145572802
D4⋊#644362
#145572602
C37×#4742
#165437