Finite Group Databasebeta

← #17993881

Subgroups — #17993881

Order 4736.

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

normal subgroups only

This group has 240 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#14558186C211yesmaximal, characteristic
2#14557929C211yesmaximal, characteristic, complemented
3#14557814C211yesmaximal, characteristic, complemented
4#14557739C211yesmaximal, characteristic, complemented
5#14557260C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#332C211yesmaximal, characteristic, complemented
8C2×#10596966—21no—
9C2×#10596930—21no—
10#11924536C2211yescharacteristic
11#11924521—22no—
12#11924512—21no—
13#11924511—21no—
14C4×D148C2211yescharacteristic
15C4×D148C2211yescharacteristic
16C4⋊C4×D37—21no—
17#11924470—21no—
18#11924467—22no—
19#11924461—21no—
20#11924458—21no—
21C4×#64436C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26#10596966—42no—
27#10596966—42no—
28C2×D148—22no—
29C2×D148D411yescharacteristic
30C2×D148D411yescharacteristic
31C2×C4×D37—22no—
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×Dic74—21no—
35C2×C8×C37—21no—
36C2×C8×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37D412yes—
39C42×C37C2311yescharacteristic
40#10596938—22no—
41#10596938—21no—
42#10596938—21no—
43C4⋊Dic37—21no—
44C4⋊Dic37—21no—
45C4⋊Dic37D411yescharacteristic
46C4⋊Dic37D411yescharacteristic
47#10596936—22no—
48C2×#64436—21no—
49#10596930—42no—
50C22×D37—21no—
51C22×D37—21no—
52Q8×C37—41no—
53Q8×C37—41no—
54C2×C4×C37—22no—
55C2×C4×C37C2×D411yescharacteristic
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×Dic37—21no—
59C2×Dic37—21no—
60C2×Dic37—41no—
61D148—21no—
62D148—21no—
63D148—21no—
64D148—44no—
65D148SD1612yescomplemented
66C4×D37—44no—
67C4×D37—41no—
68C4×D37—41no—
69C4×D37—41no—
70C4×D37—41no—
71Dic74—41no—
72Dic74—41no—
73C8×C37—41no—
74C8×C37—41no—
75#64436—22no—
76C22×C37#12011yescharacteristic
77C2×D37—22no—
78C2×D37—41no—
79C2×D37—41no—
80C2×D37—41no—
81C2×D37—41no—
82C2×D37—41no—
83C4×C37—21no—
84C4×C37—42no—
85C4×C37C2×SD1611yescharacteristic
86C4×C37#13511yescharacteristic
87C4×C37AGL(1,ℤ/8)11yescharacteristic
88C4×C37AGL(1,ℤ/8)11yescharacteristic
89Dic37—41no—
90Dic37—41no—
91Dic37—81no—
92#1654—371nomaximal, Sylow
93C2×C37#44911yescharacteristic
94C2×C37#45011yescharacteristic
95C2×C37#45611yescharacteristic
96D37—42no—
97D37—81no—
98#547—371no—
99#498—371no—
100#474—371no—
101#461—371no—
102#332D3711yescharacteristic, complemented
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×D4—371no—
115C2×C4⋊C4—741no—
116#107—741no—
117#106—742no—
118C4⋊C8C2×D3711yescharacteristic
119C4⋊C8C2×D3711yescharacteristic
120#103—741no—
121#102—741no—
122C4×C8—371no—
123#41—1482no—
124#41—1482no—
125C2×Q8—21no—
126C2×Q8—741no—
127C2×D4—371no—
128C2×D4—371no—
129C2×D4—742no—
130C22×C4—742no—
131C22×C4—741no—
132C22×C4—741no—
133SD16—1482no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—741no—
137C4⋊C4—21no—
138C4⋊C4—371no—
139C4⋊C4—371no—
140C4⋊C4—742no—
141C4⋊C4—741no—
142C4⋊C4—741no—
143C4⋊C4D14812yes—
144C22⋊C4—742no—
145C22⋊C4—741no—
146C22⋊C4—741no—
147C42C22×D3711yescharacteristic
148C23—741no—
149C23—741no—
150Q8—41no—
151Q8—41no—
152Q8—1481no—
153Q8—1481no—
154D4—372no—
155D4—741no—
156D4—741no—
157D4—741no—
158D4—1484no—
159C2×C4—22no—
160C2×C4—741no—
161C2×C4—741no—
162C2×C4—1484no—
163C2×C4—1481no—
164C2×C4—1481no—
165C2×C4—1481no—
166C2×C4—1481no—
167C2×C4—1481no—
168C2×C4C2×D14811yescharacteristic
169C2×C4D4×D3711yescharacteristic
170C2×C4D4×D3711yescharacteristic
171C8—41no—
172C8—41no—
173C8—742no—
174C22—742no—
175C22—1481no—
176C22—1481no—
177C22—1481no—
178C22—1481no—
179C22—1481no—
180C22#1192450611yescharacteristic
181C4—21no—
182C4—42no—
183C4—2961no—
184C4—1481no—
185C4—1481no—
186C4SD16×D3711yescharacteristic
187C4#1192455911yescharacteristic
188C4#1192456011yescharacteristic
189C4#1192456311yescharacteristic
190C2—2961no—
191C2—1482no—
192C2#1455768111yescharacteristic
193C2#1455768511yescharacteristic
194C2#1455771811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#332C2
socleC22×C37#120
prime radical#14558186C2
hypercenter#332D37
hypocenterC37#1654
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #14557929C2semidirect
3. #14557814C2semidirect
4. #14557739C2semidirect
5. #14557260C2semidirect
6. #14557260C2semidirect
7. C37×#332C2semidirect
65. D148SD16semidirect
102. #332D37semidirect
105. C37#1654semidirect

Maximal subgroups

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

subgroupindex
#145581862
#145579292
#145578142
#145577392
#145572602
C37×#3322
#165437