Finite Group Databasebeta

← #17993744

Subgroups — #17993744

Order 4736.

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

normal subgroups only

This group has 234 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#14557820C211yesmaximal, characteristic, complemented
3#14557820C211yesmaximal, characteristic, complemented
4#14557279C211yesmaximal, characteristic, complemented
5#14557262C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic, complemented
7C37×#487C211yesmaximal, characteristic, complemented
8C2×#10596966—21no—
9#11924521—22no—
10#11924512—21no—
11#11924511—21no—
12C4×D148C2211yescharacteristic
13C4×D148C2211yescharacteristic
14C4⋊C4×D37—21no—
15#11924467—21no—
16#11924467—21no—
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924456—21no—
20#11924456—21no—
21C4⋊Q8×C37C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23#103×C37—22no—
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×Q8×C37—21no—
27#10596966—42no—
28#10596966—42no—
29C2×D148—22no—
30C2×D148D411yescharacteristic
31C2×D148D411yescharacteristic
32C2×C4×D37—22no—
33C2×C4×D37—21no—
34C2×C4×D37—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37D412yes—
40C42×C37C2311yescharacteristic
41#10596938—22no—
42#10596938—21no—
43#10596938—21no—
44C4⋊Dic37D411yescharacteristic
45C4⋊Dic37D411yescharacteristic
46#10596936—22no—
47C2×#64436—21no—
48C2×#64436—21no—
49C22×D37—21no—
50C22×D37—21no—
51Q8×C37—42no—
52Q8×C37—41no—
53Q8×C37—41no—
54C2×C4×C37—22no—
55C2×C4×C37—41no—
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×Dic37—21no—
60C2×Dic37—21no—
61D148—21no—
62D148—21no—
63D148—21no—
64D148—44no—
65D148SD1612yes—
66C4×D37—44no—
67C4×D37—41no—
68C4×D37—41no—
69C4×D37—41no—
70C4×D37—41no—
71C8×C37—41no—
72#64436—41no—
73#64436—41no—
74C22×C37#12011yescharacteristic
75C2×D37—22no—
76C2×D37—41no—
77C2×D37—41no—
78C2×D37—41no—
79C2×D37—41no—
80C2×D37—41no—
81C4×C37—21no—
82C4×C37—42no—
83C4×C37—81no—
84C4×C37C2×SD1611yescharacteristic
85C4×C37#13511yescharacteristic
86C4×C37AGL(1,ℤ/8)11yescharacteristic
87C4×C37#13711yescharacteristic
88Dic37—41no—
89Dic37—41no—
90#1635—371nomaximal, Sylow
91C2×C37#45011yescharacteristic
92C2×C37#45211yescharacteristic
93C2×C37#45411yescharacteristic
94D37—42no—
95D37—81no—
96#547—371no—
97#487D3711yescharacteristic, complemented
98#476—371no—
99#476—371no—
100#332—371no—
101D4⋊C8—371no—
102D4⋊C8—371no—
103C37#163511yescharacteristic, complemented, Sylow
104C2×#41—741no—
105C4⋊Q8C2×D3711yescharacteristic
106C4⋊Q8C2×D3711yescharacteristic
107#123—742no—
108C22⋊Q8—741no—
109#121—741no—
110C4×D4—371no—
111C4×D4—371no—
112C2×C4⋊C4—741no—
113#106—741no—
114#106—741no—
115C4⋊C8—371no—
116C4⋊C8—371no—
117#103—22no—
118#102—741no—
119#102—741no—
120C4×C8C2×D3711yescharacteristic
121#41—1482no—
122#41—1482no—
123C2×Q8—21no—
124C2×Q8—21no—
125C2×D4—371no—
126C2×D4—371no—
127C2×D4—742no—
128C22×C4—742no—
129C22×C4—741no—
130C22×C4—741no—
131C2×C8—21no—
132C2×C8—741no—
133C2×C8—741no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—371no—
138C4⋊C4—371no—
139C4⋊C4—742no—
140C4⋊C4C22⋊D3712yes—
141C22⋊C4—742no—
142C22⋊C4—741no—
143C22⋊C4—741no—
144C42C22×D3711yescharacteristic
145C23—741no—
146C23—741no—
147Q8—42no—
148Q8—41no—
149Q8—41no—
150D4—372no—
151D4—741no—
152D4—741no—
153D4—741no—
154D4—1484no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—741no—
158C2×C4—741no—
159C2×C4—1484no—
160C2×C4—1481no—
161C2×C4—1481no—
162C2×C4—1481no—
163C2×C4—1481no—
164C2×C4D4×D3711yescharacteristic
165C2×C4D4×D3711yescharacteristic
166C2×C4C2×C22⋊D3711yescharacteristic
167C8—41no—
168C8—1481no—
169C8—1481no—
170C22—742no—
171C22—1481no—
172C22—1481no—
173C22—1481no—
174C22—1481no—
175C22—1481no—
176C22#1192450411yescharacteristic
177C4—21no—
178C4—42no—
179C4—81no—
180C4—1481no—
181C4—1481no—
182C4SD16×D3711yescharacteristic
183C4#1192455911yescharacteristic
184C4#1192456311yescharacteristic
185C4#1192456811yescharacteristic
186C2—2961no—
187C2—1482no—
188C2#1455768211yescharacteristic
189C2#1455769411yescharacteristic
190C2#1455770511yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#487C2
socleC22×C37#120
prime radical#14558186C2
hypercenter#487D37
hypocenterC37#1635
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #14557820C2semidirect
3. #14557820C2semidirect
4. #14557279C2semidirect
5. #14557262C2semidirect
6. #14557262C2semidirect
7. C37×#487C2semidirect
97. #487D37semidirect
103. C37#1635semidirect

Maximal subgroups

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

subgroupindex
#145581862
#145578202
#145572792
#145572622
C37×#4872
#163537