Finite Group Databasebeta

← #17993720

Subgroups — #17993720

Order 4736.

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

normal subgroups only

This group has 256 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#14558203C211yesmaximal, characteristic
2#14557825C211yesmaximal, characteristic, complemented
3#14557820C211yesmaximal, characteristic, complemented
4#14557277C211yesmaximal, characteristic, complemented
5#14557265C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic, complemented
7C37×#492C211yesmaximal, characteristic, complemented
8C2×#10596964—21no—
9#11924532—21no—
10#11924508—22no—
11#11924507—21no—
12C4×Dic74C2211yescharacteristic
13C4×D148C2211yescharacteristic
14D4×Dic37—21no—
15#11924469—21no—
16#11924467—21no—
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924459—21no—
20#11924456—21no—
21C2×SD16×C37—22no—
22C4⋊Q8×C37C2211yescharacteristic
23#127×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37D412yes—
29C2×C22⋊D37—22no—
30C2×C22⋊D37—22no—
31C22×Dic37—22no—
32#10596964—42no—
33#10596964—42no—
34C2×D148D411yescharacteristic
35C2×C4×D37—21no—
36C2×Dic74D411yescharacteristic
37SD16×C37—44no—
38C2×C8×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37—21no—
41C42×C37C2311yescharacteristic
42C22⋊Dic37—22no—
43#10596938—21no—
44C4⋊Dic37D411yescharacteristic
45C4⋊Dic37D411yescharacteristic
46#10596936—21no—
47C4×Dic37—21no—
48C2×#64436—21no—
49C2×#64436—21no—
50C23×C37—22no—
51C22×D37—21no—
52Q8×C37—42no—
53D4×C37—42no—
54D4×C37—41no—
55D4×C37—41no—
56D4×C37—41no—
57D4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C22⋊D37—44no—
63C22⋊D37—82no—
64C2×Dic37—21no—
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37—44no—
68D148—21no—
69D148—21no—
70C4×D37—41no—
71C4×D37—41no—
72Dic74—21no—
73Dic74SD1612yescomplemented
74C8×C37—22no—
75#64436—41no—
76#64436—41no—
77C22×C37—42no—
78C22×C37—42no—
79C22×C37—42no—
80C22×C37#12011yescharacteristic
81C2×D37—41no—
82C2×D37—41no—
83C2×D37—41no—
84C4×C37—21no—
85C4×C37—81no—
86C4×C37C2×SD1611yescharacteristic
87C4×C37#13511yescharacteristic
88C4×C37AGL(1,ℤ/8)11yescharacteristic
89C4×C37#13711yescharacteristic
90Dic37—22no—
91Dic37—41no—
92Dic37—41no—
93#1631—371nomaximal, Sylow
94C2×C37—82no—
95C2×C37#45011yescharacteristic
96C2×C37#45211yescharacteristic
97C2×C37#45311yescharacteristic
98D37—81no—
99#550—371no—
100#492D3711yescharacteristic, complemented
101#477—371no—
102#476—371no—
103#331—371no—
104Q8⋊C8—371no—
105D4⋊C8—371no—
106C37#163111yescharacteristic, complemented, Sylow
107C2×#41—741no—
108C2×SD16—22no—
109C4⋊Q8C2×D3711yescharacteristic
110#127—741no—
111#127C2×D3711yescharacteristic
112#121—741no—
113#121—742no—
114C4×Q8—371no—
115C4×D4—371no—
116C4×D4—741no—
117#107—741no—
118#106—741no—
119C4⋊C8—371no—
120C4⋊C8—371no—
121#103—741no—
122#102—741no—
123C4×C8C2×D3711yescharacteristic
124#41—1482no—
125#41—1482no—
126C2×Q8—21no—
127C2×Q8—371no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—371no—
131C2×D4—742no—
132C2×D4—742no—
133C2×D4C22⋊D3712yes—
134C22×C4—742no—
135C22×C4—741no—
136SD16—44no—
137C2×C8—21no—
138C2×C8—741no—
139C2×C8—741no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—371no—
143C4⋊C4—371no—
144C4⋊C4—741no—
145C22⋊C4—742no—
146C22⋊C4—741no—
147C42—741no—
148C42C22×D3711yescharacteristic
149C23—22no—
150C23—741no—
151Q8—42no—
152Q8—372no—
153Q8—741no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—2962no—
160D4—741no—
161D4—741no—
162D4—1484no—
163C2×C4—41no—
164C2×C4—741no—
165C2×C4—741no—
166C2×C4—741no—
167C2×C4—1484no—
168C2×C4—1481no—
169C2×C4—1481no—
170C2×C4D4×D3711yescharacteristic
171C2×C4D4×D3711yescharacteristic
172C2×C4C2×C22⋊D3711yescharacteristic
173C8—22no—
174C8—1481no—
175C8—1481no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—1481no—
180C22—1481no—
181C22—1481no—
182C22#1192450411yescharacteristic
183C4—21no—
184C4—81no—
185C4—742no—
186C4—1481no—
187C4—1481no—
188C4SD16×D3711yescharacteristic
189C4#1192455711yescharacteristic
190C4#1192456311yescharacteristic
191C4#1192456511yescharacteristic
192C2—82no—
193C2—2961no—
194C2#1455768211yescharacteristic
195C2#1455769211yescharacteristic
196C2#1455770011yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#492C2
socleC22×C37#120
prime radical#14558203C2
hypercenter#492D37
hypocenterC37#1631
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #14557825C2semidirect
3. #14557820C2semidirect
4. #14557277C2semidirect
5. #14557265C2semidirect
6. #14557262C2semidirect
7. C37×#492C2semidirect
73. Dic74SD16semidirect
100. #492D37semidirect
106. C37#1631semidirect

Maximal subgroups

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

subgroupindex
#145582032
#145578252
#145578202
#145572772
#145572652
#145572622
C37×#4922
#163137