Finite Group Databasebeta

← #17993724

Subgroups — #17993724

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#14557905C211yesmaximal, characteristic, complemented
3#14557829C211yesmaximal, characteristic, complemented
4#14557824C211yesmaximal, characteristic, complemented
5#14557263C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#331C211yesmaximal, characteristic, complemented
8C2×#10596964—21no—
9C2×#10596940—22no—
10#11924536C2211yescharacteristic
11#11924532—21no—
12#11924508—22no—
13#11924507—21no—
14C4×Dic74C2211yescharacteristic
15C4×D148C2211yescharacteristic
16D4×Dic37—21no—
17#11924470—21no—
18#11924468—21no—
19#11924461—21no—
20#11924458—21no—
21C4×#64436C2211yescharacteristic
22#127×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×D4×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37D412yes—
28C2×C22⋊D37—22no—
29C2×C22⋊D37—22no—
30C22×Dic37—22no—
31#10596964—42no—
32#10596964—42no—
33C2×D148D411yescharacteristic
34C2×C4×D37—21no—
35C2×Dic74—21no—
36C2×Dic74D411yescharacteristic
37C2×C8×C37—21no—
38C2×C8×C37—21no—
39C42×C37C2311yescharacteristic
40C22⋊Dic37—22no—
41#10596940—44no—
42#10596938—21no—
43C4⋊Dic37—21no—
44C4⋊Dic37—21no—
45C4⋊Dic37D411yescharacteristic
46C4⋊Dic37D411yescharacteristic
47#10596936—21no—
48C4×Dic37—21no—
49C2×#64436—21no—
50C23×C37—22no—
51C22×D37—21no—
52D4×C37—42no—
53D4×C37—41no—
54D4×C37—41no—
55D4×C37—41no—
56D4×C37—41no—
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C22⋊D37—44no—
61C22⋊D37—82no—
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—21no—
65C2×Dic37—44no—
66C2×Dic37—41no—
67D148—21no—
68D148—21no—
69C4×D37—41no—
70C4×D37—41no—
71Dic74—21no—
72Dic74—42no—
73Dic74SD1612yescomplemented
74C8×C37—41no—
75C8×C37—41no—
76#64436—22no—
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×C37C2×SD1611yescharacteristic
86C4×C37#13511yescharacteristic
87C4×C37AGL(1,ℤ/8)11yescharacteristic
88C4×C37#13711yescharacteristic
89Dic37—22no—
90Dic37—41no—
91Dic37—41no—
92Dic37—81no—
93#1631—371nomaximal, Sylow
94C2×C37—82no—
95C2×C37#45011yescharacteristic
96C2×C37#45211yescharacteristic
97C2×C37#45311yescharacteristic
98D37—81no—
99#550—371no—
100#492—371no—
101#477—371no—
102#476—371no—
103#331D3711yescharacteristic, complemented
104Q8⋊C8—371no—
105D4⋊C8—371no—
106C37#163111yescharacteristic, complemented, Sylow
107C2×#41—741no—
108C2×SD16—742no—
109C4⋊Q8—371no—
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⋊C8C2×D3711yescharacteristic
120C4⋊C8C2×D3711yescharacteristic
121#103—741no—
122#102—741no—
123C4×C8—371no—
124#41—1482no—
125#41—1482no—
126C2×Q8—371no—
127C2×Q8—741no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—371no—
131C2×D4—742no—
132C2×D4—742no—
133C2×D4D14812yes—
134C22×C4—742no—
135C22×C4—741no—
136SD16—1484no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—741no—
140C4⋊C4—371no—
141C4⋊C4—371no—
142C4⋊C4—741no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C22⋊C4—742no—
146C22⋊C4—741no—
147C42—741no—
148C42C22×D3711yescharacteristic
149C23—22no—
150C23—741no—
151Q8—372no—
152Q8—741no—
153Q8—1482no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—2962no—
160D4—741no—
161D4—741no—
162D4—1484no—
163C2×C4—741no—
164C2×C4—741no—
165C2×C4—741no—
166C2×C4—1481no—
167C2×C4—1484no—
168C2×C4—1481no—
169C2×C4—1481no—
170C2×C4C2×D14811yescharacteristic
171C2×C4D4×D3711yescharacteristic
172C2×C4D4×D3711yescharacteristic
173C8—41no—
174C8—41no—
175C8—742no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—1481no—
180C22—1481no—
181C22—1481no—
182C22#1192450611yescharacteristic
183C4—21no—
184C4—2961no—
185C4—742no—
186C4—1481no—
187C4—1481no—
188C4SD16×D3711yescharacteristic
189C4#1192455511yescharacteristic
190C4#1192456011yescharacteristic
191C4#1192456511yescharacteristic
192C2—82no—
193C2—2961no—
194C2#1455768511yescharacteristic
195C2#1455769611yescharacteristic
196C2#1455770311yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#331C2
socleC22×C37#120
prime radical#14558203C2
hypercenter#331D37
hypocenterC37#1631
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #14557905C2semidirect
3. #14557829C2semidirect
4. #14557824C2semidirect
5. #14557263C2semidirect
6. #14557260C2semidirect
7. C37×#331C2semidirect
73. Dic74SD16semidirect
103. #331D37semidirect
106. C37#1631semidirect

Maximal subgroups

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

subgroupindex
#145582032
#145579052
#145578292
#145578242
#145572632
#145572602
C37×#3312
#163137