Finite Group Databasebeta

← #17993823

Subgroups — #17993823

Order 4736.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#14558248C211yesmaximal, characteristic
2#14557885C211yesmaximal, characteristic, complemented
3#14557735C211yesmaximal, characteristic, complemented
4#14557281C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#474C211yesmaximal, characteristic, complemented
8C2×#10596941—21no—
9#11924536C2211yescharacteristic
10#11924522—22no—
11#11924510—21no—
12#11924507—21no—
13C4×D148C2211yescharacteristic
14#11924495—21no—
15#11924494—21no—
16C4⋊#64436C2211yescharacteristic
17#11924460—21no—
18#11924459—22no—
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—
29C2×D148D411yescharacteristic
30C2×C4×D37—21no—
31C2×Dic74D412yes—
32C2×C8×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37D411yescharacteristic
36C22⋊C4×C37—21no—
37C42×C37C2311yescharacteristic
38C22⋊Dic37—22no—
39#10596941—42no—
40#10596938—22no—
41#10596938—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37—21no—
44C4⋊Dic37D411yescharacteristic
45C4×Dic37—22no—
46C2×#64436—21no—
47C2×#64436—21no—
48C23×C37—21no—
49C22×D37—21no—
50Q8×C37—41no—
51Q8×C37—41no—
52D4×C37—21no—
53D4×C37—21no—
54C2×C4×C37—21no—
55C2×C4×C37—41no—
56C2×C4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C22⋊D37—82no—
62C2×Dic37—21no—
63C2×Dic37—22no—
64D148—21no—
65D148—21no—
66C4×D37—41no—
67C4×D37—41no—
68Dic74—42no—
69C8×C37—41no—
70#64436—41no—
71#64436—41no—
72C22×C37—41no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37#12011yescharacteristic
76C2×D37—41no—
77C2×D37—41no—
78C2×D37—41no—
79C4×C37—21no—
80C4×C37—41no—
81C4×C37—81no—
82C4×C37#13511yescharacteristic
83C4×C37#13511yescharacteristic
84C4×C37AGL(1,ℤ/8)11yescharacteristic
85C4×C37#13711yescharacteristic
86Dic37—41no—
87Dic37—42no—
88#1646—371nomaximal, Sylow
89C2×C37—81no—
90C2×C37#44911yescharacteristic
91C2×C37#45211yescharacteristic
92C2×C37#45511yescharacteristic
93D37—81no—
94#555—371no—
95#487—371no—
96#474D3711yescharacteristic, complemented
97#461—371no—
98#333—371no—
99D4⋊C8—371no—
100D4⋊C8—371no—
101C37#164611yescharacteristic, complemented, Sylow
102C2×SD16—741no—
103C4⋊Q8—371no—
104C4⋊Q8C2×D3711yescharacteristic
105#124—742no—
106#121—741no—
107#121—741no—
108C4×D4—371no—
109C4×D4C2×D3711yescharacteristic
110#117—741no—
111#117—741no—
112#107—21no—
113C4⋊C8—371no—
114C4⋊C8C2×D3711yescharacteristic
115#103—742no—
116#103—741no—
117#102—21no—
118C4×C8—371no—
119C2×Q8—21no—
120C2×Q8—372no—
121C2×D4—371no—
122C2×D4—742no—
123C2×D4C22⋊D3711yescharacteristic
124C22×C4—21no—
125C22×C4—741no—
126SD16—1482no—
127C2×C8—21no—
128C2×C8—741no—
129C2×C8—741no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—371no—
133C4⋊C4—741no—
134C4⋊C4—741no—
135C4⋊C4C22⋊D3711yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—742no—
138C22⋊C4—742no—
139C22⋊C4—741no—
140C42—742no—
141C42C22×D3711yescharacteristic
142C23—21no—
143C23—741no—
144Q8—41no—
145Q8—41no—
146Q8—1482no—
147D4—21no—
148D4—21no—
149D4—2962no—
150D4—741no—
151D4—741no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—741no—
157C2×C4—742no—
158C2×C4—1481no—
159C2×C4—1481no—
160C2×C4D4×D3711yescharacteristic
161C2×C4D4×D3711yescharacteristic
162C2×C4C2×C22⋊D3711yescharacteristic
163C8—41no—
164C8—1481no—
165C8—1481no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—1481no—
170C22—1481no—
171C22—1481no—
172C22#1192450411yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—1482no—
177C4—1481no—
178C4#1192455511yescharacteristic
179C4#1192455611yescharacteristic
180C4#1192456011yescharacteristic
181C4#1192456711yescharacteristic
182C2—81no—
183C2—2961no—
184C2#1455767511yescharacteristic
185C2#1455769311yescharacteristic
186C2#1455770911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#474C2
socleC22×C37#120
prime radical#14558248C2
hypercenter#474D37
hypocenterC37#1646
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. #14557885C2semidirect
3. #14557735C2semidirect
4. #14557281C2semidirect
5. D4⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×#474C2semidirect
96. #474D37semidirect
101. C37#1646semidirect

Maximal subgroups

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

subgroupindex
#145582482
#145578852
#145577352
#145572812
D4⋊#644362
#145572602
C37×#4742
#164637