Finite Group Databasebeta

← #17993901

Subgroups — #17993901

Order 4736.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#14558275C211yesmaximal, characteristic
2#14557925C211yesmaximal, characteristic, complemented
3#14557895C211yesmaximal, characteristic, complemented
4#14557273C211yesmaximal, characteristic, complemented
5#14557272C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic, complemented
7C37×#489C211yesmaximal, characteristic, complemented
8C2×#10596942—21no—
9C2×#10596941—21no—
10#11924525—21no—
11#11924524C2211yescharacteristic
12#11924524C2211yescharacteristic
13#11924522—21no—
14#11924522—21no—
15#11924506—21no—
16#11924506—21no—
17#11924504—21no—
18#11924459—21no—
19#11924456—21no—
20#11924447C2211yescharacteristic, complemented
21#11924447C2211yescharacteristic, complemented
22C4⋊Q8×C37C2211yescharacteristic, complemented
23#124×C37C2211yescharacteristic
24#103×C37—21no—
25#102×C37—21no—
26#97×C37C2211yescharacteristic, complemented
27C23×D37—21no—
28C2×Q8×C37—21no—
29C2×Q8×C37D411yescharacteristic
30C2×D4×C37D411yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×D148—21no—
34C2×D148D411yescharacteristic
35C2×D148D411yescharacteristic
36C2×Dic74D411yescharacteristic
37C2×Dic74D411yescharacteristic
38C2×C8×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37—21no—
41C22⋊C4×C37—21no—
42C22⋊C4×C37—21no—
43C42×C37C2311yescharacteristic
44C22⋊Dic37—21no—
45#10596942—42no—
46#10596941—42no—
47#10596938—21no—
48#10596938—21no—
49#10596938—21no—
50#10596938—21no—
51#10596938—21no—
52#10596938—21no—
53C4×Dic37—21no—
54C2×#64436—21no—
55C2×#64436—21no—
56C23×C37—21no—
57C22×D37—21no—
58C22×D37—21no—
59C22×D37—81no—
60C22×D37—81no—
61C22×D37—81no—
62Q8×C37—41no—
63Q8×C37—41no—
64Q8×C37—41no—
65D4×C37—41no—
66C2×C4×C37—21no—
67C2×C4×C37—41no—
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C22⋊D37—81no—
72C22⋊D37—81no—
73C2×Dic37—21no—
74C2×Dic37—21no—
75D148—41no—
76D148—41no—
77D148—81no—
78Dic74—41no—
79Dic74—41no—
80C8×C37—41no—
81#64436—22no—
82#64436—41no—
83C22×C37—41no—
84C22×C37—41no—
85C22×C37—41no—
86C22×C37#12011yescharacteristic
87C2×D37—41no—
88C2×D37—41no—
89C2×D37—41no—
90C2×D37—41no—
91C2×D37—41no—
92C2×D37—41no—
93C2×D37—84no—
94C4×C37—21no—
95C4×C37—21no—
96C4×C37—21no—
97C4×C37—41no—
98C4×C37—81no—
99Dic37—41no—
100Dic37—41no—
101#1659—371nomaximal, Sylow
102C2×C37—81no—
103C2×C37#45311yescharacteristic
104C2×C37#45511yescharacteristic
105C2×C37#45511yescharacteristic
106D37—81no—
107D37—81no—
108H(3,𝔽4)—371no—
109#497—371no—
110#489—371no—
111#489D3711yescharacteristic, complemented
112#329—371no—
113#329—371no—
114#329—371no—
115C37#165911yescharacteristic, complemented, Sylow
116C2×Q16—741no—
117C2×SD16—741no—
118C4⋊Q8C2×D3711yescharacteristic, complemented
119#124—371no—
120#124—371no—
121#124—741no—
122#124—741no—
123#124—741no—
124#124C2×D3711yescharacteristic
125#120—741no—
126#120—741no—
127#120—741no—
128#103—21no—
129#103—741no—
130#102—21no—
131#102—741no—
132#97—371no—
133#97—371no—
134#97C2×D3711yescharacteristic, complemented
135C24—741no—
136C2×Q8—21no—
137C2×Q8—371no—
138C2×Q8—371no—
139C2×Q8C22⋊D3711yescharacteristic
140C2×D4—371no—
141C2×D4—371no—
142C2×D4—741no—
143C2×D4—741no—
144C2×D4—741no—
145C2×D4C22⋊D3711yescharacteristic
146Q16—1482no—
147SD16—1482no—
148C2×C8—21no—
149C2×C8—741no—
150C2×C8—741no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—741no—
156C22⋊C4—741no—
157C22⋊C4—741no—
158C22⋊C4—741no—
159C22⋊C4—741no—
160C22⋊C4—741no—
161C22⋊C4—741no—
162C42—741no—
163C42C22×D3711yescharacteristic
164C23—21no—
165C23—2961no—
166C23—2961no—
167C23—2961no—
168C23—741no—
169C23—741no—
170Q8—41no—
171Q8—41no—
172Q8—41no—
173Q8—1481no—
174Q8—1481no—
175D4—41no—
176D4—2961no—
177D4—2961no—
178D4—2961no—
179D4—1481no—
180D4—1481no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4D4×D3711yescharacteristic
186C2×C4D4×D3711yescharacteristic
187C2×C4C2×C22⋊D3711yescharacteristic
188C8—41no—
189C8—742no—
190C8—1481no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—2964no—
195C22—1481no—
196C22—1481no—
197C22—1481no—
198C22—1481no—
199C22—1481no—
200C22—1481no—
201C22#1192450411yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—81no—
207C4—1481no—
208C4—1481no—
209C2—81no—
210C2—2961no—
211C2—2961no—
212C2#1455769911yescharacteristic
213C2#1455770911yescharacteristic
214C2#1455771011yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#489C2
socleC22×C37#120
prime radical#14558275C2
hypercenter#489D37
hypocenterC37#1659
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #14557925C2semidirect
3. #14557895C2semidirect
4. #14557273C2semidirect
5. #14557272C2semidirect
6. #14557272C2semidirect
7. C37×#489C2semidirect
20. #11924447C22semidirect
21. #11924447C22semidirect
22. C4⋊Q8×C37C22semidirect
26. #97×C37C22semidirect
111. #489D37semidirect
115. C37#1659semidirect
118. C4⋊Q8C2×D37semidirect
134. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582752
#145579252
#145578952
#145572732
#145572722
C37×#4892
#165937