Finite Group Databasebeta

← #17993772

Subgroups — #17993772

Order 4736.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#14558168C211yesmaximal, characteristic
2#14557810C211yesmaximal, characteristic, complemented
3#14557735C211yesmaximal, characteristic, complemented
4#14557277C211yesmaximal, characteristic, complemented
5#14557262C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic, complemented
7C37×#486C211yesmaximal, characteristic, complemented
8C2×D4×D37—21no—
9C2×D4×D37—21no—
10C2×#10596941—21no—
11#11924507—21no—
12#11924507—21no—
13#11924504—22no—
14C4×D148C2211yescharacteristic
15C4×D148C2211yescharacteristic
16#11924469—21no—
17C4⋊#64436C2211yescharacteristic, complemented
18C4⋊#64436C2211yescharacteristic, complemented
19#11924460—21no—
20#11924456—21no—
21C4⋊Q8×C37C2211yescharacteristic, complemented
22#127×C37C2211yescharacteristic
23#102×C37—22no—
24C4×C8×C37C2211yescharacteristic, complemented
25C23×D37—22no—
26C2×Q8×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29C2×D4×C37D412yes—
30C2×C22⋊D37—22no—
31C2×C22⋊D37—22no—
32D4×D37—42no—
33D4×D37—42no—
34D4×D37—42no—
35D4×D37—42no—
36C2×D148D411yescharacteristic
37C2×D148D411yescharacteristic
38C2×C4×D37—21no—
39C2×C4×D37—21no—
40C2×C8×C37—21no—
41C4⋊C4×C37—21no—
42C4⋊C4×C37—21no—
43C42×C37C2311yescharacteristic
44C22⋊Dic37—22no—
45#10596941—42no—
46#10596938—21no—
47#10596938—21no—
48C4⋊Dic37D411yescharacteristic
49C4⋊Dic37D411yescharacteristic
50C2×#64436—21no—
51C2×#64436—21no—
52C23×C37—22no—
53C22×D37—21no—
54C22×D37—21no—
55C22×D37—44no—
56C22×D37—44no—
57C22×D37—82no—
58Q8×C37—41no—
59Q8×C37—41no—
60D4×C37—42no—
61D4×C37—41no—
62D4×C37—41no—
63D4×C37—41no—
64D4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C22⋊D37—44no—
70C22⋊D37—44no—
71C2×Dic37—21no—
72C2×Dic37—21no—
73D148—21no—
74D148—21no—
75D148D812yes—
76D148SD1612yescomplemented
77C4×D37—41no—
78C4×D37—41no—
79C4×D37—41no—
80C4×D37—41no—
81C8×C37—41no—
82#64436—41no—
83#64436—41no—
84C22×C37—42no—
85C22×C37—42no—
86C22×C37—42no—
87C22×C37#12011yescharacteristic
88C2×D37—22no—
89C2×D37—22no—
90C2×D37—41no—
91C2×D37—41no—
92C2×D37—41no—
93C2×D37—41no—
94C2×D37—88no—
95C4×C37—21no—
96C4×C37—81no—
97C4×C37C2×D811yescharacteristic
98C4×C37C2×SD1611yescharacteristic
99C4×C37AGL(1,ℤ/8)11yescharacteristic
100C4×C37AGL(1,ℤ/8)11yescharacteristic
101Dic37—41no—
102Dic37—41no—
103#1639—371nomaximal, Sylow
104C2×C37—82no—
105C2×C37#44711yescharacteristic
106C2×C37#45011yescharacteristic
107C2×C37#45511yescharacteristic
108D37—42no—
109D37—42no—
110D42—371no—
111#486D3711yescharacteristic, complemented
112#474—371no—
113#461—371no—
114#331—371no—
115D4⋊C8—371no—
116D4⋊C8—371no—
117C37#163911yescharacteristic, complemented, Sylow
118C22×D4—741no—
119C22×D4—741no—
120C2×SD16—741no—
121C4⋊Q8C2×D3711yescharacteristic, complemented
122#127C2×D3711yescharacteristic
123#121—741no—
124#121—741no—
125#120—742no—
126C4×D4—371no—
127C4×D4—371no—
128#107—741no—
129C4⋊C8—371no—
130C4⋊C8—371no—
131#103—741no—
132#102—22no—
133#102—741no—
134C4×C8C2×D3711yescharacteristic, complemented
135C24—742no—
136C2×Q8—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—371no—
140C2×D4—371no—
141C2×D4—742no—
142C2×D4—742no—
143C2×D4—1482no—
144C2×D4—1482no—
145C2×D4—1482no—
146C2×D4—1482no—
147C2×D4C22⋊D3712yes—
148C22×C4—741no—
149C22×C4—741no—
150SD16—1482no—
151C2×C8—21no—
152C2×C8—741no—
153C2×C8—741no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—371no—
157C4⋊C4—371no—
158C22⋊C4—742no—
159C22⋊C4—741no—
160C22⋊C4—741no—
161C42C22×D3711yescharacteristic
162C23—22no—
163C23—2962no—
164C23—741no—
165C23—741no—
166C23—1484no—
167C23—1484no—
168Q8—41no—
169Q8—41no—
170D4—42no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—372no—
176D4—372no—
177D4—741no—
178D4—741no—
179D4—1484no—
180D4—1484no—
181C2×C4—41no—
182C2×C4—741no—
183C2×C4—741no—
184C2×C4—1481no—
185C2×C4—1481no—
186C2×C4—1481no—
187C2×C4—1481no—
188C2×C4D4×D3711yescharacteristic
189C2×C4D4×D3711yescharacteristic
190C2×C4C2×C22⋊D3711yescharacteristic
191C8—41no—
192C8—1481no—
193C8—1481no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—2968no—
198C22—742no—
199C22—742no—
200C22—1481no—
201C22—1481no—
202C22—1481no—
203C22—1481no—
204C22#1192450411yescharacteristic
205C4—21no—
206C4—81no—
207C4—1481no—
208C4—1481no—
209C4D8×D3711yescharacteristic
210C4SD16×D3711yescharacteristic
211C4#1192456011yescharacteristic
212C4#1192456311yescharacteristic
213C2—82no—
214C2—1482no—
215C2—1482no—
216C2#1455766511yescharacteristic
217C2#1455768211yescharacteristic
218C2#1455771011yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#486C2
socleC22×C37#120
prime radical#14558168C2
hypercenter#486D37
hypocenterC37#1639
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #14557810C2semidirect
3. #14557735C2semidirect
4. #14557277C2semidirect
5. #14557262C2semidirect
6. #14557262C2semidirect
7. C37×#486C2semidirect
17. C4⋊#64436C22semidirect
18. C4⋊#64436C22semidirect
21. C4⋊Q8×C37C22semidirect
24. C4×C8×C37C22semidirect
76. D148SD16semidirect
111. #486D37semidirect
117. C37#1639semidirect
121. C4⋊Q8C2×D37semidirect
134. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581682
#145578102
#145577352
#145572772
#145572622
C37×#4862
#163937