Finite Group Databasebeta

← #17993566

Subgroups — #17993566

Order 4736.

282 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 51 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#14558110C211yesmaximal, characteristic
2#14557674C211yesmaximal, characteristic, complemented
3#14557671C211yesmaximal, characteristic, complemented
4#14557454C211yesmaximal, characteristic, complemented
5#14557266C211yesmaximal, characteristic, complemented
6#14557258C211yesmaximal, characteristic, complemented
7C37×#327C211yesmaximal, characteristic, complemented
8C2×#10596964—21no—
9C22×Dic74C2211yescharacteristic
10C2×#10596930—21no—
11C2×#10596940—21no—
12#11924514—21no—
13#11924513—21no—
14#11924510C2211yescharacteristic
15#11924509—21no—
16#11924508—21no—
17#11924508—21no—
18C2×C4⋊Dic37—21no—
19C2×#10596936C2211yescharacteristic
20#11924461—21no—
21#11924459—21no—
22C22⋊#64436C2211yescharacteristic
23#11924443—21no—
24#121×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C2×D4×C37—21no—
28C2×D4×C37D411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C22×Dic37—21no—
35C22×Dic37—21no—
36C22×Dic37D411yescharacteristic
37C22×Dic37D411yescharacteristic
38#10596964—42no—
39#10596964—42no—
40C2×D148D411yescharacteristic
41C2×C4×D37—21no—
42C2×Dic74—21no—
43C2×Dic74—21no—
44C2×Dic74—21no—
45C2×Dic74—42no—
46C2×C8×C37—21no—
47C4⋊C4×C37D411yescharacteristic
48C22⋊C4×C37—21no—
49C22⋊Dic37—21no—
50#10596940—42no—
51#10596938—21no—
52#10596938—21no—
53C4⋊Dic37—42no—
54C4⋊Dic37D411yescharacteristic
55#10596936—21no—
56#10596936—21no—
57#10596936—21no—
58C2×#64436—21no—
59#10596930—42no—
60C23×C37—21no—
61C23×C37C2×D411yescharacteristic
62C22×D37—21no—
63D4×C37—41no—
64D4×C37—41no—
65D4×C37—41no—
66C2×C4×C37—22no—
67C2×C4×C37—21no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37—41no—
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C22⋊D37—42no—
74C22⋊D37—41no—
75C22⋊D37—41no—
76C22⋊D37—81no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—22no—
80C2×Dic37—21no—
81C2×Dic37—21no—
82C2×Dic37—42no—
83C2×Dic37—41no—
84C2×Dic37—41no—
85C2×Dic37—41no—
86C2×Dic37SD1612yescomplemented
87D148—41no—
88C4×D37—42no—
89Dic74—22no—
90Dic74—22no—
91Dic74—42no—
92Dic74—41no—
93Dic74—41no—
94C8×C37—41no—
95#64436—41no—
96C22×C37—21no—
97C22×C37—21no—
98C22×C37—41no—
99C22×C37—41no—
100C22×C37—41no—
101C22×C37#12011yescharacteristic
102C22×C37C2×SD1611yescharacteristic
103C22×C37AGL(1,ℤ/8)11yescharacteristic
104C2×D37—41no—
105C2×D37—41no—
106C2×D37—41no—
107C4×C37—21no—
108C4×C37—21no—
109C4×C37—42no—
110C4×C37—41no—
111Dic37—22no—
112Dic37—41no—
113Dic37—42no—
114Dic37—41no—
115#1604—371nomaximal, Sylow
116C2×C37—21no—
117C2×C37—21no—
118C2×C37—81no—
119C2×C37#45011yescharacteristic
120C2×C37#45611yescharacteristic
121C2×C37B(4,𝔽2)11yescharacteristic
122D37—81no—
123#537—371no—
124#448—371no—
125#448—371no—
126#395—371no—
127#327—371no—
128#327D3711yescharacteristic, complemented
129#324—371no—
130C37#160411yescharacteristic, complemented, Sylow
131C2×#41—741no—
132C22×Q8—371no—
133C2×SD16—741no—
134C2×SD16—741no—
135C22⋊Q8—741no—
136C22⋊Q8—741no—
137#121—371no—
138#121—741no—
139#121—741no—
140#121—741no—
141#121C2×D3711yescharacteristic
142C2×C4⋊C4—371no—
143C2×C4⋊C4—741no—
144#103—741no—
145#103—741no—
146C22⋊C8—371no—
147C22⋊C8C2×D3711yescharacteristic
148#95—741no—
149#95C2×D3711yescharacteristic
150#41—1482no—
151#41—1482no—
152C2×Q8—741no—
153C2×Q8—741no—
154C2×Q8—741no—
155C2×Q8—1482no—
156C2×D4—21no—
157C2×D4—371no—
158C2×D4—741no—
159C2×D4—741no—
160C2×D4—741no—
161C2×D4D14811yescharacteristic
162C22×C4—21no—
163C22×C4—371no—
164C22×C4—371no—
165C22×C4—741no—
166C22×C4—741no—
167C22×C4—741no—
168C22×C4C22×D3711yescharacteristic
169SD16—1482no—
170SD16—1482no—
171C2×C8—21no—
172C2×C8—741no—
173C4⋊C4—371no—
174C4⋊C4—741no—
175C4⋊C4—741no—
176C4⋊C4—741no—
177C4⋊C4—1482no—
178C4⋊C4D14811yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—741no—
181C22⋊C4—741no—
182C22⋊C4—741no—
183C23—21no—
184C23—741no—
185C23D4×D3711yescharacteristic
186Q8—742no—
187Q8—742no—
188Q8—1481no—
189Q8—1481no—
190Q8—1482no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—2961no—
195D4—1481no—
196D4—1482no—
197D4—1481no—
198D4—1481no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—372no—
205C2×C4—741no—
206C2×C4—741no—
207C2×C4—742no—
208C2×C4—741no—
209C2×C4—741no—
210C2×C4—1482no—
211C2×C4—1482no—
212C2×C4—1481no—
213C2×C4—1481no—
214C2×C4—1481no—
215C2×C4C2×D14811yescharacteristic
216C2×C4D4×D3711yescharacteristic
217C8—41no—
218C8—1481no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—1481no—
225C22—1481no—
226C22—1481no—
227C22#1192450611yescharacteristic
228C22SD16×D3711yescharacteristic
229C22#1192456011yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—41no—
234C4—742no—
235C4—1482no—
236C4—1481no—
237C4—1481no—
238C2—21no—
239C2—21no—
240C2—81no—
241C2—2961no—
242C2#1455768511yescharacteristic
243C2#1455771711yescharacteristic
244C2#1455772111yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#327C2
socleC22×C37#120
prime radical#14558110C2
hypercenter#327D37
hypocenterC37#1604
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14557674C2semidirect
3. #14557671C2semidirect
4. #14557454C2semidirect
5. #14557266C2semidirect
6. #14557258C2semidirect
7. C37×#327C2semidirect
86. C2×Dic37SD16semidirect
128. #327D37semidirect
130. C37#1604semidirect

Maximal subgroups

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

subgroupindex
#145581102
#145576742
#145576712
#145574542
#145572662
#145572582
C37×#3272
#160437