Finite Group Databasebeta

← #17993617

Subgroups — #17993617

Order 4736.

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

normal subgroups only

This group has 288 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#14558091C211yesmaximal, characteristic
2#14557852C211yesmaximal, characteristic, complemented
3#14557849C211yesmaximal, characteristic, complemented
4#14557470C211yesmaximal, characteristic, complemented
5#14557266C211yesmaximal, characteristic, complemented
6#14557256C211yesmaximal, characteristic, complemented
7C37×#327C211yesmaximal, characteristic, complemented
8C2×D4×D37—21no—
9#11924521—21no—
10#11924518—21no—
11#11924510C2211yescharacteristic
12#11924508—21no—
13#11924506—21no—
14#11924504—21no—
15C2×C4⋊Dic37—21no—
16C2×C4⋊Dic37C2211yescharacteristic, complemented
17C2×#10596938—21no—
18C2×#10596938C2211yescharacteristic
19#11924468—21no—
20#11924467—21no—
21#11924458—21no—
22#11924457—21no—
23C22⋊#64436C2211yescharacteristic, complemented
24#121×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic, complemented
26#95×C37C2211yescharacteristic, complemented
27C23×D37—21no—
28C23×D37D411yescharacteristic
29C2×D4×C37—21no—
30C2×D4×C37D411yescharacteristic
31C22×C4×C37—21no—
32C22×C4×C37C2311yescharacteristic
33C2×C22⋊D37—21no—
34C2×C22⋊D37—21no—
35C2×C22⋊D37—21no—
36C22×Dic37—21no—
37C22×Dic37D411yescharacteristic
38D4×D37—42no—
39D4×D37—42no—
40C2×D148—21no—
41C2×D148D411yescharacteristic
42C2×C4×D37—21no—
43C2×C8×C37—21no—
44C4⋊C4×C37D411yescharacteristic
45C22⋊C4×C37—21no—
46C22⋊Dic37—21no—
47#10596938—21no—
48#10596938—21no—
49#10596938—21no—
50#10596938—21no—
51#10596938—42no—
52C4⋊Dic37—21no—
53C4⋊Dic37—21no—
54C4⋊Dic37—42no—
55C4⋊Dic37D411yescharacteristic
56#10596936—21no—
57C2×#64436—21no—
58C23×C37—21no—
59C23×C37C2×D411yescharacteristic
60C22×D37—21no—
61C22×D37—21no—
62C22×D37—21no—
63C22×D37—42no—
64C22×D37—41no—
65C22×D37—41no—
66C22×D37—81no—
67C22×D37—81no—
68C22×D37SD1612yes—
69D4×C37—41no—
70D4×C37—41no—
71D4×C37—41no—
72C2×C4×C37—22no—
73C2×C4×C37—21no—
74C2×C4×C37—41no—
75C2×C4×C37—41no—
76C2×C4×C37—41no—
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C22⋊D37—42no—
80C22⋊D37—41no—
81C22⋊D37—41no—
82C22⋊D37—81no—
83C2×Dic37—21no—
84C2×Dic37—21no—
85C2×Dic37—41no—
86C2×Dic37—41no—
87C2×Dic37—41no—
88C2×Dic37—41no—
89D148—41no—
90D148—42no—
91C4×D37—42no—
92C8×C37—41no—
93#64436—41no—
94C22×C37—21no—
95C22×C37—21no—
96C22×C37—41no—
97C22×C37—41no—
98C22×C37—41no—
99C22×C37#12011yescharacteristic
100C22×C37C2×SD1611yescharacteristic
101C22×C37AGL(1,ℤ/8)11yescharacteristic
102C2×D37—22no—
103C2×D37—41no—
104C2×D37—41no—
105C2×D37—42no—
106C2×D37—41no—
107C2×D37—41no—
108C2×D37—41no—
109C2×D37—81no—
110C2×D37—84no—
111C4×C37—21no—
112C4×C37—21no—
113C4×C37—42no—
114C4×C37—41no—
115Dic37—41no—
116Dic37—41no—
117Dic37—81no—
118#1613—371nomaximal, Sylow
119C2×C37—21no—
120C2×C37—21no—
121C2×C37—81no—
122C2×C37#45011yescharacteristic
123C2×C37#45311yescharacteristic
124C2×C37#45811yescharacteristic
125D37—42no—
126D37—81no—
127#534—371no—
128#481—371no—
129#481—371no—
130#399—371no—
131#327—371no—
132#327D3711yescharacteristic, complemented
133#323—371no—
134C37#161311yescharacteristic, complemented, Sylow
135C22×D4—741no—
136#123—741no—
137#123—741no—
138#121—371no—
139#121—741no—
140#121C2×D3711yescharacteristic
141#120—741no—
142#120—741no—
143C2×C4⋊C4—371no—
144C2×C4⋊C4—741no—
145C2×C22⋊C4—371no—
146C2×C22⋊C4—741no—
147#106—741no—
148#106—741no—
149#102—741no—
150#102—741no—
151C22⋊C8—371no—
152C22⋊C8C2×D3711yescharacteristic, complemented
153#95C2×D3711yescharacteristic, complemented
154C24—371no—
155C24—741no—
156C2×D4—21no—
157C2×D4—371no—
158C2×D4—741no—
159C2×D4—741no—
160C2×D4—741no—
161C2×D4—741no—
162C2×D4—1482no—
163C2×D4—1482no—
164C2×D4D14811yescharacteristic
165C22×C4—21no—
166C22×C4—371no—
167C22×C4—741no—
168C22×C4—741no—
169C22×C4C22×D3711yescharacteristic
170C2×C8—21no—
171C2×C8—741no—
172C4⋊C4—371no—
173C4⋊C4—741no—
174C4⋊C4—741no—
175C4⋊C4—741no—
176C4⋊C4—1482no—
177C4⋊C4D14811yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—741no—
180C22⋊C4—741no—
181C22⋊C4—741no—
182C22⋊C4—741no—
183C22⋊C4—741no—
184C22⋊C4—1482no—
185C23—21no—
186C23—372no—
187C23—2961no—
188C23—2961no—
189C23—741no—
190C23—741no—
191C23—741no—
192C23—1481no—
193C23—1481no—
194C23—1482no—
195C23D4×D3711yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—2961no—
200D4—1481no—
201D4—1482no—
202D4—1482no—
203D4—1481no—
204D4—1481no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—741no—
211C2×C4—741no—
212C2×C4—1482no—
213C2×C4—1481no—
214C2×C4—1481no—
215C2×C4—1481no—
216C2×C4—1481no—
217C2×C4C2×D14811yescharacteristic
218C2×C4D4×D3711yescharacteristic
219C8—41no—
220C8—1481no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—2961no—
227C22—2964no—
228C22—742no—
229C22—1482no—
230C22—1481no—
231C22—1481no—
232C22—1481no—
233C22—1481no—
234C22—1481no—
235C22#1192450611yescharacteristic
236C22SD16×D3711yescharacteristic
237C22#1192456011yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—41no—
242C4—2961no—
243C4—1481no—
244C4—1481no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—2961no—
249C2—1482no—
250C2#1455768511yescharacteristic
251C2#1455770211yescharacteristic
252C2#1455772411yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#327C2
socleC22×C37#120
prime radical#14558091C2
hypercenter#327D37
hypocenterC37#1613
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. #14557852C2semidirect
3. #14557849C2semidirect
4. #14557470C2semidirect
5. #14557266C2semidirect
6. #14557256C2semidirect
7. C37×#327C2semidirect
16. C2×C4⋊Dic37C22semidirect
23. C22⋊#64436C22semidirect
25. C22⋊C8×C37C22semidirect
26. #95×C37C22semidirect
132. #327D37semidirect
134. C37#1613semidirect
152. C22⋊C8C2×D37semidirect
153. #95C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580912
#145578522
#145578492
#145574702
#145572662
#145572562
C37×#3272
#161337