Finite Group Databasebeta

← #17996263

Subgroups — #17996263

Order 4736.

286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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#14558100C211yesmaximal, characteristic
2C2×#11924451C211yesmaximal, characteristic, complemented
3#14557327C212yesmaximal, complemented
4#14557325C212yesmaximal, complemented
5C2×#99×C37C211yesmaximal, characteristic, complemented
6C2×#10596962C411yescharacteristic, complemented
7#11924532C411yescharacteristic, complemented
8#11924532C2211yescharacteristic
9#11924523C411yescharacteristic, complemented
10#11924523C2211yescharacteristic
11#11924507—21no—
12#11924507—21no—
13#11924505—21no—
14#11924505—21no—
15#11924495C411yescharacteristic, complemented
16C2×C22⋊Dic37—21no—
17#11924451—21no—
18#11924451C2212yes—
19C22×D4×C37C2211yescharacteristic
20C2×C22⋊C4×C37—21no—
21#99×C37—21no—
22#99×C37C2212yes—
23C24×C37D411yescharacteristic
24C24×C37D411yescharacteristic
25C2×D4×C37—41no—
26C2×D4×C37—41no—
27C2×D4×C37C2×C411yescharacteristic
28C2×D4×C37D411yescharacteristic
29C2×D4×C37D411yescharacteristic
30C2×D4×C37C2311yescharacteristic
31C22×C4×C37—41no—
32C22×C4×C37C2×C411yescharacteristic
33C2×C22⋊D37—21no—
34C2×C22⋊D37—21no—
35C2×C22⋊D37—21no—
36C2×C22⋊D37—21no—
37C2×C22⋊D37—21no—
38C22×Dic37—41no—
39#10596962—41no—
40#10596962—41no—
41C2×D148C2×C411yescharacteristic, complemented
42C2×C4×D37—21no—
43C2×Dic74C2×C411yescharacteristic, complemented
44C22⋊C4×C37—22no—
45C22⋊C4×C37—41no—
46C22⋊Dic37—21no—
47C22⋊Dic37—21no—
48C22⋊Dic37—21no—
49C22⋊Dic37—21no—
50C22⋊Dic37—21no—
51C22⋊Dic37—22no—
52C22⋊Dic37—41no—
53C4⋊Dic37—21no—
54C4×Dic37C2×C411yescharacteristic, complemented
55C4×Dic37C2×C411yescharacteristic, complemented
56C23×C37—21no—
57C23×C37—21no—
58C23×C37—21no—
59C23×C37—21no—
60C23×C37—81no—
61C23×C37—81no—
62C23×C37C22⋊C411yescharacteristic
63C23×C37C22⋊C411yescharacteristic
64C23×C37C22⋊C411yescharacteristic
65C23×C37C2×D411yescharacteristic
66C23×C37C2×D411yescharacteristic
67C22×D37—21no—
68D4×C37—41no—
69D4×C37—41no—
70D4×C37—41no—
71D4×C37—41no—
72C2×C4×C37—21no—
73C2×C4×C37—21no—
74C2×C4×C37—42no—
75C2×C4×C37—82no—
76C2×C4×C37C22⋊C411yescharacteristic
77C2×C4×C37C22×C411yescharacteristic
78C22⋊D37—41no—
79C22⋊D37—41no—
80C22⋊D37—81no—
81C22⋊D37—81no—
82C22⋊D37—81no—
83C22⋊D37—81no—
84C2×Dic37—21no—
85C2×Dic37—21no—
86C2×Dic37—21no—
87C2×Dic37—42no—
88C2×Dic37—82no—
89D148—41no—
90C4×D37—42no—
91Dic74—41no—
92C22×C37—21no—
93C22×C37—21no—
94C22×C37—21no—
95C22×C37—21no—
96C22×C37—41no—
97C22×C37—41no—
98C22×C37—41no—
99C22×C37—41no—
100C22×C37—41no—
101C22×C37—42no—
102C22×C37—42no—
103C22×C37—81no—
104C22×C37—81no—
105C22×C37#9911yescharacteristic
106C22×C37#9911yescharacteristic
107C22×C37C2×C22⋊C411yescharacteristic
108C2×D37—41no—
109C2×D37—41no—
110C2×D37—41no—
111C4×C37—21no—
112C4×C37—21no—
113C4×C37—82no—
114Dic37—41no—
115Dic37—41no—
116Dic37—41no—
117Dic37—82no—
118#2127—371nomaximal, Sylow
119C2×C37—21no—
120C2×C37—21no—
121C2×C37—21no—
122C2×C37—41no—
123C2×C37—41no—
124C2×C37—41no—
125C2×C37—41no—
126C2×C37C2×#9911yescharacteristic
127D37—81no—
128#535—371no—
129C2×#99—371no—
130C2×#99D3711yescharacteristic, complemented
131#354—372no—
132#353—372no—
133C37#212711yescharacteristic, complemented, Sylow
134C2×#41—371no—
135C22×D4C2×D3711yescharacteristic
136#127—371no—
137#127—371no—
138#124—371no—
139#124—371no—
140#121—741no—
141#121—741no—
142#120—741no—
143#120—741no—
144#117—371no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—741no—
147#99—21no—
148#99—372no—
149#99—741no—
150#99C2×D3712yes—
151C24D14811yescharacteristic
152C24C22⋊D3711yescharacteristic
153#41—1481no—
154#41—1481no—
155C2×Q8—371no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—371no—
159C2×D4—741no—
160C2×D4—741no—
161C2×D4—741no—
162C2×D4—741no—
163C2×D4—741no—
164C2×D4C4×D3711yescharacteristic
165C2×D4D14811yescharacteristic
166C2×D4C22⋊D3711yescharacteristic
167C2×D4C22×D3711yescharacteristic
168C22×C4—41no—
169C22×C4—741no—
170C22×C4—1481no—
171C22×C4C4×D3711yescharacteristic
172C4⋊C4—741no—
173C22⋊C4—22no—
174C22⋊C4—41no—
175C22⋊C4—741no—
176C22⋊C4—741no—
177C22⋊C4—741no—
178C22⋊C4—741no—
179C22⋊C4—741no—
180C22⋊C4—742no—
181C22⋊C4—1481no—
182C42—371no—
183C42—371no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—81no—
189C23—81no—
190C23—741no—
191C23#1059693811yescharacteristic
192C23#1059693811yescharacteristic
193C23#1059693811yescharacteristic
194C23C2×D14811yescharacteristic
195C23C2×C22⋊D3711yescharacteristic
196Q8—1481no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—2961no—
202D4—2961no—
203D4—2961no—
204D4—2961no—
205D4—1481no—
206D4—1481no—
207D4—1481no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—2962no—
213C2×C4—741no—
214C2×C4—741no—
215C2×C4—741no—
216C2×C4—1482no—
217C2×C4—1482no—
218C2×C4#1059693811yescharacteristic
219C2×C4C2×C4×D3711yescharacteristic
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—1481no—
234C22—1481no—
235C22—1481no—
236C22#1192445011yescharacteristic
237C22#1192445011yescharacteristic
238C22C2×#1059693811yescharacteristic
239C4—21no—
240C4—21no—
241C4—82no—
242C4—2962no—
243C4—1481no—
244C4—1481no—
245C4—1481no—
246C2—21no—
247C2—21no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—41no—
252C2—41no—
253C2—2961no—
254C2C2×#1192445011yescharacteristic
subgroupG/H
centerC2C2×#11924450
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
FittingC2×#99×C37C2
socleC2×C37C2×#99
prime radical#14558100C2
cosocleC2×D4×C37C23
hypercenterC2×#99D37
hypocenterC37#2127
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#11924451C2semidirect
3. #14557327C2semidirect
4. #14557325C2semidirect
5. C2×#99×C37C2semidirect
6. C2×#10596962C4semidirect
7. #11924532C4semidirect
9. #11924523C4semidirect
15. #11924495C4semidirect
41. C2×D148C2×C4semidirect
43. C2×Dic74C2×C4semidirect
54. C4×Dic37C2×C4semidirect
55. C4×Dic37C2×C4semidirect
130. C2×#99D37semidirect
133. C37#2127semidirect

Maximal subgroups

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

subgroupindex
#145581002
C2×#119244512
#145573272
#145573252
C2×#99×C372
#212737