Finite Group Databasebeta

← #17994898

Subgroups — #17994898

Order 4736.

376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 97 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#14558044C211yesmaximal, characteristic
2C2×#11924462C212yesmaximal, complemented
3C4×C22⋊Dic37C211yesmaximal, characteristic, complemented
4#14557294C212yesmaximal, complemented
5C22×M16×C37C211yesmaximal, characteristic, complemented
6C2×#10596962C2211yescharacteristic
7#11924519—21no—
8#11924515C411yescharacteristic, complemented
9#11924515C411yescharacteristic, complemented
10#11924510C411yescharacteristic, complemented
11#11924510C411yescharacteristic, complemented
12#11924505—21no—
13C4×C22⋊D37—21no—
14C4×C22⋊D37—21no—
15#11924495C2211yescharacteristic
16C2×C22⋊Dic37—21no—
17C2×C4×Dic37C2212yes—
18#11924462—24no—
19#11924443—21no—
20C23×C4×C37C2211yescharacteristic
21C2×M16×C37—21no—
22C2×M16×C37—24no—
23C2×M16×C37C2212yes—
24C22×C8×C37—21no—
25C24×C37D411yescharacteristic
26C22×C4×C37—22no—
27C22×C4×C37—22no—
28C22×C4×C37C2×C411yescharacteristic
29C22×C4×C37C2×C411yescharacteristic
30C22×C4×C37D411yescharacteristic
31C22×C4×C37D411yescharacteristic
32C22×C4×C37D411yescharacteristic
33C22×C4×C37C2311yescharacteristic
34C2×C22⋊D37—21no—
35C2×C22⋊D37—21no—
36C2×C22⋊D37—21no—
37C22×Dic37—22no—
38#10596962—22no—
39#10596962—22no—
40C2×D148C2×C411yescharacteristic
41C2×C4×D37—21no—
42C2×Dic74C2×C411yescharacteristic
43M16×C37—24no—
44M16×C37—22no—
45M16×C37D414yescomplemented
46C2×C8×C37—24no—
47C2×C8×C37—22no—
48C22⋊Dic37—24no—
49C22⋊Dic37—21no—
50C22⋊Dic37—21no—
51C22⋊Dic37—21no—
52#10596938—21no—
53#10596938—21no—
54C4⋊Dic37C2×C411yescharacteristic
55C4⋊Dic37C2×C411yescharacteristic
56#10596936—21no—
57#10596936—21no—
58C4×Dic37—21no—
59C4×Dic37—22no—
60C4×Dic37—22no—
61C23×C37—22no—
62C23×C37—22no—
63C23×C37—41no—
64C23×C37C22⋊C411yescharacteristic
65C23×C37C22⋊C411yescharacteristic
66C23×C37C2×D411yescharacteristic
67C22×D37—21no—
68C2×C4×C37—22no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37—21no—
72C2×C4×C37—21no—
73C2×C4×C37—21no—
74C2×C4×C37—21no—
75C2×C4×C37C22⋊C411yescharacteristic
76C2×C4×C37C22⋊C411yescharacteristic
77C2×C4×C37C22×C411yescharacteristic
78C2×C4×C37C2×D412yes—
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37#4112yes—
81C22⋊D37—42no—
82C22⋊D37—42no—
83C22⋊D37—42no—
84C2×Dic37—24no—
85C2×Dic37—21no—
86C2×Dic37—21no—
87C2×Dic37—21no—
88C2×Dic37—42no—
89C2×Dic37—42no—
90D148—22no—
91C4×D37—41no—
92C4×D37—41no—
93Dic74—22no—
94C8×C37—24no—
95C22×C37—21no—
96C22×C37—21no—
97C22×C37—21no—
98C22×C37—21no—
99C22×C37—21no—
100C22×C37—21no—
101C22×C37—21no—
102C22×C37—44no—
103C22×C37#10412yescomplemented
104C22×C37C2×C22⋊C411yescharacteristic
105C22×C37#12112yes—
106C2×D37—41no—
107C2×D37—41no—
108C2×D37—41no—
109C4×C37—21no—
110C4×C37—21no—
111C4×C37C4×D412yes—
112C4×C37#12011yescharacteristic
113C4×C37#12311yescharacteristic
114Dic37—44no—
115Dic37—41no—
116Dic37—41no—
117Dic37—41no—
118#1871—371nomaximal, Sylow
119C2×C37—22no—
120C2×C37—22no—
121C2×C37—41no—
122C2×C37#38611yescharacteristic
123C2×C37C2×#10411yescharacteristic
124C2×C37#42111yescharacteristic
125D37—81no—
126C22×M16D3711yescharacteristic, complemented
127#525—371no—
128C2×#104—372no—
129C4×C22⋊C4—371no—
130#339—372no—
131C37#187111yescharacteristic, complemented, Sylow
132C2×#41—371no—
133C23×C4C2×D3711yescharacteristic
134C2×M16—21no—
135C2×M16—24no—
136C2×M16C2×D3712yes—
137C22×C8—21no—
138#123—741no—
139C22⋊Q8—371no—
140C22⋊Q8—371no—
141#121—371no—
142#121—371no—
143#120—741no—
144C4×D4—741no—
145C4×D4—741no—
146#117—371no—
147C2×C22⋊C4—741no—
148C2×C42—372no—
149#104—744no—
150#95—741no—
151C24D14811yescharacteristic
152#41—742no—
153#41—742no—
154C2×Q8—371no—
155C2×D4—371no—
156C2×D4—741no—
157C2×D4—741no—
158C2×D4—741no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—742no—
162C22×C4—741no—
163C22×C4C4×D3711yescharacteristic
164C22×C4C4×D3711yescharacteristic
165C22×C4D14811yescharacteristic
166C22×C4C22⋊D3711yescharacteristic
167C22×C4C22⋊D3711yescharacteristic
168C22×C4C22×D3711yescharacteristic
169M16—24no—
170M16—22no—
171M16C22⋊D3714yescomplemented
172C2×C8—24no—
173C2×C8—22no—
174C4⋊C4—371no—
175C4⋊C4—371no—
176C4⋊C4—741no—
177C4⋊C4—741no—
178C22⋊C4—744no—
179C22⋊C4—741no—
180C22⋊C4—741no—
181C22⋊C4—741no—
182C22⋊C4—741no—
183C22⋊C4—741no—
184C42—741no—
185C42—742no—
186C42—742no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23—741no—
191C23#1059693811yescharacteristic
192C23#1059693811yescharacteristic
193C23C2×D14811yescharacteristic
194Q8—742no—
195D4—742no—
196D4—1482no—
197D4—1482no—
198D4—1482no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—744no—
207C2×C4—741no—
208C2×C4—741no—
209C2×C4—741no—
210C2×C4—1482no—
211C2×C4—1482no—
212C2×C4—1481no—
213C2×C4—1481no—
214C2×C4#1059693811yescharacteristic
215C2×C4#1059693811yescharacteristic
216C2×C4C2×C4×D3711yescharacteristic
217C2×C4#1059696212yes—
218C2×C4C2×C22⋊D3712yes—
219C2×C4C2×C22⋊D3711yescharacteristic
220C8—24no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—1481no—
230C22—1481no—
231C22—1481no—
232C22#1192446212yescomplemented
233C22C2×#1059693811yescharacteristic
234C22#1192451012yes—
235C4—21no—
236C4—21no—
237C4—1484no—
238C4—1481no—
239C4—1481no—
240C4—1481no—
241C4C4×C22⋊D3712yes—
242C4#1192450511yescharacteristic
243C4#1192451911yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—2961no—
248C2#1455741211yescharacteristic
249C2C2×#1192446211yescharacteristic
250C2#1455754911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC22×M16×C37C2
socleC22×C37C2×C22⋊C4
prime radical#14558044C2
cosocleC22×C4×C37C23
hypercenterC22×M16D37
hypocenterC37#1871
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#11924462C2semidirect
3. C4×C22⋊Dic37C2semidirect
4. #14557294C2semidirect
5. C22×M16×C37C2semidirect
8. #11924515C4semidirect
9. #11924515C4semidirect
10. #11924510C4semidirect
11. #11924510C4semidirect
45. M16×C37D4semidirect
103. C22×C37#104semidirect
126. C22×M16D37semidirect
131. C37#1871semidirect
171. M16C22⋊D37semidirect
232. C22#11924462semidirect

Maximal subgroups

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

subgroupindex
#145580442
C2×#119244622
C4×C22⋊Dic372
#145572942
C22×M16×C372
#187137