Finite Group Databasebeta

← #18004114

Subgroups — #18004114

Order 4736.

490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#11924567C211yesmaximal, characteristic, complemented
2#14558100C211yesmaximal, characteristic
3#14558011C211yesmaximal, characteristic, complemented
4#14557753C214yesmaximal, complemented
5#14557731C214yesmaximal, complemented
6#14557559C211yesmaximal, characteristic, complemented
7#14557538C211yesmaximal, characteristic, complemented
8#14557530C211yesmaximal, characteristic, complemented
9C22×SD16×C37C211yesmaximal, characteristic, complemented
10C2×#10596962C2211yescharacteristic
11#11924567—24no—
12C2×#10596942C2212yescomplemented
13C2×#10596941C2212yescomplemented
14C2×#10596934C2211yescharacteristic
15#11924532C2212yes—
16#11924523C2212yes—
17#11924507—22no—
18#11924505—22no—
19Q8×Dic37—22no—
20Q8×Dic37C2214yescomplemented
21#11924495—22no—
22#11924495C2211yescharacteristic
23#11924495C2211yescharacteristic
24#11924465C2214yescomplemented
25#11924461C2212yescomplemented
26#11924458C2212yescomplemented
27#11924457C2214yes—
28C22×Q8×C37C2211yescharacteristic
29C22×D4×C37C2211yescharacteristic
30C2×SD16×C37—24no—
31C2×SD16×C37C2214yes—
32C22×C8×C37C2211yescharacteristic
33C24×C37—21no—
34C2×Q8×C37—21no—
35C2×Q8×C37—22no—
36C2×Q8×C37D414yescomplemented
37C2×Q8×C37C2312yes—
38C2×D4×C37—22no—
39C2×D4×C37—21no—
40C2×D4×C37—22no—
41C2×D4×C37C2312yes—
42C22×C4×C37—21no—
43C22×C4×C37C2311yescharacteristic
44C2×C22⋊D37—21no—
45C2×C22⋊D37—24no—
46#10596962—22no—
47#10596962—22no—
48C2×D148C2311yescharacteristic
49C2×C4×D37—21no—
50C2×Dic74C2311yescharacteristic
51SD16×C37—28no—
52C2×C8×C37—22no—
53C2×C8×C37C2312yes—
54C22⋊Dic37—21no—
55C22⋊Dic37—24no—
56C22⋊Dic37D412yes—
57#10596942—24no—
58#10596941—24no—
59C4⋊Dic37—24no—
60C4⋊Dic37D412yes—
61C4⋊Dic37C2312yes—
62C4×Dic37—21no—
63C4×Dic37—24no—
64C4×Dic37C2312yes—
65#10596934—22no—
66C2×#64436C2312yes—
67C23×C37—22no—
68C23×C37—42no—
69C23×C37—82no—
70C23×C37C2×D411yescharacteristic
71C22×D37—21no—
72Q8×C37—24no—
73Q8×C37—22no—
74Q8×C37C2×D414yes—
75D4×C37—22no—
76D4×C37—22no—
77D4×C37—42no—
78C2×C4×C37—24no—
79C2×C4×C37—22no—
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D412yes—
82C2×C4×C37#4112yes—
83C2×C4×C37C2411yescharacteristic
84C22⋊D37—42no—
85C22⋊D37—84no—
86C2×Dic37—22no—
87C2×Dic37—21no—
88C2×Dic37C2×D414yes—
89D148—21no—
90D148—21no—
91C4×D37—42no—
92Dic74—21no—
93Dic74—21no—
94C8×C37—22no—
95#64436—22no—
96C22×C37—22no—
97C22×C37—42no—
98C22×C37—44no—
99C22×C37—84no—
100C22×C37#12112yes—
101C22×C37C22×D411yescharacteristic
102C2×D37—41no—
103C2×D37—42no—
104C4×C37—24no—
105C4×C37#12112yes—
106C4×C37C22×D411yescharacteristic
107C4×C37C2×#4111yescharacteristic
108Dic37—24no—
109Dic37—41no—
110Dic37—42no—
111#3043—371nomaximal, Sylow
112C2×C37—22no—
113C2×C37—82no—
114C2×C37C2×#12111yescharacteristic
115C2×C37#57712yes—
116D37—81no—
117C2×#137—371no—
118C22×SD16D3711yescharacteristic, complemented
119#535—371no—
120#519—371no—
121#464—374no—
122#460—374no—
123#424—371no—
124#418—371no—
125#416—371no—
126C37#304311yescharacteristic, complemented, Sylow
127C2×#41—371no—
128C22×Q8C2×D3711yescharacteristic
129C22×D4C2×D3711yescharacteristic
130#137—744no—
131C2×Q16—372no—
132C2×SD16—24no—
133C2×SD16—372no—
134C2×SD16C2×D3714yes—
135C2×M16—371no—
136C22×C8C2×D3711yescharacteristic
137#127—372no—
138#124—372no—
139#121—742no—
140#120—742no—
141C4×Q8—374no—
142C4×Q8—742no—
143#117—371no—
144#117—371no—
145#117—742no—
146C4⋊C8—374no—
147#103—372no—
148#102—374no—
149#102—372no—
150C24—21no—
151#41—742no—
152#41—742no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—371no—
156C2×Q8C22⋊D3714yescomplemented
157C2×Q8C22×D3712yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—22no—
161C2×D4—371no—
162C2×D4—744no—
163C2×D4—741no—
164C2×D4C22×D3712yes—
165C22×C4—21no—
166C22×C4—741no—
167C22×C4C22×D3711yescharacteristic
168Q16—744no—
169SD16—28no—
170SD16—744no—
171M16—742no—
172C2×C8—22no—
173C2×C8—372no—
174C2×C8C22×D3712yes—
175C4⋊C4—372no—
176C4⋊C4—372no—
177C4⋊C4—744no—
178C22⋊C4—372no—
179C22⋊C4—744no—
180C22⋊C4—741no—
181C42—372no—
182C42—744no—
183C42—741no—
184C23—22no—
185C23—42no—
186C23—82no—
187C23—741no—
188C23D4×D3711yescharacteristic
189Q8—24no—
190Q8—22no—
191Q8—741no—
192Q8—741no—
193Q8C2×C22⋊D3714yes—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—2964no—
198D4—741no—
199D4—741no—
200D4—1482no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—374no—
204C2×C4—742no—
205C2×C4—741no—
206C2×C4—1482no—
207C2×C4D4×D3711yescharacteristic
208C2×C4#1059696412yes—
209C2×C4C2×C22⋊D3712yes—
210C2×C4C23×D3711yescharacteristic
211C8—22no—
212C8—742no—
213C22—22no—
214C22—42no—
215C22—44no—
216C22—84no—
217C22—1481no—
218C22—1482no—
219C22#1192450812yes—
220C22C2×D4×D3711yescharacteristic
221C4—24no—
222C4—744no—
223C4—1481no—
224C4—1482no—
225C4#1192450812yes—
226C4C22×C22⋊D3711yescharacteristic
227C4C2×#1059696411yescharacteristic
228C2—22no—
229C2—82no—
230C2—2961no—
231C2C2×#1192450811yescharacteristic
232C2#1455833912yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC22×SD16×C37C2
socleC22×C37C22×D4
prime radical#14558100C2
hypercenterC22×SD16D37
hypocenterC37#3043
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#11924567C2semidirect
3. #14558011C2semidirect
4. #14557753C2semidirect
5. #14557731C2semidirect
6. #14557559C2semidirect
7. #14557538C2semidirect
8. #14557530C2semidirect
9. C22×SD16×C37C2semidirect
12. C2×#10596942C22semidirect
13. C2×#10596941C22semidirect
20. Q8×Dic37C22semidirect
24. #11924465C22semidirect
25. #11924461C22semidirect
26. #11924458C22semidirect
36. C2×Q8×C37D4semidirect
118. C22×SD16D37semidirect
126. C37#3043semidirect
156. C2×Q8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
#145581002
#145580112
#145577532
#145577312
#145575592
#145575382
#145575302
C22×SD16×C372
#304337