Finite Group Databasebeta

← #18005196

Subgroups — #18005196

Order 4736.

364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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#14558067C211yesmaximal, characteristic
2#14557939C211yesmaximal, characteristic, complemented
3#14557925C211yesmaximal, characteristic, complemented
4#14557901C211yesmaximal, characteristic, complemented
5#14557895C211yesmaximal, characteristic, complemented
6#14557789C212yesmaximal, complemented
7#14557781C212yesmaximal
8C4×#10596942C212yesmaximal, complemented
9C4×#10596941C212yesmaximal, complemented
10C4×#10596934C211yesmaximal, characteristic, complemented
11C37×#533C211yesmaximal, characteristic, complemented
12C2×#10596942C2212yes—
13C2×#10596941C2212yes—
14C2×#10596934C2212yes—
15#11924530—21no—
16#11924528C2211yescharacteristic
17#11924524C2211yescharacteristic
18#11924519—21no—
19#11924515C2211yescharacteristic
20#11924510C2211yescharacteristic
21C4×Dic74C2211yescharacteristic
22C4×D148C2211yescharacteristic
23C4×C22⋊D37—21no—
24#11924493—21no—
25#11924469C2212yes—
26#11924467C2212yes—
27#11924460C2212yes—
28#11924460C2212yes—
29#11924459C2212yes—
30#11924456C2212yes—
31#11924447C2211yescharacteristic
32#11924447C2211yescharacteristic
33C4×#64436C2212yes—
34C4⋊Q8×C37C2211yescharacteristic
35C4⋊Q8×C37C2211yescharacteristic
36#125×C37—21no—
37C22⋊Q8×C37—21no—
38C22⋊Q8×C37C2212yes—
39C4×Q8×C37—21no—
40C4×Q8×C37C2212yes—
41#117×C37—21no—
42C2×C42×C37C2211yescharacteristic
43C2×Q8×C37—21no—
44C2×Q8×C37C2312yes—
45C22×C4×C37D411yescharacteristic
46C22×C4×C37D411yescharacteristic
47C22×C4×C37C2311yescharacteristic
48C2×C22⋊D37—21no—
49C2×D148C2311yescharacteristic
50C2×C4×D37—21no—
51C2×Dic74C2311yescharacteristic
52C4⋊C4×C37—21no—
53C4⋊C4×C37—21no—
54C4⋊C4×C37—21no—
55C4⋊C4×C37—22no—
56C4⋊C4×C37—22no—
57C4⋊C4×C37C2312yes—
58C22⋊C4×C37—22no—
59C42×C37—22no—
60C42×C37D411yescharacteristic
61C42×C37D411yescharacteristic
62C42×C37C2311yescharacteristic
63C42×C37C2311yescharacteristic
64C22⋊Dic37—21no—
65#10596942—24no—
66#10596941—24no—
67#10596938—21no—
68#10596938—21no—
69#10596938—21no—
70#10596938—21no—
71C4⋊Dic37C2311yescharacteristic
72C4⋊Dic37C2311yescharacteristic
73#10596936—21no—
74#10596936—21no—
75#10596936—21no—
76#10596936—21no—
77C4×Dic37—21no—
78#10596934—24no—
79C2×#64436C2312yes—
80C2×#64436C2312yes—
81C23×C37C2×D411yescharacteristic
82C22×D37—21no—
83Q8×C37—22no—
84Q8×C37—22no—
85Q8×C37—42no—
86C2×C4×C37—22no—
87C2×C4×C37—22no—
88C2×C4×C37—22no—
89C2×C4×C37—22no—
90C2×C4×C37—41no—
91C2×C4×C37C2×D411yescharacteristic
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2×D411yescharacteristic
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2411yescharacteristic
97C22⋊D37—42no—
98C2×Dic37—21no—
99C2×Dic37—21no—
100C2×Dic37—21no—
101D148—22no—
102C4×D37—42no—
103Dic74—22no—
104#64436—22no—
105#64436#4114yes—
106C22×C37—21no—
107C22×C37—21no—
108C22×C37—21no—
109C22×C37C22×D411yescharacteristic
110C2×D37—41no—
111C2×D37—41no—
112C2×D37—41no—
113C4×C37—21no—
114C4×C37—21no—
115C4×C37—21no—
116C4×C37—21no—
117C4×C37—42no—
118C4×C37—42no—
119C4×C37#13712yes—
120C4×C37C2×#4112yes—
121Dic37—41no—
122Dic37—41no—
123Dic37—41no—
124#3172—371nomaximal, Sylow
125C2×C37—41no—
126C2×C37#53211yescharacteristic
127C2×C37C2×#13711yescharacteristic
128C2×C37#57511yescharacteristic
129D37—81no—
130#533D3711yescharacteristic, complemented
131#529—371no—
132#501—371no—
133#497—371no—
134#491—371no—
135#489—371no—
136#470—372no—
137#468—372no—
138C4×Q16—372no—
139C4×SD16—372no—
140C4×M16—371no—
141C37#317211yescharacteristic, complemented, Sylow
142C2×Q16—372no—
143C2×SD16—372no—
144C2×M16—372no—
145C4⋊Q8C2×D3711yescharacteristic
146C4⋊Q8C2×D3711yescharacteristic
147#126—741no—
148#125—21no—
149#125—371no—
150#124—371no—
151#123—741no—
152C22⋊Q8—21no—
153C22⋊Q8—371no—
154C22⋊Q8C2×D3712yes—
155#121—371no—
156C4×Q8—21no—
157C4×Q8—371no—
158C4×Q8C2×D3712yes—
159C4×D4—371no—
160C4×D4—741no—
161#117—21no—
162#117—741no—
163C2×C42C2×D3711yescharacteristic
164#107—372no—
165#106—372no—
166#103—372no—
167#103—372no—
168#103—372no—
169#102—372no—
170#97—371no—
171#97—371no—
172C4×C8—372no—
173C2×Q8—21no—
174C2×Q8—371no—
175C2×Q8C22×D3712yes—
176C2×D4—371no—
177C2×D4—741no—
178C22×C4—741no—
179C22×C4C22⋊D3711yescharacteristic
180C22×C4C22⋊D3711yescharacteristic
181C22×C4C22×D3711yescharacteristic
182Q16—744no—
183SD16—744no—
184M16—744no—
185C2×C8—372no—
186C2×C8—372no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—371no—
193C4⋊C4—371no—
194C4⋊C4—741no—
195C4⋊C4—741no—
196C4⋊C4—741no—
197C4⋊C4—741no—
198C4⋊C4C22×D3712yes—
199C22⋊C4—22no—
200C22⋊C4—741no—
201C22⋊C4—741no—
202C22⋊C4—741no—
203C22⋊C4—741no—
204C22⋊C4—741no—
205C42—22no—
206C42—741no—
207C42C22⋊D3711yescharacteristic
208C42C22⋊D3711yescharacteristic
209C42C22×D3711yescharacteristic
210C42C22×D3711yescharacteristic
211C23—741no—
212C23C2×C22⋊D3711yescharacteristic
213Q8—22no—
214Q8—22no—
215Q8—42no—
216Q8—742no—
217D4—742no—
218D4—1482no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—741no—
225C2×C4—741no—
226C2×C4—741no—
227C2×C4—1482no—
228C2×C4C2×C22⋊D3711yescharacteristic
229C2×C4C2×C22⋊D3711yescharacteristic
230C2×C4C2×C22⋊D3711yescharacteristic
231C2×C4C2×C22⋊D3711yescharacteristic
232C2×C4C2×C22⋊D3711yescharacteristic
233C2×C4C23×D3711yescharacteristic
234C8—374no—
235C8—742no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—1481no—
240C22—1481no—
241C22—1481no—
242C22C22×C22⋊D3711yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—1481no—
250C4—1481no—
251C4—1481no—
252C4#1192456712yes—
253C4#41×D3712yes—
254C2—41no—
255C2—2961no—
256C2#1455807911yescharacteristic
257C2C2×#1192456711yescharacteristic
258C2#1455833111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#533C2
socleC22×C37C22×D4
prime radical#11924510C22
hypercenter#533D37
hypocenterC37#3172
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #14557939C2semidirect
3. #14557925C2semidirect
4. #14557901C2semidirect
5. #14557895C2semidirect
6. #14557789C2semidirect
8. C4×#10596942C2semidirect
9. C4×#10596941C2semidirect
10. C4×#10596934C2semidirect
11. C37×#533C2semidirect
130. #533D37semidirect
141. C37#3172semidirect

Maximal subgroups

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

subgroupindex
#145580672
#145579392
#145579252
#145579012
#145578952
#145577892
#145577812
C4×#105969422
C4×#105969412
C4×#105969342
C37×#5332
#317237