Finite Group Databasebeta

← #18004993

Subgroups — #18004993

Order 4736.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#14558082C211yesmaximal, characteristic
2#125×D37C211yesmaximal, characteristic, complemented
3#14557900C212yesmaximal, complemented
4#14557896C212yesmaximal, complemented
5#14557890C211yesmaximal, characteristic, complemented
6#14557888C211yesmaximal, characteristic, complemented
7#14557887C211yesmaximal, characteristic, complemented
8#14557533C212yesmaximal, complemented
9#14557531C212yesmaximal, complemented
10C4×#10596929C211yesmaximal, characteristic, complemented
11C37×#488C211yesmaximal, characteristic, complemented
12C2×#10596966C2211yescharacteristic
13C2×#10596964C2211yescharacteristic
14C2×#10596929C2212yes—
15#11924534C2211yescharacteristic
16#11924532C2211yescharacteristic
17#11924528C2211yescharacteristic
18#11924527C2212yes—
19#11924526—22no—
20#11924524C2211yescharacteristic
21#11924509—22no—
22#11924496—22no—
23C4⋊C4×D37—22no—
24C4⋊C4×D37C2212yes—
25C42×D37C2211yescharacteristic
26#11924461C2212yes—
27#11924460C2212yes—
28#11924459C2212yes—
29#11924458C2212yes—
30#11924457C2212yes—
31#11924456C2212yes—
32#11924446C2212yes—
33C4×#64436C2211yescharacteristic
34#125×C37C2211yescharacteristic
35#124×C37C2211yescharacteristic
36#103×C37C2212yes—
37#102×C37C2212yes—
38C4×C8×C37C2211yescharacteristic
39C2×Q8×C37C2311yescharacteristic
40C2×D4×C37C2311yescharacteristic
41C2×C22⋊D37—21no—
42C2×C22⋊D37—22no—
43C22×Dic37—21no—
44#10596966—24no—
45#10596964—24no—
46C2×D148—21no—
47C2×D148C2311yescharacteristic
48C2×C4×D37—22no—
49C2×C4×D37—21no—
50C2×C4×D37D412yes—
51C2×C4×D37C2311yescharacteristic
52C2×Dic74C2311yescharacteristic
53C2×C8×C37C2312yes—
54C4⋊C4×C37—22no—
55C4⋊C4×C37C2312yes—
56C22⋊C4×C37—22no—
57C42×C37C2311yescharacteristic
58#10596938—22no—
59C4⋊Dic37—22no—
60C4⋊Dic37C2312yes—
61#10596936—22no—
62#10596936—22no—
63#10596936—22no—
64#10596936—22no—
65C4×Dic37D412yes—
66C4×Dic37C2311yescharacteristic
67C2×#64436C2312yes—
68#10596929—24no—
69C23×C37—21no—
70C22×D37—21no—
71C22×D37C2×D411yescharacteristic
72Q8×C37—22no—
73D4×C37—22no—
74C2×C4×C37—22no—
75C2×C4×C37—21no—
76C2×C4×C37C2×D412yes—
77C2×C4×C37C2411yescharacteristic
78C22⋊D37—44no—
79C22⋊D37—42no—
80C2×Dic37—22no—
81C2×Dic37—21no—
82C2×Dic37—42no—
83C2×Dic37C2×D412yes—
84C2×Dic37C2×D411yescharacteristic
85D148—22no—
86D148—42no—
87C4×D37—42no—
88C4×D37—44no—
89C4×D37—42no—
90C4×D37#4114yes—
91Dic74—22no—
92C8×C37—22no—
93#64436—22no—
94C22×C37—41no—
95C22×C37—42no—
96C22×C37C22×D411yescharacteristic
97C2×D37—22no—
98C2×D37—41no—
99C2×D37—42no—
100C2×D37#12412yes—
101C4×C37—22no—
102C4×C37—41no—
103C4×C37—42no—
104C4×C37C2×#4112yes—
105Dic37—22no—
106Dic37—41no—
107Dic37—42no—
108Dic37#12412yes—
109#3142—371nomaximal, Sylow
110C2×C37—81no—
111C2×C37C2×#12411yescharacteristic
112C2×C37#57512yes—
113D37—22no—
114D37—81no—
115#532—371no—
116C2×#125—371no—
117#491—372no—
118#490—372no—
119#488—371no—
120#488—371no—
121#488—371no—
122#488D3711yescharacteristic, complemented
123#417—372no—
124#417—372no—
125C4×M16—371no—
126C37#314211yescharacteristic, complemented, Sylow
127C2×#41—371no—
128C2×#41—371no—
129C2×M16—372no—
130C4⋊Q8—371no—
131#127—371no—
132#125—372no—
133#125—371no—
134#125—742no—
135#125C2×D3711yescharacteristic
136#124—371no—
137#124C2×D3711yescharacteristic
138#121—742no—
139C4×D4—742no—
140C2×C4⋊C4—372no—
141C2×C4⋊C4—742no—
142C2×C42—371no—
143#103—372no—
144#103—372no—
145#103—372no—
146#103C2×D3712yes—
147#102—372no—
148#102—372no—
149#102—372no—
150#102C2×D3712yes—
151#97—372no—
152C4×C8—371no—
153C4×C8C2×D3711yescharacteristic
154#41—744no—
155#41—744no—
156C2×Q8—371no—
157C2×Q8C22×D3711yescharacteristic
158C2×D4—371no—
159C2×D4—741no—
160C2×D4—742no—
161C2×D4—741no—
162C2×D4C22×D3711yescharacteristic
163C22×C4—371no—
164C22×C4—372no—
165C22×C4—741no—
166C22×C4—742no—
167C22×C4—741no—
168M16—744no—
169C2×C8—372no—
170C2×C8C22×D3712yes—
171C4⋊C4—22no—
172C4⋊C4—372no—
173C4⋊C4—742no—
174C4⋊C4—742no—
175C4⋊C4—742no—
176C4⋊C4—742no—
177C4⋊C4—742no—
178C4⋊C4C22×D3712yes—
179C22⋊C4—22no—
180C22⋊C4—742no—
181C42—372no—
182C42—371no—
183C42C22×D3711yescharacteristic
184C23—21no—
185C23—371no—
186C23—741no—
187Q8—22no—
188Q8—742no—
189D4—22no—
190D4—742no—
191D4—1482no—
192D4—1484no—
193D4—1482no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—371no—
197C2×C4—374no—
198C2×C4—372no—
199C2×C4—741no—
200C2×C4—742no—
201C2×C4—1482no—
202C2×C4—1482no—
203C2×C4—1484no—
204C2×C4—1482no—
205C2×C4D4×D3712yes—
206C2×C4C23×D3711yescharacteristic
207C8—22no—
208C8—742no—
209C22—41no—
210C22—42no—
211C22—372no—
212C22—742no—
213C22—1481no—
214C22—1482no—
215C22C2×D4×D3711yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—372no—
220C4—742no—
221C4—1481no—
222C4—1482no—
223C4#41×D3712yes—
224C2—81no—
225C2—2961no—
226C2—742no—
227C2#124×D3711yescharacteristic
228C2#1455833012yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#488C2
socleC22×C37C22×D4
prime radical#14558082C2
hypercenter#488D37
hypocenterC37#3142
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #125×D37C2semidirect
3. #14557900C2semidirect
4. #14557896C2semidirect
5. #14557890C2semidirect
6. #14557888C2semidirect
7. #14557887C2semidirect
8. #14557533C2semidirect
9. #14557531C2semidirect
10. C4×#10596929C2semidirect
11. C37×#488C2semidirect
122. #488D37semidirect
126. C37#3142semidirect

Maximal subgroups

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

subgroupindex
#145580822
#125×D372
#145579002
#145578962
#145578902
#145578882
#145578872
#145575332
#145575312
C4×#105969292
C37×#4882
#314237