Finite Group Databasebeta

← #18004986

Subgroups — #18004986

Order 4736.

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

normal subgroups only

This group has 424 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#14558081C211yesmaximal, characteristic
2C4⋊Q8×D37C211yesmaximal, characteristic, complemented
3#14557891C214yesmaximal, complemented
4#14557885C211yesmaximal, characteristic, complemented
5#14557884C211yesmaximal, characteristic, complemented
6#14557879C211yesmaximal, characteristic, complemented
7#14557531C214yesmaximal, complemented
8C4×#10596929C211yesmaximal, characteristic, complemented
9C37×#486C211yesmaximal, characteristic, complemented
10C2×#10596964C2212yes—
11C2×Q8×D37—21no—
12C2×#10596929C2212yes—
13#11924536C2211yescharacteristic
14#11924536C2211yescharacteristic
15#11924535—21no—
16#11924535C2212yes—
17#11924534—21no—
18#11924523C2212yes—
19#11924507—21no—
20#11924507—21no—
21D4×Dic37—21no—
22D4×Dic37—21no—
23C4⋊C4×D37—21no—
24C4⋊C4×D37C2212yes—
25C42×D37C2211yescharacteristic
26#11924461C2214yes—
27#11924459C2214yes—
28#11924457C2214yes—
29#11924446C2212yes—
30C4×#64436C2211yescharacteristic
31C4⋊Q8×C37C2211yescharacteristic
32#127×C37C2211yescharacteristic
33#102×C37C2214yes—
34C4×C8×C37C2211yescharacteristic
35C2×Q8×C37—21no—
36C2×D4×C37—21no—
37C2×D4×C37—21no—
38C2×D4×C37C2312yes—
39C2×C22⋊D37—22no—
40C22×Dic37—22no—
41Q8×D37—44no—
42#10596964—28no—
43C2×C4×D37—22no—
44C2×C4×D37D411yescharacteristic
45C2×C4×D37D411yescharacteristic
46C2×C4×D37C2311yescharacteristic
47C2×Dic74—21no—
48C2×Dic74—22no—
49C2×Dic74C2312yes—
50C2×C8×C37C2312yes—
51C4⋊C4×C37—21no—
52C4⋊C4×C37C2312yes—
53C42×C37C2311yescharacteristic
54C22⋊Dic37—22no—
55C22⋊Dic37—22no—
56C4⋊Dic37—21no—
57C4⋊Dic37—21no—
58C4⋊Dic37—21no—
59C4⋊Dic37C2312yes—
60#10596936—22no—
61#10596936—22no—
62C4×Dic37D411yescharacteristic
63C4×Dic37D411yescharacteristic
64C4×Dic37C2311yescharacteristic
65C2×#64436C2312yes—
66#10596929—24no—
67C23×C37—22no—
68C22×D37C2×D411yescharacteristic
69Q8×C37—42no—
70D4×C37—24no—
71D4×C37—42no—
72D4×C37—42no—
73C2×C4×C37—22no—
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2411yescharacteristic
77C22⋊D37—44no—
78C2×Dic37—22no—
79C2×Dic37—22no—
80C2×Dic37—44no—
81C2×Dic37C2×D411yescharacteristic
82C2×Dic37C2×D411yescharacteristic
83C2×Dic37C2×D411yescharacteristic
84C4×D37—22no—
85C4×D37—22no—
86C4×D37—44no—
87C4×D37#4114yes—
88Dic74—24no—
89Dic74—44no—
90Dic74—42no—
91C8×C37—22no—
92#64436—22no—
93C22×C37—42no—
94C22×C37—42no—
95C22×C37—42no—
96C22×C37C22×D411yescharacteristic
97C2×D37—21no—
98C2×D37—21no—
99C2×D37#12412yes—
100C4×C37—42no—
101C4×C37AGL(1,ℤ/8)12yes—
102C4×C37#13712yes—
103C4×C37C2×#4112yes—
104Dic37—21no—
105Dic37—21no—
106Dic37—42no—
107Dic37—42no—
108Dic37#12412yes—
109#3141—371nomaximal, Sylow
110C2×C37—82no—
111C2×C37C2×#12411yescharacteristic
112C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
113C2×C37C2×#13711yescharacteristic
114D37—22no—
115#532—371no—
116C2×C4⋊Q8—371no—
117#489—374no—
118#487—371no—
119#487—371no—
120#486—371no—
121#486D3711yescharacteristic, complemented
122#417—374no—
123C4×M16—371no—
124C37#314111yescharacteristic, complemented, Sylow
125C2×#41—372no—
126C22×Q8—741no—
127C2×M16—372no—
128C4⋊Q8—372no—
129C4⋊Q8—371no—
130C4⋊Q8—371no—
131C4⋊Q8—741no—
132C4⋊Q8—741no—
133C4⋊Q8C2×D3711yescharacteristic
134#127C2×D3711yescharacteristic
135#124—372no—
136#121—741no—
137#121—741no—
138C4×D4—741no—
139C4×D4—741no—
140C2×C4⋊C4—372no—
141C2×C4⋊C4—741no—
142C2×C42—371no—
143#103—374no—
144#103—374no—
145#102—374no—
146#102C2×D3714yes—
147#97—372no—
148C4×C8—371no—
149C4×C8C2×D3711yescharacteristic
150#41—748no—
151C2×Q8—21no—
152C2×Q8—372no—
153C2×Q8—742no—
154C2×Q8—741no—
155C2×Q8—1484no—
156C2×D4—21no—
157C2×D4—21no—
158C2×D4—742no—
159C2×D4C22×D3712yes—
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—371no—
163C22×C4—742no—
164C22×C4—742no—
165M16—744no—
166C2×C8—372no—
167C2×C8C22×D3712yes—
168C4⋊C4—21no—
169C4⋊C4—372no—
170C4⋊C4—742no—
171C4⋊C4—742no—
172C4⋊C4—741no—
173C4⋊C4—741no—
174C4⋊C4—741no—
175C4⋊C4C22×D3712yes—
176C22⋊C4—742no—
177C22⋊C4—742no—
178C42—371no—
179C42—371no—
180C42—371no—
181C42C22×D3711yescharacteristic
182C23—22no—
183C23—371no—
184Q8—42no—
185Q8—744no—
186Q8—1484no—
187Q8—1482no—
188D4—24no—
189D4—42no—
190D4—42no—
191D4—1484no—
192C2×C4—22no—
193C2×C4—371no—
194C2×C4—374no—
195C2×C4—371no—
196C2×C4—371no—
197C2×C4—742no—
198C2×C4—742no—
199C2×C4—742no—
200C2×C4—742no—
201C2×C4—1484no—
202C2×C4—1484no—
203C2×C4D4×D3711yescharacteristic
204C2×C4D4×D3711yescharacteristic
205C2×C4C23×D3711yescharacteristic
206C8—22no—
207C8—742no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—372no—
212C22—741no—
213C22—741no—
214C22C2×D4×D3711yescharacteristic
215C4—42no—
216C4—372no—
217C4—741no—
218C4—741no—
219C4—1482no—
220C4—1482no—
221C4#1192456012yes—
222C4#1192456512yes—
223C4#41×D3712yes—
224C2—82no—
225C2—742no—
226C2#124×D3711yescharacteristic
227C2C2×#1192456011yescharacteristic
228C2C2×#1192456511yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#486C2
socleC22×C37C22×D4
prime radical#14558081C2
hypercenter#486D37
hypocenterC37#3141
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D37C2semidirect
3. #14557891C2semidirect
4. #14557885C2semidirect
5. #14557884C2semidirect
6. #14557879C2semidirect
7. #14557531C2semidirect
8. C4×#10596929C2semidirect
9. C37×#486C2semidirect
121. #486D37semidirect
124. C37#3141semidirect

Maximal subgroups

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

subgroupindex
#145580812
C4⋊Q8×D372
#145578912
#145578852
#145578842
#145578792
#145575312
C4×#105969292
C37×#4862
#314137