Finite Group Databasebeta

← #18007308

Subgroups — #18007308

Order 4736.

396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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#14558244C211yesmaximal, characteristic, complemented
2#14558203C211yesmaximal, characteristic, complemented
3#14557896C212yesmaximal, complemented
4#14557831C212yesmaximal, complemented
5#14557820C211yesmaximal, characteristic, complemented
6#14557727C212yesmaximal, complemented
7#14557725C211yesmaximal, characteristic, complemented
8#14557663C211yesmaximal, characteristic, complemented
9#14557642C212yesmaximal, complemented
10C4×D296C211yesmaximal, characteristic, complemented
11C37×#486C211yesmaximal, characteristic, complemented
12C2×#10596964—21no—
13C2×D296C2211yescharacteristic
14C2×#10596939C2212yes—
15#11924532C2212yes—
16#11924527C2212yes—
17#11924516—21no—
18#11924512—22no—
19#11924508—22no—
20#11924507—21no—
21C4×Dic74C2211yescharacteristic
22C4×D148C2211yescharacteristic
23C4×D148C2211yescharacteristic
24D4×Dic37C2212yes—
25#11924498C2212yes—
26C4⋊C4×D37—21no—
27#11924470C2211yescharacteristic
28#11924467C2212yes—
29C4⋊#64436C2211yescharacteristic
30#11924465C2212yes—
31#11924458C2211yescharacteristic
32#11924458C2211yescharacteristic
33#11924457C2212yes—
34#11924456C2212yes—
35#11924446C2212yes—
36C4⋊Q8×C37C2211yescharacteristic
37#127×C37C2211yescharacteristic
38#102×C37C2212yes—
39#102×C37C2212yes—
40C4×C8×C37C2211yescharacteristic
41C2×Q8×C37—21no—
42C2×D4×C37—21no—
43C2×D4×C37—21no—
44C2×D4×C37C2312yes—
45C2×C22⋊D37—22no—
46C2×C22⋊D37—22no—
47C22×Dic37—22no—
48#10596964—44no—
49C2×D148C2311yescharacteristic
50C2×D148C2311yescharacteristic
51C2×C4×D37—21no—
52C2×C4×D37—21no—
53C2×C4×D37—22no—
54C2×Dic74D411yescharacteristic
55C2×C8×C37C2311yescharacteristic
56C2×C8×C37C2311yescharacteristic
57C4⋊C4×C37—21no—
58C4⋊C4×C37C2312yes—
59C42×C37C2311yescharacteristic
60C22⋊Dic37—22no—
61#10596939—24no—
62#10596938—21no—
63#10596938—21no—
64#10596938—22no—
65C4⋊Dic37—22no—
66C4⋊Dic37D411yescharacteristic
67C4⋊Dic37C2311yescharacteristic
68C4⋊Dic37C2311yescharacteristic
69#10596936—22no—
70#10596936D412yes—
71C4×Dic37C2312yes—
72C2×#64436C2312yes—
73D296—22no—
74C23×C37—22no—
75C22×D37—21no—
76C22×D37—21no—
77Q8×C37—81no—
78D4×C37—22no—
79D4×C37—22no—
80D4×C37—42no—
81D4×C37—81no—
82C2×C4×C37—22no—
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37C2411yescharacteristic
86C22⋊D37—44no—
87C22⋊D37—82no—
88C2×Dic37—21no—
89C2×Dic37—21no—
90C2×Dic37—44no—
91C2×Dic37C2×D412yes—
92C2×Dic37C2×D412yes—
93D148—21no—
94D148—21no—
95D148—21no—
96D148#4112yescomplemented
97C4×D37—42no—
98C4×D37—42no—
99C4×D37—82no—
100Dic74—22no—
101C8×C37—21no—
102C8×C37—21no—
103#64436—22no—
104C22×C37—42no—
105C22×C37—42no—
106C22×C37—42no—
107C22×C37C22×D411yescharacteristic
108C2×D37—22no—
109C2×D37—41no—
110C2×D37—41no—
111C2×D37—41no—
112C2×D37—41no—
113C2×D37—41no—
114C4×C37—21no—
115C4×C37—42no—
116C4×C37AGL(1,ℤ/8)12yes—
117C4×C37C2×#4111yescharacteristic
118C4×C372−1+411yescharacteristic
119Dic37—22no—
120Dic37—22no—
121Dic37—41no—
122Dic37—41no—
123#3366—371nomaximal, Sylow
124C2×C37—82no—
125C2×C37#54811yescharacteristic
126C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C37#57611yescharacteristic
128D37—42no—
129D37—81no—
130#554—371no—
131#550—371no—
132#490—372no—
133#486D3711yescharacteristic, complemented
134#478—372no—
135#476—371no—
136#459—371no—
137#459—372no—
138#446—371no—
139#442—372no—
140C4×D8—371no—
141C37#336611yescharacteristic, complemented, Sylow
142C2×#41—741no—
143C2×D8—372no—
144C2×D8—371no—
145C4⋊Q8C2×D3711yescharacteristic
146#127—372no—
147#127C2×D3711yescharacteristic
148#125—372no—
149C22⋊Q8—741no—
150C22⋊Q8—742no—
151#121—741no—
152#121—742no—
153C4×Q8—371no—
154C4×D4—372no—
155C4×D4—372no—
156C4×D4—371no—
157C4×D4—371no—
158C2×C4⋊C4—741no—
159#107—371no—
160#106—372no—
161C4⋊C8—372no—
162C4⋊C8—371no—
163#102—372no—
164#102—371no—
165#102—371no—
166#102—372no—
167#102C2×D3712yes—
168#102C2×D3712yes—
169#97—372no—
170C4×C8C2×D3711yescharacteristic
171#41—1484no—
172C2×Q8—21no—
173C2×Q8—371no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—371no—
177C2×D4—371no—
178C2×D4—742no—
179C2×D4—742no—
180C2×D4C22×D3712yes—
181C22×C4—742no—
182C22×C4—742no—
183C22×C4—741no—
184C22×C4—741no—
185D8—742no—
186D8—744no—
187C2×C8—372no—
188C2×C8C22×D3711yescharacteristic
189C2×C8C22×D3711yescharacteristic
190C4⋊C4—21no—
191C4⋊C4—372no—
192C4⋊C4—371no—
193C4⋊C4—371no—
194C4⋊C4—371no—
195C4⋊C4—742no—
196C4⋊C4—742no—
197C4⋊C4C22×D3712yes—
198C22⋊C4—742no—
199C22⋊C4—742no—
200C22⋊C4—741no—
201C22⋊C4—741no—
202C42—372no—
203C42C22×D3711yescharacteristic
204C23—22no—
205C23—741no—
206C23—741no—
207Q8—81no—
208Q8—742no—
209D4—22no—
210D4—22no—
211D4—42no—
212D4—81no—
213D4—372no—
214D4—2962no—
215D4—741no—
216D4—741no—
217D4—741no—
218D4—1484no—
219C2×C4—22no—
220C2×C4—372no—
221C2×C4—372no—
222C2×C4—2962no—
223C2×C4—741no—
224C2×C4—741no—
225C2×C4—1484no—
226C2×C4—1482no—
227C2×C4—1482no—
228C2×C4D4×D3711yescharacteristic
229C2×C4D4×D3711yescharacteristic
230C2×C4C23×D3711yescharacteristic
231C8—21no—
232C8—21no—
233C8—742no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—742no—
238C22—1481no—
239C22—1481no—
240C22—1481no—
241C22—1481no—
242C22—1481no—
243C22C2×D4×D3711yescharacteristic
244C4—21no—
245C4—42no—
246C4—742no—
247C4—742no—
248C4—1481no—
249C4—1481no—
250C4#1192456312yes—
251C4#41×D3711yescharacteristic
252C4#1192458311yescharacteristic
253C2—82no—
254C2—2961no—
255C2—1482no—
256C2#1455819111yescharacteristic
257C2C2×#1192456311yescharacteristic
258C2#1455833411yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#486C2
socleC22×C37C22×D4
hypercenter#486D37
hypocenterC37#3366
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
1. #14558244C2semidirect
2. #14558203C2semidirect
3. #14557896C2semidirect
4. #14557831C2semidirect
5. #14557820C2semidirect
6. #14557727C2semidirect
7. #14557725C2semidirect
8. #14557663C2semidirect
9. #14557642C2semidirect
10. C4×D296C2semidirect
11. C37×#486C2semidirect
96. D148#41semidirect
133. #486D37semidirect
141. C37#3366semidirect

Maximal subgroups

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

subgroupindex
#145582442
#145582032
#145578962
#145578312
#145578202
#145577272
#145577252
#145576632
#145576422
C4×D2962
C37×#4862
#336637