Finite Group Databasebeta

← #18005343

Subgroups — #18005343

Order 4736.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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#121×D37C212yesmaximal, complemented
2#14557848C212yesmaximal, complemented
3#14557845C212yesmaximal, complemented
4#14557769C211yesmaximal, characteristic, complemented
5#14557767C212yesmaximal, complemented
6#14557668C212yesmaximal, complemented
7#14557665C212yesmaximal, complemented
8C2×#11924448C211yesmaximal, characteristic, complemented
9C37×#466C211yesmaximal, characteristic, complemented
10C2×D4×D37—22no—
11C2×D4×D37C2212yescomplemented
12C22×C4×D37C2211yescharacteristic
13C2×D296C2211yescharacteristic, complemented
14C2×#10596939C2212yescomplemented
15C22×#64436C2211yescharacteristic, complemented
16#11924511C2212yes—
17#11924510C2212yescomplemented
18#11924509—22no—
19#11924508—22no—
20#11924507C2212yes—
21C4⋊C4×D37C2212yescomplemented
22C22⋊C4×D37—22no—
23#11924470C2211yescharacteristic, complemented
24#11924469C2212yescomplemented
25#11924458C2212yescomplemented
26#11924457C2212yescomplemented
27#11924456C2212yescomplemented
28#11924448C2212yescomplemented
29#11924448C2212yescomplemented
30C2×D8×C37C2211yescharacteristic, complemented
31C22×C8×C37C2211yescharacteristic, complemented
32#121×C37C2212yescomplemented
33#107×C37C2211yescharacteristic, complemented
34#102×C37C2212yescomplemented
35C23×D37—22no—
36C23×D37D411yescharacteristic
37C2×D4×C37—22no—
38C2×D4×C37C2312yes—
39C22×C4×C37C2311yescharacteristic
40C2×C22⋊D37—22no—
41C2×C22⋊D37—22no—
42C2×C22⋊D37—22no—
43C22×Dic37D411yescharacteristic
44D4×D37—42no—
45D4×D37—42no—
46D4×D37—48no—
47C2×D148—22no—
48C2×D148C2312yes—
49C2×C4×D37—22no—
50C2×C4×D37—41no—
51C2×C4×D37—41no—
52C2×C4×D37D412yes—
53C2×C4×D37C2312yes—
54D8×C37—41no—
55C2×C8×C37—41no—
56C2×C8×C37C2311yescharacteristic
57C2×C8×C37C2311yescharacteristic
58C4⋊C4×C37C2312yes—
59C22⋊C4×C37—22no—
60C22⋊Dic37—22no—
61#10596939—42no—
62#10596938—22no—
63#10596938—22no—
64C4⋊Dic37C2312yes—
65#10596936—22no—
66C2×#64436—41no—
67C2×#64436C2312yes—
68D296—41no—
69C23×C37—22no—
70C23×C37C2×D411yescharacteristic
71C22×D37—22no—
72C22×D37—41no—
73C22×D37—41no—
74C22×D37—44no—
75C22×D37—44no—
76C22×D37—44no—
77C22×D37D814yescomplemented
78C22×D37C2×D412yes—
79D4×C37—22no—
80D4×C37—22no—
81D4×C37—44no—
82C2×C4×C37—21no—
83C2×C4×C37—21no—
84C2×C4×C37—22no—
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37C2411yescharacteristic
87C22⋊D37—44no—
88C22⋊D37—44no—
89C22⋊D37—44no—
90C2×Dic37—22no—
91C2×Dic37—41no—
92C2×Dic37C2×D412yes—
93D148—22no—
94D148—22no—
95D148—44no—
96C4×D37—22no—
97C4×D37—22no—
98C4×D37—42no—
99C4×D37—44no—
100C8×C37—21no—
101C8×C37—21no—
102#64436—22no—
103C22×C37—21no—
104C22×C37—21no—
105C22×C37—42no—
106C22×C37—42no—
107C22×C37—42no—
108C22×C37C2×D812yes—
109C22×C37C22×D411yescharacteristic
110C2×D37—22no—
111C2×D37—22no—
112C2×D37—44no—
113C2×D37—42no—
114C2×D37—42no—
115C2×D37—42no—
116C2×D37—88no—
117C2×D37C2×D814yes—
118C4×C37—21no—
119C4×C37—42no—
120C4×C37H(5,𝔽2)11yescharacteristic
121C4×C37H(5,𝔽2)11yescharacteristic
122Dic37—22no—
123Dic37—42no—
124#3186—371nomaximal, Sylow
125C2×C37—22no—
126C2×C37—82no—
127C2×C37#53411yescharacteristic
128C2×C37C22×D811yescharacteristic
129C2×C37#57511yescharacteristic
130D37—24no—
131D37—82no—
132C2×#121—372no—
133#480—372no—
134#480—372no—
135#466—371no—
136#466—372no—
137#466D3711yescharacteristic, complemented
138#447—372no—
139#447—372no—
140C2×C22⋊C8—371no—
141C37#318611yescharacteristic, complemented, Sylow
142C22×D4—372no—
143C22×D4—742no—
144C23×C4—371no—
145C2×D8—372no—
146C2×D8—371no—
147C2×D8C2×D3711yescharacteristic, complemented
148C22×C8—371no—
149C22×C8C2×D3711yescharacteristic, complemented
150#121—372no—
151#121—372no—
152#121—372no—
153#121—742no—
154#121—742no—
155#121C2×D3712yescomplemented
156C2×C4⋊C4—372no—
157C2×C22⋊C4—742no—
158#107—371no—
159#107—372no—
160#107C2×D3711yescharacteristic, complemented
161#102—372no—
162#102—372no—
163#102—372no—
164#102C2×D3712yescomplemented
165C22⋊C8—372no—
166C22⋊C8—372no—
167C24—371no—
168C24—742no—
169C2×D4—22no—
170C2×D4—372no—
171C2×D4—742no—
172C2×D4—742no—
173C2×D4—742no—
174C2×D4—742no—
175C2×D4—1482no—
176C2×D4—1482no—
177C2×D4—1488no—
178C2×D4C22×D3712yes—
179C22×C4—371no—
180C22×C4—372no—
181C22×C4—372no—
182C22×C4—742no—
183C22×C4—1481no—
184C22×C4—1481no—
185C22×C4C22×D3711yescharacteristic
186D8—41no—
187D8—1481no—
188D8—1482no—
189C2×C8—41no—
190C2×C8—372no—
191C2×C8—1481no—
192C2×C8C22×D3711yescharacteristic
193C2×C8C22×D3711yescharacteristic
194C4⋊C4—372no—
195C4⋊C4—742no—
196C4⋊C4C22×D3712yes—
197C22⋊C4—22no—
198C22⋊C4—742no—
199C22⋊C4—742no—
200C22⋊C4—742no—
201C23—22no—
202C23—372no—
203C23—374no—
204C23—742no—
205C23—1481no—
206C23—1481no—
207C23—1484no—
208C23—1484no—
209C23—1484no—
210C23D4×D3711yescharacteristic
211D4—22no—
212D4—22no—
213D4—44no—
214D4—742no—
215D4—742no—
216D4—1484no—
217D4—1484no—
218D4—1484no—
219D4—1484no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—372no—
224C2×C4—742no—
225C2×C4—742no—
226C2×C4—742no—
227C2×C4—1482no—
228C2×C4—1484no—
229C2×C4—1481no—
230C2×C4D4×D3711yescharacteristic
231C2×C4C23×D3711yescharacteristic
232C8—21no—
233C8—21no—
234C8—742no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—374no—
241C22—2968no—
242C22—742no—
243C22—742no—
244C22—1484no—
245C22—1482no—
246C22—1482no—
247C22—1482no—
248C22D8×D3712yes—
249C22C2×D4×D3711yescharacteristic
250C4—21no—
251C4—42no—
252C4—742no—
253C4—1482no—
254C4#1192458111yescharacteristic
255C4#1192458211yescharacteristic
256C2—22no—
257C2—82no—
258C2—2962no—
259C2—744no—
260C2#1455809111yescharacteristic
261C2C2×D8×D3711yescharacteristic
262C2#1455833011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#466C2
socleC22×C37C22×D4
hypercenter#466D37
hypocenterC37#3186
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #121×D37C2semidirect
2. #14557848C2semidirect
3. #14557845C2semidirect
4. #14557769C2semidirect
5. #14557767C2semidirect
6. #14557668C2semidirect
7. #14557665C2semidirect
8. C2×#11924448C2semidirect
9. C37×#466C2semidirect
11. C2×D4×D37C22semidirect
13. C2×D296C22semidirect
14. C2×#10596939C22semidirect
15. C22×#64436C22semidirect
17. #11924510C22semidirect
21. C4⋊C4×D37C22semidirect
23. #11924470C22semidirect
24. #11924469C22semidirect
25. #11924458C22semidirect
26. #11924457C22semidirect
27. #11924456C22semidirect
28. #11924448C22semidirect
29. #11924448C22semidirect
30. C2×D8×C37C22semidirect
31. C22×C8×C37C22semidirect
32. #121×C37C22semidirect
33. #107×C37C22semidirect
34. #102×C37C22semidirect
77. C22×D37D8semidirect
137. #466D37semidirect
141. C37#3186semidirect
147. C2×D8C2×D37semidirect
149. C22×C8C2×D37semidirect
155. #121C2×D37semidirect
160. #107C2×D37semidirect
164. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
#121×D372
#145578482
#145578452
#145577692
#145577672
#145576682
#145576652
C2×#119244482
C37×#4662
#318637