Finite Group Databasebeta

← #18005078

Subgroups — #18005078

Order 4736.

596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#11924563C212yesmaximal, complemented
2C2×#11924559C211yesmaximal, characteristic, complemented
3C2×D8×D37C211yesmaximal, characteristic, complemented
4#14558101C212yesmaximal, complemented
5#14557923C212yesmaximal, complemented
6#14557919C212yesmaximal, complemented
7#14557918C211yesmaximal, characteristic, complemented
8#14557910C211yesmaximal, characteristic, complemented
9#14557908C211yesmaximal, characteristic, complemented
10#14557487C211yesmaximal, characteristic, complemented
11C37×#495C211yesmaximal, characteristic, complemented
12C2×#10596966C2212yes—
13C2×D4×D37C2212yes—
14#11924563—28no—
15#11924559—24no—
16C2×#10596941C2212yescomplemented
17C2×#10596941C2212yescomplemented
18C2×D296C2211yescharacteristic
19C2×D296C2211yescharacteristic, complemented
20C2×D296C2212yescomplemented
21C2×#10596939C2212yes—
22C2×#10596939C2212yescomplemented
23D8×D37—24no—
24C2×#10596929C2211yescharacteristic
25C2×C8×D37C2211yescharacteristic
26#11924533C2212yescomplemented
27#11924532C2212yescomplemented
28#11924525C2212yescomplemented
29#11924509—24no—
30#11924506—24no—
31#11924493C2211yescharacteristic
32#11924447C2211yescharacteristic, complemented
33#11924446C2211yescharacteristic, complemented
34C8×Dic37C2211yescharacteristic, complemented
35C2×Q16×C37C2211yescharacteristic, complemented
36C2×SD16×C37C2212yescomplemented
37C2×D8×C37C2211yescharacteristic
38#124×C37C2212yescomplemented
39C4×C8×C37C2211yescharacteristic, complemented
40C23×D37—22no—
41C2×Q8×C37C2312yes—
42C2×D4×C37C2312yes—
43C2×C22⋊D37—22no—
44C2×C22⋊D37—24no—
45#10596966—24no—
46#10596966—24no—
47D4×D37—24no—
48D4×D37—24no—
49C2×D148—22no—
50C2×D148—24no—
51C2×D148C2312yes—
52C2×D148C2312yes—
53C2×C4×D37—22no—
54C2×C4×D37C2311yescharacteristic
55Q16×C37—22no—
56SD16×C37—24no—
57D8×C37—22no—
58C2×C8×C37C2311yescharacteristic
59C2×C8×C37C2311yescharacteristic
60C22⋊C4×C37—24no—
61C42×C37C2311yescharacteristic
62#10596941—24no—
63#10596941—24no—
64#10596939—24no—
65#10596939—24no—
66#10596938—24no—
67#10596938D412yes—
68#10596936D412yes—
69C4×Dic37C2311yescharacteristic
70C2×#64436C2311yescharacteristic
71C2×#64436C2311yescharacteristic
72D296—22no—
73D296—22no—
74D296—24no—
75#10596929D414yescomplemented
76C8×D37D414yescomplemented
77C23×C37—22no—
78C22×D37—22no—
79C22×D37—22no—
80C22×D37—44no—
81C22×D37—84no—
82C22×D37C2×D411yescharacteristic
83Q8×C37—22no—
84Q8×C37—22no—
85D4×C37—22no—
86D4×C37—22no—
87C2×C4×C37—22no—
88C2×C4×C37C2×D412yes—
89C2×C4×C37C2411yescharacteristic
90C22⋊D37—44no—
91C22⋊D37—84no—
92C2×Dic37C2×D412yes—
93C2×Dic37C2×D411yescharacteristic
94D148—22no—
95D148—22no—
96D148—22no—
97D148—22no—
98D148—44no—
99D148—84no—
100C4×D37—44no—
101C4×D37C2×D412yes—
102C4×D37C2×D412yes—
103C8×C37C2×D412yes—
104C8×C37C2×D412yes—
105#64436C2×D412yes—
106#64436C2×D412yes—
107C22×C37—42no—
108C22×C37—44no—
109C22×C37C22×D411yescharacteristic
110C2×D37—22no—
111C2×D37—42no—
112C2×D37—42no—
113C2×D37—44no—
114C2×D37—44no—
115C2×D37—88no—
116C2×D37#12712yes—
117C4×C37—22no—
118C4×C37—42no—
119C4×C37C22×D411yescharacteristic
120C4×C37C22×D411yescharacteristic
121Dic37—22no—
122Dic37#12712yes—
123#3155—371nomaximal, Sylow
124C2×C37—82no—
125C2×C37C2×#12711yescharacteristic
126C2×C37#57612yes—
127D37—22no—
128D37—82no—
129D37—82no—
130C2×AGL(1,ℤ/8)—372no—
131C2×#135—371no—
132C22×D8—371no—
133#535—372no—
134#496—372no—
135#496—372no—
136#495—371no—
137#495D3711yescharacteristic, complemented
138#493—371no—
139#493—371no—
140#405—371no—
141C37#315511yescharacteristic, complemented, Sylow
142C2×#41—372no—
143C22×D4—372no—
144AGL(1,ℤ/8)—748no—
145#135—744no—
146C2×Q16C2×D3711yescharacteristic, complemented
147C2×SD16—372no—
148C2×SD16—372no—
149C2×SD16C2×D3712yescomplemented
150C2×D8—372no—
151C2×D8—372no—
152C2×D8—371no—
153C2×D8—371no—
154C2×D8—372no—
155C2×D8—744no—
156C2×D8C2×D3711yescharacteristic
157C2×M16—371no—
158C22×C8—371no—
159#127—372no—
160#127—372no—
161#124—372no—
162#124C2×D3712yescomplemented
163#121—744no—
164#120—744no—
165#117—371no—
166#97—371no—
167#97—371no—
168C4×C8—371no—
169C4×C8C2×D3711yescharacteristic, complemented
170C24—742no—
171#41—744no—
172#41—744no—
173C2×Q8C22×D3712yes—
174C2×D4—372no—
175C2×D4—372no—
176C2×D4—742no—
177C2×D4—744no—
178C2×D4—744no—
179C2×D4—744no—
180C2×D4—742no—
181C2×D4—744no—
182C2×D4C22×D3712yes—
183C22×C4—371no—
184C22×C4—742no—
185Q16—22no—
186SD16—24no—
187SD16—744no—
188SD16—744no—
189D8—22no—
190D8—744no—
191D8—744no—
192D8—742no—
193D8—742no—
194D8—744no—
195M16—374no—
196C2×C8—371no—
197C2×C8—371no—
198C2×C8—374no—
199C2×C8C22×D3711yescharacteristic
200C2×C8C22×D3711yescharacteristic
201C4⋊C4—372no—
202C22⋊C4—24no—
203C22⋊C4—372no—
204C22⋊C4—744no—
205C42—371no—
206C42C22×D3711yescharacteristic
207C23—22no—
208C23—371no—
209C23—2964no—
210C23—742no—
211C23—742no—
212C23—1484no—
213Q8—22no—
214Q8—22no—
215D4—22no—
216D4—22no—
217D4—2964no—
218D4—2964no—
219D4—742no—
220D4—742no—
221D4—742no—
222D4—742no—
223D4—1484no—
224D4—1484no—
225C2×C4—22no—
226C2×C4—371no—
227C2×C4—372no—
228C2×C4—372no—
229C2×C4—372no—
230C2×C4—1484no—
231C2×C4D4×D3712yes—
232C2×C4C23×D3711yescharacteristic
233C8—372no—
234C8—372no—
235C8D4×D3712yes—
236C8D4×D3712yes—
237C22—42no—
238C22—44no—
239C22—372no—
240C22—2968no—
241C22—742no—
242C22—1482no—
243C22—1482no—
244C22—1484no—
245C22—1484no—
246C22C2×D4×D3711yescharacteristic
247C4—22no—
248C4—42no—
249C4—372no—
250C4—742no—
251C4C2×D4×D3711yescharacteristic
252C4C2×D4×D3711yescharacteristic
253C2—82no—
254C2—2962no—
255C2—2962no—
256C2—742no—
257C2#127×D3711yescharacteristic
258C2#1455833512yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#495C2
socleC22×C37C22×D4
hypercenter#495D37
hypocenterC37#3155
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#11924563C2semidirect
2. C2×#11924559C2semidirect
3. C2×D8×D37C2semidirect
4. #14558101C2semidirect
5. #14557923C2semidirect
6. #14557919C2semidirect
7. #14557918C2semidirect
8. #14557910C2semidirect
9. #14557908C2semidirect
10. #14557487C2semidirect
11. C37×#495C2semidirect
16. C2×#10596941C22semidirect
17. C2×#10596941C22semidirect
19. C2×D296C22semidirect
20. C2×D296C22semidirect
22. C2×#10596939C22semidirect
26. #11924533C22semidirect
27. #11924532C22semidirect
28. #11924525C22semidirect
32. #11924447C22semidirect
33. #11924446C22semidirect
34. C8×Dic37C22semidirect
35. C2×Q16×C37C22semidirect
36. C2×SD16×C37C22semidirect
38. #124×C37C22semidirect
39. C4×C8×C37C22semidirect
75. #10596929D4semidirect
76. C8×D37D4semidirect
137. #495D37semidirect
141. C37#3155semidirect
146. C2×Q16C2×D37semidirect
149. C2×SD16C2×D37semidirect
162. #124C2×D37semidirect
169. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245632
C2×#119245592
C2×D8×D372
#145581012
#145579232
#145579192
#145579182
#145579102
#145579082
#145574872
C37×#4952
#315537