Finite Group Databasebeta

← #18006205

Subgroups — #18006205

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
1C2×#11924563C212yesmaximal, complemented
2#14558176C212yesmaximal, complemented
3#14557776C212yesmaximal, complemented
4#14557745C212yesmaximal, complemented
5#14557694C212yesmaximal, complemented
6#14557665C212yesmaximal, complemented
7C4×D296C211yesmaximal, characteristic, complemented
8#14557612C211yesmaximal, characteristic, complemented
9C37×#495C211yesmaximal, characteristic, complemented
10C2×#10596966C2212yes—
11C2×D4×D37C2212yescomplemented
12#11924563—28no—
13C2×#10596941C2212yescomplemented
14C2×D296C2211yescharacteristic
15C2×#10596939C2212yes—
16C2×#10596929C2212yescomplemented
17#11924518—22no—
18#11924512C2212yescomplemented
19#11924509—22no—
20#11924507C2212yes—
21#11924506—22no—
22C4×D148C2211yescharacteristic
23C4×D148C2212yescomplemented
24C22⋊C4×D37—22no—
25#11924470C2211yescharacteristic, complemented
26C4⋊#64436C2211yescharacteristic, complemented
27#11924460C2212yescomplemented
28#11924458C2212yescomplemented
29#11924457C2212yescomplemented
30#11924448C2212yescomplemented
31C2×Q16×C37C2211yescharacteristic, complemented
32C2×SD16×C37C2212yescomplemented
33C2×D8×C37C2211yescharacteristic
34#124×C37C2212yescomplemented
35C4×C8×C37C2211yescharacteristic, complemented
36C23×D37—22no—
37C2×Q8×C37C2312yes—
38C2×D4×C37C2312yes—
39C2×C22⋊D37—22no—
40C2×C22⋊D37—22no—
41#10596966—24no—
42#10596966—42no—
43D4×D37—24no—
44D4×D37—42no—
45C2×D148—22no—
46C2×D148D411yescharacteristic
47C2×D148C2312yes—
48C2×C4×D37—22no—
49C2×C4×D37—22no—
50C2×C4×D37C2312yes—
51Q16×C37—41no—
52SD16×C37—24no—
53D8×C37—41no—
54C2×C8×C37C2311yescharacteristic
55C2×C8×C37C2311yescharacteristic
56C22⋊C4×C37—22no—
57C22⋊C4×C37—22no—
58C42×C37C2311yescharacteristic
59C22⋊Dic37—22no—
60#10596941—24no—
61#10596939—24no—
62#10596938—22no—
63#10596938—22no—
64#10596938D412yes—
65C4⋊Dic37D411yescharacteristic
66C4⋊Dic37C2312yes—
67#10596936—22no—
68C2×#64436C2312yes—
69D296D414yescomplemented
70#10596929—24no—
71C23×C37—22no—
72C22×D37—22no—
73C22×D37—44no—
74C22×D37—44no—
75C22×D37—82no—
76C22×D37C2×D412yes—
77Q8×C37—22no—
78Q8×C37—22no—
79D4×C37—22no—
80D4×C37—22no—
81C2×C4×C37—22no—
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2411yescharacteristic
85C22⋊D37—44no—
86C22⋊D37—82no—
87C2×Dic37—22no—
88C2×Dic37C2×D412yes—
89D148—22no—
90D148—41no—
91D148—44no—
92D148C2×D414yes—
93C4×D37—22no—
94C4×D37—22no—
95C4×D37—44no—
96C4×D37—82no—
97C8×C37—21no—
98C8×C37C2×D412yes—
99#64436—22no—
100C22×C37—42no—
101C22×C37—42no—
102C22×C37—42no—
103C22×C37C22×D411yescharacteristic
104C2×D37—22no—
105C2×D37—24no—
106C2×D37—22no—
107C2×D37—22no—
108C2×D37—42no—
109C2×D37—42no—
110C2×D37—88no—
111C4×C37—21no—
112C4×C37—21no—
113C4×C37—42no—
114C4×C37C22×D411yescharacteristic
115C4×C37H(5,𝔽2)11yescharacteristic
116Dic37—22no—
117Dic37—42no—
118#3273—371nomaximal, Sylow
119C2×C37—82no—
120C2×C37D4211yescharacteristic
121C2×C37#57511yescharacteristic
122C2×C37#57611yescharacteristic
123D37—42no—
124D37—44no—
125C2×AGL(1,ℤ/8)—372no—
126#546—372no—
127#495D3711yescharacteristic, complemented
128#468—372no—
129#463—372no—
130#452—372no—
131#447—372no—
132C4×D8—371no—
133#436—371no—
134C37#327311yescharacteristic, complemented, Sylow
135C2×#41—372no—
136C22×D4—372no—
137AGL(1,ℤ/8)—748no—
138C2×Q16C2×D3711yescharacteristic, complemented
139C2×SD16—372no—
140C2×SD16C2×D3712yescomplemented
141C2×D8—372no—
142C2×D8—371no—
143C2×D8C2×D3711yescharacteristic
144C2×M16—372no—
145#124C2×D3712yescomplemented
146#123—742no—
147C22⋊Q8—372no—
148#121—372no—
149#121—742no—
150#120—742no—
151C4×D4—371no—
152C4×D4—372no—
153C2×C22⋊C4—742no—
154#107—371no—
155C4⋊C8—371no—
156#103—372no—
157#102—372no—
158#102—372no—
159C22⋊C8—372no—
160C4×C8C2×D3711yescharacteristic, complemented
161C24—742no—
162#41—744no—
163#41—1482no—
164C2×Q8C22×D3712yes—
165C2×D4—371no—
166C2×D4—372no—
167C2×D4—742no—
168C2×D4—742no—
169C2×D4—744no—
170C2×D4—742no—
171C2×D4—1482no—
172C2×D4C22×D3712yes—
173C22×C4—372no—
174C22×C4—742no—
175C22×C4—742no—
176Q16—41no—
177SD16—24no—
178SD16—744no—
179D8—41no—
180D8—374no—
181D8—744no—
182M16—744no—
183C2×C8—372no—
184C2×C8C22×D3711yescharacteristic
185C2×C8C22×D3711yescharacteristic
186C4⋊C4—371no—
187C4⋊C4—372no—
188C4⋊C4—742no—
189C22⋊C4—22no—
190C22⋊C4—22no—
191C22⋊C4—372no—
192C22⋊C4—742no—
193C22⋊C4—742no—
194C22⋊C4—742no—
195C42C22×D3711yescharacteristic
196C23—22no—
197C23—372no—
198C23—2962no—
199C23—742no—
200C23—1484no—
201C23—1484no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—22no—
206D4—374no—
207D4—2962no—
208D4—742no—
209D4—1481no—
210D4—1484no—
211D4—1484no—
212C2×C4—22no—
213C2×C4—372no—
214C2×C4—2962no—
215C2×C4—742no—
216C2×C4—742no—
217C2×C4—742no—
218C2×C4—1484no—
219C2×C4D4×D3711yescharacteristic
220C2×C4D4×D3711yescharacteristic
221C2×C4C23×D3711yescharacteristic
222C8—21no—
223C8—742no—
224C8D4×D3712yes—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—2968no—
229C22—742no—
230C22—742no—
231C22—742no—
232C22—744no—
233C22—1482no—
234C22—1482no—
235C22C2×D4×D3711yescharacteristic
236C4—21no—
237C4—21no—
238C4—42no—
239C4—742no—
240C4—1482no—
241C4C2×D4×D3711yescharacteristic
242C4#1192458111yescharacteristic
243C2—82no—
244C2—1482no—
245C2—1484no—
246C2#1455816811yescharacteristic
247C2#1455833011yescharacteristic
248C2#1455833511yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#495C2
socleC22×C37C22×D4
hypercenter#495D37
hypocenterC37#3273
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. #14558176C2semidirect
3. #14557776C2semidirect
4. #14557745C2semidirect
5. #14557694C2semidirect
6. #14557665C2semidirect
7. C4×D296C2semidirect
8. #14557612C2semidirect
9. C37×#495C2semidirect
11. C2×D4×D37C22semidirect
13. C2×#10596941C22semidirect
16. C2×#10596929C22semidirect
18. #11924512C22semidirect
23. C4×D148C22semidirect
25. #11924470C22semidirect
26. C4⋊#64436C22semidirect
27. #11924460C22semidirect
28. #11924458C22semidirect
29. #11924457C22semidirect
30. #11924448C22semidirect
31. C2×Q16×C37C22semidirect
32. C2×SD16×C37C22semidirect
34. #124×C37C22semidirect
35. C4×C8×C37C22semidirect
69. D296D4semidirect
127. #495D37semidirect
134. C37#3273semidirect
138. C2×Q16C2×D37semidirect
140. C2×SD16C2×D37semidirect
145. #124C2×D37semidirect
160. 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
#145581762
#145577762
#145577452
#145576942
#145576652
C4×D2962
#145576122
C37×#4952
#327337