Finite Group Databasebeta

← #18004075

Subgroups — #18004075

Order 4736.

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

normal subgroups only

This group has 584 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×#11924564C211yesmaximal, characteristic, complemented
2C2×#11924562C211yesmaximal, characteristic, complemented
3C2×#11924532C211yesmaximal, characteristic, complemented
4#14558001C211yesmaximal, characteristic, complemented
5#14557732C214yesmaximal, complemented
6#14557727C214yesmaximal, complemented
7#14557556C211yesmaximal, characteristic, complemented
8#14557537C211yesmaximal, characteristic, complemented
9C37×#418C211yesmaximal, characteristic, complemented
10C2×#10596962C2211yescharacteristic
11C22×D148C2211yescharacteristic
12C22×C22⋊D37—22no—
13#11924564—24no—
14#11924562—24no—
15C2×#10596930C2212yescomplemented
16C2×#10596940C2212yescomplemented
17C2×D296C2212yescomplemented
18C2×#10596939C2212yescomplemented
19C2×#10596934C2211yescharacteristic
20#11924532—21no—
21#11924532—21no—
22#11924532C2214yes—
23#11924501C2212yescomplemented
24#11924498C2212yescomplemented
25#11924496—22no—
26#11924493—21no—
27C2×C4×Dic37C2211yescharacteristic
28C42×D37—21no—
29#11924465C2214yescomplemented
30#11924456C2214yescomplemented
31C22×D4×C37C2211yescharacteristic
32C2×M16×C37C2211yescharacteristic
33#117×C37C2211yescharacteristic
34#102×C37C2214yescomplemented
35C24×C37—21no—
36C23×D37—21no—
37C2×D4×C37—22no—
38C2×D4×C37—21no—
39C2×D4×C37—22no—
40C2×D4×C37C2312yes—
41C22×C4×C37C2311yescharacteristic
42C2×C22⋊D37—21no—
43C2×C22⋊D37—24no—
44C2×C22⋊D37—24no—
45C2×C22⋊D37—48no—
46C22×Dic37D412yes—
47#10596962—22no—
48#10596962D414yescomplemented
49C2×D148—22no—
50C2×D148—22no—
51C2×D148—21no—
52C2×D148C2312yes—
53C2×D148C2311yescharacteristic
54C2×C4×D37—21no—
55C2×C4×D37—22no—
56C2×Dic74C2311yescharacteristic
57M16×C37—22no—
58C2×C8×C37C2312yes—
59C4⋊C4×C37C2312yes—
60C22⋊C4×C37—21no—
61C42×C37—21no—
62#10596940—24no—
63#10596939—24no—
64#10596938—22no—
65#10596936—22no—
66C4×Dic37—22no—
67C4×Dic37D411yescharacteristic
68C4×Dic37D411yescharacteristic
69C4×Dic37C2312yes—
70#10596934—22no—
71C2×#64436C2312yes—
72D296—24no—
73#10596930—24no—
74C23×C37—22no—
75C23×C37—44no—
76C23×C37—42no—
77C23×C37C2×D411yescharacteristic
78C22×D37—21no—
79C22×D37—22no—
80C22×D37—44no—
81C22×D37—42no—
82D4×C37—22no—
83D4×C37—22no—
84D4×C37—42no—
85C2×C4×C37—22no—
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37C2×D412yes—
88C2×C4×C37#4112yes—
89C2×C4×C37C2411yescharacteristic
90C22⋊D37—24no—
91C22⋊D37—48no—
92C22⋊D37—48no—
93C2×Dic37—21no—
94C2×Dic37—24no—
95C2×Dic37C2×D412yes—
96C2×Dic37C2×D412yes—
97D148—22no—
98D148—21no—
99D148—22no—
100D148—42no—
101D148C2×D412yescomplemented
102C4×D37—24no—
103C4×D37—44no—
104Dic74—21no—
105Dic74C2×D412yescomplemented
106C8×C37—22no—
107#64436—22no—
108C22×C37—22no—
109C22×C37—42no—
110C22×C37—44no—
111C22×C37—84no—
112C22×C37#12112yes—
113C22×C37C22×D411yescharacteristic
114C2×D37—22no—
115C2×D37—42no—
116C2×D37—42no—
117C2×D37—44no—
118C2×D37—84no—
119C4×C37—42no—
120C4×C37#12112yes—
121C4×C37C22×D411yescharacteristic
122C4×C37C2×#4111yescharacteristic
123Dic37—22no—
124Dic37—22no—
125Dic37AGL(1,ℤ/8)14yescomplemented
126#3038—371nomaximal, Sylow
127C2×C37—22no—
128C2×C37—82no—
129C2×C37C2×#12111yescharacteristic
130C2×C37C2×AGL(1,ℤ/8)12yes—
131D37—42no—
132D37—82no—
133C2×AGL(1,ℤ/8)—371no—
134C2×AGL(1,ℤ/8)—371no—
135C2×#127—371no—
136C4×#41—371no—
137#460—374no—
138#459—374no—
139#423—371no—
140#418—371no—
141#418D3711yescharacteristic, complemented
142C37#303811yescharacteristic, complemented, Sylow
143C2×#41—371no—
144C22×D4—371no—
145C22×D4—742no—
146C22×D4C2×D3711yescharacteristic
147AGL(1,ℤ/8)—744no—
148AGL(1,ℤ/8)—744no—
149C2×SD16—372no—
150C2×SD16—372no—
151C2×D8—372no—
152C2×D8—372no—
153C2×M16—371no—
154C2×M16C2×D3711yescharacteristic
155#127—374no—
156#127—741no—
157#127—741no—
158C4×Q8—372no—
159C4×D4—372no—
160C4×D4—742no—
161#117—741no—
162#117C2×D3711yescharacteristic
163C2×C42—371no—
164C2×C42—741no—
165C4⋊C8—374no—
166#102—374no—
167#102C2×D3714yescomplemented
168C24—21no—
169C24—741no—
170#41—374no—
171#41—742no—
172C2×Q8—371no—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—21no—
176C2×D4—371no—
177C2×D4—372no—
178C2×D4—744no—
179C2×D4—744no—
180C2×D4—741no—
181C2×D4—742no—
182C2×D4—742no—
183C2×D4—741no—
184C2×D4—1488no—
185C2×D4C22×D3712yes—
186C22×C4—372no—
187C22×C4—742no—
188C22×C4—741no—
189C22×C4C22×D3711yescharacteristic
190SD16—744no—
191SD16—744no—
192D8—744no—
193D8—744no—
194M16—22no—
195M16—742no—
196C2×C8—372no—
197C2×C8C22×D3712yes—
198C4⋊C4—742no—
199C4⋊C4C22×D3712yes—
200C22⋊C4—21no—
201C22⋊C4—742no—
202C42—21no—
203C42—371no—
204C42—371no—
205C42—372no—
206C42—742no—
207C23—22no—
208C23—44no—
209C23—42no—
210C23—741no—
211C23—742no—
212C23—1484no—
213C23—1482no—
214C23D4×D3711yescharacteristic
215Q8—372no—
216Q8—741no—
217D4—22no—
218D4—22no—
219D4—42no—
220D4—372no—
221D4—744no—
222D4—742no—
223D4—741no—
224D4—742no—
225D4—1488no—
226D4—1488no—
227D4—1482no—
228C2×C4—22no—
229C2×C4—372no—
230C2×C4—372no—
231C2×C4—744no—
232C2×C4—741no—
233C2×C4—744no—
234C2×C4—1484no—
235C2×C4#1059696212yes—
236C2×C4D4×D3711yescharacteristic
237C2×C4D4×D3712yes—
238C2×C4C23×D3711yescharacteristic
239C8—22no—
240C8—742no—
241C22—22no—
242C22—42no—
243C22—44no—
244C22—84no—
245C22—2964no—
246C22—742no—
247C22—1482no—
248C22—1484no—
249C22—1482no—
250C22#1192450912yes—
251C22C2×D4×D3711yescharacteristic
252C4—42no—
253C4—374no—
254C4—742no—
255C4—742no—
256C4#1192450912yes—
257C4C2×D4×D3711yescharacteristic
258C4C2×#1059696211yescharacteristic
259C2—22no—
260C2—82no—
261C2—2962no—
262C2—1482no—
263C2C2×#1192450911yescharacteristic
264C2AGL(1,ℤ/8)×D3712yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#418C2
socleC22×C37C22×D4
hypercenter#418D37
hypocenterC37#3038
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#11924564C2semidirect
2. C2×#11924562C2semidirect
3. C2×#11924532C2semidirect
4. #14558001C2semidirect
5. #14557732C2semidirect
6. #14557727C2semidirect
7. #14557556C2semidirect
8. #14557537C2semidirect
9. C37×#418C2semidirect
15. C2×#10596930C22semidirect
16. C2×#10596940C22semidirect
17. C2×D296C22semidirect
18. C2×#10596939C22semidirect
23. #11924501C22semidirect
24. #11924498C22semidirect
29. #11924465C22semidirect
30. #11924456C22semidirect
34. #102×C37C22semidirect
48. #10596962D4semidirect
101. D148C2×D4semidirect
105. Dic74C2×D4semidirect
125. Dic37AGL(1,ℤ/8)semidirect
141. #418D37semidirect
142. C37#3038semidirect
167. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
C2×#119245622
C2×#119245322
#145580012
#145577322
#145577272
#145575562
#145575372
C37×#4182
#303837