Finite Group Databasebeta

← #18005060

Subgroups — #18005060

Order 4736.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924567C212yesmaximal, complemented
2C2×#11924562C212yesmaximal, complemented
3#14558083C211yesmaximal, characteristic, complemented
4#14557928C212yesmaximal, complemented
5#14557923C212yesmaximal, complemented
6#14557915C214yesmaximal, complemented
7C4×#10596934C211yesmaximal, characteristic, complemented
8C2×#124×C37C211yesmaximal, characteristic, complemented
9C2×#10596962C2212yes—
10#11924567—28no—
11#11924562—28no—
12C2×#10596942C2214yescomplemented
13C2×#10596940C2214yes—
14C2×#10596941C2214yescomplemented
15C2×#10596939C2214yes—
16C2×#10596934C2212yes—
17#11924536C2211yescharacteristic, complemented
18#11924533C2211yescharacteristic, complemented
19#11924524C2212yescomplemented
20#11924510—22no—
21C4×D148—22no—
22#11924447C2212yescomplemented
23C4×#64436C2212yescomplemented
24C22×Q8×C37C2211yescharacteristic
25C22×D4×C37C2211yescharacteristic
26#124×C37—22no—
27#124×C37C2212yes—
28#124×C37C2212yes—
29C2×C22⋊C4×C37—22no—
30C2×C42×C37C2211yescharacteristic
31C24×C37—21no—
32C2×Q8×C37—21no—
33C2×Q8×C37—24no—
34C2×Q8×C37C2312yes—
35C2×D4×C37—24no—
36C2×D4×C37—21no—
37C2×D4×C37C2312yes—
38C22×C4×C37—21no—
39C22×C4×C37D412yes—
40C22×C4×C37C2311yescharacteristic
41C2×C22⋊D37—22no—
42#10596962—24no—
43#10596962—24no—
44C2×D148—22no—
45C2×D148C2312yes—
46C2×C4×D37—22no—
47C2×Dic74C2312yes—
48C22⋊C4×C37—24no—
49C22⋊C4×C37—24no—
50C42×C37D412yes—
51C42×C37C2311yescharacteristic
52C42×C37C2311yescharacteristic
53#10596942—28no—
54#10596941—28no—
55#10596940—28no—
56#10596939—28no—
57#10596938—24no—
58C4⋊Dic37—22no—
59#10596934D418yescomplemented
60C2×#64436C2314yes—
61C23×C37—22no—
62C23×C37—44no—
63C23×C37—42no—
64C23×C37C2×D411yescharacteristic
65C22×D37—22no—
66Q8×C37—24no—
67Q8×C37—42no—
68D4×C37—24no—
69D4×C37—42no—
70C2×C4×C37—22no—
71C2×C4×C37—42no—
72C2×C4×C37—42no—
73C2×C4×C37C2×D414yes—
74C2×C4×C37C2×D412yes—
75C2×C4×C37C2×D412yes—
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2411yescharacteristic
78C22⋊D37—44no—
79C2×Dic37—22no—
80D148—22no—
81D148—22no—
82D148—44no—
83C4×D37—44no—
84Dic74—22no—
85Dic74—22no—
86#64436C2×D418yes—
87C22×C37—22no—
88C22×C37—42no—
89C22×C37—44no—
90C22×C37—84no—
91C22×C37#12712yes—
92C22×C37C22×D411yescharacteristic
93C2×D37—42no—
94C2×D37—44no—
95C4×C37—22no—
96C4×C37—22no—
97C4×C37—42no—
98C4×C37#12712yes—
99C4×C37C22×D412yes—
100Dic37—42no—
101#3153—371nomaximal, Sylow
102C2×C37—22no—
103C2×C37—82no—
104C2×C37C2×#12711yescharacteristic
105C2×C37#57512yes—
106D37—82no—
107C2×#137—372no—
108C2×AGL(1,ℤ/8)—372no—
109#532—371no—
110C2×#124D3711yescharacteristic, complemented
111#497—372no—
112#496—372no—
113#495—374no—
114C4×M16—371no—
115C37#315311yescharacteristic, complemented, Sylow
116C2×#41—372no—
117C22×Q8C2×D3711yescharacteristic
118C22×D4C2×D3711yescharacteristic
119#137—748no—
120AGL(1,ℤ/8)—748no—
121C2×Q16—374no—
122C2×SD16—374no—
123C2×SD16—374no—
124C2×D8—374no—
125C2×M16—372no—
126C4⋊Q8—371no—
127#127—371no—
128#124—22no—
129#124—372no—
130#124C2×D3712yes—
131#124C2×D3712yes—
132#121—742no—
133C4×D4—742no—
134C2×C22⋊C4—22no—
135C2×C42C2×D3711yescharacteristic
136#97—372no—
137C4×C8—372no—
138C24—21no—
139#41—744no—
140#41—744no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—372no—
144C2×Q8C22×D3712yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—372no—
148C2×D4—742no—
149C2×D4—742no—
150C2×D4C22×D3712yes—
151C22×C4—21no—
152C22×C4—742no—
153C22×C4C22⋊D3712yes—
154C22×C4C22×D3711yescharacteristic
155Q16—748no—
156SD16—748no—
157SD16—748no—
158D8—748no—
159M16—378no—
160C2×C8—374no—
161C4⋊C4—742no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—744no—
165C42C22⋊D3712yes—
166C42C22×D3711yescharacteristic
167C42C22×D3711yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—742no—
172C23C2×C22⋊D3711yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—742no—
176Q8—742no—
177D4—24no—
178D4—42no—
179D4—742no—
180D4—742no—
181D4—1484no—
182D4—1484no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—742no—
187C2×C4—1484no—
188C2×C4D4×D3714yes—
189C2×C4C2×C22⋊D3712yes—
190C2×C4C2×C22⋊D3712yes—
191C2×C4C2×C22⋊D3711yescharacteristic
192C2×C4C23×D3711yescharacteristic
193C8—378no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—1482no—
199C22—1484no—
200C22#1192453212yes—
201C22C22×C22⋊D3711yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—1482no—
206C4#1192453212yes—
207C4C2×D4×D3712yes—
208C2—22no—
209C2—82no—
210C2—2962no—
211C2C2×#1192453211yescharacteristic
212C2#1455833112yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#124×C37C2
socleC22×C37C22×D4
hypercenterC2×#124D37
hypocenterC37#3153
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#11924567C2semidirect
2. C2×#11924562C2semidirect
3. #14558083C2semidirect
4. #14557928C2semidirect
5. #14557923C2semidirect
6. #14557915C2semidirect
7. C4×#10596934C2semidirect
8. C2×#124×C37C2semidirect
12. C2×#10596942C22semidirect
14. C2×#10596941C22semidirect
17. #11924536C22semidirect
18. #11924533C22semidirect
19. #11924524C22semidirect
22. #11924447C22semidirect
23. C4×#64436C22semidirect
59. #10596934D4semidirect
110. C2×#124D37semidirect
115. C37#3153semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
C2×#119245622
#145580832
#145579282
#145579232
#145579152
C4×#105969342
C2×#124×C372
#315337