Finite Group Databasebeta

← #18005083

Subgroups — #18005083

Order 4736.

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

normal subgroups only

This group has 596 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×#11924561C212yesmaximal, complemented
2C22×D296C211yesmaximal, characteristic, complemented
3#14558097C212yesmaximal, complemented
4#14557919C214yesmaximal, complemented
5#14557918C212yesmaximal, complemented
6#14557908C212yesmaximal, complemented
7#14557488C211yesmaximal, characteristic, complemented
8C2×#135×C37C211yesmaximal, characteristic, complemented
9C22×D148C2212yes—
10#11924561—28no—
11C2×#10596941C2214yescomplemented
12C2×D296—24no—
13C2×D296C2212yes—
14C2×D296C2212yes—
15C2×#10596939C2214yescomplemented
16C2×#10596934C2211yescharacteristic
17#11924532C2214yescomplemented
18#11924525C2214yescomplemented
19#11924510—24no—
20#11924504—24no—
21#11924495C2211yescharacteristic
22#11924446C2212yescomplemented
23C8×Dic37C2212yescomplemented
24C2×#41×C37C2212yes—
25#135×C37—24no—
26C2×Q16×C37C2211yescharacteristic, complemented
27C2×SD16×C37C2212yescomplemented
28C2×D8×C37C2211yescharacteristic, complemented
29C22×C8×C37C2211yescharacteristic
30C23×D37—22no—
31#41×C37—24no—
32#41×C37—24no—
33C2×Q8×C37C2312yes—
34C2×D4×C37—22no—
35C2×D4×C37C2312yes—
36C22×C4×C37—22no—
37C22×C4×C37C2311yescharacteristic
38C2×C22⋊D37—28no—
39C2×D148—24no—
40C2×D148—24no—
41C2×D148—22no—
42C2×D148C2314yes—
43Q16×C37—22no—
44SD16×C37—24no—
45D8×C37—22no—
46C2×C8×C37D414yescomplemented
47C2×C8×C37C2311yescharacteristic
48C2×C8×C37C2311yescharacteristic
49C22⋊Dic37D412yes—
50#10596941—28no—
51#10596939—28no—
52#10596938—28no—
53C4⋊Dic37D412yes—
54C4×Dic37C2312yes—
55#10596934D414yescomplemented
56C2×#64436C2312yes—
57D296—24no—
58D296—24no—
59C23×C37—22no—
60C23×C37C2×D411yescharacteristic
61C22×D37—24no—
62C22×D37—44no—
63C22×D37—84no—
64Q8×C37—22no—
65Q8×C37—22no—
66D4×C37—22no—
67D4×C37—22no—
68D4×C37—44no—
69C2×C4×C37—22no—
70C2×C4×C37—44no—
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D412yes—
73C2×C4×C37C2×D412yes—
74C2×C4×C37C2411yescharacteristic
75C22⋊D37—88no—
76C2×Dic37C2×D414yes—
77D148—24no—
78D148—24no—
79D148—44no—
80C8×C37C2×D412yes—
81C8×C37C2×D412yes—
82#64436C2×D414yes—
83C22×C37—22no—
84C22×C37—42no—
85C22×C37—44no—
86C22×C37#12712yes—
87C22×C37C22×D411yescharacteristic
88C2×D37—44no—
89C2×D37—48no—
90C2×D37—88no—
91C4×C37—42no—
92C4×C37#12712yes—
93C4×C37C22×D411yescharacteristic
94C4×C37C22×D411yescharacteristic
95Dic37—24no—
96#3155—371nomaximal, Sylow
97C2×C37—22no—
98C2×C37—82no—
99C2×C37C2×#12711yescharacteristic
100C2×C37#57612yes—
101D37—84no—
102C2×AGL(1,ℤ/8)—372no—
103C2×#135D3711yescharacteristic, complemented
104C22×D8—371no—
105#535—372no—
106#496—374no—
107#495—372no—
108#493—372no—
109#405—371no—
110C37#315511yescharacteristic, complemented, Sylow
111C2×#41C2×D3712yes—
112C22×D4—372no—
113AGL(1,ℤ/8)—748no—
114#135—24no—
115C2×Q16C2×D3711yescharacteristic, complemented
116C2×SD16—374no—
117C2×SD16C2×D3712yescomplemented
118C2×D8—374no—
119C2×D8—372no—
120C2×D8—372no—
121C2×D8—744no—
122C2×D8C2×D3711yescharacteristic, complemented
123C2×M16—371no—
124C22×C8C2×D3711yescharacteristic
125#127—374no—
126#124—374no—
127#121—744no—
128#120—744no—
129#117—371no—
130#97—372no—
131C4×C8—372no—
132C24—742no—
133#41—24no—
134#41—24no—
135C2×Q8C22×D3712yes—
136C2×D4—22no—
137C2×D4—374no—
138C2×D4—748no—
139C2×D4—744no—
140C2×D4—742no—
141C2×D4—744no—
142C2×D4C22×D3712yes—
143C22×C4—22no—
144C22×C4C22×D3711yescharacteristic
145Q16—22no—
146SD16—24no—
147SD16—748no—
148D8—22no—
149D8—748no—
150D8—744no—
151D8—744no—
152M16—374no—
153C2×C8—372no—
154C2×C8C22⋊D3714yescomplemented
155C2×C8C22×D3711yescharacteristic
156C2×C8C22×D3711yescharacteristic
157C4⋊C4—372no—
158C22⋊C4—372no—
159C22⋊C4—748no—
160C42—372no—
161C23—22no—
162C23—2964no—
163C23—744no—
164C23—1484no—
165C23D4×D3711yescharacteristic
166Q8—22no—
167Q8—22no—
168D4—22no—
169D4—22no—
170D4—44no—
171D4—2968no—
172D4—744no—
173D4—744no—
174D4—1484no—
175C2×C4—22no—
176C2×C4—44no—
177C2×C4—374no—
178C2×C4D4×D3711yescharacteristic
179C2×C4D4×D3712yes—
180C2×C4C2×C22⋊D3712yes—
181C2×C4C23×D3711yescharacteristic
182C8—374no—
183C8C2×C22⋊D3712yes—
184C8C2×C22⋊D3712yes—
185C22—22no—
186C22—42no—
187C22—44no—
188C22—2968no—
189C22—1484no—
190C22—1488no—
191C22#1192453212yes—
192C22C2×D4×D3711yescharacteristic
193C4—42no—
194C4—744no—
195C4#1192453212yes—
196C4C2×D4×D3711yescharacteristic
197C4C22×C22⋊D3711yescharacteristic
198C2—22no—
199C2—82no—
200C2—2964no—
201C2C2×#1192453211yescharacteristic
202C2#1455833512yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#135×C37C2
socleC22×C37C22×D4
hypercenterC2×#135D37
hypocenterC37#3155
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#11924561C2semidirect
2. C22×D296C2semidirect
3. #14558097C2semidirect
4. #14557919C2semidirect
5. #14557918C2semidirect
6. #14557908C2semidirect
7. #14557488C2semidirect
8. C2×#135×C37C2semidirect
11. C2×#10596941C22semidirect
15. C2×#10596939C22semidirect
17. #11924532C22semidirect
18. #11924525C22semidirect
22. #11924446C22semidirect
23. C8×Dic37C22semidirect
26. C2×Q16×C37C22semidirect
27. C2×SD16×C37C22semidirect
28. C2×D8×C37C22semidirect
46. C2×C8×C37D4semidirect
55. #10596934D4semidirect
103. C2×#135D37semidirect
110. C37#3155semidirect
115. C2×Q16C2×D37semidirect
117. C2×SD16C2×D37semidirect
122. C2×D8C2×D37semidirect
154. C2×C8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245612
C22×D2962
#145580972
#145579192
#145579182
#145579082
#145574882
C2×#135×C372
#315537