Finite Group Databasebeta

← #18005048

Subgroups — #18005048

Order 4736.

656 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 173 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×#11924564C214yesmaximal, complemented
2#14558083C211yesmaximal, characteristic, complemented
3C2×#11924533C211yesmaximal, characteristic, complemented
4#14557922C214yesmaximal, complemented
5#14557910C212yesmaximal, complemented
6#14557906C212yesmaximal, complemented
7C4×M16×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2212yes—
9C22×D148—22no—
10C22×D148C2212yes—
11#11924564—216no—
12C2×#10596930C2218yescomplemented
13C2×D296C2218yescomplemented
14#11924536C2211yescharacteristic, complemented
15#11924533—22no—
16#11924533C2212yes—
17#11924533C2212yes—
18#11924533C2211yescharacteristic, complemented
19#11924524C2212yescomplemented
20#11924510—22no—
21C4×D148—22no—
22C2×M16×C37C2212yes—
23C2×C42×C37C2211yescharacteristic
24#97×C37C2212yescomplemented
25C4×C8×C37C2212yescomplemented
26C23×D37—22no—
27C22×C4×C37D412yes—
28C22×C4×C37C2311yescharacteristic
29C2×C22⋊D37—22no—
30#10596962—28no—
31C2×D148—28no—
32C2×D148—22no—
33C2×D148—22no—
34C2×D148—24no—
35C2×D148—24no—
36C2×D148—48no—
37C2×D148C2312yes—
38C2×D148C2314yes—
39C2×C4×D37—22no—
40C2×Dic74C2312yes—
41M16×C37D418yescomplemented
42C2×C8×C37C2314yes—
43C42×C37D412yes—
44C42×C37C2311yescharacteristic
45C42×C37C2311yescharacteristic
46#10596938—24no—
47C4⋊Dic37—22no—
48D296—216no—
49#10596930—216no—
50C23×C37C2×D411yescharacteristic
51C22×D37—22no—
52C22×D37—24no—
53C22×D37—48no—
54C22×D37—44no—
55C2×C4×C37—24no—
56C2×C4×C37C2×D412yes—
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D414yes—
59C2×C4×C37C2×D412yes—
60C2×C4×C37C2411yescharacteristic
61C22⋊D37—44no—
62C2×Dic37—22no—
63D148—28no—
64D148—24no—
65D148—48no—
66D148—44no—
67D148—44no—
68D148—48no—
69C4×D37—44no—
70Dic74—24no—
71C8×C37C2×D418yescomplemented
72C22×C37—22no—
73C22×C37#12712yes—
74C22×C37C22×D411yescharacteristic
75C2×D37—42no—
76C2×D37—44no—
77C2×D37—48no—
78C2×D37—44no—
79C2×D37—88no—
80C4×C37—22no—
81C4×C37#12712yes—
82C4×C37AGL(1,ℤ/8)14yescomplemented
83C4×C37C22×D412yes—
84Dic37—42no—
85#3151—371nomaximal, Sylow
86C2×C37—22no—
87C2×C37C2×#12711yescharacteristic
88C2×C37C2×AGL(1,ℤ/8)12yes—
89D37—82no—
90D37—84no—
91C2×AGL(1,ℤ/8)—374no—
92#532—371no—
93C2×#127—371no—
94#496—374no—
95#493—372no—
96#492—372no—
97C4×M16D3711yescharacteristic, complemented
98C37#315111yescharacteristic, complemented, Sylow
99C2×#41—372no—
100C22×D4—372no—
101C22×D4—742no—
102AGL(1,ℤ/8)—7416no—
103C2×SD16—378no—
104C2×D8—378no—
105C2×M16C2×D3712yes—
106C4⋊Q8—371no—
107#127—372no—
108#127—372no—
109#127—371no—
110#127—742no—
111#124—372no—
112#121—742no—
113C4×D4—742no—
114C2×C42C2×D3711yescharacteristic
115#97C2×D3712yescomplemented
116C4×C8C2×D3712yescomplemented
117C24—742no—
118#41—748no—
119C2×Q8—372no—
120C2×D4—372no—
121C2×D4—374no—
122C2×D4—742no—
123C2×D4—748no—
124C2×D4—742no—
125C2×D4—744no—
126C2×D4—744no—
127C2×D4—742no—
128C2×D4—1488no—
129C22×C4—742no—
130C22×C4D14812yes—
131C22×C4C22×D3711yescharacteristic
132SD16—7416no—
133D8—7416no—
134M16D14818yescomplemented
135C2×C8C22×D3714yes—
136C4⋊C4—742no—
137C22⋊C4—744no—
138C42D14812yes—
139C42C22×D3711yescharacteristic
140C42C22×D3711yescharacteristic
141C23—742no—
142C23—744no—
143C23—1488no—
144C23—1484no—
145C23C2×D14811yescharacteristic
146Q8—744no—
147D4—744no—
148D4—748no—
149D4—1488no—
150D4—1484no—
151D4—1484no—
152D4—1488no—
153D4—1484no—
154C2×C4—24no—
155C2×C4—742no—
156C2×C4—1484no—
157C2×C4C2×D14812yes—
158C2×C4C2×D14811yescharacteristic
159C2×C4C2×D14814yes—
160C2×C4C2×D14812yes—
161C2×C4C23×D3711yescharacteristic
162C8C2×D14818yescomplemented
163C22—22no—
164C22—2968no—
165C22—1488no—
166C22—1484no—
167C22—1482no—
168C22—1484no—
169C22#1192453312yes—
170C22C22×D14811yescharacteristic
171C4—22no—
172C4—1482no—
173C4#1192453312yes—
174C4#1192456414yescomplemented
175C4C22×D14812yes—
176C2—22no—
177C2—2964no—
178C2—2962no—
179C2C2×#1192453311yescharacteristic
180C2C2×#1192456412yes—
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×M16×C37C2
socleC22×C37C22×D4
hypercenterC4×M16D37
hypocenterC37#3151
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#11924564C2semidirect
2. #14558083C2semidirect
3. C2×#11924533C2semidirect
4. #14557922C2semidirect
5. #14557910C2semidirect
6. #14557906C2semidirect
7. C4×M16×C37C2semidirect
12. C2×#10596930C22semidirect
13. C2×D296C22semidirect
14. #11924536C22semidirect
18. #11924533C22semidirect
19. #11924524C22semidirect
24. #97×C37C22semidirect
25. C4×C8×C37C22semidirect
41. M16×C37D4semidirect
71. C8×C37C2×D4semidirect
82. C4×C37AGL(1,ℤ/8)semidirect
97. C4×M16D37semidirect
98. C37#3151semidirect
115. #97C2×D37semidirect
116. C4×C8C2×D37semidirect
134. M16D148semidirect
162. C8C2×D148semidirect
174. C4#11924564semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
#145580832
C2×#119245332
#145579222
#145579102
#145579062
C4×M16×C372
#315137