Finite Group Databasebeta

← #18004943

Subgroups — #18004943

Order 4736.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#14558089C211yesmaximal, characteristic, complemented
2#14558084C211yesmaximal, characteristic
3#14557901C211yesmaximal, characteristic, complemented
4#14557899C211yesmaximal, characteristic, complemented
5#14557898C211yesmaximal, characteristic, complemented
6#14557894C214yesmaximal, complemented
7#14557528C214yesmaximal, complemented
8#97×D37C211yesmaximal, characteristic, complemented
9C37×#491C211yesmaximal, characteristic, complemented
10C2×#10596966C2212yes—
11C2×C8×D37C2212yes—
12#11924535C2212yes—
13#11924533C2211yescharacteristic
14#11924528C2211yescharacteristic
15#11924525C2212yes—
16#11924514—22no—
17#11924511—22no—
18#11924501—22no—
19#11924498—22no—
20#11924494C2212yes—
21C42×D37C2211yescharacteristic
22#11924460C2214yes—
23#11924458C2214yes—
24#11924456C2214yes—
25#11924447C2211yescharacteristic
26#11924446C2212yes—
27C4⋊Q8×C37C2211yescharacteristic
28#125×C37C2211yescharacteristic
29#103×C37C2214yes—
30#97×C37C2211yescharacteristic
31C2×Q8×C37C2312yes—
32#10596966—28no—
33C2×D148—22no—
34C2×D148—22no—
35C2×D148C2312yes—
36C2×C4×D37—22no—
37C2×C4×D37D412yes—
38C2×C4×D37C2311yescharacteristic
39C2×Dic74—22no—
40C2×C8×C37C2312yes—
41C4⋊C4×C37—22no—
42C4⋊C4×C37—22no—
43C4⋊C4×C37C2312yes—
44C42×C37C2311yescharacteristic
45#10596938—22no—
46#10596938—24no—
47C4⋊Dic37C2312yes—
48#10596936—22no—
49#10596936—22no—
50C4×Dic37—22no—
51C4×Dic37D412yes—
52C4×Dic37C2311yescharacteristic
53C2×#64436C2312yes—
54C8×D37—24no—
55C22×D37—22no—
56C22×D37C2×D411yescharacteristic
57Q8×C37—24no—
58C2×C4×C37—22no—
59C2×C4×C37—22no—
60C2×C4×C37C2×D412yes—
61C2×C4×C37C2411yescharacteristic
62C2×Dic37—22no—
63C2×Dic37C2×D412yes—
64C2×Dic37C2×D411yescharacteristic
65D148—24no—
66D148—44no—
67D148—44no—
68C4×D37—42no—
69C4×D37—44no—
70C4×D37#4114yes—
71Dic74—44no—
72C8×C37—22no—
73#64436—22no—
74C22×C37C22×D411yescharacteristic
75C2×D37—22no—
76C2×D37—42no—
77C2×D37—44no—
78C2×D37#12412yes—
79C4×C37—22no—
80C4×C37—42no—
81C4×C37—42no—
82C4×C37C2×#4112yes—
83Dic37—22no—
84Dic37—42no—
85Dic37#12412yes—
86#3135—371nomaximal, Sylow
87C2×C37C2×#12411yescharacteristic
88C2×C37#57512yes—
89D37—22no—
90D37—82no—
91#533—371no—
92#532—371no—
93#491—371no—
94#491D3711yescharacteristic, complemented
95#490—371no—
96#490—371no—
97#489—374no—
98#416—374no—
99C2×#97—371no—
100C37#313511yescharacteristic, complemented, Sylow
101C2×#41—372no—
102C22×C8—372no—
103C4⋊Q8—372no—
104C4⋊Q8C2×D3711yescharacteristic
105#127—371no—
106#125—371no—
107#125C2×D3711yescharacteristic
108#124—372no—
109C22⋊Q8—742no—
110#121—742no—
111C4×Q8—742no—
112C4×D4—742no—
113#117—372no—
114C2×C42—371no—
115#103—374no—
116#103C2×D3714yes—
117#102—374no—
118#102—374no—
119#97—372no—
120#97—371no—
121#97C2×D3711yescharacteristic
122#41—748no—
123C2×Q8—742no—
124C2×Q8C22×D3712yes—
125C2×D4—372no—
126C2×D4—742no—
127C2×D4—742no—
128C22×C4—371no—
129C22×C4—372no—
130C22×C4—742no—
131C2×C8—372no—
132C2×C8—744no—
133C2×C8C22×D3712yes—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—372no—
137C4⋊C4—742no—
138C4⋊C4—742no—
139C4⋊C4C22×D3712yes—
140C22⋊C4—744no—
141C22⋊C4—742no—
142C42—372no—
143C42—371no—
144C42—742no—
145C42C22×D3711yescharacteristic
146C23—371no—
147C23—742no—
148Q8—24no—
149Q8—1484no—
150D4—744no—
151D4—1484no—
152D4—1484no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—371no—
156C2×C4—374no—
157C2×C4—372no—
158C2×C4—742no—
159C2×C4—1482no—
160C2×C4—1484no—
161C2×C4D4×D3712yes—
162C2×C4C23×D3711yescharacteristic
163C8—22no—
164C8—742no—
165C22—372no—
166C22—742no—
167C22—1482no—
168C22—1484no—
169C22C2×D4×D3711yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—372no—
174C4—742no—
175C4—1482no—
176C4#41×D3712yes—
177C2—2962no—
178C2—742no—
179C2#124×D3711yescharacteristic
180C2#1455833212yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#491C2
socleC22×C37C22×D4
prime radical#14558084C2
hypercenter#491D37
hypocenterC37#3135
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #14558089C2semidirect
3. #14557901C2semidirect
4. #14557899C2semidirect
5. #14557898C2semidirect
6. #14557894C2semidirect
7. #14557528C2semidirect
8. #97×D37C2semidirect
9. C37×#491C2semidirect
94. #491D37semidirect
100. C37#3135semidirect

Maximal subgroups

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

subgroupindex
#145580892
#145580842
#145579012
#145578992
#145578982
#145578942
#145575282
#97×D372
C37×#4912
#313537