Finite Group Databasebeta

← #17996260

Subgroups — #17996260

Order 4736.

258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558082C211yesmaximal, characteristic
2#14557505C212yesmaximal, complemented
3#14557328C211yesmaximal, characteristic, complemented
4#14557325C212yesmaximal, complemented
5C37×#354C211yesmaximal, characteristic, complemented
6C2×#10596966C411yescharacteristic, complemented
7C2×#10596964C2211yescharacteristic
8#11924534C411yescharacteristic, complemented
9#11924532C2211yescharacteristic
10#11924524C411yescharacteristic, complemented
11#11924509—22no—
12#11924496—22no—
13#11924492—22no—
14C42×D37C411yescharacteristic, complemented
15#11924451C2212yes—
16#11924450—22no—
17#124×C37C2211yescharacteristic
18#99×C37C2212yes—
19C2×Q8×C37C2×C411yescharacteristic
20C2×D4×C37C2311yescharacteristic
21C2×C22⋊D37—22no—
22C2×C22⋊D37D412yes—
23C22×Dic37D412yes—
24#10596966—41no—
25#10596966—41no—
26#10596964—41no—
27#10596964—41no—
28C2×D148—21no—
29C2×D148C2×C411yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37—21no—
32C2×C4×D37C2×C411yescharacteristic
33C2×Dic74C2×C411yescharacteristic
34C22⋊C4×C37—22no—
35C22⋊C4×C37—22no—
36C42×C37C2×C411yescharacteristic
37C22⋊Dic37—22no—
38#10596938—22no—
39#10596936—22no—
40#10596936—42no—
41C4×Dic37—21no—
42C4×Dic37—42no—
43C4×Dic37C2×C411yescharacteristic
44C23×C37C2×D412yes—
45C22×D37—21no—
46C22×D37C22⋊C411yescharacteristic
47Q8×C37—41no—
48D4×C37—41no—
49C2×C4×C37—21no—
50C2×C4×C37—21no—
51C2×C4×C37—42no—
52C2×C4×C37C22×C411yescharacteristic
53C22⋊D37—42no—
54C22⋊D37—44no—
55C2×Dic37—21no—
56C2×Dic37—22no—
57C2×Dic37—22no—
58C2×Dic37—42no—
59C2×Dic37C22⋊C412yes—
60C2×Dic37C22⋊C411yescharacteristic
61D148—41no—
62D148—42no—
63C4×D37—21no—
64C4×D37—21no—
65C4×D37—42no—
66C4×D37—41no—
67C4×D37—41no—
68Dic74—41no—
69C22×C37—22no—
70C22×C37—42no—
71C22×C37C2×C22⋊C411yescharacteristic
72C2×D37—21no—
73C2×D37—41no—
74C2×D37—42no—
75C2×D37—41no—
76C4×C37—21no—
77C4×C37—41no—
78C4×C37—41no—
79C4×C37—82no—
80Dic37—22no—
81Dic37—22no—
82Dic37—82no—
83Dic37#9911yescharacteristic
84Dic37#9911yescharacteristic
85#2126—371nomaximal, Sylow
86C2×C37—21no—
87C2×C37—42no—
88C2×C37C2×#9911yescharacteristic
89D37—41no—
90D37—81no—
91#532—371no—
92#410—372no—
93#354—371no—
94#354D3711yescharacteristic, complemented
95#353—372no—
96C37#212611yescharacteristic, complemented, Sylow
97C2×#41—371no—
98C2×#41—371no—
99C4⋊Q8—371no—
100#127—371no—
101#124—371no—
102#124C2×D3711yescharacteristic
103#121—742no—
104C4×D4—742no—
105#117—742no—
106C2×C42—371no—
107#99—372no—
108#99—742no—
109#99C2×D3712yes—
110#41—1481no—
111#41—1481no—
112#41—1481no—
113#41—1481no—
114C2×Q8—371no—
115C2×Q8C4×D3711yescharacteristic
116C2×D4—372no—
117C2×D4—371no—
118C2×D4—741no—
119C2×D4—742no—
120C2×D4C22×D3711yescharacteristic
121C22×C4—372no—
122C22×C4—371no—
123C22×C4—741no—
124C22×C4—741no—
125C4⋊C4—742no—
126C4⋊C4—1482no—
127C22⋊C4—22no—
128C22⋊C4—22no—
129C22⋊C4—742no—
130C22⋊C4—742no—
131C42—371no—
132C42—741no—
133C42—1482no—
134C42C4×D3711yescharacteristic
135C23—371no—
136C23—741no—
137C23D4×D3712yes—
138Q8—41no—
139Q8—1481no—
140D4—41no—
141D4—1481no—
142D4—1482no—
143D4—1482no—
144D4—1484no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—371no—
149C2×C4—372no—
150C2×C4—741no—
151C2×C4—741no—
152C2×C4—742no—
153C2×C4—742no—
154C2×C4—741no—
155C2×C4—1481no—
156C2×C4—1481no—
157C2×C4—1482no—
158C2×C4—1482no—
159C2×C4C2×C4×D3711yescharacteristic
160C22—22no—
161C22—42no—
162C22—741no—
163C22—1482no—
164C22—1481no—
165C22—1481no—
166C22C22⋊C4×D3711yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—371no—
172C4—371no—
173C4—2962no—
174C4—742no—
175C4—742no—
176C2—21no—
177C2—42no—
178C2—2961no—
179C2—1481no—
180C2#99×D3711yescharacteristic
subgroupG/H
centerC2#99×D37
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#354C2
socleC2×C37C2×#99
prime radical#14558082C2
cosocleC2×D4×C37C23
hypercenter#354D37
hypocenterC37#2126
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #14557505C2semidirect
3. #14557328C2semidirect
4. #14557325C2semidirect
5. C37×#354C2semidirect
6. C2×#10596966C4semidirect
8. #11924534C4semidirect
10. #11924524C4semidirect
14. C42×D37C4semidirect
94. #354D37semidirect
96. C37#2126semidirect

Maximal subgroups

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

subgroupindex
#145580822
#145575052
#145573282
#145573252
C37×#3542
#212637