Finite Group Databasebeta

← #17996258

Subgroups — #17996258

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#14558081C211yesmaximal, characteristic
2#14557505C212yesmaximal, complemented
3#14557327C212yesmaximal, complemented
4#14557326C211yesmaximal, characteristic, complemented
5C37×#353C211yesmaximal, characteristic, complemented
6C2×#10596964C411yescharacteristic, complemented
7C2×#10596964C2211yescharacteristic
8#11924536C411yescharacteristic, complemented
9#11924523C411yescharacteristic, complemented
10#11924523C2211yescharacteristic
11#11924507—22no—
12D4×Dic37—22no—
13#11924492—22no—
14C42×D37C411yescharacteristic, complemented
15#11924451C2212yes—
16#11924450—22no—
17#127×C37C2211yescharacteristic
18#99×C37C2212yes—
19C2×D4×C37—22no—
20C2×D4×C37C2×C411yescharacteristic
21C2×D4×C37C2311yescharacteristic
22C2×C22⋊D37—21no—
23C2×C22⋊D37D412yes—
24C22×Dic37—21no—
25C22×Dic37D412yes—
26#10596964—41no—
27#10596964—41no—
28#10596964—41no—
29#10596964—41no—
30C2×C4×D37—21no—
31C2×C4×D37C2×C411yescharacteristic
32C2×Dic74C2×C411yescharacteristic
33C2×Dic74C2×C411yescharacteristic
34C22⋊C4×C37—22no—
35C42×C37C2×C411yescharacteristic
36C22⋊Dic37—22no—
37C22⋊Dic37—22no—
38C22⋊Dic37—22no—
39C4⋊Dic37—22no—
40#10596936—42no—
41C4×Dic37—21no—
42C4×Dic37—42no—
43C4×Dic37C2×C411yescharacteristic
44C23×C37—21no—
45C23×C37C2×D412yes—
46C22×D37C22⋊C411yescharacteristic
47D4×C37—41no—
48D4×C37—41no—
49D4×C37—44no—
50C2×C4×C37—21no—
51C2×C4×C37—42no—
52C2×C4×C37C22×C411yescharacteristic
53C22⋊D37—42no—
54C22⋊D37—42no—
55C2×Dic37—22no—
56C2×Dic37—22no—
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37—41no—
60C2×Dic37—41no—
61C2×Dic37—42no—
62C2×Dic37C22⋊C412yes—
63C2×Dic37C22⋊C411yescharacteristic
64C4×D37—21no—
65C4×D37—21no—
66C4×D37—42no—
67Dic74—41no—
68Dic74—41no—
69C22×C37—22no—
70C22×C37—42no—
71C22×C37—42no—
72C22×C37—41no—
73C22×C37C2×C22⋊C411yescharacteristic
74C2×D37—21no—
75C2×D37—41no—
76C4×C37—22no—
77C4×C37—21no—
78C4×C37—82no—
79Dic37—22no—
80Dic37—41no—
81Dic37—41no—
82Dic37—82no—
83Dic37#9911yescharacteristic
84Dic37#9911yescharacteristic
85#2126—371nomaximal, Sylow
86C2×C37—21no—
87C2×C37—42no—
88C2×C37—81no—
89C2×C37C2×#9911yescharacteristic
90D37—41no—
91#532—371no—
92#410—372no—
93#354—372no—
94#353—371no—
95#353D3711yescharacteristic, complemented
96C37#212611yescharacteristic, complemented, Sylow
97C2×#41—371no—
98C2×#41—371no—
99C4⋊Q8—371no—
100#127C2×D3711yescharacteristic
101#124—371no—
102#124—371no—
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×Q8—371no—
116C2×D4—22no—
117C2×D4—372no—
118C2×D4—741no—
119C2×D4C4×D3711yescharacteristic
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—742no—
129C22⋊C4—742no—
130C22⋊C4—742no—
131C42—371no—
132C42—741no—
133C42—1482no—
134C42C4×D3711yescharacteristic
135C23—21no—
136C23—371no—
137C23D4×D3712yes—
138Q8—1481no—
139Q8—1481no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—1482no—
144D4—1482no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—371no—
148C2×C4—372no—
149C2×C4—741no—
150C2×C4—741no—
151C2×C4—742no—
152C2×C4—742no—
153C2×C4—741no—
154C2×C4—741no—
155C2×C4—1482no—
156C2×C4—1481no—
157C2×C4—1481no—
158C2×C4—1482no—
159C2×C4C2×C4×D3711yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—741no—
165C22—1481no—
166C22C22⋊C4×D3711yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—371no—
171C4—371no—
172C4—2962no—
173C4—742no—
174C4—1481no—
175C4—1481no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—1481no—
180C2#99×D3711yescharacteristic
subgroupG/H
centerC2#99×D37
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#353C2
socleC2×C37C2×#99
prime radical#14558081C2
cosocleC2×D4×C37C23
hypercenter#353D37
hypocenterC37#2126
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #14557505C2semidirect
3. #14557327C2semidirect
4. #14557326C2semidirect
5. C37×#353C2semidirect
6. C2×#10596964C4semidirect
8. #11924536C4semidirect
9. #11924523C4semidirect
14. C42×D37C4semidirect
95. #353D37semidirect
96. C37#2126semidirect

Maximal subgroups

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

subgroupindex
#145580812
#145575052
#145573272
#145573262
C37×#3532
#212637