Finite Group Databasebeta

← #18010062

Subgroups — #18010062

Order 4736.

216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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#14558553C211yesmaximal, characteristic, complemented
2C4×#10596957C211yesmaximal, characteristic, complemented
3#14558390C212yesmaximal, complemented
4#14558388C212yesmaximal, complemented
5#14558064C211yesmaximal, characteristic
6C2×#10596957—21no—
7#11924603—21no—
8C22⋊#64438—21no—
9#11924591C2212yes—
10#11924591C2212yes—
11C4×#64438—21no—
12#11924529—21no—
13#11924527C2211yescharacteristic
14#11924523C2211yescharacteristic
15#11924517—21no—
16#11924515C411yescharacteristic
17#11924501C411yescharacteristic
18D4×Dic37—21no—
19D4×Dic37C411yescharacteristic
20#11924492—21no—
21C2×C4×Dic37C2211yescharacteristic
22#121×C37C411yescharacteristic
23C2×D4×C37—21no—
24C2×D4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C22×Dic37—21no—
27C22×Dic37D411yescharacteristic
28C22×Dic37D411yescharacteristic
29C2×Dic74C2×C411yescharacteristic
30#10596957—24no—
31C2×#64438—22no—
32C2×#64438—22no—
33C4⋊C4×C37C2×C411yescharacteristic
34C22⋊C4×C37—21no—
35C22⋊Dic37—21no—
36C22⋊Dic37—21no—
37C22⋊Dic37—21no—
38C22⋊Dic37—21no—
39C4⋊Dic37—21no—
40C4⋊Dic37C2×C411yescharacteristic
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44C4×Dic37—21no—
45C4×Dic37C2×C411yescharacteristic
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37C2311yescharacteristic
49C23×C37—21no—
50C23×C37C22⋊C411yescharacteristic
51D4×C37—41no—
52D4×C37—42no—
53C2×C4×C37—21no—
54C2×C4×C37—41no—
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22×C411yescharacteristic
57C2×Dic37—22no—
58C2×Dic37—21no—
59C2×Dic37—21no—
60C2×Dic37—41no—
61C2×Dic37—42no—
62C2×Dic37C22⋊C411yescharacteristic
63C2×Dic37C22⋊C411yescharacteristic
64C2×Dic37C2×D411yescharacteristic
65C2×Dic37C2×D411yescharacteristic
66Dic74—41no—
67#64438—24no—
68#64438—42no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37—21no—
72C22×C37—41no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37C2×C22⋊C411yescharacteristic
76C4×C37—21no—
77C4×C37—21no—
78C4×C37—41no—
79Dic37—21no—
80Dic37—21no—
81Dic37—21no—
82Dic37—41no—
83Dic37—41no—
84Dic37#10412yes—
85#1529—371nomaximal, Sylow
86C2×C37—41no—
87C2×C37—81no—
88C2×C37#41311yescharacteristic
89C2×C37C2×#10411yescharacteristic
90C2×C37#42111yescharacteristic
91#529—371no—
92#432—371no—
93C4×M16—371no—
94#330—372no—
95#329—372no—
96C37#152911yescharacteristic, complemented, Sylow
97C2×M16—741no—
98#126—741no—
99#125—371no—
100#124—371no—
101#123—741no—
102C22⋊Q8—371no—
103#121#386611yescharacteristic
104C4×Q8—371no—
105C4×D4—371no—
106C4×D4—741no—
107#117—741no—
108C2×C42—371no—
109C4⋊C8—741no—
110C22⋊C8—741no—
111#97—372no—
112#97—372no—
113C4×C8—741no—
114C2×Q8—371no—
115C2×D4—21no—
116C2×D4C2×#386611yescharacteristic
117C22×C4—371no—
118C22×C4—371no—
119C22×C4—741no—
120C22×C4C2×#386611yescharacteristic
121M16—744no—
122C2×C8—742no—
123C2×C8—742no—
124C4⋊C4—371no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4C2×#386611yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—741no—
132C22⋊C4—741no—
133C22⋊C4—741no—
134C22⋊C4—741no—
135C42—371no—
136C42—371no—
137C42—371no—
138C42—371no—
139C42—741no—
140C23—21no—
141C23C22⋊#386611yescharacteristic
142Q8—1481no—
143D4—41no—
144D4—42no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—371no—
148C2×C4—371no—
149C2×C4—371no—
150C2×C4—371no—
151C2×C4—742no—
152C2×C4—741no—
153C2×C4—741no—
154C2×C4—1482no—
155C2×C4—1481no—
156C2×C4C22⋊#386611yescharacteristic
157C2×C4C22×#386611yescharacteristic
158C8—744no—
159C8—1482no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22C2×C22⋊#386611yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—372no—
171C4—741no—
172C4—741no—
173C4—741no—
174C4—1481no—
175C4—1481no—
176C2—41no—
177C2—81no—
178C2#1455852011yescharacteristic
179C2D37⋊#10411yescharacteristic
180C2#1455853111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting, prime radical#121×C37C4
socleC22×C37C2×C22⋊C4
cosocleC4×Dic37C23
hypercenter#121#3866
hypocenterC37#1529
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #14558553C2semidirect
2. C4×#10596957C2semidirect
3. #14558390C2semidirect
4. #14558388C2semidirect
96. C37#1529semidirect

Maximal subgroups

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

subgroupindex
#145585532
C4×#105969572
#145583902
#145583882
#145580642
#152937