Finite Group Databasebeta

← #17993204

Subgroups — #17993204

Order 4736.

216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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#14558067C211yesmaximal, characteristic
2C4×#10596934C211yesmaximal, characteristic, complemented
3#14557274C212yesmaximal, complemented
4#14557272C212yesmaximal, complemented
5C37×#432C211yesmaximal, characteristic, complemented
6C2×#10596934—21no—
7#11924530—21no—
8#11924528C2211yescharacteristic
9#11924524C2211yescharacteristic
10#11924519—21no—
11#11924515C411yescharacteristic
12#11924510C411yescharacteristic
13C4×Dic74C411yescharacteristic
14C4×D148C411yescharacteristic
15C4×C22⋊D37—21no—
16#11924493—21no—
17#11924447C2212yes—
18C4×#64436—21no—
19C2×C42×C37C2211yescharacteristic
20C4⋊C8×C37—21no—
21C22⋊C8×C37—21no—
22#97×C37C2212yes—
23C22×C4×C37C2×C411yescharacteristic
24C22×C4×C37D411yescharacteristic
25C22×C4×C37D411yescharacteristic
26C2×C22⋊D37—21no—
27C2×D148C2×C411yescharacteristic
28C2×C4×D37—21no—
29C2×Dic74C2×C411yescharacteristic
30C2×C8×C37—22no—
31C42×C37C2×C411yescharacteristic
32C42×C37D411yescharacteristic
33C42×C37D411yescharacteristic
34C42×C37C2311yescharacteristic
35C22⋊Dic37—21no—
36#10596938—21no—
37#10596938—21no—
38#10596938—21no—
39#10596938—21no—
40C4⋊Dic37C2×C411yescharacteristic
41C4⋊Dic37C2×C411yescharacteristic
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46C4×Dic37—21no—
47#10596934—24no—
48C2×#64436—22no—
49C23×C37C22⋊C411yescharacteristic
50C22×D37—21no—
51C2×C4×C37—22no—
52C2×C4×C37—41no—
53C2×C4×C37—41no—
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22×C411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C22⋊D37—42no—
61C2×Dic37—21no—
62C2×Dic37—21no—
63C2×Dic37—21no—
64D148—41no—
65C4×D37—42no—
66Dic74—41no—
67C8×C37—42no—
68#64436—24no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37—21no—
72C22×C37C2×C22⋊C411yescharacteristic
73C2×D37—41no—
74C2×D37—41no—
75C2×D37—41no—
76C4×C37—21no—
77C4×C37—21no—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37#10412yes—
82Dic37—41no—
83Dic37—41no—
84Dic37—41no—
85#1529—371nomaximal, Sylow
86C2×C37—41no—
87C2×C37#41311yescharacteristic
88C2×C37C2×#10411yescharacteristic
89C2×C37#42111yescharacteristic
90D37—81no—
91#529—371no—
92#432D3711yescharacteristic, complemented
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—371no—
104C4×Q8—371no—
105C4×D4—371no—
106C4×D4—741no—
107#117—741no—
108C2×C42C2×D3711yescharacteristic
109C4⋊C8—21no—
110C22⋊C8—21no—
111#97—372no—
112#97C2×D3712yes—
113C4×C8—741no—
114C2×Q8—371no—
115C2×D4—371no—
116C2×D4—741no—
117C22×C4—741no—
118C22×C4C4×D3711yescharacteristic
119C22×C4D14811yescharacteristic
120C22×C4C22⋊D3711yescharacteristic
121M16—744no—
122C2×C8—22no—
123C2×C8—742no—
124C4⋊C4—371no—
125C4⋊C4—371no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C22⋊C4—741no—
131C22⋊C4—741no—
132C22⋊C4—741no—
133C22⋊C4—741no—
134C22⋊C4—741no—
135C42—741no—
136C42C4×D3711yescharacteristic
137C42D14811yescharacteristic
138C42C22⋊D3711yescharacteristic
139C42C22×D3711yescharacteristic
140C23—741no—
141C23#1059693811yescharacteristic
142Q8—1481no—
143D4—1481no—
144D4—1482no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—741no—
149C2×C4—741no—
150C2×C4—741no—
151C2×C4—1482no—
152C2×C4#1059693811yescharacteristic
153C2×C4#1059693811yescharacteristic
154C2×C4#1059693811yescharacteristic
155C2×C4C2×C4×D3711yescharacteristic
156C2×C4C2×D14811yescharacteristic
157C2×C4C2×C22⋊D3711yescharacteristic
158C8—42no—
159C8—744no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—1481no—
164C22—1481no—
165C22—1481no—
166C22C2×#1059693811yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—1481no—
173C4—1481no—
174C4—1481no—
175C4#1192446212yes—
176C2—41no—
177C2—2961no—
178C2#1455751511yescharacteristic
179C2C2×#1192446211yescharacteristic
180C2#1455755111yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#432C2
socleC22×C37C2×C22⋊C4
prime radical#11924510C4
cosocleC42×C37C23
hypercenter#432D37
hypocenterC37#1529
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×#10596934C2semidirect
3. #14557274C2semidirect
4. #14557272C2semidirect
5. C37×#432C2semidirect
92. #432D37semidirect
96. C37#1529semidirect

Maximal subgroups

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

subgroupindex
#145580672
C4×#105969342
#145572742
#145572722
C37×#4322
#152937