Finite Group Databasebeta

← #17993616

Subgroups — #17993616

Order 4736.

288 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 57 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#14557849C212yesmaximal, complemented
2#14557469C211yesmaximal, characteristic, complemented
3#14557267C212yesmaximal, complemented
4#14557257C211yesmaximal, characteristic, complemented
5C37×#534C211yesmaximal, characteristic
6C2×C4⋊Dic37C2211yescharacteristic, complemented
7C2×#10596936—21no—
8C2×C22⋊Dic37—21no—
9#11924467—22no—
10#11924457—22no—
11C22⋊#64436C2212yescomplemented
12#11924443C2211yescharacteristic, complemented
13C22×D4×C37—21no—
14#123×C37—22no—
15#121×C37—21no—
16#121×C37C2212yes—
17#120×C37—22no—
18C2×C22⋊C4×C37C2211yescharacteristic
19C24×C37—21no—
20C24×C37D411yescharacteristic
21C2×D4×C37—22no—
22C2×D4×C37—22no—
23C2×D4×C37—21no—
24C2×D4×C37—42no—
25C2×D4×C37—42no—
26C2×D4×C37D412yes—
27C22×C4×C37—21no—
28C22×C4×C37D411yescharacteristic
29C22×C4×C37C2311yescharacteristic
30C22×Dic37—21no—
31C22×Dic37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37D412yes—
34C22⋊C4×C37—22no—
35C22⋊C4×C37—22no—
36C22⋊C4×C37—22no—
37C22⋊Dic37—42no—
38C4⋊Dic37—22no—
39#10596936—42no—
40C2×#64436—22no—
41C23×C37—21no—
42C23×C37—21no—
43C23×C37—22no—
44C23×C37—41no—
45C23×C37—41no—
46C23×C37—42no—
47C23×C37—81no—
48C23×C37—81no—
49C23×C37SD1612yes—
50C23×C37C2×D411yescharacteristic
51D4×C37—42no—
52D4×C37—44no—
53D4×C37—42no—
54D4×C37—42no—
55D4×C37—81no—
56C2×C4×C37—21no—
57C2×C4×C37—22no—
58C2×C4×C37—41no—
59C2×C4×C37—42no—
60C2×C4×C37—41no—
61C2×C4×C37C2×D412yes—
62C2×Dic37—22no—
63C2×Dic37—41no—
64C2×Dic37—41no—
65C2×Dic37—41no—
66C2×Dic37—41no—
67C2×Dic37—41no—
68#64436—42no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37—22no—
72C22×C37—42no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37—42no—
76C22×C37—42no—
77C22×C37—42no—
78C22×C37—81no—
79C22×C37—84no—
80C22×C37#12011yescharacteristic
81C22×C37C2×SD1611yescharacteristic
82C22×C37AGL(1,ℤ/8)11yescharacteristic
83C4×C37—22no—
84C4×C37—42no—
85C4×C37—41no—
86Dic37—42no—
87Dic37—81no—
88#1613—371nomaximal, Sylow
89C2×C37—21no—
90C2×C37—21no—
91C2×C37—42no—
92C2×C37—82no—
93C2×C37#45011yescharacteristic
94C2×C37#45311yescharacteristic
95C2×C37#45811yescharacteristic
96#534D3711yescharacteristic
97#481—372no—
98#399—371no—
99#327—372no—
100#323—371no—
101C37#161311yescharacteristic, complemented, Sylow
102C22×D4—21no—
103#123—22no—
104#121—21no—
105#121C2×D3712yes—
106#120—22no—
107C2×C4⋊C4—371no—
108C2×C4⋊C4—741no—
109C2×C22⋊C4—741no—
110C2×C22⋊C4C2×D3711yescharacteristic
111#106—742no—
112#102—742no—
113C22⋊C8—372no—
114#95—371no—
115C24—21no—
116C24C22⋊D3711yescharacteristic
117C2×D4—22no—
118C2×D4—22no—
119C2×D4—21no—
120C2×D4—42no—
121C2×D4—42no—
122C2×D4C22⋊D3712yes—
123C22×C4—21no—
124C22×C4—741no—
125C22×C4—741no—
126C22×C4C22⋊D3711yescharacteristic
127C22×C4C22×D3711yescharacteristic
128C2×C8—742no—
129C4⋊C4—21no—
130C4⋊C4—742no—
131C4⋊C4—1482no—
132C4⋊C4C22⋊D3712yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—1482no—
137C23—21no—
138C23—21no—
139C23—22no—
140C23—41no—
141C23—41no—
142C23—42no—
143C23—81no—
144C23—81no—
145C23#1059694012yes—
146C23C2×C22⋊D3711yescharacteristic
147D4—42no—
148D4—44no—
149D4—42no—
150D4—42no—
151D4—81no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—742no—
158C2×C4—1481no—
159C2×C4—1481no—
160C2×C4—1481no—
161C2×C4—1481no—
162C2×C4—1481no—
163C2×C4C2×C22⋊D3712yes—
164C8—1482no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—42no—
172C22—42no—
173C22—42no—
174C22—81no—
175C22—84no—
176C22#1192450511yescharacteristic
177C22C2×#1059694011yescharacteristic
178C22#1192456211yescharacteristic
179C4—22no—
180C4—41no—
181C4—42no—
182C4—2961no—
183C4—1482no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—82no—
188C2#1455768411yescharacteristic
189C2#1455770111yescharacteristic
190C2#1455772311yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
Fitting, prime radicalC37×#534C2
socleC22×C37#120
hypercenter#534D37
hypocenterC37#1613
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #14557849C2semidirect
2. #14557469C2semidirect
3. #14557267C2semidirect
4. #14557257C2semidirect
6. C2×C4⋊Dic37C22semidirect
11. C22⋊#64436C22semidirect
12. #11924443C22semidirect
101. C37#1613semidirect

Maximal subgroups

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

subgroupindex
#145578492
#145574692
#145572672
#145572572
C37×#5342
#161337