Finite Group Databasebeta

← #17993615

Subgroups — #17993615

Order 4736.

288 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 53 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#14558095C211yesmaximal, characteristic
2#14557851C212yesmaximal, complemented
3#14557266C212yesmaximal, complemented
4#14557257C211yesmaximal, characteristic, complemented
5C37×#399C211yesmaximal, characteristic, complemented
6C22×C22⋊D37—21no—
7#11924520—22no—
8#11924510—21no—
9#11924510C2212yes—
10#11924506—22no—
11#11924467—22no—
12#11924456—22no—
13C22⋊#64436C2212yescomplemented
14C2×C4⋊C4×C37—21no—
15C2×C4⋊C4×C37C2211yescharacteristic, complemented
16C2×C22⋊C4×C37—21no—
17C2×C22⋊C4×C37C2211yescharacteristic
18#95×C37C2211yescharacteristic, complemented
19C24×C37D411yescharacteristic
20C23×D37—21no—
21C22×C4×C37—21no—
22C22×C4×C37—21no—
23C22×C4×C37D411yescharacteristic
24C22×C4×C37C2311yescharacteristic
25C2×C22⋊D37—22no—
26C2×C22⋊D37—22no—
27C2×C22⋊D37—42no—
28C2×C22⋊D37—42no—
29C22×Dic37—21no—
30C2×D148—21no—
31C2×D148D412yes—
32C4⋊C4×C37—22no—
33C4⋊C4×C37—42no—
34C22⋊C4×C37—22no—
35C22⋊C4×C37—42no—
36#10596938—22no—
37#10596938—22no—
38C4⋊Dic37—21no—
39C4⋊Dic37D412yes—
40C2×#64436—22no—
41C23×C37—21no—
42C23×C37—21no—
43C23×C37—41no—
44C23×C37—41no—
45C23×C37SD1612yes—
46C23×C37C2×D411yescharacteristic
47C22×D37—22no—
48C22×D37—42no—
49C22×D37—81no—
50C22×D37—81no—
51C2×C4×C37—22no—
52C2×C4×C37—21no—
53C2×C4×C37—41no—
54C2×C4×C37—41no—
55C2×C4×C37—41no—
56C2×C4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37C2×D412yes—
61C22⋊D37—44no—
62C22⋊D37—42no—
63C22⋊D37—42no—
64C2×Dic37—22no—
65C2×Dic37—42no—
66D148—42no—
67D148—81no—
68#64436—42no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37—22no—
72C22×C37—42no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37—81no—
76C22×C37#12011yescharacteristic
77C22×C37C2×SD1611yescharacteristic
78C22×C37AGL(1,ℤ/8)11yescharacteristic
79C2×D37—42no—
80C2×D37—42no—
81C2×D37—42no—
82C2×D37—84no—
83C4×C37—22no—
84C4×C37—42no—
85C4×C37—41no—
86C4×C37—81no—
87Dic37—42no—
88#1613—371nomaximal, Sylow
89C2×C37—21no—
90C2×C37—21no—
91C2×C37—42no—
92C2×C37#45011yescharacteristic
93C2×C37#45311yescharacteristic
94C2×C37#45811yescharacteristic
95D37—82no—
96#534—371no—
97#481—372no—
98#399D3711yescharacteristic, complemented
99#327—372no—
100#323—371no—
101C37#161311yescharacteristic, complemented, Sylow
102C22×D4—741no—
103#123—742no—
104#121—372no—
105#121—741no—
106#120—742no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4C2×D3711yescharacteristic, complemented
109C2×C22⋊C4—21no—
110C2×C22⋊C4C2×D3711yescharacteristic
111#106—742no—
112#102—742no—
113C22⋊C8—372no—
114#95C2×D3711yescharacteristic, complemented
115C24—741no—
116C24C22⋊D3711yescharacteristic
117C2×D4—372no—
118C2×D4—741no—
119C2×D4—742no—
120C2×D4—742no—
121C2×D4—1482no—
122C2×D4—1482no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—741no—
126C22×C4C22⋊D3711yescharacteristic
127C22×C4C22×D3711yescharacteristic
128C2×C8—742no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4—372no—
132C4⋊C4—741no—
133C22⋊C4—22no—
134C22⋊C4—42no—
135C22⋊C4—742no—
136C22⋊C4—742no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—2961no—
142C23—2961no—
143C23—742no—
144C23—1482no—
145C23#1059694112yes—
146C23C2×C22⋊D3711yescharacteristic
147D4—2961no—
148D4—1482no—
149D4—1484no—
150D4—1482no—
151D4—1482no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—742no—
162C2×C4—1482no—
163C2×C4D4×D3712yes—
164C8—1482no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—2964no—
173C22—1482no—
174C22—1482no—
175C22—1482no—
176C22#1192450411yescharacteristic
177C22C2×#1059694111yescharacteristic
178C22#1192456111yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—81no—
183C4—1482no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—2962no—
188C2#1455768311yescharacteristic
189C2#1455770011yescharacteristic
190C2#1455772211yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#399C2
socleC22×C37#120
prime radical#14558095C2
hypercenter#399D37
hypocenterC37#1613
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #14557851C2semidirect
3. #14557266C2semidirect
4. #14557257C2semidirect
5. C37×#399C2semidirect
13. C22⋊#64436C22semidirect
15. C2×C4⋊C4×C37C22semidirect
18. #95×C37C22semidirect
98. #399D37semidirect
101. C37#1613semidirect
108. C2×C4⋊C4C2×D37semidirect
114. #95C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580952
#145578512
#145572662
#145572572
C37×#3992
#161337