Finite Group Databasebeta

← #17995014

Subgroups — #17995014

Order 4736.

342 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 89 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#14558040C211yesmaximal, characteristic
2#14557517C211yesmaximal, characteristic, complemented
3#14557496C212yesmaximal, complemented
4#14557304C212yesmaximal, complemented
5C37×#568C211yesmaximal, characteristic, complemented
6C22×C4×D37C2211yescharacteristic
7C2×#10596934C2212yes—
8#11924517C412yes—
9#11924512—21no—
10#11924507—21no—
11#11924504C412yes—
12C4×C22⋊D37—22no—
13#11924495C2211yescharacteristic
14#11924455—21no—
15#11924453—21no—
16#11924448—24no—
17C2×#41×C37C2211yescharacteristic
18#131×C37—24no—
19C2×M16×C37—22no—
20C2×M16×C37C2212yes—
21C23×D37C2×C411yescharacteristic
22#41×C37—22no—
23#41×C37—22no—
24C2×Q8×C37D411yescharacteristic
25C2×D4×C37C2×C412yes—
26C2×D4×C37D411yescharacteristic
27C22×C4×C37D412yes—
28C22×C4×C37C2311yescharacteristic
29C2×C22⋊D37—22no—
30C22×Dic37C2×C411yescharacteristic
31C2×C4×D37—21no—
32C2×C4×D37—21no—
33C2×C4×D37—22no—
34C2×C4×D37—22no—
35M16×C37—24no—
36M16×C37—22no—
37M16×C37—22no—
38C2×C8×C37—24no—
39C2×C8×C37D414yescomplemented
40C22⋊Dic37—22no—
41C22⋊Dic37C2×C412yes—
42#10596938—22no—
43C4⋊Dic37—21no—
44#10596936—22no—
45C4×Dic37—21no—
46#10596934—22no—
47#10596934—22no—
48C2×#64436—22no—
49C23×C37C22⋊C412yes—
50C23×C37C22×C411yescharacteristic
51C22×D37—21no—
52C22×D37—22no—
53C22×D37—42no—
54Q8×C37—22no—
55D4×C37—24no—
56D4×C37—22no—
57C2×C4×C37—22no—
58C2×C4×C37—22no—
59C2×C4×C37C22⋊C412yes—
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D412yes—
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37#4112yes—
64C22⋊D37—44no—
65C2×Dic37—22no—
66C2×Dic37—21no—
67C2×Dic37—22no—
68C4×D37—41no—
69C4×D37—42no—
70C4×D37—41no—
71C8×C37—24no—
72#64436—42no—
73C22×C37—22no—
74C22×C37—41no—
75C22×C37—42no—
76C22×C37C2×C22⋊C411yescharacteristic
77C22×C37C4×D412yes—
78C2×D37—22no—
79C2×D37—24no—
80C2×D37—41no—
81C2×D37—42no—
82C2×D37—41no—
83C4×C37—22no—
84C4×C37#12011yescharacteristic
85C4×C37#12112yes—
86C4×C37#12311yescharacteristic
87Dic37—42no—
88Dic37—41no—
89#1891—371nomaximal, Sylow
90C2×C37—21no—
91C2×C37—22no—
92C2×C37—42no—
93C2×C37#38611yescharacteristic
94D37—42no—
95#568D3711yescharacteristic, complemented
96#525—371no—
97#413—371no—
98#407—372no—
99#344—372no—
100C37#189111yescharacteristic, complemented, Sylow
101C2×#41C2×D3711yescharacteristic
102C23×C4—371no—
103#131—24no—
104C2×M16—22no—
105C2×M16—372no—
106C2×M16C2×D3712yes—
107#123—372no—
108C22⋊Q8—741no—
109#121—741no—
110#120—372no—
111C4×D4—742no—
112#117—371no—
113#101—741no—
114#100—741no—
115C22⋊C8—744no—
116C24—371no—
117#41—22no—
118#41—22no—
119C2×Q8D14811yescharacteristic
120C2×D4—742no—
121C2×D4C4×D3712yes—
122C2×D4D14811yescharacteristic
123C22×C4—371no—
124C22×C4—741no—
125C22×C4—742no—
126C22×C4—742no—
127C22×C4—741no—
128C22×C4C22⋊D3712yes—
129C22×C4C22×D3711yescharacteristic
130M16—24no—
131M16—22no—
132M16—22no—
133M16—742no—
134M16—742no—
135C2×C8—24no—
136C2×C8—742no—
137C2×C8C22⋊D3714yescomplemented
138C4⋊C4—742no—
139C4⋊C4—741no—
140C22⋊C4—372no—
141C22⋊C4—742no—
142C22⋊C4—742no—
143C42—741no—
144C23—741no—
145C23—742no—
146C23—1482no—
147C23#1059693812yes—
148C23C2×C4×D3711yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—1484no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—742no—
156C2×C4—741no—
157C2×C4—742no—
158C2×C4—1481no—
159C2×C4—1482no—
160C2×C4—1481no—
161C2×C4#1059693812yes—
162C2×C4C2×D14811yescharacteristic
163C2×C4#1059696212yes—
164C2×C4C2×C22⋊D3712yes—
165C2×C4C2×C22⋊D3711yescharacteristic
166C8—24no—
167C8—1482no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—742no—
172C22—744no—
173C22—1481no—
174C22—1482no—
175C22—1481no—
176C22C2×#1059693811yescharacteristic
177C22C4×C22⋊D3712yes—
178C4—22no—
179C4—1482no—
180C4—1481no—
181C4#1192450511yescharacteristic
182C4#1192451012yes—
183C4#1192451911yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—1482no—
188C2#1455741211yescharacteristic
subgroupG/H
centerC4#11924505
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#568C2
socleC2×C37#386
prime radical#14558040C2
cosocleC22×C4×C37C23
hypercenter#568D37
hypocenterC37#1891
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #14557517C2semidirect
3. #14557496C2semidirect
4. #14557304C2semidirect
5. C37×#568C2semidirect
39. C2×C8×C37D4semidirect
95. #568D37semidirect
100. C37#1891semidirect
137. C2×C8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145580402
#145575172
#145574962
#145573042
C37×#5682
#189137