Finite Group Databasebeta

← #17995760

Subgroups — #17995760

Order 4736.

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

normal subgroups only

This group has 466 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#14558159C211yesmaximal, characteristic, complemented
2#14557389C212yesmaximal
3#14557300C211yesmaximal, characteristic, complemented
4#14557299C212yesmaximal, complemented
5C37×#379C211yesmaximal, characteristic
6#11924515—22no—
7#11924513—24no—
8C2×C22⋊Dic37—24no—
9C2×C22⋊Dic37C2212yes—
10C2×C22⋊Dic37C2212yes—
11C25×C37C2211yescharacteristic
12C2×C22⋊C4×C37—22no—
13C2×C22⋊C4×C37C2211yescharacteristic
14C2×C22⋊C4×C37C2211yescharacteristic
15C24×C37—22no—
16C24×C37—21no—
17C24×C37—21no—
18C24×C37—22no—
19C24×C37—44no—
20C24×C37Q812yescomplemented
21C24×C37C2311yescharacteristic
22C22×C4×C37—21no—
23C22×C4×C37D412yes—
24C22×Dic37—22no—
25C22×Dic37D414yes—
26C2×Dic74—22no—
27C22⋊C4×C37—22no—
28C22⋊C4×C37—22no—
29C22⋊C4×C37—44no—
30C22⋊Dic37—22no—
31C22⋊Dic37—22no—
32C22⋊Dic37—22no—
33C22⋊Dic37—22no—
34C22⋊Dic37—48no—
35C4⋊Dic37—22no—
36#10596936—24no—
37C23×C37—28no—
38C23×C37—24no—
39C23×C37—24no—
40C23×C37—22no—
41C23×C37—44no—
42C23×C37—42no—
43C23×C37—44no—
44C23×C37—42no—
45C23×C37—44no—
46C23×C37—48no—
47C23×C37—41no—
48C23×C37—42no—
49C23×C37—41no—
50C23×C37C2×D412yes—
51C23×C37C2×D411yescharacteristic
52C23×C37C2×Q811yescharacteristic
53C23×C37#4111yescharacteristic
54C23×C37#4112yes—
55C2×C4×C37—22no—
56C2×C4×C37—42no—
57C2×C4×C37—42no—
58C2×C4×C37—41no—
59C2×Dic37—24no—
60C2×Dic37—44no—
61C2×Dic37—44no—
62C2×Dic37—42no—
63Dic74—82no—
64C22×C37—24no—
65C22×C37—22no—
66C22×C37—28no—
67C22×C37—24no—
68C22×C37—41no—
69C22×C37—41no—
70C22×C37—42no—
71C22×C37—48no—
72C22×C37—44no—
73C22×C37—44no—
74C22×C37—42no—
75C22×C37—42no—
76C22×C37—44no—
77C22×C37#12011yescharacteristic
78C22×C37C22⋊Q812yes—
79C22×C37C22⋊Q811yescharacteristic
80C22×C37#12412yes—
81C22×C37#12411yescharacteristic
82C4×C37—42no—
83C4×C37—81no—
84Dic37—44no—
85Dic37—82no—
86#2029—371nomaximal, Sylow
87C2×C37—22no—
88C2×C37—21no—
89C2×C37—22no—
90C2×C37—21no—
91C2×C37—44no—
92C2×C37#39311yescharacteristic
93C2×C37B(4,𝔽2)12yes—
94#543—371no—
95#379—372no—
96#379D3711yescharacteristic
97#342—372no—
98#342—371no—
99C37#202911yescharacteristic, complemented, Sylow
100C25C2×D3711yescharacteristic
101C22⋊Q8—744no—
102C22⋊Q8—742no—
103C2×C22⋊C4—22no—
104C2×C22⋊C4—372no—
105C2×C22⋊C4—372no—
106C2×C22⋊C4—744no—
107C2×C22⋊C4C2×D3711yescharacteristic
108C2×C22⋊C4C2×D3711yescharacteristic
109C24—22no—
110C24—21no—
111C24—21no—
112C24—22no—
113C24—44no—
114C24Dic7412yescomplemented
115C24C22×D3711yescharacteristic
116C2×Q8—742no—
117C22×C4—21no—
118C22×C4—374no—
119C22×C4—742no—
120C22×C4C22⋊D3712yes—
121C4⋊C4—744no—
122C4⋊C4—742no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—44no—
126C22⋊C4—742no—
127C22⋊C4—742no—
128C22⋊C4—742no—
129C22⋊C4—742no—
130C22⋊C4—1488no—
131C23—24no—
132C23—28no—
133C23—24no—
134C23—22no—
135C23—44no—
136C23—42no—
137C23—42no—
138C23—44no—
139C23—44no—
140C23—48no—
141C23—41no—
142C23—42no—
143C23—41no—
144C23C2×Dic7411yescharacteristic
145C23#1059696211yescharacteristic
146C23D4×D3712yes—
147C23#1059696412yes—
148C23C2×C22⋊D3711yescharacteristic
149Q8—2962no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—744no—
155C2×C4—1484no—
156C2×C4—1482no—
157C2×C4—1484no—
158C22—22no—
159C22—24no—
160C22—28no—
161C22—24no—
162C22—41no—
163C22—41no—
164C22—42no—
165C22—44no—
166C22—48no—
167C22—44no—
168C22—42no—
169C22—42no—
170C22—44no—
171C22#1192450411yescharacteristic
172C22#1192451312yes—
173C22#1192451511yescharacteristic
174C22#1192452212yes—
175C22#1192452311yescharacteristic
176C4—42no—
177C4—81no—
178C4—2962no—
179C4—1484no—
180C2—21no—
181C2—22no—
182C2—22no—
183C2—21no—
184C2—44no—
185C2#1455744511yescharacteristic
186C2#1455771912yes—
subgroupG/H
centerC22#11924504
commutator, cosocleC24×C37C23
FrattiniC24C22×D37
FittingC37×#379C2
socleC22×C37#120
prime radicalC25×C37C22
hypercenter#379D37
hypocenterC37#2029
LCSG ▷ C24×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #14558159C2semidirect
3. #14557300C2semidirect
4. #14557299C2semidirect
20. C24×C37Q8semidirect
99. C37#2029semidirect
114. C24Dic74semidirect

Maximal subgroups

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

subgroupindex
#145581592
#145573892
#145573002
#145572992
C37×#3792
#202937