Finite Group Databasebeta

← #18010568

Subgroups — #18010568

Order 4736.

260 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 66 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#14558611C211yesmaximal, characteristic
2#14558539C212yesmaximal, complemented
3#14558506C211yesmaximal, characteristic
4#14558414C212yesmaximal, complemented
5#14557505C211yesmaximal, characteristic
6#11924623—22no—
7#11924623—22no—
8D37⋊M16—21no—
9C2×#10596957—21no—
10C2×#10596957C2211yescharacteristic
11C2×#10596957C2212yes—
12C22×#64438C2211yescharacteristic
13#11924603—22no—
14C4⋊#64438—22no—
15#11924593—21no—
16C22⋊#64438—21no—
17C2×#10596964C2211yescharacteristic
18#11924492C2212yes—
19#11924451C411yescharacteristic
20#11924450C412yes—
21#99×C37C411yescharacteristic
22C2×D4×C37C2×C411yescharacteristic
23C2×C22⋊D37C2×C411yescharacteristic
24C2×C22⋊D37Q811yescharacteristic
25C22×Dic37D411yescharacteristic
26C22×Dic37C2311yescharacteristic
27#10596964—22no—
28#10596964—22no—
29C2×C4×D37D411yescharacteristic
30C2×Dic74Q811yescharacteristic
31#10596957—22no—
32#10596957—22no—
33#10596957—22no—
34#10596957—22no—
35C2×#64438—21no—
36C2×#64438—21no—
37C2×#64438—21no—
38C2×#64438—21no—
39C2×#64438—22no—
40C2×#64438D412yes—
41C2×#64438D412yes—
42#10596953—21no—
43#10596953—21no—
44D37⋊C8—22no—
45C22⋊C4×C37C2×C412yes—
46C22⋊Dic37C2×C412yes—
47#10596936—22no—
48C4×Dic37—22no—
49C23×C37C4⋊C411yescharacteristic
50C23×C37C22×C411yescharacteristic
51C22×D37C4⋊C411yescharacteristic
52D4×C37—22no—
53C2×C4×C37—22no—
54C2×C4×C37C4⋊C411yescharacteristic
55C22⋊D37—22no—
56C22⋊D37—22no—
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37—22no—
60C2×Dic37C4⋊C411yescharacteristic
61C2×Dic37C2×D412yes—
62C2×Dic37C2×D411yescharacteristic
63C2×Dic37C2×Q811yescharacteristic
64C2×Dic37#4112yes—
65C4×D37—21no—
66C4×D37—21no—
67Dic74—22no—
68#64438—22no—
69#64438—22no—
70#64438—41no—
71#64438—41no—
72C22×C37—21no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37C2×C4⋊C411yescharacteristic
76C22×C37C4×D412yes—
77C2×D37—21no—
78C2×D37—41no—
79C4×C37—21no—
80C4×C37—42no—
81Dic37—21no—
82Dic37—42no—
83Dic37#12011yescharacteristic
84Dic37C22⋊Q812yes—
85Dic37#12311yescharacteristic
86#1868—371nomaximal, Sylow
87C2×C37—22no—
88C2×C37—21no—
89C2×C37—41no—
90C2×C37#38511yescharacteristic
91D37—41no—
92#568—371no—
93#424—372no—
94#410—371no—
95#408—371no—
96#344—372no—
97C37#186811yescharacteristic, complemented, Sylow
98C2×#41—371no—
99#131—742no—
100#131—742no—
101C2×M16—372no—
102C2×M16—371no—
103C2×M16—741no—
104C2×M16—741no—
105C22×C8—371no—
106#117—372no—
107C4⋊C8—742no—
108C4⋊C8—742no—
109#99—371no—
110#99—372no—
111#99#386611yescharacteristic
112C22⋊C8—741no—
113C22⋊C8—741no—
114#41—742no—
115#41—742no—
116C2×Q8—371no—
117C2×D4—371no—
118C2×D4—371no—
119C2×D4C2×#386611yescharacteristic
120C22×C4—371no—
121C22×C4—371no—
122C22×C4—371no—
123M16—742no—
124M16—742no—
125M16—741no—
126M16—741no—
127M16—742no—
128M16—742no—
129C2×C8—372no—
130C2×C8—372no—
131C2×C8—742no—
132C2×C8—741no—
133C2×C8—741no—
134C2×C8—741no—
135C2×C8—741no—
136C2×C8—742no—
137C4⋊C4—742no—
138C22⋊C4—372no—
139C22⋊C4C2×#386612yes—
140C42—742no—
141C23—371no—
142C23C4⋊#386611yescharacteristic
143C23C22×#386611yescharacteristic
144Q8—742no—
145D4—22no—
146D4—742no—
147D4—742no—
148C2×C4—22no—
149C2×C4—371no—
150C2×C4—371no—
151C2×C4—372no—
152C2×C4—372no—
153C2×C4—371no—
154C2×C4—741no—
155C2×C4—741no—
156C2×C4—741no—
157C2×C4—741no—
158C2×C4—742no—
159C2×C4C4⋊#386611yescharacteristic
160C8—742no—
161C8—742no—
162C8—1481no—
163C8—1481no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—741no—
168C22—1481no—
169C22C2×C4⋊#386611yescharacteristic
170C22D4×#386612yes—
171C4—21no—
172C4—42no—
173C4—371no—
174C4—371no—
175C4—372no—
176C4—741no—
177C4—1482no—
178C2—22no—
179C2—21no—
180C2—41no—
181C2—1481no—
182C2#1455848011yescharacteristic
subgroupG/H
centerC2#14558480
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#99×C37C4
socleC2×C37#385
prime radicalC2×#10596964C22
cosocleC22×Dic37C23
hypercenter#99#3866
hypocenterC37#1868
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #14558539C2semidirect
4. #14558414C2semidirect
97. C37#1868semidirect

Maximal subgroups

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

subgroupindex
#145586112
#145585392
#145585062
#145584142
#145575052
#186837