Finite Group Databasebeta

← #17997775

Subgroups — #17997775

Order 4736.

424 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#11924534C211yesmaximal, characteristic
2#14557440C211yesmaximal, characteristic
3#14557437C212yesmaximal
4#14557420C212yesmaximal
5#14557417C212yesmaximal
6#14557415C212yesmaximal
7#14557414C212yesmaximal
8#14557400C212yesmaximal
9C37×#391C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11#11924534C418yescomplemented
12C2×C4⋊Dic37C2211yescharacteristic
13C2×#10596936C2212yes—
14C2×#10596936C2212yes—
15C2×#10596936C2212yes—
16C2×C4×Dic37C2211yescharacteristic
17C2×C4×Dic37C2212yes—
18C2×C4×Dic37C2211yescharacteristic
19#11924443C2212yes—
20#11924443C2212yes—
21#11924443C2212yes—
22#11924443C2212yes—
23#11924443C2212yes—
24#11924443C2212yes—
25#11924443C2212yes—
26#11924443C2212yes—
27C22×Q8×C37C2211yescharacteristic
28C2×C4⋊C4×C37C2211yescharacteristic
29C2×C42×C37C2211yescharacteristic
30#95×C37C2212yes—
31#95×C37C2212yes—
32C2×Q8×C37—41no—
33C2×Q8×C37—41no—
34C2×Q8×C37C2×C414yes—
35C22×C4×C37C2312yes—
36C22×C4×C37C2312yes—
37C22×C4×C37C2311yescharacteristic
38C22×C4×C37C2311yescharacteristic
39C22×C4×C37C2311yescharacteristic
40C22×Dic37C2312yes—
41C22×Dic37C2312yes—
42C22×Dic37C2312yes—
43C22×Dic37C2312yes—
44C2×Dic74—41no—
45C2×Dic74—41no—
46C2×Dic74C2×C414yes—
47C4⋊C4×C37—41no—
48C42×C37—41no—
49C4⋊Dic37—41no—
50#10596936—42no—
51#10596936C2×C418yes—
52#10596936C2×C418yes—
53C4×Dic37—42no—
54C4×Dic37—41no—
55C4×Dic37C2×C414yes—
56C23×C37C2411yescharacteristic
57Q8×C37—44no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—24no—
67C2×C4×C37—22no—
68C2×C4×C37—22no—
69C2×C4×C37C22×C412yes—
70C2×C4×C37C22×C412yes—
71C2×C4×C37C22×C412yes—
72C2×Dic37—22no—
73C2×Dic37—22no—
74C2×Dic37—22no—
75C2×Dic37—22no—
76C2×Dic37—22no—
77C2×Dic37—22no—
78C2×Dic37—22no—
79C2×Dic37—22no—
80C2×Dic37—24no—
81C2×Dic37C22×C414yes—
82C2×Dic37C22×C414yes—
83Dic74—44no—
84C22×C37C23×C411yescharacteristic
85C22×C37H(5,𝔽2)11yescharacteristic
86C22×C37H(5,𝔽2)11yescharacteristic
87C22×C372−1+412yes—
88C22×C372−1+412yes—
89C4×C37—22no—
90C4×C37—22no—
91C4×C37—22no—
92C4×C37—42no—
93C4×C37—42no—
94Dic37—24no—
95Dic37—24no—
96Dic37—42no—
97Dic37—42no—
98#2381—371nomaximal, Sylow
99C2×C37#51811yescharacteristic
100C2×C37#51912yes—
101C2×C37#56311yescharacteristic
102C2×C37#56311yescharacteristic
103C2×C37#56312yes—
104C2×C4⋊Q8—371no—
105#391—371no—
106#391—372no—
107#391D3711yescharacteristic
108#387—372no—
109#387—372no—
110#387—372no—
111#387—372no—
112#383—372no—
113C37#238111yescharacteristic, complemented, Sylow
114C22×Q8—371no—
115C22×Q8C2×D3711yescharacteristic
116C4⋊Q8—378no—
117C2×C4⋊C4—372no—
118C2×C4⋊C4—372no—
119C2×C4⋊C4—372no—
120C2×C4⋊C4—371no—
121C2×C4⋊C4C2×D3711yescharacteristic
122C2×C42—371no—
123C2×C42—372no—
124C2×C42—371no—
125C2×C42C2×D3711yescharacteristic
126#95—372no—
127#95—372no—
128#95—372no—
129#95—372no—
130#95—372no—
131#95—372no—
132#95—372no—
133#95—372no—
134#95C2×D3712yes—
135#95C2×D3712yes—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—374no—
139C2×Q8—1481no—
140C2×Q8—1481no—
141C2×Q8C4×D3714yes—
142C22×C4—372no—
143C22×C4—372no—
144C22×C4—372no—
145C22×C4—372no—
146C22×C4C22×D3712yes—
147C22×C4C22×D3712yes—
148C22×C4C22×D3711yescharacteristic
149C22×C4C22×D3711yescharacteristic
150C22×C4C22×D3711yescharacteristic
151C4⋊C4—41no—
152C4⋊C4—378no—
153C4⋊C4—378no—
154C4⋊C4—1482no—
155C4⋊C4—1481no—
156C42—41no—
157C42—374no—
158C42—1481no—
159C42—1482no—
160C23C23×D3711yescharacteristic
161Q8—44no—
162Q8—1484no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—374no—
175C2×C4—374no—
176C2×C4—742no—
177C2×C4—742no—
178C2×C4—742no—
179C2×C4—742no—
180C2×C4—742no—
181C2×C4—742no—
182C2×C4—742no—
183C2×C4—744no—
184C2×C4—742no—
185C2×C4C2×C4×D3712yes—
186C2×C4C2×C4×D3712yes—
187C2×C4C2×C4×D3712yes—
188C22C22×C4×D3711yescharacteristic
189C22#1192458111yescharacteristic
190C22#1192458111yescharacteristic
191C22#1192458312yes—
192C22#1192458412yes—
193C4—22no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—42no—
198C4—744no—
199C4—744no—
200C4—1482no—
201C4—1482no—
202C2#1455800611yescharacteristic
203C2#1455800912yes—
204C2#1455828211yescharacteristic
205C2#1455828311yescharacteristic
206C2#1455828412yes—
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#391C2
socle, prime radical, cosocleC23×C37C24
hypercenter#391D37
hypocenterC37#2381
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #11924534C4semidirect
113. C37#2381semidirect

Maximal subgroups

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

subgroupindex
C2×#119245342
#145574402
#145574372
#145574202
#145574172
#145574152
#145574142
#145574002
C37×#3912
#238137