Finite Group Databasebeta

← #17997781

Subgroups — #17997781

Order 4736.

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

normal subgroups only

This group has 408 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×#11924528C211yesmaximal, characteristic
2#14557430C212yesmaximal
3#14557428C212yesmaximal
4#14557420C212yesmaximal
5#14557418C212yesmaximal
6#14557416C212yesmaximal
7#14557414C212yesmaximal
8#14557399C211yesmaximal, characteristic
9C37×#382C211yesmaximal, characteristic
10#11924528C418yescomplemented
11C2×C4⋊Dic37C2211yescharacteristic
12C2×C4⋊Dic37C2211yescharacteristic
13C2×C4⋊Dic37C2211yescharacteristic
14C2×C4⋊Dic37C2211yescharacteristic
15C2×#10596936C2212yes—
16C2×#10596936C2212yes—
17C2×#10596936C2212yes—
18C2×#10596936C2212yes—
19C2×C4×Dic37C2212yes—
20C2×C4×Dic37C2212yes—
21#11924443C2212yes—
22#11924443C2212yes—
23#11924443C2212yes—
24#11924443C2212yes—
25#11924443C2212yes—
26#11924443C2212yes—
27C2×C4⋊C4×C37C2211yescharacteristic
28C2×C4⋊C4×C37C2211yescharacteristic
29C2×C42×C37C2211yescharacteristic
30#95×C37C2212yes—
31#95×C37C2212yes—
32C22×C4×C37C2312yes—
33C22×C4×C37C2312yes—
34C22×C4×C37C2311yescharacteristic
35C22×C4×C37C2311yescharacteristic
36C22×C4×C37C2311yescharacteristic
37C22×Dic37C2312yes—
38C22×Dic37C2312yes—
39C22×Dic37C2312yes—
40C22×Dic37C2312yes—
41C4⋊C4×C37—41no—
42C4⋊C4×C37—41no—
43C42×C37C2×C414yes—
44C4⋊Dic37—41no—
45C4⋊Dic37—41no—
46C4⋊Dic37C2×C414yes—
47C4⋊Dic37C2×C414yes—
48#10596936—42no—
49#10596936—42no—
50#10596936C2×C418yes—
51#10596936C2×C418yes—
52C4×Dic37—42no—
53C4×Dic37—42no—
54C23×C37C2411yescharacteristic
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—22no—
62C2×C4×C37—22no—
63C2×C4×C37—22no—
64C2×C4×C37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—22no—
67C2×C4×C37C22×C412yes—
68C2×C4×C37C22×C412yes—
69C2×C4×C37C22×C412yes—
70C2×Dic37—22no—
71C2×Dic37—22no—
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×Dic37C22×C414yes—
81C2×Dic37C22×C414yes—
82C22×C37C23×C411yescharacteristic
83C22×C37H(5,𝔽2)11yescharacteristic
84C22×C37H(5,𝔽2)11yescharacteristic
85C22×C372−1+411yescharacteristic
86C22×C372−1+411yescharacteristic
87C22×C372−1+411yescharacteristic
88C22×C372−1+411yescharacteristic
89C4×C37—22no—
90C4×C37—22no—
91C4×C37—22no—
92C4×C37—42no—
93C4×C37—42no—
94Dic37—24no—
95Dic37—24no—
96Dic37—42no—
97Dic37—42no—
98#2382—371nomaximal, Sylow
99C2×C37#51911yescharacteristic
100C2×C37#52011yescharacteristic
101C2×C37#52011yescharacteristic
102C2×C37#56211yescharacteristic
103C2×C37#56311yescharacteristic
104C2×C37#56311yescharacteristic
105C2×C37#56411yescharacteristic
106C2×#125—371no—
107#389—372no—
108#389—372no—
109#387—372no—
110#387—372no—
111#387—372no—
112#387—372no—
113#382—371no—
114#382D3711yescharacteristic
115C37#238211yescharacteristic, complemented, Sylow
116#125—378no—
117C2×C4⋊C4—372no—
118C2×C4⋊C4—372no—
119C2×C4⋊C4—371no—
120C2×C4⋊C4—371no—
121C2×C4⋊C4—372no—
122C2×C4⋊C4—372no—
123C2×C4⋊C4—371no—
124C2×C4⋊C4—371no—
125C2×C4⋊C4C2×D3711yescharacteristic
126C2×C4⋊C4C2×D3711yescharacteristic
127C2×C42—372no—
128C2×C42—372no—
129C2×C42C2×D3711yescharacteristic
130#95—372no—
131#95—372no—
132#95—372no—
133#95—372no—
134#95—372no—
135#95—372no—
136#95C2×D3712yes—
137#95C2×D3712yes—
138C22×C4—372no—
139C22×C4—372no—
140C22×C4—372no—
141C22×C4—372no—
142C22×C4C22×D3712yes—
143C22×C4C22×D3712yes—
144C22×C4C22×D3711yescharacteristic
145C22×C4C22×D3711yescharacteristic
146C22×C4C22×D3711yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—378no—
150C4⋊C4—378no—
151C4⋊C4—374no—
152C4⋊C4—374no—
153C4⋊C4—1482no—
154C4⋊C4—1482no—
155C4⋊C4—1481no—
156C4⋊C4—1481no—
157C42—1482no—
158C42—1482no—
159C42C4×D3714yes—
160C23C23×D3711yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—374no—
174C2×C4—374no—
175C2×C4—742no—
176C2×C4—742no—
177C2×C4—742no—
178C2×C4—742no—
179C2×C4—742no—
180C2×C4—742no—
181C2×C4—742no—
182C2×C4—742no—
183C2×C4—742no—
184C2×C4—742no—
185C2×C4C2×C4×D3712yes—
186C2×C4C2×C4×D3712yes—
187C2×C4C2×C4×D3712yes—
188C22C22×C4×D3711yescharacteristic
189C22#1192458111yescharacteristic
190C22#1192458211yescharacteristic
191C22#1192458311yescharacteristic
192C22#1192458311yescharacteristic
193C22#1192458311yescharacteristic
194C22#1192458411yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—744no—
201C4—744no—
202C4—1482no—
203C4—1482no—
204C2#1455801011yescharacteristic
205C2#1455801311yescharacteristic
206C2#1455801411yescharacteristic
207C2#1455827711yescharacteristic
208C2#1455828311yescharacteristic
209C2#1455828711yescharacteristic
210C2C37⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#382C2
socle, prime radical, cosocleC23×C37C24
hypercenter#382D37
hypocenterC37#2382
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
10. #11924528C4semidirect
115. C37#2382semidirect

Maximal subgroups

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

subgroupindex
C2×#119245282
#145574302
#145574282
#145574202
#145574182
#145574162
#145574142
#145573992
C37×#3822
#238237