Finite Group Databasebeta

← #18006066

Subgroups — #18006066

Order 4736.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#14558150C212yesmaximal, complemented
2#14557821C212yesmaximal, complemented
3#14557817C212yesmaximal, complemented
4#14557791C211yesmaximal, characteristic, complemented
5#14557760C212yesmaximal, complemented
6#14557754C212yesmaximal, complemented
7#14557746C212yesmaximal, complemented
8#14557561C211yesmaximal, characteristic, complemented
9C37×#469C211yesmaximal, characteristic
10C2×Dic148C2211yescharacteristic
11C2×#10596940C2212yes—
12C22×#64436C2211yescharacteristic
13#11924535C2212yes—
14#11924529—22no—
15#11924523—22no—
16#11924523C2212yes—
17#11924517—22no—
18#11924515C2212yes—
19#11924513—22no—
20#11924501C2212yes—
21D4×Dic37C2212yes—
22#11924495C2211yescharacteristic
23#11924468C2211yescharacteristic
24#11924467C2212yes—
25#11924465C2212yes—
26#11924465C2212yes—
27#11924461C2212yes—
28#11924459C2212yes—
29#11924457C2212yes—
30C2×D8×C37C2211yescharacteristic
31C2×M16×C37C2211yescharacteristic
32#121×C37C2212yes—
33#106×C37C2211yescharacteristic
34#102×C37C2212yes—
35C2×D4×C37—22no—
36C2×D4×C37C2312yes—
37C22×C4×C37C2311yescharacteristic
38C22×Dic37—22no—
39C2×Dic74—22no—
40C2×Dic74C2312yes—
41D8×C37—41no—
42M16×C37—41no—
43C2×C8×C37C2311yescharacteristic
44C2×C8×C37C2311yescharacteristic
45C4⋊C4×C37C2312yes—
46C22⋊C4×C37—22no—
47C22⋊Dic37—22no—
48C22⋊Dic37—22no—
49C22⋊Dic37—22no—
50C22⋊Dic37—22no—
51C22⋊Dic37D411yescharacteristic
52C22⋊Dic37D411yescharacteristic
53#10596940—42no—
54C4⋊Dic37D412yes—
55C4⋊Dic37C2312yes—
56#10596936—22no—
57#10596936—22no—
58#10596936—22no—
59C4×Dic37—22no—
60C4×Dic37C2312yes—
61C2×#64436—41no—
62C2×#64436C2312yes—
63Dic148—41no—
64C23×C37—22no—
65C23×C37C2×D411yescharacteristic
66D4×C37—22no—
67D4×C37—22no—
68D4×C37—82no—
69C2×C4×C37—21no—
70C2×C4×C37—21no—
71C2×C4×C37—22no—
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2411yescharacteristic
74C2×Dic37—22no—
75C2×Dic37—22no—
76C2×Dic37—82no—
77C2×Dic37C2×D412yes—
78C2×Dic37C2×D412yes—
79Dic74—22no—
80Dic74—22no—
81Dic74—82no—
82C8×C37—21no—
83C8×C37—21no—
84#64436—22no—
85C22×C37—21no—
86C22×C37—22no—
87C22×C37—42no—
88C22×C37—42no—
89C22×C37—42no—
90C22×C37C22×D411yescharacteristic
91C4×C37—21no—
92C4×C37—42no—
93C4×C37H(5,𝔽2)11yescharacteristic
94C4×C372−1+411yescharacteristic
95Dic37—22no—
96Dic37—22no—
97Dic37—42no—
98Dic37—42no—
99#3263—371nomaximal, Sylow
100C2×C37—41no—
101C2×C37—82no—
102C2×C37#53711yescharacteristic
103C2×C37#57712yes—
104#542—372no—
105#476—372no—
106#475—372no—
107#470—371no—
108#469D3711yescharacteristic
109#465—372no—
110#464—372no—
111#463—372no—
112#424—371no—
113C37#326311yescharacteristic, complemented, Sylow
114C2×Q16—371no—
115C2×SD16—372no—
116C2×D8C2×D3711yescharacteristic
117C2×M16C2×D3711yescharacteristic
118C22×C8—371no—
119C4⋊Q8—372no—
120#126—742no—
121#124—372no—
122#124—742no—
123#123—742no—
124C22⋊Q8—372no—
125C22⋊Q8—742no—
126#121C2×D3712yes—
127C4×Q8—372no—
128C4×D4—372no—
129#117—371no—
130#106—371no—
131#106—372no—
132#106C2×D3711yescharacteristic
133C4⋊C8—372no—
134C4⋊C8—372no—
135#103—372no—
136#103—372no—
137#102—372no—
138#102C2×D3712yes—
139C2×Q8—372no—
140C2×Q8—742no—
141C2×D4—22no—
142C2×D4C22×D3712yes—
143C22×C4—742no—
144C22×C4C22×D3711yescharacteristic
145Q16—1481no—
146SD16—1482no—
147D8—41no—
148M16—41no—
149C2×C8—372no—
150C2×C8—1481no—
151C2×C8C22×D3711yescharacteristic
152C2×C8C22×D3711yescharacteristic
153C4⋊C4—372no—
154C4⋊C4—372no—
155C4⋊C4—742no—
156C4⋊C4—742no—
157C4⋊C4—742no—
158C4⋊C4C22×D3712yes—
159C22⋊C4—22no—
160C22⋊C4—371no—
161C22⋊C4—371no—
162C22⋊C4—742no—
163C22⋊C4—742no—
164C22⋊C4—742no—
165C22⋊C4—742no—
166C42—372no—
167C42—742no—
168C23—22no—
169C23D4×D3711yescharacteristic
170Q8—2962no—
171Q8—742no—
172Q8—742no—
173D4—22no—
174D4—22no—
175D4—82no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—372no—
180C2×C4—372no—
181C2×C4—2962no—
182C2×C4—742no—
183C2×C4—742no—
184C2×C4D4×D3711yescharacteristic
185C2×C4C23×D3711yescharacteristic
186C8—21no—
187C8—21no—
188C8—742no—
189C22—22no—
190C22—21no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D3711yescharacteristic
195C4—21no—
196C4—42no—
197C4—742no—
198C4—742no—
199C4—1482no—
200C4—1482no—
201C4#1192458111yescharacteristic
202C4#1192458311yescharacteristic
203C2—41no—
204C2—82no—
205C2#1455811011yescharacteristic
206C2#1455834312yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC37×#469C2
socleC22×C37C22×D4
hypercenter#469D37
hypocenterC37#3263
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14558150C2semidirect
2. #14557821C2semidirect
3. #14557817C2semidirect
4. #14557791C2semidirect
5. #14557760C2semidirect
6. #14557754C2semidirect
7. #14557746C2semidirect
8. #14557561C2semidirect
113. C37#3263semidirect

Maximal subgroups

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

subgroupindex
#145581502
#145578212
#145578172
#145577912
#145577602
#145577542
#145577462
#145575612
C37×#4692
#326337