Finite Group Databasebeta

← #18006058

Subgroups — #18006058

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#14558156C212yesmaximal, complemented
2#14557826C212yesmaximal, complemented
3#14557812C212yesmaximal, complemented
4#14557781C212yesmaximal, complemented
5#14557769C211yesmaximal, characteristic
6#14557757C212yesmaximal, complemented
7#14557751C212yesmaximal, complemented
8#14557559C211yesmaximal, characteristic, complemented
9C37×#467C211yesmaximal, characteristic, complemented
10C2×#10596941C2212yes—
11C2×D296C2211yescharacteristic
12C2×#10596934C2211yescharacteristic
13#11924535C2212yes—
14#11924531—22no—
15#11924525C2212yes—
16#11924522—22no—
17#11924518—22no—
18#11924516—22no—
19#11924510C2212yes—
20Q8×Dic37C2212yes—
21#11924498C2212yes—
22#11924495C2211yescharacteristic
23#11924470C2211yescharacteristic
24#11924469C2212yes—
25#11924465C2212yes—
26#11924465C2212yes—
27#11924460C2212yes—
28#11924458C2212yes—
29#11924456C2212yes—
30C2×Q16×C37C2211yescharacteristic
31C22×C8×C37C2211yescharacteristic
32C22⋊Q8×C37C2212yes—
33#107×C37C2211yescharacteristic
34#103×C37C2212yes—
35C2×Q8×C37C2312yes—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—22no—
38C2×D148C2312yes—
39C2×C4×D37—22no—
40C2×Dic74—22no—
41Q16×C37—41no—
42C2×C8×C37—41no—
43C2×C8×C37C2311yescharacteristic
44C2×C8×C37C2311yescharacteristic
45C4⋊C4×C37—22no—
46C4⋊C4×C37C2312yes—
47C22⋊C4×C37—22no—
48C22⋊Dic37D412yes—
49#10596941—42no—
50#10596938—22no—
51#10596938—22no—
52#10596938—22no—
53#10596938—22no—
54C4⋊Dic37—22no—
55C4⋊Dic37D411yescharacteristic
56C4⋊Dic37D411yescharacteristic
57C4⋊Dic37C2312yes—
58#10596936—22no—
59C4×Dic37—22no—
60C4×Dic37C2312yes—
61#10596934—41no—
62C2×#64436C2312yes—
63D296—41no—
64C23×C37C2×D411yescharacteristic
65C22×D37—22no—
66Q8×C37—22no—
67Q8×C37—22no—
68C2×C4×C37—21no—
69C2×C4×C37—21no—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2411yescharacteristic
74C22⋊D37—82no—
75C2×Dic37—22no—
76C2×Dic37C2×D412yes—
77C2×Dic37C2×D412yes—
78D148—22no—
79D148—22no—
80C4×D37—82no—
81Dic74—82no—
82C8×C37—21no—
83C8×C37—21no—
84#64436—22no—
85C22×C37—21no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37C22×D411yescharacteristic
89C2×D37—42no—
90C2×D37—42no—
91C2×D37—42no—
92C4×C37—21no—
93C4×C37—42no—
94C4×C37—42no—
95C4×C37H(5,𝔽2)11yescharacteristic
96C4×C372−1+411yescharacteristic
97Dic37—22no—
98Dic37—22no—
99Dic37—42no—
100#3262—371nomaximal, Sylow
101C2×C37—41no—
102C2×C37#53711yescharacteristic
103C2×C37#57611yescharacteristic
104C2×C37#57811yescharacteristic
105D37—82no—
106#542—372no—
107#477—372no—
108#474—372no—
109#468—372no—
110#467D3711yescharacteristic, complemented
111#466—371no—
112#464—372no—
113#463—372no—
114#424—371no—
115C37#326211yescharacteristic, complemented, Sylow
116C2×Q16C2×D3711yescharacteristic
117C2×SD16—372no—
118C2×D8—371no—
119C2×M16—371no—
120C22×C8C2×D3711yescharacteristic
121C4⋊Q8—372no—
122#126—742no—
123#124—372no—
124#124—742no—
125#123—742no—
126C22⋊Q8—742no—
127C22⋊Q8C2×D3712yes—
128#121—372no—
129C4×Q8—372no—
130C4×D4—372no—
131#117—371no—
132#107—371no—
133#107—372no—
134#107C2×D3711yescharacteristic
135C4⋊C8—372no—
136C4⋊C8—372no—
137#103—372no—
138#103C2×D3712yes—
139#102—372no—
140#102—372no—
141C2×Q8—742no—
142C2×Q8C22×D3712yes—
143C2×D4—372no—
144C2×D4—742no—
145C22×C4—742no—
146C22×C4C22×D3711yescharacteristic
147Q16—41no—
148SD16—1482no—
149D8—1481no—
150M16—1481no—
151C2×C8—41no—
152C2×C8—372no—
153C2×C8C22×D3711yescharacteristic
154C2×C8C22×D3711yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—371no—
157C4⋊C4—371no—
158C4⋊C4—372no—
159C4⋊C4—742no—
160C4⋊C4—742no—
161C4⋊C4C22×D3712yes—
162C22⋊C4—22no—
163C22⋊C4—372no—
164C22⋊C4—742no—
165C22⋊C4—742no—
166C22⋊C4—742no—
167C22⋊C4—742no—
168C42—372no—
169C42—742no—
170C23—742no—
171C23D4×D3711yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—2962no—
175D4—2962no—
176D4—742no—
177D4—742no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—372no—
183C2×C4—372no—
184C2×C4—2962no—
185C2×C4—742no—
186C2×C4D4×D3711yescharacteristic
187C2×C4C23×D3711yescharacteristic
188C8—21no—
189C8—21no—
190C8—742no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—1482no—
195C22—1482no—
196C22—1482no—
197C22C2×D4×D3711yescharacteristic
198C4—21no—
199C4—42no—
200C4—42no—
201C4—742no—
202C4—742no—
203C4—1482no—
204C4#1192458111yescharacteristic
205C4#1192458311yescharacteristic
206C2—41no—
207C2—2962no—
208C2#1455811011yescharacteristic
209C2#1455833511yescharacteristic
210C2#1455834611yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#467C2
socleC22×C37C22×D4
prime radical#14557769C2
hypercenter#467D37
hypocenterC37#3262
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #14558156C2semidirect
2. #14557826C2semidirect
3. #14557812C2semidirect
4. #14557781C2semidirect
6. #14557757C2semidirect
7. #14557751C2semidirect
8. #14557559C2semidirect
9. C37×#467C2semidirect
110. #467D37semidirect
115. C37#3262semidirect

Maximal subgroups

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

subgroupindex
#145581562
#145578262
#145578122
#145577812
#145577692
#145577572
#145577512
#145575592
C37×#4672
#326237