Finite Group Databasebeta

← #18006051

Subgroups — #18006051

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#14557827C212yesmaximal, complemented
3#14557811C212yesmaximal, complemented
4#14557777C212yesmaximal, complemented
5#14557774C211yesmaximal, characteristic, complemented
6#14557754C212yesmaximal, complemented
7#14557746C212yesmaximal, complemented
8#14557559C211yesmaximal, characteristic, complemented
9C37×#466C211yesmaximal, characteristic
10C2×Dic148C2211yescharacteristic
11C2×#10596940C2212yes—
12C2×#10596934C2211yescharacteristic
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#11924470C2211yescharacteristic
24#11924469C2212yes—
25#11924465C2212yes—
26#11924465C2212yes—
27#11924461C2212yes—
28#11924459C2212yes—
29#11924457C2212yes—
30C2×D8×C37C2211yescharacteristic
31C22×C8×C37C2211yescharacteristic
32#121×C37C2212yes—
33#107×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—
42C2×C8×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⋊Dic37D412yes—
52#10596940—42no—
53C4⋊Dic37D411yescharacteristic
54C4⋊Dic37D411yescharacteristic
55C4⋊Dic37C2312yes—
56#10596936—22no—
57#10596936—22no—
58#10596936—22no—
59C4×Dic37—22no—
60C4×Dic37C2312yes—
61#10596934—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—21no—
87C22×C37—21no—
88C22×C37—42no—
89C22×C37—42no—
90C22×C37—42no—
91C22×C37C22×D411yescharacteristic
92C4×C37—21no—
93C4×C37—42no—
94C4×C37H(5,𝔽2)11yescharacteristic
95C4×C372−1+411yescharacteristic
96Dic37—22no—
97Dic37—22no—
98Dic37—42no—
99Dic37—42no—
100#3262—371nomaximal, Sylow
101C2×C37—41no—
102C2×C37—82no—
103C2×C37#53711yescharacteristic
104C2×C37#57611yescharacteristic
105C2×C37#57811yescharacteristic
106#542—372no—
107#477—372no—
108#474—372no—
109#468—372no—
110#467—371no—
111#466D3711yescharacteristic
112#464—372no—
113#463—372no—
114#424—371no—
115C37#326211yescharacteristic, complemented, Sylow
116C2×Q16—371no—
117C2×SD16—372no—
118C2×D8C2×D3711yescharacteristic
119C2×M16—371no—
120C22×C8C2×D3711yescharacteristic
121C4⋊Q8—372no—
122#126—742no—
123#124—372no—
124#124—742no—
125#123—742no—
126C22⋊Q8—372no—
127C22⋊Q8—742no—
128#121C2×D3712yes—
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#103—372no—
139#102—372no—
140#102C2×D3712yes—
141C2×Q8—372no—
142C2×Q8—742no—
143C2×D4—22no—
144C2×D4C22×D3712yes—
145C22×C4—742no—
146C22×C4C22×D3711yescharacteristic
147Q16—1481no—
148SD16—1482no—
149D8—41no—
150M16—1481no—
151C2×C8—41no—
152C2×C8—372no—
153C2×C8C22×D3711yescharacteristic
154C2×C8C22×D3711yescharacteristic
155C4⋊C4—371no—
156C4⋊C4—371no—
157C4⋊C4—372no—
158C4⋊C4—742no—
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—22no—
171C23D4×D3711yescharacteristic
172Q8—2962no—
173Q8—742no—
174Q8—742no—
175D4—22no—
176D4—22no—
177D4—82no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—372no—
182C2×C4—372no—
183C2×C4—2962no—
184C2×C4—742no—
185C2×C4—742no—
186C2×C4D4×D3711yescharacteristic
187C2×C4C23×D3711yescharacteristic
188C8—21no—
189C8—21no—
190C8—742no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C2×D4×D3711yescharacteristic
198C4—21no—
199C4—42no—
200C4—742no—
201C4—742no—
202C4—1482no—
203C4—1482no—
204C4#1192458111yescharacteristic
205C4#1192458311yescharacteristic
206C2—41no—
207C2—82no—
208C2#1455811011yescharacteristic
209C2#1455833411yescharacteristic
210C2#1455834711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC37×#466C2
socleC22×C37C22×D4
hypercenter#466D37
hypocenterC37#3262
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #14558150C2semidirect
2. #14557827C2semidirect
3. #14557811C2semidirect
4. #14557777C2semidirect
5. #14557774C2semidirect
6. #14557754C2semidirect
7. #14557746C2semidirect
8. #14557559C2semidirect
115. C37#3262semidirect

Maximal subgroups

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

subgroupindex
#145581502
#145578272
#145578112
#145577772
#145577742
#145577542
#145577462
#145575592
C37×#4662
#326237