Finite Group Databasebeta

← #18004128

Subgroups — #18004128

Order 4736.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#10596942C211yesmaximal, characteristic, complemented
2#14558104C211yesmaximal, characteristic
3#14558011C211yesmaximal, characteristic, complemented
4#14557753C214yesmaximal, complemented
5#14557741C214yesmaximal, complemented
6#14557561C211yesmaximal, characteristic, complemented
7#14557543C211yesmaximal, characteristic, complemented
8#14557529C211yesmaximal, characteristic
9C2×#137×C37C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11C2×#10596942—24no—
12C2×#10596942C2214yes—
13C22×#64436C2211yescharacteristic
14#11924534C2212yes—
15#11924523C2212yes—
16#11924517—22no—
17#11924515—22no—
18Q8×Dic37—22no—
19Q8×Dic37C2214yes—
20#11924495—22no—
21#11924495C2211yescharacteristic
22#11924495C2211yescharacteristic
23#11924465C2214yes—
24#11924461C2214yes—
25#11924460C2212yes—
26#11924457C2212yes—
27C2×#41×C37C2211yescharacteristic
28C22×Q8×C37C2211yescharacteristic
29#137×C37—24no—
30C2×Q16×C37C2212yes—
31C2×SD16×C37C2212yes—
32C2×M16×C37C2211yescharacteristic
33#41×C37—22no—
34#41×C37—22no—
35C2×Q8×C37—21no—
36C2×Q8×C37—22no—
37C2×Q8×C37D414yes—
38C2×Q8×C37C2311yescharacteristic
39C2×Q8×C37C2312yes—
40C2×D4×C37—21no—
41C2×D4×C37C2311yescharacteristic
42C22×C4×C37—21no—
43C22×C4×C37—21no—
44C22×C4×C37C2311yescharacteristic
45C22×Dic37—21no—
46C2×Dic74—22no—
47C2×Dic74—22no—
48C2×Dic74—21no—
49C2×Dic74C2312yes—
50Q16×C37—24no—
51SD16×C37—24no—
52M16×C37—22no—
53C2×C8×C37C2312yes—
54C22⋊Dic37—21no—
55C22⋊Dic37—24no—
56C22⋊Dic37D412yes—
57#10596942—28no—
58C4⋊Dic37—24no—
59C4⋊Dic37D412yes—
60C4⋊Dic37C2312yes—
61#10596936—24no—
62C4×Dic37—21no—
63C4×Dic37—24no—
64C4×Dic37C2312yes—
65C2×#64436—22no—
66C2×#64436C2312yes—
67C23×C37—21no—
68C23×C37C2×D411yescharacteristic
69Q8×C37—24no—
70Q8×C37—22no—
71Q8×C37—21no—
72Q8×C37—21no—
73Q8×C37C2×D414yes—
74D4×C37—21no—
75D4×C37—21no—
76D4×C37—42no—
77C2×C4×C37—24no—
78C2×C4×C37—22no—
79C2×C4×C37—21no—
80C2×C4×C37—42no—
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D412yes—
83C2×C4×C37#4112yes—
84C2×C4×C37C2411yescharacteristic
85C2×Dic37—22no—
86C2×Dic37—22no—
87C2×Dic37—42no—
88C2×Dic37C2×D414yes—
89Dic74—22no—
90Dic74—22no—
91Dic74—42no—
92C8×C37—22no—
93#64436—22no—
94C22×C37—22no—
95C22×C37—41no—
96C22×C37—42no—
97C22×C37#12112yes—
98C22×C37C22×D411yescharacteristic
99C4×C37—24no—
100C4×C37—41no—
101C4×C37#12112yes—
102C4×C37C22×D411yescharacteristic
103C4×C37C2×#4111yescharacteristic
104Dic37—24no—
105Dic37—42no—
106Dic37—42no—
107#3044—371nomaximal, Sylow
108C2×C37—22no—
109C2×C37—81no—
110C2×C37C2×#12111yescharacteristic
111C2×C37#57812yes—
112C2×#137D3711yescharacteristic
113C22×Q16—371no—
114#536—371no—
115#519—371no—
116#464—374no—
117#462—374no—
118#424—371no—
119#419—371no—
120#416—371no—
121C37#304411yescharacteristic, complemented, Sylow
122C2×#41C2×D3711yescharacteristic
123C22×Q8—371no—
124C22×Q8C2×D3711yescharacteristic
125#137—24no—
126C2×Q16—374no—
127C2×Q16—744no—
128C2×Q16C2×D3712yes—
129C2×SD16C2×D3712yes—
130C2×M16C2×D3711yescharacteristic
131C22×C8—371no—
132C4⋊Q8—372no—
133#124—372no—
134#123—742no—
135C22⋊Q8—742no—
136C4×Q8—374no—
137C4×Q8—742no—
138#117—371no—
139#117—371no—
140#117—742no—
141C4⋊C8—374no—
142#103—372no—
143#103—374no—
144#102—372no—
145#41—22no—
146#41—22no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—372no—
150C2×Q8—741no—
151C2×Q8—742no—
152C2×Q8—742no—
153C2×Q8C22⋊D3714yes—
154C2×Q8C22×D3711yescharacteristic
155C2×Q8C22×D3712yes—
156C2×D4—21no—
157C2×D4C22×D3711yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—741no—
161C22×C4C22×D3711yescharacteristic
162Q16—24no—
163Q16—748no—
164SD16—24no—
165M16—22no—
166C2×C8—372no—
167C2×C8—742no—
168C2×C8C22×D3712yes—
169C4⋊C4—372no—
170C4⋊C4—372no—
171C4⋊C4—744no—
172C4⋊C4—744no—
173C22⋊C4—372no—
174C22⋊C4—744no—
175C22⋊C4—741no—
176C42—372no—
177C42—744no—
178C42—741no—
179C23—21no—
180C23D4×D3711yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—21no—
184Q8—21no—
185Q8—742no—
186Q8—742no—
187Q8—1482no—
188Q8C2×C22⋊D3714yes—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—42no—
196C2×C4—374no—
197C2×C4—742no—
198C2×C4—742no—
199C2×C4—1482no—
200C2×C4D4×D3711yescharacteristic
201C2×C4#1059696412yes—
202C2×C4C2×C22⋊D3712yes—
203C2×C4C23×D3711yescharacteristic
204C8—22no—
205C8—742no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22#1192450812yes—
210C22C2×D4×D3711yescharacteristic
211C4—24no—
212C4—41no—
213C4—744no—
214C4—1482no—
215C4—1482no—
216C4#1192450812yes—
217C4C22×C22⋊D3711yescharacteristic
218C4C2×#1059696411yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#1192450811yescharacteristic
222C2#1455834912yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#137×C37C2
socleC22×C37C22×D4
prime radicalC2×#41×C37C22
hypercenterC2×#137D37
hypocenterC37#3044
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#10596942C2semidirect
3. #14558011C2semidirect
4. #14557753C2semidirect
5. #14557741C2semidirect
6. #14557561C2semidirect
7. #14557543C2semidirect
121. C37#3044semidirect

Maximal subgroups

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

subgroupindex
C22×#105969422
#145581042
#145580112
#145577532
#145577412
#145575612
#145575432
#145575292
C2×#137×C372
#304437