Finite Group Databasebeta

← #18004126

Subgroups — #18004126

Order 4736.

458 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924567C211yesmaximal, characteristic
2C22×#10596942C211yesmaximal, characteristic, complemented
3#14558109C211yesmaximal, characteristic
4#14557755C214yesmaximal, complemented
5#14557743C214yesmaximal, complemented
6#14557560C211yesmaximal, characteristic, complemented
7#14557541C211yesmaximal, characteristic, complemented
8#14557527C211yesmaximal, characteristic
9C37×#519C211yesmaximal, characteristic, complemented
10C2×#10596962C2211yescharacteristic
11C22×Dic74C2211yescharacteristic
12#11924567—24no—
13C2×#10596942—24no—
14C2×#10596942C2212yes—
15C2×#10596942C2214yes—
16C2×#10596941C2212yes—
17C2×#10596934C2211yescharacteristic
18C22×#64436C2211yescharacteristic
19#11924536C2212yes—
20#11924524C2212yes—
21#11924520—22no—
22#11924516—22no—
23C4⋊#64436C2214yes—
24#11924459C2212yes—
25#11924459C2214yes—
26#11924456C2212yes—
27C22×Q8×C37C2211yescharacteristic
28C4×Q8×C37—22no—
29C4×Q8×C37C2214yes—
30#117×C37—22no—
31#117×C37C2211yescharacteristic
32#117×C37C2211yescharacteristic
33C2×Q8×C37—21no—
34C2×Q8×C37—22no—
35C2×Q8×C37D414yes—
36C2×Q8×C37C2312yes—
37C22×C4×C37—21no—
38C22×C4×C37C2311yescharacteristic
39C2×C22⋊D37—21no—
40C22×Dic37—21no—
41#10596962—22no—
42#10596962—22no—
43C2×D148C2311yescharacteristic
44C2×C4×D37—21no—
45C2×Dic74—22no—
46C2×Dic74—22no—
47C2×Dic74—21no—
48C2×Dic74C2312yes—
49C2×Dic74C2311yescharacteristic
50C4⋊C4×C37—24no—
51C4⋊C4×C37D412yes—
52C4⋊C4×C37C2312yes—
53C22⋊C4×C37—21no—
54C22⋊C4×C37D412yes—
55C42×C37—24no—
56C42×C37—21no—
57C42×C37C2312yes—
58#10596942—28no—
59#10596942—24no—
60#10596941—24no—
61#10596938—24no—
62C4⋊Dic37—24no—
63#10596934—22no—
64C2×#64436—22no—
65C2×#64436C2312yes—
66C2×#64436C2312yes—
67C23×C37C2×D411yescharacteristic
68C22×D37—21no—
69Q8×C37—24no—
70Q8×C37—22no—
71Q8×C37C2×D414yes—
72C2×C4×C37—24no—
73C2×C4×C37—22no—
74C2×C4×C37—22no—
75C2×C4×C37C2×D412yes—
76C2×C4×C37C2×D414yes—
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37#4112yes—
79C2×C4×C37C2411yescharacteristic
80C22⋊D37—42no—
81C2×Dic37—21no—
82C2×Dic37—22no—
83C2×Dic37—42no—
84D148—21no—
85D148—21no—
86C4×D37—42no—
87Dic74—22no—
88Dic74—21no—
89Dic74—22no—
90Dic74—21no—
91Dic74—42no—
92#64436—22no—
93#64436—22no—
94C22×C37—22no—
95C22×C37#12112yes—
96C22×C37C22×D411yescharacteristic
97C2×D37—41no—
98C2×D37—42no—
99C4×C37—24no—
100C4×C37—24no—
101C4×C37—42no—
102C4×C37#12112yes—
103C4×C37C22×D411yescharacteristic
104C4×C37C2×#4111yescharacteristic
105Dic37—42no—
106Dic37—41no—
107#3044—371nomaximal, Sylow
108C2×C37—22no—
109C2×C37C2×#12111yescharacteristic
110C2×C37#57812yes—
111D37—81no—
112C2×#137—371no—
113C22×Q16—371no—
114#536—371no—
115#519D3711yescharacteristic, complemented
116#464—374no—
117#462—374no—
118#424—371no—
119#419—371no—
120#416—371no—
121C37#304411yescharacteristic, complemented, Sylow
122C2×#41—371no—
123C22×Q8—371no—
124C22×Q8C2×D3711yescharacteristic
125#137—744no—
126C2×Q16—374no—
127C2×Q16—372no—
128C2×Q16—744no—
129C2×SD16—372no—
130C2×M16—371no—
131C22×C8—371no—
132C4⋊Q8—372no—
133#124—372no—
134#123—742no—
135C22⋊Q8—742no—
136C4×Q8—22no—
137C4×Q8C2×D3714yes—
138#117—22no—
139#117C2×D3711yescharacteristic
140#117C2×D3711yescharacteristic
141C4⋊C8—374no—
142#103—372no—
143#103—374no—
144#102—372no—
145#41—742no—
146#41—742no—
147C2×Q8—22no—
148C2×Q8—21no—
149C2×Q8—372no—
150C2×Q8—371no—
151C2×Q8—741no—
152C2×Q8—742no—
153C2×Q8—742no—
154C2×Q8D14814yes—
155C2×Q8C22×D3712yes—
156C2×D4—371no—
157C2×D4—741no—
158C22×C4—21no—
159C22×C4—741no—
160C22×C4—741no—
161C22×C4C22×D3711yescharacteristic
162Q16—748no—
163Q16—744no—
164SD16—744no—
165M16—742no—
166C2×C8—372no—
167C2×C8—372no—
168C2×C8—742no—
169C4⋊C4—24no—
170C4⋊C4—744no—
171C4⋊C4C22⋊D3712yes—
172C4⋊C4C22×D3712yes—
173C22⋊C4—21no—
174C22⋊C4—744no—
175C22⋊C4C22⋊D3712yes—
176C42—24no—
177C42—21no—
178C42C22×D3712yes—
179C23—741no—
180C23C2×C22⋊D3711yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—742no—
184Q8—741no—
185Q8—742no—
186Q8—741no—
187Q8—1482no—
188Q8C2×D14814yes—
189D4—741no—
190D4—741no—
191D4—1482no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—742no—
196C2×C4—741no—
197C2×C4—1482no—
198C2×C4—1482no—
199C2×C4C2×D14812yes—
200C2×C4#1059696212yes—
201C2×C4C2×C22⋊D3714yes—
202C2×C4C2×C22⋊D3711yescharacteristic
203C2×C4C23×D3711yescharacteristic
204C8—742no—
205C8—742no—
206C22—22no—
207C22—1481no—
208C22—1482no—
209C22#1192451012yes—
210C22C22×C22⋊D3711yescharacteristic
211C4—24no—
212C4—24no—
213C4—42no—
214C4—1481no—
215C4—1482no—
216C4#1192451012yes—
217C4C22×D14811yescharacteristic
218C4C2×#1059696211yescharacteristic
219C2—22no—
220C2—2961no—
221C2C2×#1192451011yescharacteristic
222C2#1455834812yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#519C2
socleC22×C37C22×D4
prime radicalC2×#10596962C22
hypercenter#519D37
hypocenterC37#3044
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. C22×#10596942C2semidirect
4. #14557755C2semidirect
5. #14557743C2semidirect
6. #14557560C2semidirect
7. #14557541C2semidirect
9. C37×#519C2semidirect
115. #519D37semidirect
121. C37#3044semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
C22×#105969422
#145581092
#145577552
#145577432
#145575602
#145575412
#145575272
C37×#5192
#304437