Finite Group Databasebeta

← #18004108

Subgroups — #18004108

Order 4736.

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

normal subgroups only

This group has 494 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×#11924562C211yesmaximal, characteristic
2C22×#10596940C211yesmaximal, characteristic, complemented
3#14558109C211yesmaximal, characteristic, complemented
4#14557748C214yesmaximal, complemented
5#14557738C214yesmaximal, complemented
6#14557560C211yesmaximal, characteristic, complemented
7#14557541C211yesmaximal, characteristic, complemented
8#14557527C211yesmaximal, characteristic, complemented
9C37×#518C211yesmaximal, characteristic, complemented
10C2×#10596962C2211yescharacteristic
11C22×Dic74C2211yescharacteristic
12#11924562—24no—
13C2×#10596940—24no—
14C2×#10596940C2212yes—
15C2×#10596940C2214yes—
16C2×#10596939C2212yes—
17C2×#10596934C2211yescharacteristic
18C22×#64436C2211yescharacteristic
19#11924536C2212yescomplemented
20#11924524C2212yescomplemented
21#11924520—22no—
22#11924516—22no—
23C4⋊#64436C2214yescomplemented
24#11924459C2212yescomplemented
25#11924459C2214yescomplemented
26#11924456C2212yescomplemented
27C22×D4×C37C2211yescharacteristic
28C4×D4×C37—22no—
29C4×D4×C37C2214yes—
30#117×C37C2211yescharacteristic
31#117×C37C2211yescharacteristic
32C2×C22⋊C4×C37—22no—
33C24×C37—21no—
34C2×D4×C37—21no—
35C2×D4×C37—22no—
36C2×D4×C37D414yes—
37C2×D4×C37C2312yes—
38C22×C4×C37—24no—
39C22×C4×C37C2311yescharacteristic
40C2×C22⋊D37—21no—
41C22×Dic37—21no—
42#10596962—22no—
43#10596962—22no—
44C2×D148C2311yescharacteristic
45C2×C4×D37—21no—
46C2×Dic74—22no—
47C2×Dic74—22no—
48C2×Dic74—21no—
49C2×Dic74C2312yes—
50C2×Dic74C2311yescharacteristic
51C4⋊C4×C37D412yes—
52C4⋊C4×C37C2312yes—
53C22⋊C4×C37—21no—
54C22⋊C4×C37—24no—
55C22⋊C4×C37D412yes—
56C42×C37—21no—
57C42×C37C2312yes—
58#10596940—28no—
59#10596940—24no—
60#10596939—24no—
61#10596938—24no—
62C4⋊Dic37—24no—
63#10596934—22no—
64C2×#64436—22no—
65C2×#64436C2312yes—
66C2×#64436C2312yes—
67C23×C37—22no—
68C23×C37—24no—
69C23×C37—82no—
70C23×C37C2×D411yescharacteristic
71C22×D37—21no—
72D4×C37—24no—
73D4×C37—22no—
74D4×C37C2×D414yes—
75C2×C4×C37—22no—
76C2×C4×C37—84no—
77C2×C4×C37C2×D412yes—
78C2×C4×C37C2×D414yes—
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37#4112yes—
81C2×C4×C37C2411yescharacteristic
82C22⋊D37—42no—
83C2×Dic37—21no—
84C2×Dic37—22no—
85C2×Dic37—42no—
86D148—21no—
87D148—21no—
88C4×D37—42no—
89Dic74—22no—
90Dic74—21no—
91Dic74—22no—
92Dic74—21no—
93Dic74—42no—
94#64436—22no—
95#64436—22no—
96C22×C37—22no—
97C22×C37—24no—
98C22×C37—44no—
99C22×C37—84no—
100C22×C37#12112yes—
101C22×C37C22×D411yescharacteristic
102C2×D37—41no—
103C2×D37—42no—
104C4×C37—24no—
105C4×C37—42no—
106C4×C37#12112yes—
107C4×C37C22×D411yescharacteristic
108C4×C37C2×#4111yescharacteristic
109Dic37—42no—
110Dic37—41no—
111#3042—371nomaximal, Sylow
112C2×C37—22no—
113C2×C37—44no—
114C2×C37C2×#12111yescharacteristic
115C2×C37#57712yes—
116D37—81no—
117C2×AGL(1,ℤ/8)—371no—
118C22×SD16—371no—
119#536—371no—
120#518D3711yescharacteristic, complemented
121#463—374no—
122#461—374no—
123#424—371no—
124#419—371no—
125#416—371no—
126C37#304211yescharacteristic, complemented, Sylow
127C2×#41—371no—
128C22×Q8—371no—
129C22×D4C2×D3711yescharacteristic
130AGL(1,ℤ/8)—744no—
131C2×SD16—374no—
132C2×SD16—372no—
133C2×SD16—744no—
134C2×D8—372no—
135C2×M16—371no—
136C22×C8—371no—
137C4⋊Q8—372no—
138#124—372no—
139#123—742no—
140C22⋊Q8—742no—
141C4×D4—22no—
142C4×D4C2×D3714yes—
143#117C2×D3711yescharacteristic
144#117C2×D3711yescharacteristic
145C2×C22⋊C4—22no—
146C4⋊C8—374no—
147#103—372no—
148#103—374no—
149#102—372no—
150C24—21no—
151#41—742no—
152#41—742no—
153C2×Q8—372no—
154C2×Q8—371no—
155C2×Q8—741no—
156C2×Q8—742no—
157C2×Q8—742no—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—371no—
161C2×D4—741no—
162C2×D4D14814yes—
163C2×D4C22×D3712yes—
164C22×C4—24no—
165C22×C4—741no—
166C22×C4—741no—
167C22×C4C22×D3711yescharacteristic
168SD16—748no—
169SD16—744no—
170D8—744no—
171M16—742no—
172C2×C8—372no—
173C2×C8—372no—
174C2×C8—742no—
175C4⋊C4—744no—
176C4⋊C4C22⋊D3712yes—
177C4⋊C4C22×D3712yes—
178C22⋊C4—21no—
179C22⋊C4—24no—
180C22⋊C4—744no—
181C22⋊C4C22⋊D3712yes—
182C42—21no—
183C42C22×D3712yes—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—741no—
188C23C2×C22⋊D3711yescharacteristic
189Q8—742no—
190Q8—741no—
191Q8—742no—
192Q8—741no—
193Q8—1482no—
194D4—24no—
195D4—22no—
196D4—741no—
197D4—741no—
198D4—1482no—
199D4C2×D14814yes—
200C2×C4—22no—
201C2×C4—84no—
202C2×C4—742no—
203C2×C4—741no—
204C2×C4—1482no—
205C2×C4—1482no—
206C2×C4C2×D14812yes—
207C2×C4#1059696212yes—
208C2×C4C2×C22⋊D3714yes—
209C2×C4C2×C22⋊D3711yescharacteristic
210C2×C4C23×D3711yescharacteristic
211C8—742no—
212C8—742no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—1481no—
218C22—1482no—
219C22#1192451012yes—
220C22C22×C22⋊D3711yescharacteristic
221C4—24no—
222C4—42no—
223C4—1481no—
224C4—1482no—
225C4#1192451012yes—
226C4C22×D14811yescharacteristic
227C4C2×#1059696211yescharacteristic
228C2—22no—
229C2—44no—
230C2—2961no—
231C2C2×#1192451011yescharacteristic
232C2#1455834412yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#518C2
socleC22×C37C22×D4
prime radicalC2×#11924562C2
hypercenter#518D37
hypocenterC37#3042
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C22×#10596940C2semidirect
3. #14558109C2semidirect
4. #14557748C2semidirect
5. #14557738C2semidirect
6. #14557560C2semidirect
7. #14557541C2semidirect
8. #14557527C2semidirect
9. C37×#518C2semidirect
19. #11924536C22semidirect
20. #11924524C22semidirect
23. C4⋊#64436C22semidirect
24. #11924459C22semidirect
25. #11924459C22semidirect
26. #11924456C22semidirect
120. #518D37semidirect
126. C37#3042semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C22×#105969402
#145581092
#145577482
#145577382
#145575602
#145575412
#145575272
C37×#5182
#304237