Finite Group Databasebeta

← #17995038

Subgroups — #17995038

Order 4736.

442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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#14558045C211yesmaximal, characteristic
2C2×C42×D37C211yesmaximal, characteristic, complemented
3C2×#11924464C211yesmaximal, characteristic, complemented
4C2×#11924462C211yesmaximal, characteristic, complemented
5#14557496C211yesmaximal, characteristic, complemented
6#14557292C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×C4×D37—21no—
10C22×C4×D37C2211yescharacteristic
11C2×#10596934C2211yescharacteristic
12#11924520—21no—
13#11924516C412yescomplemented
14#11924511C412yescomplemented
15#11924506—21no—
16C4×D148—22no—
17C2×C4×Dic37—21no—
18C2×C4×Dic37C2211yescharacteristic
19C42×D37—22no—
20C42×D37—22no—
21#11924464—22no—
22#11924462—22no—
23#11924448—22no—
24C2×M16×C37C2211yescharacteristic
25#117×C37C2211yescharacteristic
26C2×C42×C37C2211yescharacteristic
27C23×D37D411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37C2311yescharacteristic
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32C22×Dic37D411yescharacteristic
33#10596962—21no—
34#10596962—21no—
35#10596962—21no—
36#10596962—21no—
37C2×D148—22no—
38C2×D148C2×C411yescharacteristic, complemented
39C2×C4×D37—24no—
40C2×C4×D37—28no—
41C2×C4×D37—21no—
42C2×C4×D37—21no—
43C2×C4×D37—21no—
44C2×C4×D37—21no—
45C2×C4×D37—21no—
46C2×C4×D37C2×C412yes—
47C2×C4×D37D412yes—
48C2×Dic74C2×C411yescharacteristic, complemented
49M16×C37—21no—
50M16×C37—21no—
51C2×C8×C37—21no—
52C4⋊C4×C37C2×C412yescomplemented
53C22⋊C4×C37—21no—
54C42×C37—21no—
55C42×C37—21no—
56C42×C37D412yescomplemented
57#10596938—22no—
58#10596938—22no—
59C4⋊Dic37—22no—
60C4×Dic37—24no—
61C4×Dic37—21no—
62C4×Dic37D412yescomplemented
63#10596934—21no—
64#10596934—21no—
65C2×#64436—21no—
66C23×C37C2×D411yescharacteristic
67C22×D37—21no—
68C22×D37—21no—
69C22×D37—24no—
70C22×D37—21no—
71C22×D37C22⋊C412yes—
72C2×C4×C37—24no—
73C2×C4×C37—22no—
74C2×C4×C37—22no—
75C2×C4×C37C22×C411yescharacteristic
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37#4111yescharacteristic
80C2×C4×C37#4111yescharacteristic
81C22⋊D37—41no—
82C22⋊D37—41no—
83C2×Dic37—24no—
84C2×Dic37—21no—
85C2×Dic37—22no—
86C2×Dic37—21no—
87C2×Dic37—21no—
88C2×Dic37C22⋊C412yes—
89D148—21no—
90D148—21no—
91D148—44no—
92C4×D37—216no—
93C4×D37—22no—
94C4×D37—22no—
95C4×D37—22no—
96C4×D37—22no—
97C4×D37—41no—
98C4×D37—41no—
99Dic74—21no—
100Dic74—21no—
101C8×C37—41no—
102#64436—41no—
103C22×C37—22no—
104C22×C37C2×C22⋊C411yescharacteristic
105C22×C37#12011yescharacteristic
106C22×C37#12311yescharacteristic
107C2×D37—24no—
108C2×D37—24no—
109C2×D37—22no—
110C2×D37—22no—
111C2×D37—41no—
112C2×D37—42no—
113C2×D37#10414yescomplemented
114C4×C37—24no—
115C4×C37—42no—
116C4×C37C4×D411yescharacteristic
117C4×C37C4×D411yescharacteristic
118C4×C37#12111yescharacteristic
119C4×C37#12111yescharacteristic
120Dic37—24no—
121Dic37—22no—
122Dic37—41no—
123#1896—371nomaximal, Sylow
124C2×C37—21no—
125C2×C37—21no—
126C2×C37#38611yescharacteristic
127C2×C37C2×#10412yes—
128D37—24no—
129D37—81no—
130#525—371no—
131C22×C42—371no—
132C2×#104—371no—
133C2×#104—371no—
134#407—371no—
135#339—371no—
136#339D3711yescharacteristic, complemented
137C37#189611yescharacteristic, complemented, Sylow
138C2×#41—371no—
139C23×C4—371no—
140C23×C4—741no—
141C2×M16—371no—
142C2×M16C2×D3711yescharacteristic
143#123—741no—
144C22⋊Q8—372no—
145#121—372no—
146#120—741no—
147C4×D4—742no—
148#117C2×D3711yescharacteristic
149C2×C42—371no—
150C2×C42—742no—
151C2×C42—741no—
152C2×C42—742no—
153C2×C42C2×D3711yescharacteristic
154#104—742no—
155#104—742no—
156C22⋊C8—742no—
157C24—371no—
158#41—741no—
159#41—741no—
160#41—741no—
161#41—741no—
162C2×Q8—371no—
163C2×D4—371no—
164C2×D4—742no—
165C2×D4—741no—
166C22×C4—21no—
167C22×C4—371no—
168C22×C4—372no—
169C22×C4—372no—
170C22×C4—744no—
171C22×C4—748no—
172C22×C4—741no—
173C22×C4—741no—
174C22×C4—741no—
175C22×C4—741no—
176C22×C4—741no—
177C22×C4—741no—
178C22×C4C22×D3711yescharacteristic
179M16—21no—
180M16—21no—
181M16—741no—
182M16—741no—
183C2×C8—21no—
184C2×C8—741no—
185C4⋊C4—742no—
186C4⋊C4C4×D3712yescomplemented
187C22⋊C4—21no—
188C22⋊C4—742no—
189C22⋊C4—742no—
190C42—21no—
191C42—21no—
192C42—372no—
193C42—744no—
194C42—741no—
195C42D14812yescomplemented
196C23—372no—
197C23—744no—
198C23—741no—
199C23—741no—
200C23—741no—
201C23D4×D3711yescharacteristic
202Q8—741no—
203Q8—741no—
204D4—741no—
205D4—741no—
206D4—1484no—
207D4—1481no—
208D4—1481no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—372no—
213C2×C4—7416no—
214C2×C4—744no—
215C2×C4—742no—
216C2×C4—741no—
217C2×C4—741no—
218C2×C4—742no—
219C2×C4—742no—
220C2×C4—742no—
221C2×C4—742no—
222C2×C4—741no—
223C2×C4—1481no—
224C2×C4—1481no—
225C2×C4C2×C4×D3711yescharacteristic
226C2×C4C2×D14811yescharacteristic
227C2×C4#1059696211yescharacteristic
228C2×C4D4×D3711yescharacteristic
229C2×C4D4×D3711yescharacteristic
230C2×C4#1059696611yescharacteristic
231C8—41no—
232C8—1481no—
233C22—22no—
234C22—374no—
235C22—744no—
236C22—744no—
237C22—742no—
238C22—742no—
239C22—1482no—
240C22—1481no—
241C22C22⋊C4×D3711yescharacteristic
242C22#1192450611yescharacteristic
243C22#1192452111yescharacteristic
244C4—24no—
245C4—42no—
246C4—744no—
247C4—742no—
248C4—1481no—
249C4#1192449811yescharacteristic
250C4C4×D14811yescharacteristic
251C4#1192450911yescharacteristic
252C4#1192451111yescharacteristic
253C2—21no—
254C2—21no—
255C2—2961no—
256C2—744no—
257C2#1455741111yescharacteristic
258C2#104×D3712yes—
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37C2×C22⋊C4
prime radical#14558045C2
cosocleC22×C4×C37C23
hypercenter#339D37
hypocenterC37#1896
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×C42×D37C2semidirect
3. C2×#11924464C2semidirect
4. C2×#11924462C2semidirect
5. #14557496C2semidirect
6. #14557292C2semidirect
7. C37×#339C2semidirect
13. #11924516C4semidirect
14. #11924511C4semidirect
38. C2×D148C2×C4semidirect
48. C2×Dic74C2×C4semidirect
52. C4⋊C4×C37C2×C4semidirect
56. C42×C37D4semidirect
62. C4×Dic37D4semidirect
113. C2×D37#104semidirect
136. #339D37semidirect
137. C37#1896semidirect
186. C4⋊C4C4×D37semidirect
195. C42D148semidirect

Maximal subgroups

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

subgroupindex
#145580452
C2×C42×D372
C2×#119244642
C2×#119244622
#145574962
#145572922
C37×#3392
#189637