Finite Group Databasebeta

← #18010444

Subgroups — #18010444

Order 4736.

548 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 82 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#14558530C212yesmaximal, complemented
2#14558523C212yesmaximal, complemented
3#14558513C211yesmaximal, characteristic, complemented
4#14558507C211yesmaximal, characteristic, complemented
5#14558368C211yesmaximal, characteristic
6C2×#10596953C2211yescharacteristic, complemented
7C2×D37⋊C8C2211yescharacteristic, complemented
8#11924615C2212yescomplemented
9#11924601—22no—
10#11924600—22no—
11#11924599—22no—
12#11924598—22no—
13#11924594—22no—
14C22⋊#64438—22no—
15#11924583—22no—
16#11924583C412yescomplemented
17#11924581—22no—
18#11924581—22no—
19#11924581C411yescharacteristic, complemented
20C2×#10596964—22no—
21C2×#10596964—22no—
22C2×#10596964C2211yescharacteristic
23#41×D37—22no—
24#41×D37C2212yes—
25H(5,𝔽2)×C37C411yescharacteristic, complemented
26#41×C37—22no—
27#41×C37C2×C412yes—
28C2×D4×C37—22no—
29C2×D4×C37—22no—
30C2×D4×C37C2×C411yescharacteristic
31C2×C22⋊D37—24no—
32C2×C22⋊D37—22no—
33C2×C22⋊D37—22no—
34C2×C22⋊D37D412yes—
35C22×Dic37—22no—
36C22×Dic37D412yes—
37#10596966D412yes—
38Q8×D37—22no—
39Q8×D37D412yes—
40#10596964—24no—
41#10596964—24no—
42#10596964—24no—
43#10596964—22no—
44#10596964—24no—
45#10596964—22no—
46#10596964—22no—
47#10596964—22no—
48#10596964—22no—
49#10596964D412yes—
50D4×D37—24no—
51D4×D37—22no—
52D4×D37—22no—
53D4×D37D412yes—
54#10596962—24no—
55#10596962—22no—
56#10596962—22no—
57#10596962C2×C412yes—
58C2×C4×D37—22no—
59C2×C4×D37—22no—
60C2×C4×D37C2311yescharacteristic
61C2×Dic74—22no—
62C2×Dic74—22no—
63C2×Dic74C2×C411yescharacteristic
64C22⋊#3866—22no—
65C2×#64438—21no—
66C2×#64438—21no—
67C4⋊#3866—22no—
68C4×#3866—22no—
69#10596953—22no—
70D37⋊C8—22no—
71C23×C37—22no—
72C23×C37C22⋊C412yes—
73C22×D37—22no—
74C22×D37—22no—
75C22×D37C2×D411yescharacteristic
76C2×#3866—42no—
77Q8×C37C22⋊C412yes—
78D4×C37—24no—
79D4×C37—22no—
80D4×C37—22no—
81D4×C37C22⋊C412yes—
82C2×C4×C37—22no—
83C2×C4×C37—22no—
84C2×C4×C37C22×C411yescharacteristic
85C22⋊D37—24no—
86C22⋊D37—24no—
87C22⋊D37—22no—
88C22⋊D37—24no—
89C22⋊D37—22no—
90C22⋊D37—22no—
91C2×Dic37—24no—
92C2×Dic37—22no—
93C2×Dic37—22no—
94C2×Dic37—22no—
95C2×Dic37—22no—
96C2×Dic37C22⋊C412yes—
97C2×Dic37C2×D411yescharacteristic
98D148—22no—
99D148C22⋊C412yes—
100C4×D37—24no—
101C4×D37—22no—
102C4×D37—22no—
103C4×D37—22no—
104C4×D37C2×D412yes—
105C4×D37C2×D412yes—
106Dic74—24no—
107Dic74—22no—
108Dic74—22no—
109Dic74C22⋊C412yes—
110#64438—41no—
111#64438—41no—
112C22×C37—22no—
113C22×C37—22no—
114C22×C37—42no—
115C22×C37—82no—
116C22×C37C2×C22⋊C411yescharacteristic
117C2×D37—22no—
118C2×D37—41no—
119C2×D37—82no—
120C2×D37—82no—
121C2×D37#12012yes—
122#3866—82no—
123C4×C37—22no—
124C4×C37C2×C22⋊C412yes—
125Dic37—22no—
126Dic37—22no—
127Dic37#12011yescharacteristic
128Dic37#12011yescharacteristic
129#1794—371nomaximal, Sylow
130C2×C37—21no—
131C2×C37—42no—
132C2×C37—42no—
133C2×C37#37911yescharacteristic
134D37—22no—
135D37—42no—
136#585—371no—
137#421—372no—
138#416—372no—
139#410—371no—
140#408—371no—
141C37#179411yescharacteristic, complemented, Sylow
1422−1+4—372no—
1432−1+4—742no—
144H(5,𝔽2)—371no—
145H(5,𝔽2)—742no—
146H(5,𝔽2)—742no—
147H(5,𝔽2)#386611yescharacteristic, complemented
148C2×#41—371no—
149C2×#41—372no—
150C2×#41—742no—
151C2×#41—742no—
152C2×#41—742no—
153C2×M16—371no—
154C22×C8—371no—
155#117—372no—
156#104—742no—
157#104—742no—
158#103—742no—
159#102—742no—
160#99—742no—
161C22⋊C8—742no—
162#41—22no—
163#41—372no—
164#41—372no—
165#41—372no—
166#41—742no—
167#41—742no—
168#41—744no—
169#41—742no—
170#41—742no—
171#41—742no—
172#41—744no—
173#41—742no—
174#41—744no—
175#41—744no—
176#41—744no—
177#41—742no—
178#41C2×#386612yes—
179C2×Q8—371no—
180C2×Q8—372no—
181C2×Q8—742no—
182C2×Q8—742no—
183C2×Q8—742no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—372no—
187C2×D4—372no—
188C2×D4—742no—
189C2×D4—742no—
190C2×D4—744no—
191C2×D4—742no—
192C2×D4—744no—
193C2×D4—742no—
194C2×D4C2×#386611yescharacteristic
195C22×C4—371no—
196C22×C4—372no—
197C22×C4—742no—
198C22×C4—742no—
199C22×C4—742no—
200M16—742no—
201C2×C8—742no—
202C2×C8—741no—
203C2×C8—741no—
204C4⋊C4—742no—
205C22⋊C4—742no—
206C42—742no—
207C23—22no—
208C23—371no—
209C23—742no—
210C23—742no—
211C23C22⋊#386612yes—
212Q8—372no—
213Q8—742no—
214Q8—744no—
215Q8—742no—
216Q8C22⋊#386612yes—
217D4—24no—
218D4—22no—
219D4—22no—
220D4—372no—
221D4—742no—
222D4—742no—
223D4—744no—
224D4—742no—
225D4—744no—
226D4—744no—
227D4—742no—
228D4C22⋊#386612yes—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—371no—
232C2×C4—372no—
233C2×C4—372no—
234C2×C4—372no—
235C2×C4—742no—
236C2×C4—742no—
237C2×C4—744no—
238C2×C4—742no—
239C2×C4—742no—
240C2×C4—742no—
241C2×C4—744no—
242C2×C4—742no—
243C2×C4—742no—
244C2×C4—1482no—
245C2×C4C22×#386611yescharacteristic
246C8—1481no—
247C8—1481no—
248C22—22no—
249C22—22no—
250C22—42no—
251C22—82no—
252C22—372no—
253C22—2962no—
254C22—2962no—
255C22—742no—
256C22—1481no—
257C22C2×C22⋊#386611yescharacteristic
258C4—22no—
259C4—371no—
260C4—371no—
261C4—2962no—
262C4—742no—
263C4—742no—
264C4C2×C22⋊#386612yes—
265C2—21no—
266C2—42no—
267C2—42no—
268C2—742no—
269C2—1482no—
270C2#1455847411yescharacteristic
subgroupG/H
centerC2#14558474
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingH(5,𝔽2)×C37C4
socleC2×C37#379
prime radical#14558368C2
cosocleC2×C4×D37C23
hypercenterH(5,𝔽2)#3866
hypocenterC37#1794
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #14558530C2semidirect
2. #14558523C2semidirect
3. #14558513C2semidirect
4. #14558507C2semidirect
6. C2×#10596953C22semidirect
7. C2×D37⋊C8C22semidirect
8. #11924615C22semidirect
16. #11924583C4semidirect
19. #11924581C4semidirect
25. H(5,𝔽2)×C37C4semidirect
141. C37#1794semidirect
147. H(5,𝔽2)#3866semidirect

Maximal subgroups

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

subgroupindex
#145585302
#145585232
#145585132
#145585072
#145583682
#179437