Finite Group Databasebeta

← #18006362

Subgroups — #18006362

Order 4736.

464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 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#14558339C212yesmaximal, complemented
2#14558334C212yesmaximal, complemented
3#14557800C212yesmaximal, complemented
4#14557793C212yesmaximal, complemented
5#14557710C211yesmaximal, characteristic, complemented
6#14557705C211yesmaximal, characteristic, complemented
7#14557700C212yesmaximal, complemented
8#14557656C212yesmaximal, complemented
9C37×#496C211yesmaximal, characteristic, complemented
10#11924584C2211yescharacteristic, complemented
11#11924581C2211yescharacteristic
12#11924581C2212yescomplemented
13#11924567C2212yescomplemented
14#11924565—22no—
15#11924563—22no—
16#11924562C2212yes—
17#11924562C2212yescomplemented
18#11924562C2212yescomplemented
19#11924560—22no—
20#11924560—22no—
21#11924558C2212yes—
22#11924557—22no—
23#11924555—22no—
24SD16×D37—22no—
25D8×D37—22no—
26#11924542C2212yescomplemented
27#11924542C2212yescomplemented
28#11924472C2212yescomplemented
29#11924464C2212yescomplemented
30#11924464C2212yescomplemented
31#11924455C2211yescharacteristic, complemented
32#11924453C2212yescomplemented
33#11924453C2211yescharacteristic, complemented
34C2×SD16×C37C2212yescomplemented
35C2×D8×C37C2212yescomplemented
36#127×C37C2211yescharacteristic, complemented
37#124×C37C2211yescharacteristic, complemented
38#97×C37C2211yescharacteristic, complemented
39C2×Q8×C37C2311yescharacteristic
40C2×D4×C37—41no—
41C2×D4×C37C2312yes—
42C2×D4×C37C2311yescharacteristic
43C2×C22⋊D37—41no—
44C2×C22⋊D37—42no—
45#10596966—22no—
46Q8×D37—22no—
47#10596964—22no—
48#10596964—22no—
49#10596964—22no—
50D4×D37—22no—
51D4×D37—22no—
52D4×D37—22no—
53#10596962—41no—
54#10596962C2312yes—
55#10596962C2312yes—
56SD16×C37—22no—
57SD16×C37—22no—
58D8×C37—22no—
59D8×C37—22no—
60C2×C8×C37C2312yes—
61C22⋊C4×C37—41no—
62C42×C37C2311yescharacteristic
63#10596942—22no—
64#10596941—22no—
65#10596940—22no—
66#10596940—22no—
67#10596940—22no—
68#10596939—22no—
69#10596939—22no—
70#10596939—22no—
71#10596934C2312yes—
72#10596934C2312yes—
73Dic148D412yescomplemented
74D296D412yescomplemented
75#10596930D412yescomplemented
76#10596930D412yescomplemented
77#10596929—22no—
78#10596929—22no—
79C8×D37—22no—
80C8×D37—22no—
81C23×C37—21no—
82C23×C37—22no—
83C22×D37—42no—
84C22×D37—41no—
85Q8×C37—22no—
86D4×C37—22no—
87D4×C37—22no—
88D4×C37—22no—
89D4×C37—82no—
90C2×C4×C37—21no—
91C2×C4×C37—21no—
92C2×C4×C37C2411yescharacteristic
93C22⋊D37—22no—
94C22⋊D37—22no—
95C22⋊D37—42no—
96C22⋊D37—42no—
97C22⋊D37—42no—
98C2×Dic37—42no—
99C2×Dic37—41no—
100D148—41no—
101D148C2×D412yes—
102D148C2×D412yes—
103C4×D37—22no—
104C4×D37—22no—
105C4×D37—42no—
106Dic74—41no—
107Dic74C2×D412yes—
108Dic74C2×D412yes—
109C8×C37C2×D412yes—
110C8×C37C2×D412yes—
111#64436—22no—
112#64436—22no—
113C22×C37—41no—
114C22×C37—42no—
115C22×C37—82no—
116C22×C37—81no—
117C22×C37H(5,𝔽2)11yescharacteristic
118C2×D37—22no—
119C2×D37—22no—
120C2×D37—162no—
121C2×D37—161no—
122C4×C37—41no—
123C4×C37—41no—
124C4×C37C22×D412yes—
125Dic37—22no—
126Dic37—22no—
127#3288—371nomaximal, Sylow
128C2×C37—21no—
129C2×C37—82no—
130C2×C37—81no—
131C2×C37D4211yescharacteristic
132D37—42no—
133D37—42no—
134#577—372no—
135#576—372no—
136#496D3711yescharacteristic, complemented
137#472—372no—
138#471—372no—
139#455—371no—
140#454—371no—
141#453—372no—
142#444—372no—
143C37#328811yescharacteristic, complemented, Sylow
1442−1+4—371no—
145H(5,𝔽2)—371no—
146H(5,𝔽2)—372no—
147#137—372no—
148#137—742no—
149AGL(1,ℤ/8)—372no—
150AGL(1,ℤ/8)—372no—
151AGL(1,ℤ/8)—372no—
152AGL(1,ℤ/8)—742no—
153AGL(1,ℤ/8)—742no—
154AGL(1,ℤ/8)—742no—
155#135—372no—
156#135—742no—
157#135—742no—
158C2×SD16—742no—
159C2×SD16C2×D3712yescomplemented
160C2×D8—742no—
161C2×D8C2×D3712yescomplemented
162#131—372no—
163#131—372no—
164#127C2×D3711yescharacteristic, complemented
165#124C2×D3711yescharacteristic, complemented
166#108—372no—
167#104—372no—
168#104—372no—
169#101—371no—
170#100—372no—
171#100—371no—
172#97C2×D3711yescharacteristic, complemented
173#41—372no—
174#41—372no—
175#41—742no—
176#41—742no—
177#41—742no—
178#41—742no—
179#41—1481no—
180C2×Q8—742no—
181C2×Q8C22×D3711yescharacteristic
182C2×D4—41no—
183C2×D4—742no—
184C2×D4—742no—
185C2×D4—742no—
186C2×D4—1481no—
187C2×D4—1482no—
188C2×D4C22×D3711yescharacteristic
189C2×D4C22×D3712yes—
190Q16—372no—
191Q16—742no—
192SD16—22no—
193SD16—22no—
194SD16—372no—
195SD16—372no—
196SD16—742no—
197SD16—742no—
198SD16—742no—
199SD16—742no—
200D8—22no—
201D8—22no—
202D8—372no—
203D8—742no—
204D8—742no—
205D8—742no—
206M16—372no—
207M16—372no—
208M16—742no—
209M16—742no—
210C2×C8—742no—
211C2×C8—742no—
212C2×C8C22×D3712yes—
213C22⋊C4—41no—
214C42C22×D3711yescharacteristic
215C23—21no—
216C23—22no—
217C23—1482no—
218C23—1481no—
219Q8—22no—
220Q8—372no—
221Q8—372no—
222Q8—1481no—
223D4—22no—
224D4—22no—
225D4—22no—
226D4—82no—
227D4—372no—
228D4—372no—
229D4—742no—
230D4—742no—
231D4—1481no—
232D4—1482no—
233D4—1482no—
234D4—1482no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—742no—
238C2×C4—742no—
239C2×C4—1482no—
240C2×C4—1481no—
241C2×C4—1482no—
242C2×C4C23×D3711yescharacteristic
243C8—742no—
244C8—742no—
245C8D4×D3712yes—
246C8D4×D3712yes—
247C22—41no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—742no—
252C22—742no—
253C22—5921no—
254C22—5922no—
255C22#1192458111yescharacteristic
256C4—41no—
257C4—41no—
258C4—742no—
259C4—742no—
260C4C2×D4×D3712yes—
261C2—21no—
262C2—82no—
263C2—81no—
264C2—1482no—
265C2—1482no—
266C2#1455816811yescharacteristic
subgroupG/H
centerC2#14558168
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#496C2
socleC2×C37D42
hypercenter#496D37
hypocenterC37#3288
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14558339C2semidirect
2. #14558334C2semidirect
3. #14557800C2semidirect
4. #14557793C2semidirect
5. #14557710C2semidirect
6. #14557705C2semidirect
7. #14557700C2semidirect
8. #14557656C2semidirect
9. C37×#496C2semidirect
10. #11924584C22semidirect
12. #11924581C22semidirect
13. #11924567C22semidirect
17. #11924562C22semidirect
18. #11924562C22semidirect
26. #11924542C22semidirect
27. #11924542C22semidirect
28. #11924472C22semidirect
29. #11924464C22semidirect
30. #11924464C22semidirect
31. #11924455C22semidirect
32. #11924453C22semidirect
33. #11924453C22semidirect
34. C2×SD16×C37C22semidirect
35. C2×D8×C37C22semidirect
36. #127×C37C22semidirect
37. #124×C37C22semidirect
38. #97×C37C22semidirect
73. Dic148D4semidirect
74. D296D4semidirect
75. #10596930D4semidirect
76. #10596930D4semidirect
136. #496D37semidirect
143. C37#3288semidirect
159. C2×SD16C2×D37semidirect
161. C2×D8C2×D37semidirect
164. #127C2×D37semidirect
165. #124C2×D37semidirect
172. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583392
#145583342
#145578002
#145577932
#145577102
#145577052
#145577002
#145576562
C37×#4962
#328837