Finite Group Databasebeta

← #31818204

Subgroups — #31818204

Order 17792.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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#22581758C212yesmaximal, complemented
2#22581755C212yesmaximal, complemented
3#22581330C211yesmaximal, characteristic, complemented
4#22581224C212yesmaximal, complemented
5#22581223C212yesmaximal, complemented
6#22581122C214yesmaximal, complemented
7#22581071C211yesmaximal, characteristic, complemented
8#443×C139C211yesmaximal, characteristic, complemented
9#17984888C2214yescomplemented
10#17984870—24no—
11#17984870C2214yescomplemented
12#17984869—24no—
13#17984867C2214yescomplemented
14#17984865—22no—
15#17984864—22no—
16#17984864C2211yescharacteristic
17C2×D1112—22no—
18C2×D1112C2212yescomplemented
19C2×D1112C2212yescomplemented
20D8×D139—22no—
21#17984848C2212yescomplemented
22#17984839C2212yescomplemented
23#17984778C2211yescharacteristic, complemented
24#17984770C2212yescomplemented
25#17984758C2214yescomplemented
26#135×C139C2211yescharacteristic
27#131×C139C2212yescomplemented
28#108×C139C2211yescharacteristic, complemented
29#104×C139C2212yescomplemented
30C4×C8×C139C2211yescharacteristic, complemented
31#14555786—24no—
32#14555785—24no—
33#14555785C2312yes—
34C2×D556—24no—
35C2×D556—42no—
36C2×D556C2314yes—
37D4×D139—24no—
38D4×D139—44no—
39Dic556D411yescharacteristic, complemented
40#14555774—24no—
41#14555774D412yescomplemented
42#14555772—24no—
43D1112—24no—
44D1112—22no—
45D1112—22no—
46D1112—22no—
47D1112—22no—
48D1112D411yescharacteristic, complemented
49#14555770—24no—
50#14555769C2312yes—
51#14555768—22no—
52C8×D139—22no—
53#41×C139C2312yes—
54Q16×C139D411yescharacteristic, complemented
55SD16×C139D412yescomplemented
56D8×C139D411yescharacteristic, complemented
57M16×C139—22no—
58M16×C139C2312yes—
59C2×C8×C139—22no—
60C2×C8×C139C2311yescharacteristic
61C2×C8×C139C2311yescharacteristic
62C42×C139C2311yescharacteristic
63C22×D139—24no—
64C22×D139—44no—
65Dic278C2×D412yes—
66D556—24no—
67D556—24no—
68D556—44no—
69D556—84no—
70D556C2×D412yes—
71C22⋊D139—22no—
72C22⋊D139—44no—
73C4×D139—22no—
74C4×D139—44no—
75C139⋊C8—22no—
76Q8×C139C2×D412yes—
77D4×C139—22no—
78D4×C139C2×D412yes—
79C2×C4×C139—21no—
80C2×C4×C139—22no—
81C2×C4×C139C2411yescharacteristic
82C8×C139—22no—
83C8×C139C2×D411yescharacteristic
84C8×C139C2×D411yescharacteristic
85C8×C139C2×D411yescharacteristic
86C8×C139C2×D411yescharacteristic
87C22×C139—22no—
88C22×C139H(5,𝔽2)11yescharacteristic
89C2×D139—22no—
90C2×D139—44no—
91C2×D139—84no—
92C2×D139—164no—
93C4×C139—22no—
94C4×C139—22no—
95C4×C139C22×D411yescharacteristic
96C4×C139C22×D411yescharacteristic
97Dic139—22no—
98C2×C139—21no—
99C2×C139—42no—
100C2×C139D4211yescharacteristic
101D139—42no—
102D139—84no—
103C139#329211yescharacteristic, complemented, Sylow
104#3292—1391nomaximal, Sylow
105#576—1392no—
106#576—1392no—
107#493—1391no—
108#472—1392no—
109#472—1392no—
110#453—1394no—
111#443—1391no—
112#443D13911yescharacteristic, complemented
113H(5,𝔽2)—1394no—
114AGL(1,ℤ/8)—2784no—
115AGL(1,ℤ/8)—2784no—
116AGL(1,ℤ/8)—1394no—
117AGL(1,ℤ/8)—1394no—
118#135—2782no—
119#135—2782no—
120#135—1391no—
121#135C2×D13911yescharacteristic
122C2×D8—2782no—
123C2×D8—2782no—
124C2×D8—1392no—
125C2×D8—1392no—
126#131—1392no—
127#131C2×D13912yescomplemented
128#127—1392no—
129#108—1391no—
130#108C2×D13911yescharacteristic, complemented
131#104—1392no—
132#104C2×D13912yescomplemented
133#100—1394no—
134C4×C8C2×D13911yescharacteristic, complemented
135#41—2784no—
136#41—2784no—
137#41—1392no—
138#41C22×D13912yes—
139C2×D4—2784no—
140C2×D4—2784no—
141C2×D4—5562no—
142C2×D4—5564no—
143C2×D4—1394no—
144Q16—1391no—
145Q16D55611yescharacteristic, complemented
146SD16—2784no—
147SD16—2784no—
148SD16—1392no—
149SD16D55612yescomplemented
150D8—2784no—
151D8—2784no—
152D8—2782no—
153D8—2782no—
154D8—2782no—
155D8—2782no—
156D8—1391no—
157D8D55611yescharacteristic, complemented
158M16—22no—
159M16—2782no—
160M16—1392no—
161M16C22×D13912yes—
162C2×C8—22no—
163C2×C8—2782no—
164C2×C8C22×D13911yescharacteristic
165C2×C8C22×D13911yescharacteristic
166C42C22×D13911yescharacteristic
167C23—2784no—
168C23—5564no—
169Q8—1392no—
170Q8C2×D55612yes—
171D4—22no—
172D4—2782no—
173D4—2784no—
174D4—2784no—
175D4—5564no—
176D4—5564no—
177D4—11124no—
178D4—1392no—
179D4C2×D55612yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—2782no—
183C2×C4—5564no—
184C2×C4C23×D13911yescharacteristic
185C8—22no—
186C8—2782no—
187C8D4×D13911yescharacteristic
188C8D4×D13911yescharacteristic
189C8C2×D55611yescharacteristic
190C8C2×D55611yescharacteristic
191C22—22no—
192C22—2782no—
193C22—5564no—
194C22—11124no—
195C22—22244no—
196C22#1798488811yescharacteristic
197C4—22no—
198C4—22no—
199C4—2782no—
200C4C2×D4×D13911yescharacteristic
201C4C22×D55611yescharacteristic
202C2—21no—
203C2—42no—
204C2—5562no—
205C2—11124no—
206C2D4×D55611yescharacteristic
subgroupG/H
centerC2D4×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#443×C139C2
socleC2×C139D42
hypercenter#443D139
hypocenterC139#3292
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #22581758C2semidirect
2. #22581755C2semidirect
3. #22581330C2semidirect
4. #22581224C2semidirect
5. #22581223C2semidirect
6. #22581122C2semidirect
7. #22581071C2semidirect
8. #443×C139C2semidirect
9. #17984888C22semidirect
11. #17984870C22semidirect
13. #17984867C22semidirect
18. C2×D1112C22semidirect
19. C2×D1112C22semidirect
21. #17984848C22semidirect
22. #17984839C22semidirect
23. #17984778C22semidirect
24. #17984770C22semidirect
25. #17984758C22semidirect
27. #131×C139C22semidirect
28. #108×C139C22semidirect
29. #104×C139C22semidirect
30. C4×C8×C139C22semidirect
39. Dic556D4semidirect
41. #14555774D4semidirect
48. D1112D4semidirect
54. Q16×C139D4semidirect
55. SD16×C139D4semidirect
56. D8×C139D4semidirect
103. C139#3292semidirect
112. #443D139semidirect
127. #131C2×D139semidirect
130. #108C2×D139semidirect
132. #104C2×D139semidirect
134. C4×C8C2×D139semidirect
145. Q16D556semidirect
149. SD16D556semidirect
157. D8D556semidirect

Maximal subgroups

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

subgroupindex
#225817582
#225817552
#225813302
#225812242
#225812232
#225811222
#225810712
#443×C1392
#3292139