Finite Group Databasebeta

← #22581760

Subgroups — #22581760

Order 8896.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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#17984889C211yesmaximal, characteristic, complemented
2#17984888C211yesmaximal, characteristic, complemented
3#17984874C212yesmaximal, complemented
4#17984872C211yesmaximal, characteristic, complemented
5#17984867C211yesmaximal, characteristic, complemented
6#17984866C212yesmaximal, complemented
7#17984863C212yesmaximal, complemented
8C2×#14555774C211yesmaximal, characteristic, complemented
9SD16×D139C212yesmaximal, complemented
10#17984848C211yesmaximal, characteristic, complemented
11#135×C139C211yesmaximal, characteristic, complemented
12#14555786C2212yes—
13#14555785—21no—
14#14555785—21no—
15#14555785C2211yescharacteristic
16#14555784—22no—
17#14555784C2212yescomplemented
18C2×Dic278—21no—
19C2×Dic278C2211yescharacteristic, complemented
20Q8×D139C2212yescomplemented
21C2×D556—21no—
22C2×D556C2211yescharacteristic
23D4×D139—22no—
24D4×D139C2212yes—
25#14555775C2212yescomplemented
26#14555774C2212yescomplemented
27#14555774C2212yescomplemented
28#14555773C2212yescomplemented
29#14555772C2212yescomplemented
30#14555770C2212yescomplemented
31#14555769C2211yescharacteristic, complemented
32#14555768C2212yescomplemented
33C8×D139C2212yescomplemented
34#41×C139C2211yescharacteristic
35#41×C139C2211yescharacteristic, complemented
36Q16×C139C2211yescharacteristic, complemented
37SD16×C139C2211yescharacteristic, complemented
38SD16×C139C2211yescharacteristic, complemented
39D8×C139C2211yescharacteristic, complemented
40C2×C8×C139C2211yescharacteristic, complemented
41C22×D139—21no—
42C22×D139—22no—
43Dic278—21no—
44Dic278—22no—
45Dic278D411yescharacteristic
46Dic278C2312yes—
47D556—22no—
48D556—21no—
49D556D411yescharacteristic
50D556C2312yes—
51C22⋊D139—22no—
52C22⋊D139—22no—
53C22⋊D139D412yes—
54C2×Dic139—21no—
55C2×Dic139—22no—
56C4×D139—22no—
57C4×D139—22no—
58C4×D139C2312yes—
59C139⋊C8C2312yes—
60Q8×C139C2311yescharacteristic
61Q8×C139C2311yescharacteristic
62D4×C139—21no—
63D4×C139—21no—
64D4×C139C2311yescharacteristic
65D4×C139C2311yescharacteristic
66C2×C4×C139—21no—
67C2×C4×C139—21no—
68C2×C4×C139C2311yescharacteristic
69C8×C139C2311yescharacteristic
70C8×C139C2311yescharacteristic
71C22×C139—21no—
72C22×C139—21no—
73C22×C139C2×D411yescharacteristic
74C2×D139—22no—
75C2×D139—82no—
76C2×D139—81no—
77C2×D139C2×D412yes—
78C4×C139—21no—
79C4×C139—21no—
80C4×C139C2×D411yescharacteristic
81C4×C139C2411yescharacteristic
82Dic139—22no—
83Dic139C2×D412yes—
84C2×C139—21no—
85C2×C139—41no—
86C2×C139—41no—
87C2×C139C22×D411yescharacteristic
88D139—22no—
89D139—42no—
90C139#57711yescharacteristic, complemented, Sylow
91#577—1391nomaximal, Sylow
922−1+4—1391no—
93H(5,𝔽2)—1391no—
94#137—1391no—
95#137—1392no—
96AGL(1,ℤ/8)—1391no—
97AGL(1,ℤ/8)—1392no—
98#135—1392no—
99#135D13911yescharacteristic, complemented
100C2×SD16—1392no—
101C2×SD16—1391no—
102#131—1391no—
103#41—2781no—
104#41—2781no—
105#41—2782no—
106#41—1392no—
107#41—1392no—
108#41—1391no—
109#41C2×D13911yescharacteristic
110#41C2×D13911yescharacteristic, complemented
111C2×Q8—2781no—
112C2×Q8—1392no—
113C2×Q8—1391no—
114C2×D4—2781no—
115C2×D4—2782no—
116C2×D4—1392no—
117C2×D4—1391no—
118Q16—1392no—
119Q16C2×D13911yescharacteristic, complemented
120SD16—1392no—
121SD16—1392no—
122SD16—1392no—
123SD16—1392no—
124SD16C2×D13911yescharacteristic, complemented
125SD16C2×D13911yescharacteristic, complemented
126D8—1392no—
127D8C2×D13911yescharacteristic, complemented
128M16—1391no—
129M16—1392no—
130C2×C8—1392no—
131C2×C8C2×D13911yescharacteristic, complemented
132C23—2782no—
133C23—2781no—
134Q8—2782no—
135Q8—2781no—
136Q8—1392no—
137Q8—1391no—
138Q8C22×D13911yescharacteristic
139Q8C22×D13911yescharacteristic
140D4—21no—
141D4—21no—
142D4—2782no—
143D4—2782no—
144D4—2782no—
145D4—2781no—
146D4—1392no—
147D4—1391no—
148D4—1392no—
149D4C22×D13911yescharacteristic
150D4C22×D13911yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—2782no—
154C2×C4—2782no—
155C2×C4—2781no—
156C2×C4—2782no—
157C2×C4—1392no—
158C2×C4C22×D13911yescharacteristic
159C8—1392no—
160C8C22×D13911yescharacteristic
161C8C22×D13911yescharacteristic
162C22—21no—
163C22—21no—
164C22—2782no—
165C22—11121no—
166C22—11122no—
167C22—1392no—
168C22D4×D13911yescharacteristic
169C4—21no—
170C4—21no—
171C4—2782no—
172C4—1392no—
173C4D4×D13911yescharacteristic
174C4C23×D13911yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—2782no—
179C2—5562no—
180C2C2×D4×D13911yescharacteristic
subgroupG/H
centerC2C2×D4×D139
commutatorC4×C139C24
FrattiniC4C23×D139
Fitting#135×C139C2
socleC2×C139C22×D4
hypercenter#135D139
hypocenterC139#577
LCSG ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #17984889C2semidirect
2. #17984888C2semidirect
3. #17984874C2semidirect
4. #17984872C2semidirect
5. #17984867C2semidirect
6. #17984866C2semidirect
7. #17984863C2semidirect
8. C2×#14555774C2semidirect
9. SD16×D139C2semidirect
10. #17984848C2semidirect
11. #135×C139C2semidirect
17. #14555784C22semidirect
19. C2×Dic278C22semidirect
20. Q8×D139C22semidirect
25. #14555775C22semidirect
26. #14555774C22semidirect
27. #14555774C22semidirect
28. #14555773C22semidirect
29. #14555772C22semidirect
30. #14555770C22semidirect
31. #14555769C22semidirect
32. #14555768C22semidirect
33. C8×D139C22semidirect
35. #41×C139C22semidirect
36. Q16×C139C22semidirect
37. SD16×C139C22semidirect
38. SD16×C139C22semidirect
39. D8×C139C22semidirect
40. C2×C8×C139C22semidirect
90. C139#577semidirect
99. #135D139semidirect
110. #41C2×D139semidirect
119. Q16C2×D139semidirect
124. SD16C2×D139semidirect
125. SD16C2×D139semidirect
127. D8C2×D139semidirect
131. C2×C8C2×D139semidirect