Finite Group Databasebeta

← #22581759

Subgroups — #22581759

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#17984890C211yesmaximal, characteristic, complemented
2#17984887C211yesmaximal, characteristic, complemented
3#17984873C211yesmaximal, characteristic, complemented
4#17984871C212yesmaximal, complemented
5#17984869C212yesmaximal, complemented
6#17984868C211yesmaximal, characteristic, complemented
7#17984864C211yesmaximal, characteristic, complemented
8#17984863C212yesmaximal, complemented
9SD16×D139C212yesmaximal, complemented
10#17984848C211yesmaximal, characteristic, complemented
11C2×SD16×C139C211yesmaximal, characteristic, complemented
12#14555786—21no—
13#14555786C2212yescomplemented
14#14555785—22no—
15#14555785C2211yescharacteristic
16#14555785C2211yescharacteristic
17#14555785C2211yescharacteristic, complemented
18#14555784—21no—
19#14555784C2212yes—
20Q8×D139—21no—
21Q8×D139C2212yescomplemented
22C2×C22⋊D139—22no—
23D4×D139—21no—
24D4×D139C2212yes—
25Dic556C2211yescharacteristic, complemented
26#14555775C2212yescomplemented
27#14555774C2211yescharacteristic, complemented
28#14555774C2211yescharacteristic, complemented
29#14555773C2212yescomplemented
30#14555772C2212yescomplemented
31D1112C2211yescharacteristic, complemented
32#14555770C2212yescomplemented
33#14555769C2211yescharacteristic, complemented
34#14555768C2212yescomplemented
35C8×D139C2212yescomplemented
36C2×Q8×C139C2211yescharacteristic, complemented
37C2×D4×C139C2211yescharacteristic
38SD16×C139C2212yescomplemented
39SD16×C139C2212yescomplemented
40C2×C8×C139C2211yescharacteristic, complemented
41C22×D139—22no—
42Dic278—22no—
43Dic278D411yescharacteristic
44Dic278C2311yescharacteristic
45Dic278C2311yescharacteristic
46D556—22no—
47D556D411yescharacteristic
48D556C2311yescharacteristic
49D556C2311yescharacteristic
50C22⋊D139—21no—
51C22⋊D139—21no—
52C22⋊D139—22no—
53C22⋊D139—22no—
54C22⋊D139D412yes—
55C2×Dic139—22no—
56C4×D139—22no—
57C4×D139—21no—
58C4×D139—21no—
59C4×D139—22no—
60C4×D139C2312yes—
61C139⋊C8C2312yes—
62C23×C139—21no—
63Q8×C139—21no—
64Q8×C139C2312yes—
65D4×C139—21no—
66D4×C139C2312yes—
67C2×C4×C139—21no—
68C2×C4×C139C2311yescharacteristic
69C8×C139C2311yescharacteristic
70C8×C139C2311yescharacteristic
71C22×C139—22no—
72C22×C139—81no—
73C22×C139C2×D411yescharacteristic
74C2×D139—21no—
75C2×D139—21no—
76C2×D139—82no—
77C2×D139C2×D412yes—
78C4×C139—22no—
79C4×C139C2×D411yescharacteristic
80C4×C139C2411yescharacteristic
81Dic139—21no—
82Dic139—21no—
83Dic139C2×D412yes—
84C2×C139—21no—
85C2×C139—42no—
86C2×C139C22×D411yescharacteristic
87D139—22no—
88D139—41no—
89D139—41no—
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#135—1391no—
100C2×SD16—1392no—
101C2×SD16D13911yescharacteristic, complemented
102#131—1391no—
103#41—2782no—
104#41—2781no—
105#41—2781no—
106#41—1392no—
107#41—1392no—
108#41—1391no—
109#41—1391no—
110#41—1391no—
111C2×Q8—2781no—
112C2×Q8—1392no—
113C2×Q8C2×D13911yescharacteristic, complemented
114C2×D4—2781no—
115C2×D4—2782no—
116C2×D4—1392no—
117C2×D4C2×D13911yescharacteristic
118Q16—1392no—
119Q16—1391no—
120SD16—1392no—
121SD16—1392no—
122SD16—1391no—
123SD16—1391no—
124SD16C2×D13912yescomplemented
125SD16C2×D13912yescomplemented
126D8—1392no—
127D8—1391no—
128M16—1391no—
129M16—1392no—
130C2×C8—1392no—
131C2×C8C2×D13911yescharacteristic, complemented
132C23—21no—
133C23—2782no—
134Q8—21no—
135Q8—2782no—
136Q8—1391no—
137Q8—1391no—
138Q8—1391no—
139Q8C22×D13912yes—
140D4—21no—
141D4—2782no—
142D4—2782no—
143D4—2781no—
144D4—2781no—
145D4—2782no—
146D4—1392no—
147D4—1391no—
148D4—1391no—
149D4—1391no—
150D4C22×D13912yes—
151C2×C4—21no—
152C2×C4—2782no—
153C2×C4—2782no—
154C2×C4—2782no—
155C2×C4—2781no—
156C2×C4—2781no—
157C2×C4—1392no—
158C2×C4C22×D13911yescharacteristic
159C8—1392no—
160C8C22×D13911yescharacteristic
161C8C22×D13911yescharacteristic
162C22—22no—
163C22—81no—
164C22—2781no—
165C22—2781no—
166C22—11122no—
167C22—1392no—
168C22D4×D13911yescharacteristic
169C4—22no—
170C4—2781no—
171C4—2781no—
172C4—1392no—
173C4D4×D13911yescharacteristic
174C4C23×D13911yescharacteristic
175C2—21no—
176C2—42no—
177C2—2782no—
178C2—5561no—
179C2—5561no—
180C2C2×D4×D13911yescharacteristic
subgroupG/H
centerC2C2×D4×D139
commutatorC4×C139C24
FrattiniC4C23×D139
FittingC2×SD16×C139C2
socleC2×C139C22×D4
hypercenterC2×SD16D139
hypocenterC139#577
LCSG ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #17984890C2semidirect
2. #17984887C2semidirect
3. #17984873C2semidirect
4. #17984871C2semidirect
5. #17984869C2semidirect
6. #17984868C2semidirect
7. #17984864C2semidirect
8. #17984863C2semidirect
9. SD16×D139C2semidirect
10. #17984848C2semidirect
11. C2×SD16×C139C2semidirect
13. #14555786C22semidirect
17. #14555785C22semidirect
21. Q8×D139C22semidirect
25. Dic556C22semidirect
26. #14555775C22semidirect
27. #14555774C22semidirect
28. #14555774C22semidirect
29. #14555773C22semidirect
30. #14555772C22semidirect
31. D1112C22semidirect
32. #14555770C22semidirect
33. #14555769C22semidirect
34. #14555768C22semidirect
35. C8×D139C22semidirect
36. C2×Q8×C139C22semidirect
38. SD16×C139C22semidirect
39. SD16×C139C22semidirect
40. C2×C8×C139C22semidirect
90. C139#577semidirect
101. C2×SD16D139semidirect
113. C2×Q8C2×D139semidirect
124. SD16C2×D139semidirect
125. SD16C2×D139semidirect
131. C2×C8C2×D139semidirect