Finite Group Databasebeta

← #26039248

Subgroups — #26039248

Order 11456.

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#19153161C211yesmaximal, characteristic, complemented
2#19153159C211yesmaximal, characteristic, complemented
3#19153145C212yesmaximal, complemented
4#19153141C211yesmaximal, characteristic, complemented
5#19153140C212yesmaximal, complemented
6#19153136C212yesmaximal, complemented
7#19153133C211yesmaximal, characteristic, complemented
8C2×#15668246C211yesmaximal, characteristic, complemented
9SD16×D179C212yesmaximal, complemented
10#19153121C211yesmaximal, characteristic, complemented
11#137×C179C211yesmaximal, characteristic, complemented
12#15668260—21no—
13#15668260C2212yes—
14#15668260C2212yescomplemented
15#15668259—21no—
16#15668259—22no—
17#15668259C2211yescharacteristic
18#15668259C2211yescharacteristic, complemented
19Q8×D179—21no—
20Q8×D179C2212yescomplemented
21C2×D716—21no—
22C2×D716C2211yescharacteristic
23D4×D179—22no—
24D4×D179C2212yes—
25#15668249C2211yescharacteristic, complemented
26#15668248C2212yescomplemented
27#15668247C2211yescharacteristic, complemented
28#15668246C2212yescomplemented
29#15668246C2212yescomplemented
30#15668246C2211yescharacteristic, complemented
31D1432C2212yescomplemented
32#15668244C2211yescharacteristic, complemented
33#15668242C2212yescomplemented
34C2×C179⋊C8C2211yescharacteristic, complemented
35C8×D179C2212yescomplemented
36#41×C179C2211yescharacteristic
37C2×Q8×C179C2211yescharacteristic, complemented
38Q16×C179C2212yescomplemented
39SD16×C179C2212yescomplemented
40M16×C179C2211yescharacteristic, complemented
41C22×D179—21no—
42C22×D179—22no—
43Dic358—22no—
44Dic358D411yescharacteristic
45Dic358C2311yescharacteristic
46D716—22no—
47D716—22no—
48D716—21no—
49D716D411yescharacteristic
50D716C2311yescharacteristic
51D716C2312yes—
52C22⋊D179—21no—
53C22⋊D179—22no—
54C22⋊D179D412yes—
55C4×D179—22no—
56C4×D179—21no—
57C4×D179—22no—
58C4×D179—22no—
59C4×D179C2312yes—
60C179⋊C8C2311yescharacteristic
61C179⋊C8C2311yescharacteristic
62Q8×C179—21no—
63Q8×C179C2312yes—
64Q8×C179C2311yescharacteristic
65D4×C179—21no—
66D4×C179C2311yescharacteristic
67C2×C4×C179—21no—
68C2×C4×C179—21no—
69C2×C4×C179C2311yescharacteristic
70C8×C179C2312yes—
71C22×C179—21no—
72C22×C179C2×D411yescharacteristic
73C2×D179—21no—
74C2×D179—22no—
75C2×D179—82no—
76C2×D179—81no—
77C2×D179C2×D412yes—
78C4×C179—21no—
79C4×C179—22no—
80C4×C179C2×D411yescharacteristic
81C4×C179C2411yescharacteristic
82Dic179—21no—
83Dic179C2×D412yes—
84C2×C179—21no—
85C2×C179—41no—
86C2×C179C22×D411yescharacteristic
87D179—22no—
88D179—41no—
89D179—42no—
90C179#57711yescharacteristic, complemented, Sylow
91#577—1791nomaximal, Sylow
922−1+4—1791no—
93H(5,𝔽2)—1791no—
94#137—1792no—
95#137D17911yescharacteristic, complemented
96AGL(1,ℤ/8)—1792no—
97AGL(1,ℤ/8)—1791no—
98#135—1791no—
99#135—1792no—
100C2×SD16—1791no—
101C2×SD16—1792no—
102#131—1791no—
103#41—3581no—
104#41—3582no—
105#41—3581no—
106#41—1792no—
107#41—1792no—
108#41—1791no—
109#41—1791no—
110#41C2×D17911yescharacteristic
111C2×Q8—3581no—
112C2×Q8—1792no—
113C2×Q8C2×D17911yescharacteristic, complemented
114C2×D4—3581no—
115C2×D4—3582no—
116C2×D4—1792no—
117C2×D4—1791no—
118Q16—1791no—
119Q16C2×D17912yescomplemented
120SD16—1792no—
121SD16—1792no—
122SD16—1791no—
123SD16—1791no—
124SD16—1792no—
125SD16C2×D17912yescomplemented
126D8—1791no—
127D8—1792no—
128M16—1792no—
129M16C2×D17911yescharacteristic, complemented
130C2×C8—1791no—
131C2×C8—1792no—
132C23—3582no—
133C23—3581no—
134Q8—21no—
135Q8—3582no—
136Q8—1791no—
137Q8—1791no—
138Q8C22×D17912yes—
139Q8C22×D17911yescharacteristic
140D4—21no—
141D4—3582no—
142D4—3582no—
143D4—3581no—
144D4—3582no—
145D4—3581no—
146D4—1792no—
147D4—1791no—
148D4—1791no—
149D4—1792no—
150D4C22×D17911yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—3582no—
154C2×C4—3582no—
155C2×C4—3582no—
156C2×C4—3581no—
157C2×C4—1792no—
158C2×C4C22×D17911yescharacteristic
159C8—1791no—
160C8—1791no—
161C8C22×D17912yes—
162C22—21no—
163C22—3581no—
164C22—3582no—
165C22—14321no—
166C22—14322no—
167C22—1792no—
168C22D4×D17911yescharacteristic
169C4—21no—
170C4—22no—
171C4—3581no—
172C4—1792no—
173C4D4×D17911yescharacteristic
174C4C23×D17911yescharacteristic
175C2—21no—
176C2—41no—
177C2—3582no—
178C2—7162no—
179C2—7161no—
180C2C2×D4×D17911yescharacteristic
subgroupG/H
centerC2C2×D4×D179
commutator, cosocleC4×C179C24
FrattiniC4C23×D179
Fitting#137×C179C2
socleC2×C179C22×D4
hypercenter#137D179
hypocenterC179#577
LCSG ▷ C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #19153161C2semidirect
2. #19153159C2semidirect
3. #19153145C2semidirect
4. #19153141C2semidirect
5. #19153140C2semidirect
6. #19153136C2semidirect
7. #19153133C2semidirect
8. C2×#15668246C2semidirect
9. SD16×D179C2semidirect
10. #19153121C2semidirect
11. #137×C179C2semidirect
14. #15668260C22semidirect
18. #15668259C22semidirect
20. Q8×D179C22semidirect
25. #15668249C22semidirect
26. #15668248C22semidirect
27. #15668247C22semidirect
28. #15668246C22semidirect
29. #15668246C22semidirect
30. #15668246C22semidirect
31. D1432C22semidirect
32. #15668244C22semidirect
33. #15668242C22semidirect
34. C2×C179⋊C8C22semidirect
35. C8×D179C22semidirect
37. C2×Q8×C179C22semidirect
38. Q16×C179C22semidirect
39. SD16×C179C22semidirect
40. M16×C179C22semidirect
90. C179#577semidirect
95. #137D179semidirect
113. C2×Q8C2×D179semidirect
119. Q16C2×D179semidirect
125. SD16C2×D179semidirect
129. M16C2×D179semidirect

Maximal subgroups

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

subgroupindex
#191531612
#191531592
#191531452
#191531412
#191531402
#191531362
#191531332
C2×#156682462
SD16×D1792
#191531212
#137×C1792
#577179