Finite Group Databasebeta

← #26039249

Subgroups — #26039249

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#19153160C211yesmaximal, characteristic, complemented
2#19153158C211yesmaximal, characteristic, complemented
3#19153146C211yesmaximal, characteristic, complemented
4#19153142C212yesmaximal, complemented
5#19153137C212yesmaximal, complemented
6#19153133C211yesmaximal, characteristic, complemented
7#19153132C212yesmaximal, complemented
8C2×#15668247C211yesmaximal, characteristic, complemented
9SD16×D179C212yesmaximal, complemented
10#19153121C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C179C211yesmaximal, characteristic, complemented
12#15668259—21no—
13#15668259C2211yescharacteristic
14#15668259C2211yescharacteristic
15#15668258—21no—
16#15668258—22no—
17#15668258C2212yes—
18#15668258C2212yescomplemented
19C2×Dic358—21no—
20C2×Dic358C2211yescharacteristic, complemented
21Q8×D179C2212yescomplemented
22C2×C22⋊D179—22no—
23D4×D179—21no—
24D4×D179C2212yes—
25Dic716C2212yescomplemented
26#15668249C2211yescharacteristic, complemented
27#15668248C2212yescomplemented
28#15668247C2212yescomplemented
29#15668247C2212yescomplemented
30#15668247C2211yescharacteristic, complemented
31#15668246C2211yescharacteristic, complemented
32#15668244C2211yescharacteristic, complemented
33#15668242C2212yescomplemented
34C2×C179⋊C8C2211yescharacteristic, complemented
35C8×D179C2212yescomplemented
36#41×C179C2211yescharacteristic, complemented
37C2×D4×C179C2211yescharacteristic
38SD16×C179C2212yescomplemented
39D8×C179C2212yescomplemented
40M16×C179C2211yescharacteristic, complemented
41C22×D179—22no—
42Dic358—21no—
43Dic358—22no—
44Dic358D411yescharacteristic
45Dic358C2312yes—
46Dic358C2311yescharacteristic
47D716D411yescharacteristic
48D716C2311yescharacteristic
49C22⋊D179—21no—
50C22⋊D179—22no—
51C22⋊D179—22no—
52C22⋊D179—22no—
53C22⋊D179D412yes—
54C2×Dic179—21no—
55C2×Dic179—22no—
56C2×Dic179—22no—
57C4×D179—22no—
58C4×D179—21no—
59C4×D179C2312yes—
60C179⋊C8C2311yescharacteristic
61C179⋊C8C2311yescharacteristic
62C23×C179—21no—
63Q8×C179C2311yescharacteristic
64D4×C179—21no—
65D4×C179—21no—
66D4×C179C2311yescharacteristic
67D4×C179C2312yes—
68C2×C4×C179—21no—
69C2×C4×C179C2311yescharacteristic
70C8×C179C2312yes—
71C22×C179—21no—
72C22×C179—22no—
73C22×C179—81no—
74C22×C179C2×D411yescharacteristic
75C2×D179—21no—
76C2×D179—82no—
77C2×D179C2×D412yes—
78C4×C179—21no—
79C4×C179C2×D411yescharacteristic
80C4×C179C2411yescharacteristic
81Dic179—21no—
82Dic179—22no—
83Dic179C2×D412yes—
84C2×C179—21no—
85C2×C179—42no—
86C2×C179—41no—
87C2×C179C22×D411yescharacteristic
88D179—22no—
89D179—41no—
90C179#57711yescharacteristic, complemented, Sylow
91#577—1791nomaximal, Sylow
922−1+4—1791no—
93H(5,𝔽2)—1791no—
94#137—1792no—
95#137—1791no—
96AGL(1,ℤ/8)—1792no—
97AGL(1,ℤ/8)D17911yescharacteristic, complemented
98#135—1791no—
99#135—1792no—
100C2×SD16—1791no—
101C2×SD16—1792no—
102#131—1791no—
103#41—3581no—
104#41—3581no—
105#41—3582no—
106#41—1792no—
107#41—1792no—
108#41—1791no—
109#41—1791no—
110#41C2×D17911yescharacteristic, complemented
111C2×Q8—3581no—
112C2×Q8—1792no—
113C2×Q8—1791no—
114C2×D4—3581no—
115C2×D4—3582no—
116C2×D4—1792no—
117C2×D4C2×D17911yescharacteristic
118Q16—1791no—
119Q16—1792no—
120SD16—1791no—
121SD16—1792no—
122SD16—1792no—
123SD16—1791no—
124SD16—1792no—
125SD16C2×D17912yescomplemented
126D8—1791no—
127D8C2×D17912yescomplemented
128M16—1792no—
129M16C2×D17911yescharacteristic, complemented
130C2×C8—1791no—
131C2×C8—1792no—
132C23—21no—
133C23—3582no—
134Q8—3582no—
135Q8—3581no—
136Q8—1792no—
137Q8—1791no—
138Q8—1791no—
139Q8C22×D17911yescharacteristic
140D4—21no—
141D4—21no—
142D4—3582no—
143D4—3582no—
144D4—3581no—
145D4—3582no—
146D4—1792no—
147D4—1791no—
148D4—1791no—
149D4C22×D17911yescharacteristic
150D4C22×D17912yes—
151C2×C4—21no—
152C2×C4—3582no—
153C2×C4—3581no—
154C2×C4—3582no—
155C2×C4—3582no—
156C2×C4—3581no—
157C2×C4—1792no—
158C2×C4C22×D17911yescharacteristic
159C8—1791no—
160C8—1791no—
161C8C22×D17912yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—3581no—
166C22—14322no—
167C22—1792no—
168C22D4×D17911yescharacteristic
169C4—21no—
170C4—3581no—
171C4—3582no—
172C4—1792no—
173C4D4×D17911yescharacteristic
174C4C23×D17911yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—3582no—
179C2—7161no—
180C2C2×D4×D17911yescharacteristic
subgroupG/H
centerC2C2×D4×D179
commutator, cosocleC4×C179C24
FrattiniC4C23×D179
FittingAGL(1,ℤ/8)×C179C2
socleC2×C179C22×D4
hypercenterAGL(1,ℤ/8)D179
hypocenterC179#577
LCSG ▷ C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #19153160C2semidirect
2. #19153158C2semidirect
3. #19153146C2semidirect
4. #19153142C2semidirect
5. #19153137C2semidirect
6. #19153133C2semidirect
7. #19153132C2semidirect
8. C2×#15668247C2semidirect
9. SD16×D179C2semidirect
10. #19153121C2semidirect
11. AGL(1,ℤ/8)×C179C2semidirect
18. #15668258C22semidirect
20. C2×Dic358C22semidirect
21. Q8×D179C22semidirect
25. Dic716C22semidirect
26. #15668249C22semidirect
27. #15668248C22semidirect
28. #15668247C22semidirect
29. #15668247C22semidirect
30. #15668247C22semidirect
31. #15668246C22semidirect
32. #15668244C22semidirect
33. #15668242C22semidirect
34. C2×C179⋊C8C22semidirect
35. C8×D179C22semidirect
36. #41×C179C22semidirect
38. SD16×C179C22semidirect
39. D8×C179C22semidirect
40. M16×C179C22semidirect
90. C179#577semidirect
97. AGL(1,ℤ/8)D179semidirect
110. #41C2×D179semidirect
125. SD16C2×D179semidirect
127. D8C2×D179semidirect
129. M16C2×D179semidirect

Maximal subgroups

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

subgroupindex
#191531602
#191531582
#191531462
#191531422
#191531372
#191531332
#191531322
C2×#156682472
SD16×D1792
#191531212
AGL(1,ℤ/8)×C1792
#577179