Finite Group Databasebeta

← #26039243

Subgroups — #26039243

Order 11456.

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

normal subgroups only

This group has 268 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#19153159C211yesmaximal, characteristic, complemented
2#19153158C211yesmaximal, characteristic, complemented
3#19153141C211yesmaximal, characteristic, complemented
4#19153140C212yesmaximal, complemented
5#19153137C212yesmaximal, complemented
6#19153134C212yesmaximal, complemented
7#19153133C211yesmaximal, characteristic, complemented
8C2×#15668244C211yesmaximal, characteristic, complemented
9D8×D179C212yesmaximal, complemented
10#19153121C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C179C211yesmaximal, characteristic, complemented
12#15668260C2212yescomplemented
13#15668259—21no—
14#15668259C2211yescharacteristic
15#15668259C2211yescharacteristic, complemented
16#15668258—21no—
17#15668258C2212yescomplemented
18C2×D716—21no—
19C2×D716C2211yescharacteristic, complemented
20C2×C22⋊D179—22no—
21D4×D179—21no—
22D4×D179—22no—
23D4×D179C2212yescomplemented
24D4×D179C2212yescomplemented
25#15668249C2211yescharacteristic, complemented
26#15668248C2212yescomplemented
27#15668247C2211yescharacteristic, complemented
28#15668246C2211yescharacteristic, complemented
29D1432C2212yescomplemented
30#15668244C2211yescharacteristic, complemented
31#15668244C2212yescomplemented
32#15668244C2212yescomplemented
33#15668242C2212yescomplemented
34C2×C179⋊C8C2211yescharacteristic, complemented
35C8×D179C2212yescomplemented
36#41×C179C2211yescharacteristic, complemented
37C2×D4×C179C2211yescharacteristic, complemented
38SD16×C179C2212yescomplemented
39D8×C179C2212yescomplemented
40M16×C179C2211yescharacteristic, complemented
41C22×D179—21no—
42C22×D179—22no—
43C22×D179—22no—
44Dic358D411yescharacteristic
45Dic358C2311yescharacteristic
46D716—22no—
47D716—21no—
48D716D411yescharacteristic
49D716C2312yes—
50D716C2311yescharacteristic
51C22⋊D179—21no—
52C22⋊D179—22no—
53C22⋊D179—22no—
54C22⋊D179—22no—
55C22⋊D179D412yes—
56C2×Dic179—22no—
57C4×D179—21no—
58C4×D179—22no—
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—22no—
77C2×D179—82no—
78C2×D179—82no—
79C2×D179—81no—
80C2×D179C2×D412yes—
81C4×C179—21no—
82C4×C179C2×D411yescharacteristic
83C4×C179C2411yescharacteristic
84Dic179—21no—
85Dic179C2×D412yes—
86C2×C179—21no—
87C2×C179—41no—
88C2×C179—42no—
89C2×C179C22×D411yescharacteristic
90D179—22no—
91D179—41no—
92D179—42no—
93C179#57611yescharacteristic, complemented, Sylow
94#576—1791nomaximal, Sylow
95H(5,𝔽2)—1791no—
96H(5,𝔽2)—1791no—
97AGL(1,ℤ/8)—1792no—
98AGL(1,ℤ/8)—1792no—
99AGL(1,ℤ/8)—1791no—
100AGL(1,ℤ/8)D17911yescharacteristic, complemented
101#135—1791no—
102#135—1792no—
103C2×D8—1791no—
104C2×D8—1792no—
105#131—1791no—
106#41—3581no—
107#41—3581no—
108#41—1792no—
109#41—1792no—
110#41—1791no—
111#41—1791no—
112#41C2×D17911yescharacteristic, complemented
113C2×D4—3581no—
114C2×D4—3582no—
115C2×D4—3581no—
116C2×D4—3582no—
117C2×D4—1792no—
118C2×D4—1792no—
119C2×D4—1791no—
120C2×D4C2×D17911yescharacteristic, complemented
121Q16—1791no—
122SD16—1791no—
123SD16—1791no—
124SD16—1792no—
125SD16C2×D17912yescomplemented
126D8—1792no—
127D8—1791no—
128D8—1792no—
129D8—1792no—
130D8C2×D17912yescomplemented
131M16—1792no—
132M16C2×D17911yescharacteristic, complemented
133C2×C8—1791no—
134C2×C8—1792no—
135C23—21no—
136C23—3582no—
137C23—3582no—
138C23—3581no—
139Q8—1791no—
140Q8—1791no—
141Q8C22×D17911yescharacteristic
142D4—21no—
143D4—21no—
144D4—3582no—
145D4—3582no—
146D4—3581no—
147D4—3582no—
148D4—3582no—
149D4—3581no—
150D4—1792no—
151D4—1791no—
152D4—1792no—
153D4—1791no—
154D4C22×D17912yes—
155D4C22×D17911yescharacteristic
156C2×C4—21no—
157C2×C4—3582no—
158C2×C4—3582no—
159C2×C4—3581no—
160C2×C4—1792no—
161C2×C4C22×D17911yescharacteristic
162C8—1791no—
163C8—1791no—
164C8C22×D17912yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—3582no—
169C22—3581no—
170C22—14321no—
171C22—14322no—
172C22—14322no—
173C22—1792no—
174C22D4×D17911yescharacteristic
175C4—21no—
176C4—3581no—
177C4—1792no—
178C4D4×D17911yescharacteristic
179C4C23×D17911yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—3582no—
184C2—7162no—
185C2—7161no—
186C2C2×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#576
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. #19153159C2semidirect
2. #19153158C2semidirect
3. #19153141C2semidirect
4. #19153140C2semidirect
5. #19153137C2semidirect
6. #19153134C2semidirect
7. #19153133C2semidirect
8. C2×#15668244C2semidirect
9. D8×D179C2semidirect
10. #19153121C2semidirect
11. AGL(1,ℤ/8)×C179C2semidirect
12. #15668260C22semidirect
15. #15668259C22semidirect
17. #15668258C22semidirect
19. C2×D716C22semidirect
23. D4×D179C22semidirect
24. D4×D179C22semidirect
25. #15668249C22semidirect
26. #15668248C22semidirect
27. #15668247C22semidirect
28. #15668246C22semidirect
29. D1432C22semidirect
30. #15668244C22semidirect
31. #15668244C22semidirect
32. #15668244C22semidirect
33. #15668242C22semidirect
34. C2×C179⋊C8C22semidirect
35. C8×D179C22semidirect
36. #41×C179C22semidirect
37. C2×D4×C179C22semidirect
38. SD16×C179C22semidirect
39. D8×C179C22semidirect
40. M16×C179C22semidirect
93. C179#576semidirect
100. AGL(1,ℤ/8)D179semidirect
112. #41C2×D179semidirect
120. C2×D4C2×D179semidirect
125. SD16C2×D179semidirect
130. D8C2×D179semidirect
132. M16C2×D179semidirect

Maximal subgroups

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

subgroupindex
#191531592
#191531582
#191531412
#191531402
#191531372
#191531342
#191531332
C2×#156682442
D8×D1792
#191531212
AGL(1,ℤ/8)×C1792
#576179