Finite Group Databasebeta

← #43248527

Subgroups — #43248527

Order 28352.

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#28381933C211yesmaximal, characteristic, complemented
2#28381931C211yesmaximal, characteristic, complemented
3#28381919C211yesmaximal, characteristic, complemented
4#28381915C212yesmaximal, complemented
5#28381910C212yesmaximal, complemented
6#28381906C211yesmaximal, characteristic, complemented
7#28381905C212yesmaximal, complemented
8C2×#20296775C211yesmaximal, characteristic, complemented
9SD16×D443C212yesmaximal, complemented
10#28381894C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C443C211yesmaximal, characteristic, complemented
12#20296787—21no—
13#20296787C2211yescharacteristic
14#20296787C2211yescharacteristic
15#20296786—21no—
16#20296786—22no—
17#20296786C2212yes—
18#20296786C2212yescomplemented
19C2×Dic886—21no—
20C2×Dic886C2211yescharacteristic, complemented
21Q8×D443C2212yescomplemented
22C2×C22⋊D443—22no—
23D4×D443—21no—
24D4×D443C2212yes—
25Dic1772C2212yescomplemented
26#20296777C2211yescharacteristic, complemented
27#20296776C2212yescomplemented
28#20296775C2212yescomplemented
29#20296775C2212yescomplemented
30#20296775C2211yescharacteristic, complemented
31#20296774C2211yescharacteristic, complemented
32#20296772C2211yescharacteristic, complemented
33#20296770C2212yescomplemented
34C2×C443⋊C8C2211yescharacteristic, complemented
35C8×D443C2212yescomplemented
36#41×C443C2211yescharacteristic, complemented
37C2×D4×C443C2211yescharacteristic
38SD16×C443C2212yescomplemented
39D8×C443C2212yescomplemented
40M16×C443C2211yescharacteristic, complemented
41C22×D443—22no—
42Dic886—21no—
43Dic886—22no—
44Dic886D411yescharacteristic
45Dic886C2312yes—
46Dic886C2311yescharacteristic
47D1772D411yescharacteristic
48D1772C2311yescharacteristic
49C22⋊D443—21no—
50C22⋊D443—22no—
51C22⋊D443—22no—
52C22⋊D443—22no—
53C22⋊D443D412yes—
54C2×Dic443—21no—
55C2×Dic443—22no—
56C2×Dic443—22no—
57C4×D443—22no—
58C4×D443—21no—
59C4×D443C2312yes—
60C443⋊C8C2311yescharacteristic
61C443⋊C8C2311yescharacteristic
62C23×C443—21no—
63Q8×C443C2311yescharacteristic
64D4×C443—21no—
65D4×C443—21no—
66D4×C443C2311yescharacteristic
67D4×C443C2312yes—
68C2×C4×C443—21no—
69C2×C4×C443C2311yescharacteristic
70C8×C443C2312yes—
71C22×C443—21no—
72C22×C443—22no—
73C22×C443—81no—
74C22×C443C2×D411yescharacteristic
75C2×D443—21no—
76C2×D443—82no—
77C2×D443C2×D412yes—
78C4×C443—21no—
79C4×C443C2×D411yescharacteristic
80C4×C443C2411yescharacteristic
81Dic443—21no—
82Dic443—22no—
83Dic443C2×D412yes—
84C2×C443—21no—
85C2×C443—42no—
86C2×C443—41no—
87C2×C443C22×D411yescharacteristic
88D443—22no—
89D443—41no—
90C443#57711yescharacteristic, complemented, Sylow
91#577—4431nomaximal, Sylow
922−1+4—4431no—
93H(5,𝔽2)—4431no—
94#137—4432no—
95#137—4431no—
96AGL(1,ℤ/8)—4432no—
97AGL(1,ℤ/8)D44311yescharacteristic, complemented
98#135—4431no—
99#135—4432no—
100C2×SD16—4431no—
101C2×SD16—4432no—
102#131—4431no—
103#41—8861no—
104#41—8861no—
105#41—8862no—
106#41—4432no—
107#41—4432no—
108#41—4431no—
109#41—4431no—
110#41C2×D44311yescharacteristic, complemented
111C2×Q8—8861no—
112C2×Q8—4432no—
113C2×Q8—4431no—
114C2×D4—8861no—
115C2×D4—8862no—
116C2×D4—4432no—
117C2×D4C2×D44311yescharacteristic
118Q16—4431no—
119Q16—4432no—
120SD16—4431no—
121SD16—4432no—
122SD16—4432no—
123SD16—4431no—
124SD16—4432no—
125SD16C2×D44312yescomplemented
126D8—4431no—
127D8C2×D44312yescomplemented
128M16—4432no—
129M16C2×D44311yescharacteristic, complemented
130C2×C8—4431no—
131C2×C8—4432no—
132C23—21no—
133C23—8862no—
134Q8—8862no—
135Q8—8861no—
136Q8—4432no—
137Q8—4431no—
138Q8—4431no—
139Q8C22×D44311yescharacteristic
140D4—21no—
141D4—21no—
142D4—8862no—
143D4—8862no—
144D4—8861no—
145D4—8862no—
146D4—4432no—
147D4—4431no—
148D4—4431no—
149D4C22×D44311yescharacteristic
150D4C22×D44312yes—
151C2×C4—21no—
152C2×C4—8862no—
153C2×C4—8861no—
154C2×C4—8862no—
155C2×C4—8862no—
156C2×C4—8861no—
157C2×C4—4432no—
158C2×C4C22×D44311yescharacteristic
159C8—4431no—
160C8—4431no—
161C8C22×D44312yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—8861no—
166C22—4432no—
167C22—35442no—
168C22D4×D44311yescharacteristic
169C4—21no—
170C4—8861no—
171C4—8862no—
172C4—4432no—
173C4D4×D44311yescharacteristic
174C4C23×D44311yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—8862no—
179C2—17721no—
180C2C2×D4×D44311yescharacteristic
subgroupG/H
centerC2C2×D4×D443
commutator, cosocleC4×C443C24
FrattiniC4C23×D443
FittingAGL(1,ℤ/8)×C443C2
socleC2×C443C22×D4
hypercenterAGL(1,ℤ/8)D443
hypocenterC443#577
LCSG ▷ C4×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #28381933C2semidirect
2. #28381931C2semidirect
3. #28381919C2semidirect
4. #28381915C2semidirect
5. #28381910C2semidirect
6. #28381906C2semidirect
7. #28381905C2semidirect
8. C2×#20296775C2semidirect
9. SD16×D443C2semidirect
10. #28381894C2semidirect
11. AGL(1,ℤ/8)×C443C2semidirect
18. #20296786C22semidirect
20. C2×Dic886C22semidirect
21. Q8×D443C22semidirect
25. Dic1772C22semidirect
26. #20296777C22semidirect
27. #20296776C22semidirect
28. #20296775C22semidirect
29. #20296775C22semidirect
30. #20296775C22semidirect
31. #20296774C22semidirect
32. #20296772C22semidirect
33. #20296770C22semidirect
34. C2×C443⋊C8C22semidirect
35. C8×D443C22semidirect
36. #41×C443C22semidirect
38. SD16×C443C22semidirect
39. D8×C443C22semidirect
40. M16×C443C22semidirect
90. C443#577semidirect
97. AGL(1,ℤ/8)D443semidirect
110. #41C2×D443semidirect
125. SD16C2×D443semidirect
127. D8C2×D443semidirect
129. M16C2×D443semidirect

Maximal subgroups

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

subgroupindex
#283819332
#283819312
#283819192
#283819152
#283819102
#283819062
#283819052
C2×#202967752
SD16×D4432
#283818942
AGL(1,ℤ/8)×C4432
#577443