Finite Group Databasebeta

← #43248523

Subgroups — #43248523

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#28381934C211yesmaximal, characteristic, complemented
2#28381931C211yesmaximal, characteristic, complemented
3#28381917C211yesmaximal, characteristic, complemented
4#28381915C212yesmaximal, complemented
5#28381913C212yesmaximal, complemented
6#28381912C211yesmaximal, characteristic, complemented
7#28381908C211yesmaximal, characteristic, complemented
8#28381907C212yesmaximal, complemented
9SD16×D443C212yesmaximal, complemented
10#28381892C211yesmaximal, characteristic, complemented
11C2×SD16×C443C211yesmaximal, characteristic, complemented
12#20296788—21no—
13#20296788C2212yescomplemented
14#20296787—22no—
15#20296787C2211yescharacteristic
16#20296787C2211yescharacteristic
17#20296787C2211yescharacteristic, complemented
18#20296786—21no—
19#20296786C2212yes—
20Q8×D443—21no—
21Q8×D443C2212yescomplemented
22C2×C22⋊D443—22no—
23D4×D443—21no—
24D4×D443C2212yes—
25Dic1772C2211yescharacteristic, complemented
26#20296777C2212yescomplemented
27#20296776C2211yescharacteristic, complemented
28#20296776C2211yescharacteristic, complemented
29#20296775C2212yescomplemented
30#20296774C2212yescomplemented
31D3544C2211yescharacteristic, complemented
32#20296772C2212yescomplemented
33#20296771C2211yescharacteristic, complemented
34#20296770C2212yescomplemented
35C8×D443C2212yescomplemented
36C2×Q8×C443C2211yescharacteristic, complemented
37C2×D4×C443C2211yescharacteristic
38SD16×C443C2212yescomplemented
39SD16×C443C2212yescomplemented
40C2×C8×C443C2211yescharacteristic, complemented
41C22×D443—22no—
42Dic886—22no—
43Dic886D411yescharacteristic
44Dic886C2311yescharacteristic
45Dic886C2311yescharacteristic
46D1772—22no—
47D1772D411yescharacteristic
48D1772C2311yescharacteristic
49D1772C2311yescharacteristic
50C22⋊D443—21no—
51C22⋊D443—21no—
52C22⋊D443—22no—
53C22⋊D443—22no—
54C22⋊D443D412yes—
55C2×Dic443—22no—
56C4×D443—22no—
57C4×D443—21no—
58C4×D443—21no—
59C4×D443—22no—
60C4×D443C2312yes—
61C443⋊C8C2312yes—
62C23×C443—21no—
63Q8×C443—21no—
64Q8×C443C2312yes—
65D4×C443—21no—
66D4×C443C2312yes—
67C2×C4×C443—21no—
68C2×C4×C443C2311yescharacteristic
69C8×C443C2311yescharacteristic
70C8×C443C2311yescharacteristic
71C22×C443—22no—
72C22×C443—81no—
73C22×C443C2×D411yescharacteristic
74C2×D443—21no—
75C2×D443—21no—
76C2×D443—82no—
77C2×D443C2×D412yes—
78C4×C443—22no—
79C4×C443C2×D411yescharacteristic
80C4×C443C2411yescharacteristic
81Dic443—21no—
82Dic443—21no—
83Dic443C2×D412yes—
84C2×C443—21no—
85C2×C443—42no—
86C2×C443C22×D411yescharacteristic
87D443—22no—
88D443—41no—
89D443—41no—
90C443#57711yescharacteristic, complemented, Sylow
91#577—4431nomaximal, Sylow
922−1+4—4431no—
93H(5,𝔽2)—4431no—
94#137—4431no—
95#137—4432no—
96AGL(1,ℤ/8)—4431no—
97AGL(1,ℤ/8)—4432no—
98#135—4432no—
99#135—4431no—
100C2×SD16—4432no—
101C2×SD16D44311yescharacteristic, complemented
102#131—4431no—
103#41—8862no—
104#41—8861no—
105#41—8861no—
106#41—4432no—
107#41—4432no—
108#41—4431no—
109#41—4431no—
110#41—4431no—
111C2×Q8—8861no—
112C2×Q8—4432no—
113C2×Q8C2×D44311yescharacteristic, complemented
114C2×D4—8861no—
115C2×D4—8862no—
116C2×D4—4432no—
117C2×D4C2×D44311yescharacteristic
118Q16—4432no—
119Q16—4431no—
120SD16—4432no—
121SD16—4432no—
122SD16—4431no—
123SD16—4431no—
124SD16C2×D44312yescomplemented
125SD16C2×D44312yescomplemented
126D8—4432no—
127D8—4431no—
128M16—4431no—
129M16—4432no—
130C2×C8—4432no—
131C2×C8C2×D44311yescharacteristic, complemented
132C23—21no—
133C23—8862no—
134Q8—21no—
135Q8—8862no—
136Q8—4431no—
137Q8—4431no—
138Q8—4431no—
139Q8C22×D44312yes—
140D4—21no—
141D4—8862no—
142D4—8862no—
143D4—8861no—
144D4—8861no—
145D4—8862no—
146D4—4432no—
147D4—4431no—
148D4—4431no—
149D4—4431no—
150D4C22×D44312yes—
151C2×C4—21no—
152C2×C4—8862no—
153C2×C4—8862no—
154C2×C4—8862no—
155C2×C4—8861no—
156C2×C4—8861no—
157C2×C4—4432no—
158C2×C4C22×D44311yescharacteristic
159C8—4432no—
160C8C22×D44311yescharacteristic
161C8C22×D44311yescharacteristic
162C22—22no—
163C22—81no—
164C22—8861no—
165C22—8861no—
166C22—4432no—
167C22—35442no—
168C22D4×D44311yescharacteristic
169C4—22no—
170C4—8861no—
171C4—8861no—
172C4—4432no—
173C4D4×D44311yescharacteristic
174C4C23×D44311yescharacteristic
175C2—21no—
176C2—42no—
177C2—8862no—
178C2—17721no—
179C2—17721no—
180C2C2×D4×D44311yescharacteristic
subgroupG/H
centerC2C2×D4×D443
commutator, cosocleC4×C443C24
FrattiniC4C23×D443
FittingC2×SD16×C443C2
socleC2×C443C22×D4
hypercenterC2×SD16D443
hypocenterC443#577
LCSG ▷ C4×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #28381934C2semidirect
2. #28381931C2semidirect
3. #28381917C2semidirect
4. #28381915C2semidirect
5. #28381913C2semidirect
6. #28381912C2semidirect
7. #28381908C2semidirect
8. #28381907C2semidirect
9. SD16×D443C2semidirect
10. #28381892C2semidirect
11. C2×SD16×C443C2semidirect
13. #20296788C22semidirect
17. #20296787C22semidirect
21. Q8×D443C22semidirect
25. Dic1772C22semidirect
26. #20296777C22semidirect
27. #20296776C22semidirect
28. #20296776C22semidirect
29. #20296775C22semidirect
30. #20296774C22semidirect
31. D3544C22semidirect
32. #20296772C22semidirect
33. #20296771C22semidirect
34. #20296770C22semidirect
35. C8×D443C22semidirect
36. C2×Q8×C443C22semidirect
38. SD16×C443C22semidirect
39. SD16×C443C22semidirect
40. C2×C8×C443C22semidirect
90. C443#577semidirect
101. C2×SD16D443semidirect
113. C2×Q8C2×D443semidirect
124. SD16C2×D443semidirect
125. SD16C2×D443semidirect
131. C2×C8C2×D443semidirect

Maximal subgroups

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

subgroupindex
#283819342
#283819312
#283819172
#283819152
#283819132
#283819122
#283819082
#283819072
SD16×D4432
#283818922
C2×SD16×C4432
#577443