Finite Group Databasebeta

← #45688242

Subgroups — #45688242

Order 33344.

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#30659755C211yesmaximal, characteristic, complemented
2#30659753C211yesmaximal, characteristic, complemented
3#30659741C211yesmaximal, characteristic, complemented
4#30659737C212yesmaximal, complemented
5#30659732C212yesmaximal, complemented
6#30659728C211yesmaximal, characteristic, complemented
7#30659727C212yesmaximal, complemented
8C2×#22552352C211yesmaximal, characteristic, complemented
9SD16×D521C212yesmaximal, complemented
10#30659716C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C521C211yesmaximal, characteristic, complemented
12#22552364—21no—
13#22552364C2211yescharacteristic
14#22552364C2211yescharacteristic
15#22552363—21no—
16#22552363—22no—
17#22552363C2212yes—
18#22552363C2212yescomplemented
19C2×Dic1042—21no—
20C2×Dic1042C2211yescharacteristic, complemented
21Q8×D521C2212yescomplemented
22C2×C22⋊D521—22no—
23D4×D521—21no—
24D4×D521C2212yes—
25Dic2084C2212yescomplemented
26#22552354C2211yescharacteristic, complemented
27#22552353C2212yescomplemented
28#22552352C2212yescomplemented
29#22552352C2212yescomplemented
30#22552352C2211yescharacteristic, complemented
31#22552351C2211yescharacteristic, complemented
32#22552349C2211yescharacteristic, complemented
33#22552347C2212yescomplemented
34C2×#16861960C2211yescharacteristic, complemented
35C8×D521C2212yescomplemented
36#41×C521C2211yescharacteristic, complemented
37C2×D4×C521C2211yescharacteristic
38SD16×C521C2212yescomplemented
39D8×C521C2212yescomplemented
40M16×C521C2211yescharacteristic, complemented
41C22×D521—22no—
42Dic1042—21no—
43Dic1042—22no—
44Dic1042D411yescharacteristic
45Dic1042C2312yes—
46Dic1042C2311yescharacteristic
47D2084D411yescharacteristic
48D2084C2311yescharacteristic
49C22⋊D521—21no—
50C22⋊D521—22no—
51C22⋊D521—22no—
52C22⋊D521—22no—
53C22⋊D521D412yes—
54C2×Dic521—21no—
55C2×Dic521—22no—
56C2×Dic521—22no—
57C4×D521—22no—
58C4×D521—21no—
59C4×D521C2312yes—
60#16861960C2311yescharacteristic
61#16861960C2311yescharacteristic
62C23×C521—21no—
63Q8×C521C2311yescharacteristic
64D4×C521—21no—
65D4×C521—21no—
66D4×C521C2311yescharacteristic
67D4×C521C2312yes—
68C2×C4×C521—21no—
69C2×C4×C521C2311yescharacteristic
70C8×C521C2312yes—
71C22×C521—21no—
72C22×C521—22no—
73C22×C521—81no—
74C22×C521C2×D411yescharacteristic
75C2×D521—21no—
76C2×D521—82no—
77C2×D521C2×D412yes—
78C4×C521—21no—
79C4×C521C2×D411yescharacteristic
80C4×C521C2411yescharacteristic
81Dic521—21no—
82Dic521—22no—
83Dic521C2×D412yes—
84C2×C521—21no—
85C2×C521—42no—
86C2×C521—41no—
87C2×C521C22×D411yescharacteristic
88D521—22no—
89D521—41no—
90C521#57711yescharacteristic, complemented, Sylow
91#577—5211nomaximal, Sylow
922−1+4—5211no—
93H(5,𝔽2)—5211no—
94#137—5212no—
95#137—5211no—
96AGL(1,ℤ/8)—5212no—
97AGL(1,ℤ/8)D52111yescharacteristic, complemented
98#135—5211no—
99#135—5212no—
100C2×SD16—5211no—
101C2×SD16—5212no—
102#131—5211no—
103#41—5211no—
104#41—5212no—
105#41—5212no—
106#41—5211no—
107#41—10421no—
108#41—10422no—
109#41—10421no—
110#41C2×D52111yescharacteristic, complemented
111C2×Q8—5212no—
112C2×Q8—5211no—
113C2×Q8—10421no—
114C2×D4—5212no—
115C2×D4—10421no—
116C2×D4—10422no—
117C2×D4C2×D52111yescharacteristic
118Q16—5211no—
119Q16—5212no—
120SD16—5211no—
121SD16—5212no—
122SD16—5212no—
123SD16—5211no—
124SD16—5212no—
125SD16C2×D52112yescomplemented
126D8—5211no—
127D8C2×D52112yescomplemented
128M16—5212no—
129M16C2×D52111yescharacteristic, complemented
130C2×C8—5211no—
131C2×C8—5212no—
132C23—21no—
133C23—10422no—
134Q8—5211no—
135Q8—5212no—
136Q8—5211no—
137Q8—10422no—
138Q8—10421no—
139Q8C22×D52111yescharacteristic
140D4—21no—
141D4—21no—
142D4—5212no—
143D4—5211no—
144D4—5211no—
145D4—10422no—
146D4—10422no—
147D4—10422no—
148D4—10421no—
149D4C22×D52111yescharacteristic
150D4C22×D52112yes—
151C2×C4—21no—
152C2×C4—5212no—
153C2×C4—10422no—
154C2×C4—10422no—
155C2×C4—10422no—
156C2×C4—10421no—
157C2×C4—10421no—
158C2×C4C22×D52111yescharacteristic
159C8—5211no—
160C8—5211no—
161C8C22×D52112yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—5212no—
166C22—10421no—
167C22—41682no—
168C22D4×D52111yescharacteristic
169C4—21no—
170C4—5212no—
171C4—10421no—
172C4—10422no—
173C4D4×D52111yescharacteristic
174C4C23×D52111yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—10422no—
179C2—20841no—
180C2C2×D4×D52111yescharacteristic
subgroupG/H
centerC2C2×D4×D521
commutator, cosocleC4×C521C24
FrattiniC4C23×D521
FittingAGL(1,ℤ/8)×C521C2
socleC2×C521C22×D4
hypercenterAGL(1,ℤ/8)D521
hypocenterC521#577
LCSG ▷ C4×C521 ▷ C2×C521 ▷ C521
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #30659755C2semidirect
2. #30659753C2semidirect
3. #30659741C2semidirect
4. #30659737C2semidirect
5. #30659732C2semidirect
6. #30659728C2semidirect
7. #30659727C2semidirect
8. C2×#22552352C2semidirect
9. SD16×D521C2semidirect
10. #30659716C2semidirect
11. AGL(1,ℤ/8)×C521C2semidirect
18. #22552363C22semidirect
20. C2×Dic1042C22semidirect
21. Q8×D521C22semidirect
25. Dic2084C22semidirect
26. #22552354C22semidirect
27. #22552353C22semidirect
28. #22552352C22semidirect
29. #22552352C22semidirect
30. #22552352C22semidirect
31. #22552351C22semidirect
32. #22552349C22semidirect
33. #22552347C22semidirect
34. C2×#16861960C22semidirect
35. C8×D521C22semidirect
36. #41×C521C22semidirect
38. SD16×C521C22semidirect
39. D8×C521C22semidirect
40. M16×C521C22semidirect
90. C521#577semidirect
97. AGL(1,ℤ/8)D521semidirect
110. #41C2×D521semidirect
125. SD16C2×D521semidirect
127. D8C2×D521semidirect
129. M16C2×D521semidirect

Maximal subgroups

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

subgroupindex
#306597552
#306597532
#306597412
#306597372
#306597322
#306597282
#306597272
C2×#225523522
SD16×D5212
#306597162
AGL(1,ℤ/8)×C5212
#577521