Finite Group Databasebeta

← #45688238

Subgroups — #45688238

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#30659756C211yesmaximal, characteristic, complemented
2#30659753C211yesmaximal, characteristic, complemented
3#30659739C211yesmaximal, characteristic, complemented
4#30659737C212yesmaximal, complemented
5#30659735C212yesmaximal, complemented
6#30659734C211yesmaximal, characteristic, complemented
7#30659730C211yesmaximal, characteristic, complemented
8#30659729C212yesmaximal, complemented
9SD16×D521C212yesmaximal, complemented
10#30659714C211yesmaximal, characteristic, complemented
11C2×SD16×C521C211yesmaximal, characteristic, complemented
12#22552365—21no—
13#22552365C2212yescomplemented
14#22552364—22no—
15#22552364C2211yescharacteristic
16#22552364C2211yescharacteristic
17#22552364C2211yescharacteristic, complemented
18#22552363—21no—
19#22552363C2212yes—
20Q8×D521—21no—
21Q8×D521C2212yescomplemented
22C2×C22⋊D521—22no—
23D4×D521—21no—
24D4×D521C2212yes—
25Dic2084C2211yescharacteristic, complemented
26#22552354C2212yescomplemented
27#22552353C2211yescharacteristic, complemented
28#22552353C2211yescharacteristic, complemented
29#22552352C2212yescomplemented
30#22552351C2212yescomplemented
31D4168C2211yescharacteristic, complemented
32#22552349C2212yescomplemented
33#22552348C2211yescharacteristic, complemented
34#22552347C2212yescomplemented
35C8×D521C2212yescomplemented
36C2×Q8×C521C2211yescharacteristic, complemented
37C2×D4×C521C2211yescharacteristic
38SD16×C521C2212yescomplemented
39SD16×C521C2212yescomplemented
40C2×C8×C521C2211yescharacteristic, complemented
41C22×D521—22no—
42Dic1042—22no—
43Dic1042D411yescharacteristic
44Dic1042C2311yescharacteristic
45Dic1042C2311yescharacteristic
46D2084—22no—
47D2084D411yescharacteristic
48D2084C2311yescharacteristic
49D2084C2311yescharacteristic
50C22⋊D521—21no—
51C22⋊D521—21no—
52C22⋊D521—22no—
53C22⋊D521—22no—
54C22⋊D521D412yes—
55C2×Dic521—22no—
56C4×D521—22no—
57C4×D521—21no—
58C4×D521—21no—
59C4×D521—22no—
60C4×D521C2312yes—
61#16861960C2312yes—
62C23×C521—21no—
63Q8×C521—21no—
64Q8×C521C2312yes—
65D4×C521—21no—
66D4×C521C2312yes—
67C2×C4×C521—21no—
68C2×C4×C521C2311yescharacteristic
69C8×C521C2311yescharacteristic
70C8×C521C2311yescharacteristic
71C22×C521—22no—
72C22×C521—81no—
73C22×C521C2×D411yescharacteristic
74C2×D521—21no—
75C2×D521—21no—
76C2×D521—82no—
77C2×D521C2×D412yes—
78C4×C521—22no—
79C4×C521C2×D411yescharacteristic
80C4×C521C2411yescharacteristic
81Dic521—21no—
82Dic521—21no—
83Dic521C2×D412yes—
84C2×C521—21no—
85C2×C521—42no—
86C2×C521C22×D411yescharacteristic
87D521—22no—
88D521—41no—
89D521—41no—
90C521#57711yescharacteristic, complemented, Sylow
91#577—5211nomaximal, Sylow
922−1+4—5211no—
93H(5,𝔽2)—5211no—
94#137—5211no—
95#137—5212no—
96AGL(1,ℤ/8)—5211no—
97AGL(1,ℤ/8)—5212no—
98#135—5212no—
99#135—5211no—
100C2×SD16—5212no—
101C2×SD16D52111yescharacteristic, complemented
102#131—5211no—
103#41—5211no—
104#41—5212no—
105#41—5212no—
106#41—5211no—
107#41—5211no—
108#41—10422no—
109#41—10421no—
110#41—10421no—
111C2×Q8—5212no—
112C2×Q8—10421no—
113C2×Q8C2×D52111yescharacteristic, complemented
114C2×D4—5212no—
115C2×D4—10421no—
116C2×D4—10422no—
117C2×D4C2×D52111yescharacteristic
118Q16—5212no—
119Q16—5211no—
120SD16—5212no—
121SD16—5212no—
122SD16—5211no—
123SD16—5211no—
124SD16C2×D52112yescomplemented
125SD16C2×D52112yescomplemented
126D8—5212no—
127D8—5211no—
128M16—5211no—
129M16—5212no—
130C2×C8—5212no—
131C2×C8C2×D52111yescharacteristic, complemented
132C23—21no—
133C23—10422no—
134Q8—21no—
135Q8—5211no—
136Q8—5211no—
137Q8—5211no—
138Q8—10422no—
139Q8C22×D52112yes—
140D4—21no—
141D4—5212no—
142D4—5211no—
143D4—5211no—
144D4—5211no—
145D4—10422no—
146D4—10422no—
147D4—10422no—
148D4—10421no—
149D4—10421no—
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—5212no—
160C8C22×D52111yescharacteristic
161C8C22×D52111yescharacteristic
162C22—22no—
163C22—81no—
164C22—5212no—
165C22—10421no—
166C22—10421no—
167C22—41682no—
168C22D4×D52111yescharacteristic
169C4—22no—
170C4—5212no—
171C4—10421no—
172C4—10421no—
173C4D4×D52111yescharacteristic
174C4C23×D52111yescharacteristic
175C2—21no—
176C2—42no—
177C2—10422no—
178C2—20841no—
179C2—20841no—
180C2C2×D4×D52111yescharacteristic
subgroupG/H
centerC2C2×D4×D521
commutator, cosocleC4×C521C24
FrattiniC4C23×D521
FittingC2×SD16×C521C2
socleC2×C521C22×D4
hypercenterC2×SD16D521
hypocenterC521#577
LCSG ▷ C4×C521 ▷ C2×C521 ▷ C521
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #30659756C2semidirect
2. #30659753C2semidirect
3. #30659739C2semidirect
4. #30659737C2semidirect
5. #30659735C2semidirect
6. #30659734C2semidirect
7. #30659730C2semidirect
8. #30659729C2semidirect
9. SD16×D521C2semidirect
10. #30659714C2semidirect
11. C2×SD16×C521C2semidirect
13. #22552365C22semidirect
17. #22552364C22semidirect
21. Q8×D521C22semidirect
25. Dic2084C22semidirect
26. #22552354C22semidirect
27. #22552353C22semidirect
28. #22552353C22semidirect
29. #22552352C22semidirect
30. #22552351C22semidirect
31. D4168C22semidirect
32. #22552349C22semidirect
33. #22552348C22semidirect
34. #22552347C22semidirect
35. C8×D521C22semidirect
36. C2×Q8×C521C22semidirect
38. SD16×C521C22semidirect
39. SD16×C521C22semidirect
40. C2×C8×C521C22semidirect
90. C521#577semidirect
101. C2×SD16D521semidirect
113. C2×Q8C2×D521semidirect
124. SD16C2×D521semidirect
125. SD16C2×D521semidirect
131. C2×C8C2×D521semidirect

Maximal subgroups

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

subgroupindex
#306597562
#306597532
#306597392
#306597372
#306597352
#306597342
#306597302
#306597292
SD16×D5212
#306597142
C2×SD16×C5212
#577521