Finite Group Databasebeta

← #45688239

Subgroups — #45688239

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#30659754C211yesmaximal, characteristic, complemented
3#30659740C212yesmaximal, complemented
4#30659738C211yesmaximal, characteristic, complemented
5#30659733C211yesmaximal, characteristic, complemented
6#30659732C212yesmaximal, complemented
7#30659729C212yesmaximal, complemented
8C2×#22552353C211yesmaximal, characteristic, complemented
9SD16×D521C212yesmaximal, complemented
10#30659714C211yesmaximal, characteristic, complemented
11#135×C521C211yesmaximal, characteristic, complemented
12#22552365C2212yes—
13#22552364—21no—
14#22552364—21no—
15#22552364C2211yescharacteristic
16#22552363—22no—
17#22552363C2212yescomplemented
18C2×Dic1042—21no—
19C2×Dic1042C2211yescharacteristic, complemented
20Q8×D521C2212yescomplemented
21C2×D2084—21no—
22C2×D2084C2211yescharacteristic
23D4×D521—22no—
24D4×D521C2212yes—
25#22552354C2212yescomplemented
26#22552353C2212yescomplemented
27#22552353C2212yescomplemented
28#22552352C2212yescomplemented
29#22552351C2212yescomplemented
30#22552349C2212yescomplemented
31#22552348C2211yescharacteristic, complemented
32#22552347C2212yescomplemented
33C8×D521C2212yescomplemented
34#41×C521C2211yescharacteristic
35#41×C521C2211yescharacteristic, complemented
36Q16×C521C2211yescharacteristic, complemented
37SD16×C521C2211yescharacteristic, complemented
38SD16×C521C2211yescharacteristic, complemented
39D8×C521C2211yescharacteristic, complemented
40C2×C8×C521C2211yescharacteristic, complemented
41C22×D521—21no—
42C22×D521—22no—
43Dic1042—21no—
44Dic1042—22no—
45Dic1042D411yescharacteristic
46Dic1042C2312yes—
47D2084—22no—
48D2084—21no—
49D2084D411yescharacteristic
50D2084C2312yes—
51C22⋊D521—22no—
52C22⋊D521—22no—
53C22⋊D521D412yes—
54C2×Dic521—21no—
55C2×Dic521—22no—
56C4×D521—22no—
57C4×D521—22no—
58C4×D521C2312yes—
59#16861960C2312yes—
60Q8×C521C2311yescharacteristic
61Q8×C521C2311yescharacteristic
62D4×C521—21no—
63D4×C521—21no—
64D4×C521C2311yescharacteristic
65D4×C521C2311yescharacteristic
66C2×C4×C521—21no—
67C2×C4×C521—21no—
68C2×C4×C521C2311yescharacteristic
69C8×C521C2311yescharacteristic
70C8×C521C2311yescharacteristic
71C22×C521—21no—
72C22×C521—21no—
73C22×C521C2×D411yescharacteristic
74C2×D521—22no—
75C2×D521—82no—
76C2×D521—81no—
77C2×D521C2×D412yes—
78C4×C521—21no—
79C4×C521—21no—
80C4×C521C2×D411yescharacteristic
81C4×C521C2411yescharacteristic
82Dic521—22no—
83Dic521C2×D412yes—
84C2×C521—21no—
85C2×C521—41no—
86C2×C521—41no—
87C2×C521C22×D411yescharacteristic
88D521—22no—
89D521—42no—
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#135D52111yescharacteristic, complemented
100C2×SD16—5212no—
101C2×SD16—5211no—
102#131—5211no—
103#41—5211no—
104#41—5212no—
105#41—5212no—
106#41—10421no—
107#41—10421no—
108#41—10422no—
109#41C2×D52111yescharacteristic
110#41C2×D52111yescharacteristic, complemented
111C2×Q8—5212no—
112C2×Q8—5211no—
113C2×Q8—10421no—
114C2×D4—5212no—
115C2×D4—5211no—
116C2×D4—10421no—
117C2×D4—10422no—
118Q16—5212no—
119Q16C2×D52111yescharacteristic, complemented
120SD16—5212no—
121SD16—5212no—
122SD16—5212no—
123SD16—5212no—
124SD16C2×D52111yescharacteristic, complemented
125SD16C2×D52111yescharacteristic, complemented
126D8—5212no—
127D8C2×D52111yescharacteristic, complemented
128M16—5211no—
129M16—5212no—
130C2×C8—5212no—
131C2×C8C2×D52111yescharacteristic, complemented
132C23—10422no—
133C23—10421no—
134Q8—5211no—
135Q8—5212no—
136Q8—10422no—
137Q8—10421no—
138Q8C22×D52111yescharacteristic
139Q8C22×D52111yescharacteristic
140D4—21no—
141D4—21no—
142D4—5212no—
143D4—5211no—
144D4—5212no—
145D4—10422no—
146D4—10422no—
147D4—10422no—
148D4—10421no—
149D4C22×D52111yescharacteristic
150D4C22×D52111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—5212no—
154C2×C4—10422no—
155C2×C4—10422no—
156C2×C4—10422no—
157C2×C4—10421no—
158C2×C4C22×D52111yescharacteristic
159C8—5212no—
160C8C22×D52111yescharacteristic
161C8C22×D52111yescharacteristic
162C22—21no—
163C22—21no—
164C22—5212no—
165C22—10422no—
166C22—41681no—
167C22—41682no—
168C22D4×D52111yescharacteristic
169C4—21no—
170C4—21no—
171C4—5212no—
172C4—10422no—
173C4D4×D52111yescharacteristic
174C4C23×D52111yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—10422no—
179C2—20842no—
180C2C2×D4×D52111yescharacteristic
subgroupG/H
centerC2C2×D4×D521
commutator, cosocleC4×C521C24
FrattiniC4C23×D521
Fitting#135×C521C2
socleC2×C521C22×D4
hypercenter#135D521
hypocenterC521#577
LCSG ▷ C4×C521 ▷ C2×C521 ▷ C521
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #30659755C2semidirect
2. #30659754C2semidirect
3. #30659740C2semidirect
4. #30659738C2semidirect
5. #30659733C2semidirect
6. #30659732C2semidirect
7. #30659729C2semidirect
8. C2×#22552353C2semidirect
9. SD16×D521C2semidirect
10. #30659714C2semidirect
11. #135×C521C2semidirect
17. #22552363C22semidirect
19. C2×Dic1042C22semidirect
20. Q8×D521C22semidirect
25. #22552354C22semidirect
26. #22552353C22semidirect
27. #22552353C22semidirect
28. #22552352C22semidirect
29. #22552351C22semidirect
30. #22552349C22semidirect
31. #22552348C22semidirect
32. #22552347C22semidirect
33. C8×D521C22semidirect
35. #41×C521C22semidirect
36. Q16×C521C22semidirect
37. SD16×C521C22semidirect
38. SD16×C521C22semidirect
39. D8×C521C22semidirect
40. C2×C8×C521C22semidirect
90. C521#577semidirect
99. #135D521semidirect
110. #41C2×D521semidirect
119. Q16C2×D521semidirect
124. SD16C2×D521semidirect
125. SD16C2×D521semidirect
127. D8C2×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
#306597552
#306597542
#306597402
#306597382
#306597332
#306597322
#306597292
C2×#225523532
SD16×D5212
#306597142
#135×C5212
#577521