Finite Group Databasebeta

← #45688236

Subgroups — #45688236

Order 33344.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 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#30659754C211yesmaximal, characteristic, complemented
2#30659753C211yesmaximal, characteristic, complemented
3#30659736C211yesmaximal, characteristic, complemented
4#30659735C212yesmaximal, complemented
5#30659732C212yesmaximal, complemented
6#30659729C212yesmaximal, complemented
7#30659728C211yesmaximal, characteristic, complemented
8C2×#22552349C211yesmaximal, characteristic, complemented
9D8×D521C212yesmaximal, complemented
10#30659716C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C521C211yesmaximal, characteristic, complemented
12#22552365C2212yescomplemented
13#22552364—21no—
14#22552364C2211yescharacteristic
15#22552364C2211yescharacteristic, complemented
16#22552363—21no—
17#22552363C2212yescomplemented
18C2×D2084—21no—
19C2×D2084C2211yescharacteristic, complemented
20C2×C22⋊D521—22no—
21D4×D521—21no—
22D4×D521—22no—
23D4×D521C2212yescomplemented
24D4×D521C2212yescomplemented
25#22552354C2211yescharacteristic, complemented
26#22552353C2212yescomplemented
27#22552352C2211yescharacteristic, complemented
28#22552351C2211yescharacteristic, complemented
29D4168C2212yescomplemented
30#22552349C2211yescharacteristic, complemented
31#22552349C2212yescomplemented
32#22552349C2212yescomplemented
33#22552347C2212yescomplemented
34C2×#16861960C2211yescharacteristic, complemented
35C8×D521C2212yescomplemented
36#41×C521C2211yescharacteristic, complemented
37C2×D4×C521C2211yescharacteristic, complemented
38SD16×C521C2212yescomplemented
39D8×C521C2212yescomplemented
40M16×C521C2211yescharacteristic, complemented
41C22×D521—21no—
42C22×D521—22no—
43C22×D521—22no—
44Dic1042D411yescharacteristic
45Dic1042C2311yescharacteristic
46D2084—22no—
47D2084—21no—
48D2084D411yescharacteristic
49D2084C2312yes—
50D2084C2311yescharacteristic
51C22⋊D521—21no—
52C22⋊D521—22no—
53C22⋊D521—22no—
54C22⋊D521—22no—
55C22⋊D521D412yes—
56C2×Dic521—22no—
57C4×D521—21no—
58C4×D521—22no—
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—22no—
77C2×D521—82no—
78C2×D521—82no—
79C2×D521—81no—
80C2×D521C2×D412yes—
81C4×C521—21no—
82C4×C521C2×D411yescharacteristic
83C4×C521C2411yescharacteristic
84Dic521—21no—
85Dic521C2×D412yes—
86C2×C521—21no—
87C2×C521—41no—
88C2×C521—42no—
89C2×C521C22×D411yescharacteristic
90D521—22no—
91D521—41no—
92D521—42no—
93C521#57611yescharacteristic, complemented, Sylow
94#576—5211nomaximal, Sylow
95H(5,𝔽2)—5211no—
96H(5,𝔽2)—5211no—
97AGL(1,ℤ/8)—5212no—
98AGL(1,ℤ/8)—5212no—
99AGL(1,ℤ/8)—5211no—
100AGL(1,ℤ/8)D52111yescharacteristic, complemented
101#135—5211no—
102#135—5212no—
103C2×D8—5211no—
104C2×D8—5212no—
105#131—5211no—
106#41—5211no—
107#41—5212no—
108#41—5212no—
109#41—5211no—
110#41—10421no—
111#41—10421no—
112#41C2×D52111yescharacteristic, complemented
113C2×D4—5212no—
114C2×D4—5212no—
115C2×D4—5211no—
116C2×D4—10421no—
117C2×D4—10422no—
118C2×D4—10421no—
119C2×D4—10422no—
120C2×D4C2×D52111yescharacteristic, complemented
121Q16—5211no—
122SD16—5211no—
123SD16—5211no—
124SD16—5212no—
125SD16C2×D52112yescomplemented
126D8—5212no—
127D8—5211no—
128D8—5212no—
129D8—5212no—
130D8C2×D52112yescomplemented
131M16—5212no—
132M16C2×D52111yescharacteristic, complemented
133C2×C8—5211no—
134C2×C8—5212no—
135C23—21no—
136C23—10422no—
137C23—10422no—
138C23—10421no—
139Q8—5211no—
140Q8—5211no—
141Q8C22×D52111yescharacteristic
142D4—21no—
143D4—21no—
144D4—5212no—
145D4—5211no—
146D4—5212no—
147D4—5211no—
148D4—10422no—
149D4—10422no—
150D4—10422no—
151D4—10422no—
152D4—10421no—
153D4—10421no—
154D4C22×D52112yes—
155D4C22×D52111yescharacteristic
156C2×C4—21no—
157C2×C4—5212no—
158C2×C4—10422no—
159C2×C4—10422no—
160C2×C4—10421no—
161C2×C4C22×D52111yescharacteristic
162C8—5211no—
163C8—5211no—
164C8C22×D52112yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—5212no—
169C22—10422no—
170C22—10421no—
171C22—41681no—
172C22—41682no—
173C22—41682no—
174C22D4×D52111yescharacteristic
175C4—21no—
176C4—5212no—
177C4—10421no—
178C4D4×D52111yescharacteristic
179C4C23×D52111yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—10422no—
184C2—20842no—
185C2—20841no—
186C2C2×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#576
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. #30659754C2semidirect
2. #30659753C2semidirect
3. #30659736C2semidirect
4. #30659735C2semidirect
5. #30659732C2semidirect
6. #30659729C2semidirect
7. #30659728C2semidirect
8. C2×#22552349C2semidirect
9. D8×D521C2semidirect
10. #30659716C2semidirect
11. AGL(1,ℤ/8)×C521C2semidirect
12. #22552365C22semidirect
15. #22552364C22semidirect
17. #22552363C22semidirect
19. C2×D2084C22semidirect
23. D4×D521C22semidirect
24. D4×D521C22semidirect
25. #22552354C22semidirect
26. #22552353C22semidirect
27. #22552352C22semidirect
28. #22552351C22semidirect
29. D4168C22semidirect
30. #22552349C22semidirect
31. #22552349C22semidirect
32. #22552349C22semidirect
33. #22552347C22semidirect
34. C2×#16861960C22semidirect
35. C8×D521C22semidirect
36. #41×C521C22semidirect
37. C2×D4×C521C22semidirect
38. SD16×C521C22semidirect
39. D8×C521C22semidirect
40. M16×C521C22semidirect
93. C521#576semidirect
100. AGL(1,ℤ/8)D521semidirect
112. #41C2×D521semidirect
120. C2×D4C2×D521semidirect
125. SD16C2×D521semidirect
130. D8C2×D521semidirect
132. M16C2×D521semidirect

Maximal subgroups

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

subgroupindex
#306597542
#306597532
#306597362
#306597352
#306597322
#306597292
#306597282
C2×#225523492
D8×D5212
#306597162
AGL(1,ℤ/8)×C5212
#576521