Finite Group Databasebeta

← #49143062

Subgroups — #49143062

Order 36544.

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

normal subgroups only

This group has 262 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
1C2×#22603732C211yesmaximal, characteristic, complemented
2#41×D571C211yesmaximal, characteristic, complemented
3#32912727C211yesmaximal, characteristic, complemented
4#32912724C211yesmaximal, characteristic, complemented
5#32912723C212yesmaximal, complemented
6#32912720C211yesmaximal, characteristic, complemented
7#32912718C212yesmaximal, complemented
8#32912715C212yesmaximal, complemented
9#32912713C212yesmaximal, complemented
10M16×D571C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C571C211yesmaximal, characteristic, complemented
12#22603734C2211yescharacteristic, complemented
13#22603733—21no—
14#22603733C2211yescharacteristic
15#22603732—21no—
16#22603732—21no—
17#22603732—21no—
18#22603732C2212yes—
19#22603732C2211yescharacteristic, complemented
20#22603732C2212yescomplemented
21C2×Dic1142C2211yescharacteristic, complemented
22Q8×D571C2211yescharacteristic, complemented
23C2×C22⋊D571—21no—
24D4×D571—21no—
25D4×D571C2211yescharacteristic, complemented
26C22×Dic571—21no—
27C2×C4×D571—21no—
28C2×C4×D571C2211yescharacteristic
29Dic2284C2212yescomplemented
30#22603723C2212yescomplemented
31#22603722C2212yescomplemented
32#22603721C2212yescomplemented
33#22603721C2212yescomplemented
34#22603718C2212yescomplemented
35#22603717C2211yescharacteristic, complemented
36#22603716C2212yescomplemented
37C8×D571C2212yescomplemented
38#41×C571C2211yescharacteristic
39C2×D4×C571C2211yescharacteristic, complemented
40SD16×C571C2212yescomplemented
41D8×C571C2212yescomplemented
42M16×C571C2211yescharacteristic, complemented
43C22×D571—21no—
44C22×D571D411yescharacteristic
45Dic1142—21no—
46Dic1142—21no—
47Dic1142C2311yescharacteristic
48Dic1142C2312yes—
49D2284—21no—
50D2284C2311yescharacteristic
51C22⋊D571—21no—
52C22⋊D571—21no—
53C22⋊D571—22no—
54C22⋊D571—22no—
55C22⋊D571—21no—
56C2×Dic571—21no—
57C2×Dic571—21no—
58C2×Dic571—22no—
59C2×Dic571—22no—
60C2×Dic571D411yescharacteristic
61C4×D571—21no—
62C4×D571—21no—
63C4×D571—21no—
64C4×D571D411yescharacteristic
65C4×D571D411yescharacteristic
66C4×D571C2311yescharacteristic
67C4×D571C2311yescharacteristic
68C571⋊C8C2312yes—
69C23×C571—21no—
70Q8×C571C2311yescharacteristic
71D4×C571—21no—
72D4×C571—21no—
73D4×C571C2311yescharacteristic
74D4×C571C2312yes—
75C2×C4×C571—21no—
76C2×C4×C571C2311yescharacteristic
77C8×C571C2312yes—
78C22×C571—21no—
79C22×C571—22no—
80C22×C571—42no—
81C22×C571C2×D411yescharacteristic
82C2×D571—21no—
83C2×D571—41no—
84C2×D571—42no—
85C2×D571C2×D411yescharacteristic
86C2×D571C2×D411yescharacteristic
87C4×C571—21no—
88C4×C571C2×D411yescharacteristic
89C4×C571C2411yescharacteristic
90Dic571—21no—
91Dic571—22no—
92Dic571C2×D411yescharacteristic
93Dic571C2×D411yescharacteristic
94C2×C571—21no—
95C2×C571—41no—
96C2×C571—42no—
97C2×C571C22×D411yescharacteristic
98D571—21no—
99D571—21no—
100D571—41no—
101C571#57511yescharacteristic, complemented, Sylow
102#575—5711nomaximal, Sylow
103C2×#41—5711no—
104C2×#41—5711no—
105#137—5711no—
106#137—5712no—
107#137—5711no—
108AGL(1,ℤ/8)—5711no—
109AGL(1,ℤ/8)—5712no—
110AGL(1,ℤ/8)D57111yescharacteristic, complemented
111#135—5712no—
112#135—5712no—
113C2×M16—5711no—
114#41—5711no—
115#41—5712no—
116#41—5711no—
117#41—5712no—
118#41—5711no—
119#41—11421no—
120#41—11421no—
121#41—11421no—
122#41—11421no—
123#41C2×D57111yescharacteristic
124C2×Q8—5711no—
125C2×Q8—5711no—
126C2×D4—5711no—
127C2×D4—11421no—
128C2×D4—11421no—
129C2×D4C2×D57111yescharacteristic, complemented
130C22×C4—5711no—
131C22×C4—11421no—
132C22×C4—11421no—
133Q16—5712no—
134Q16—5712no—
135SD16—5712no—
136SD16—5712no—
137SD16—5712no—
138SD16C2×D57112yescomplemented
139D8—5712no—
140D8C2×D57112yescomplemented
141M16—5711no—
142M16—5712no—
143M16C2×D57111yescharacteristic, complemented
144C2×C8—5712no—
145C23—21no—
146C23—5711no—
147C23—11421no—
148Q8—5711no—
149Q8—5712no—
150Q8—11421no—
151Q8—11421no—
152Q8C22×D57111yescharacteristic
153D4—21no—
154D4—21no—
155D4—5711no—
156D4—11421no—
157D4—11421no—
158D4—11421no—
159D4—11422no—
160D4—11422no—
161D4—11421no—
162D4C22×D57112yes—
163D4C22×D57111yescharacteristic
164C2×C4—21no—
165C2×C4—5711no—
166C2×C4—5711no—
167C2×C4—5711no—
168C2×C4—5711no—
169C2×C4—5711no—
170C2×C4—11421no—
171C2×C4—11421no—
172C2×C4—11421no—
173C2×C4—11422no—
174C2×C4—11422no—
175C2×C4—11421no—
176C2×C4—11421no—
177C2×C4C22×D57111yescharacteristic
178C8—5712no—
179C8C22×D57112yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—5711no—
184C22—5711no—
185C22—11421no—
186C22—22841no—
187C22—22842no—
188C22D4×D57111yescharacteristic
189C4—21no—
190C4—5711no—
191C4—5711no—
192C4—11421no—
193C4—11422no—
194C4D4×D57111yescharacteristic
195C4C23×D57111yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—11421no—
200C2—11421no—
201C2—22841no—
202C2C2×D4×D57111yescharacteristic
subgroupG/H
centerC2C2×D4×D571
commutator, cosocleC4×C571C24
FrattiniC4C23×D571
FittingAGL(1,ℤ/8)×C571C2
socleC2×C571C22×D4
hypercenterAGL(1,ℤ/8)D571
hypocenterC571#575
LCSG ▷ C4×C571 ▷ C2×C571 ▷ C571
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#22603732C2semidirect
2. #41×D571C2semidirect
3. #32912727C2semidirect
4. #32912724C2semidirect
5. #32912723C2semidirect
6. #32912720C2semidirect
7. #32912718C2semidirect
8. #32912715C2semidirect
9. #32912713C2semidirect
10. M16×D571C2semidirect
11. AGL(1,ℤ/8)×C571C2semidirect
12. #22603734C22semidirect
19. #22603732C22semidirect
20. #22603732C22semidirect
21. C2×Dic1142C22semidirect
22. Q8×D571C22semidirect
25. D4×D571C22semidirect
29. Dic2284C22semidirect
30. #22603723C22semidirect
31. #22603722C22semidirect
32. #22603721C22semidirect
33. #22603721C22semidirect
34. #22603718C22semidirect
35. #22603717C22semidirect
36. #22603716C22semidirect
37. C8×D571C22semidirect
39. C2×D4×C571C22semidirect
40. SD16×C571C22semidirect
41. D8×C571C22semidirect
42. M16×C571C22semidirect
101. C571#575semidirect
110. AGL(1,ℤ/8)D571semidirect
129. C2×D4C2×D571semidirect
138. SD16C2×D571semidirect
140. D8C2×D571semidirect
143. M16C2×D571semidirect

Maximal subgroups

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

subgroupindex
C2×#226037322
#41×D5712
#329127272
#329127242
#329127232
#329127202
#329127182
#329127152
#329127132
M16×D5712
AGL(1,ℤ/8)×C5712
#575571