Finite Group Databasebeta

← #14583698

Subgroups — #14583698

Order 2752.

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×#10621902C211yesmaximal, characteristic, complemented
2#41×D43C211yesmaximal, characteristic, complemented
3#13063357C212yesmaximal, complemented
4#13063356C211yesmaximal, characteristic, complemented
5#13063353C211yesmaximal, characteristic, complemented
6#13063352C212yesmaximal, complemented
7#13063350C211yesmaximal, characteristic, complemented
8#13063348C212yesmaximal, complemented
9#13063346C212yesmaximal, complemented
10M16×D43C211yesmaximal, characteristic, complemented
11#137×C43C211yesmaximal, characteristic, complemented
12#41×C43C2211yescharacteristic
13C2×Q8×C43C2211yescharacteristic, complemented
14#10621902—21no—
15#10621902—21no—
16#10621902C2212yes—
17#10621902C2212yescomplemented
18#10621902C2211yescharacteristic, complemented
19Q8×D43C2211yescharacteristic, complemented
20#10621900—21no—
21#10621900C2211yescharacteristic, complemented
22D4×D43—21no—
23D4×D43C2211yescharacteristic, complemented
24#10621898—21no—
25#10621898C2211yescharacteristic
26C2×D172—21no—
27C2×D172C2211yescharacteristic, complemented
28C2×C4×D43—21no—
29C2×C4×D43—21no—
30C2×C4×D43C2211yescharacteristic
31Q16×C43C2212yescomplemented
32SD16×C43C2212yescomplemented
33M16×C43C2211yescharacteristic, complemented
34#10621885C2212yescomplemented
35#10621884C2212yescomplemented
36#10621884C2212yescomplemented
37#10621882C2212yescomplemented
38#10621877C2211yescharacteristic, complemented
39D344C2212yescomplemented
40#10621873C2212yescomplemented
41#10621872C2212yescomplemented
42C8×D43C2212yescomplemented
43C22×D43—21no—
44C22×D43—21no—
45C22×D43D411yescharacteristic
46Q8×C43—21no—
47Q8×C43C2311yescharacteristic
48Q8×C43C2312yes—
49D4×C43—21no—
50D4×C43C2311yescharacteristic
51C2×C4×C43—21no—
52C2×C4×C43—21no—
53C2×C4×C43C2311yescharacteristic
54C22⋊D43—21no—
55C22⋊D43—21no—
56C22⋊D43—21no—
57C2×Dic43—21no—
58C2×Dic43D411yescharacteristic
59D172—22no—
60D172—22no—
61D172—21no—
62D172—21no—
63D172C2312yes—
64D172C2311yescharacteristic
65C4×D43—21no—
66C4×D43—21no—
67C4×D43—21no—
68C4×D43—22no—
69C4×D43—22no—
70C4×D43D411yescharacteristic
71C4×D43D411yescharacteristic
72C4×D43C2311yescharacteristic
73C4×D43C2311yescharacteristic
74Dic86—21no—
75Dic86C2311yescharacteristic
76C8×C43C2312yes—
77C43⋊C8C2312yes—
78C22×C43—21no—
79C22×C43C2×D411yescharacteristic
80C2×D43—22no—
81C2×D43—21no—
82C2×D43—41no—
83C2×D43—42no—
84C2×D43—42no—
85C2×D43C2×D411yescharacteristic
86C2×D43C2×D411yescharacteristic
87C4×C43—21no—
88C4×C43—22no—
89C4×C43C2×D411yescharacteristic
90C4×C43C2411yescharacteristic
91Dic43—21no—
92Dic43C2×D411yescharacteristic
93Dic43C2×D411yescharacteristic
94C2×C43—21no—
95C2×C43—41no—
96C2×C43C22×D411yescharacteristic
97D43—21no—
98D43—21no—
99D43—42no—
100D43—41no—
101#575—431nomaximal, Sylow
102C43#57511yescharacteristic, complemented, Sylow
103C2×#41—431no—
104C2×#41—431no—
105#137—431no—
106#137—432no—
107#137D4311yescharacteristic, complemented
108AGL(1,ℤ/8)—431no—
109AGL(1,ℤ/8)—432no—
110AGL(1,ℤ/8)—431no—
111#135—432no—
112#135—432no—
113C2×M16—431no—
114#41—431no—
115#41—432no—
116#41—432no—
117#41—431no—
118#41—431no—
119#41—861no—
120#41—861no—
121#41—861no—
122#41—861no—
123#41C2×D4311yescharacteristic
124C2×Q8—431no—
125C2×Q8C2×D4311yescharacteristic, complemented
126C2×D4—431no—
127C2×D4—431no—
128C2×D4—861no—
129C2×D4—861no—
130C22×C4—431no—
131C22×C4—861no—
132C22×C4—861no—
133Q16—432no—
134Q16C2×D4312yescomplemented
135SD16—432no—
136SD16—432no—
137SD16—432no—
138SD16C2×D4312yescomplemented
139D8—432no—
140D8—432no—
141M16—431no—
142M16—432no—
143M16C2×D4311yescharacteristic, complemented
144C2×C8—432no—
145C23—431no—
146C23—861no—
147C23—861no—
148Q8—21no—
149Q8—431no—
150Q8—861no—
151Q8C22×D4311yescharacteristic
152Q8C22×D4312yes—
153D4—21no—
154D4—432no—
155D4—431no—
156D4—861no—
157D4—862no—
158D4—862no—
159D4—861no—
160D4—861no—
161D4—861no—
162D4—861no—
163D4C22×D4311yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—431no—
167C2×C4—431no—
168C2×C4—431no—
169C2×C4—431no—
170C2×C4—431no—
171C2×C4—861no—
172C2×C4—862no—
173C2×C4—862no—
174C2×C4—861no—
175C2×C4—861no—
176C2×C4—861no—
177C2×C4C22×D4311yescharacteristic
178C8—432no—
179C8C22×D4312yes—
180C22—21no—
181C22—431no—
182C22—431no—
183C22—862no—
184C22—861no—
185C22—1721no—
186C22—1722no—
187C22—1722no—
188C22D4×D4311yescharacteristic
189C4—21no—
190C4—22no—
191C4—431no—
192C4—431no—
193C4—861no—
194C4D4×D4311yescharacteristic
195C4C23×D4311yescharacteristic
196C2—21no—
197C2—41no—
198C2—861no—
199C2—861no—
200C2—1722no—
201C2—1721no—
202C2C2×D4×D4311yescharacteristic
subgroupG/H
centerC2C2×D4×D43
commutator, cosocleC4×C43C24
FrattiniC4C23×D43
Fitting#137×C43C2
socleC2×C43C22×D4
hypercenter#137D43
hypocenterC43#575
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#10621902C2semidirect
2. #41×D43C2semidirect
3. #13063357C2semidirect
4. #13063356C2semidirect
5. #13063353C2semidirect
6. #13063352C2semidirect
7. #13063350C2semidirect
8. #13063348C2semidirect
9. #13063346C2semidirect
10. M16×D43C2semidirect
11. #137×C43C2semidirect
13. C2×Q8×C43C22semidirect
17. #10621902C22semidirect
18. #10621902C22semidirect
19. Q8×D43C22semidirect
21. #10621900C22semidirect
23. D4×D43C22semidirect
27. C2×D172C22semidirect
31. Q16×C43C22semidirect
32. SD16×C43C22semidirect
33. M16×C43C22semidirect
34. #10621885C22semidirect
35. #10621884C22semidirect
36. #10621884C22semidirect
37. #10621882C22semidirect
38. #10621877C22semidirect
39. D344C22semidirect
40. #10621873C22semidirect
41. #10621872C22semidirect
42. C8×D43C22semidirect
102. C43#575semidirect
107. #137D43semidirect
125. C2×Q8C2×D43semidirect
134. Q16C2×D43semidirect
138. SD16C2×D43semidirect
143. M16C2×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#106219022
#41×D432
#130633572
#130633562
#130633532
#130633522
#130633502
#130633482
#130633462
M16×D432
#137×C432
#57543