Finite Group Databasebeta

← #44442883

Subgroups — #44442883

Order 29504.

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#28414165C211yesmaximal, characteristic, complemented
2#28414164C211yesmaximal, characteristic, complemented
3#28414150C212yesmaximal, complemented
4#28414148C211yesmaximal, characteristic, complemented
5#28414143C211yesmaximal, characteristic, complemented
6#28414142C212yesmaximal, complemented
7#28414139C212yesmaximal, complemented
8C2×#20301490C211yesmaximal, characteristic, complemented
9SD16×D461C212yesmaximal, complemented
10#28414124C211yesmaximal, characteristic, complemented
11#135×C461C211yesmaximal, characteristic, complemented
12#20301502C2212yes—
13#20301501—21no—
14#20301501—21no—
15#20301501C2211yescharacteristic
16#20301500—22no—
17#20301500C2212yescomplemented
18C2×Dic922—21no—
19C2×Dic922C2211yescharacteristic, complemented
20Q8×D461C2212yescomplemented
21C2×D1844—21no—
22C2×D1844C2211yescharacteristic
23D4×D461—22no—
24D4×D461C2212yes—
25#20301491C2212yescomplemented
26#20301490C2212yescomplemented
27#20301490C2212yescomplemented
28#20301489C2212yescomplemented
29#20301488C2212yescomplemented
30#20301486C2212yescomplemented
31#20301485C2211yescharacteristic, complemented
32#20301484C2212yescomplemented
33C8×D461C2212yescomplemented
34#41×C461C2211yescharacteristic
35#41×C461C2211yescharacteristic, complemented
36Q16×C461C2211yescharacteristic, complemented
37SD16×C461C2211yescharacteristic, complemented
38SD16×C461C2211yescharacteristic, complemented
39D8×C461C2211yescharacteristic, complemented
40C2×C8×C461C2211yescharacteristic, complemented
41C22×D461—21no—
42C22×D461—22no—
43Dic922—21no—
44Dic922—22no—
45Dic922D411yescharacteristic
46Dic922C2312yes—
47D1844—22no—
48D1844—21no—
49D1844D411yescharacteristic
50D1844C2312yes—
51C22⋊D461—22no—
52C22⋊D461—22no—
53C22⋊D461D412yes—
54C2×Dic461—21no—
55C2×Dic461—22no—
56C4×D461—22no—
57C4×D461—22no—
58C4×D461C2312yes—
59#16814779C2312yes—
60Q8×C461C2311yescharacteristic
61Q8×C461C2311yescharacteristic
62D4×C461—21no—
63D4×C461—21no—
64D4×C461C2311yescharacteristic
65D4×C461C2311yescharacteristic
66C2×C4×C461—21no—
67C2×C4×C461—21no—
68C2×C4×C461C2311yescharacteristic
69C8×C461C2311yescharacteristic
70C8×C461C2311yescharacteristic
71C22×C461—21no—
72C22×C461—21no—
73C22×C461C2×D411yescharacteristic
74C2×D461—22no—
75C2×D461—82no—
76C2×D461—81no—
77C2×D461C2×D412yes—
78C4×C461—21no—
79C4×C461—21no—
80C4×C461C2×D411yescharacteristic
81C4×C461C2411yescharacteristic
82Dic461—22no—
83Dic461C2×D412yes—
84C2×C461—21no—
85C2×C461—41no—
86C2×C461—41no—
87C2×C461C22×D411yescharacteristic
88D461—22no—
89D461—42no—
90C461#57711yescharacteristic, complemented, Sylow
91#577—4611nomaximal, Sylow
922−1+4—4611no—
93H(5,𝔽2)—4611no—
94#137—4611no—
95#137—4612no—
96AGL(1,ℤ/8)—4611no—
97AGL(1,ℤ/8)—4612no—
98#135—4612no—
99#135D46111yescharacteristic, complemented
100C2×SD16—4612no—
101C2×SD16—4611no—
102#131—4611no—
103#41—9221no—
104#41—9221no—
105#41—9222no—
106#41—4612no—
107#41—4612no—
108#41—4611no—
109#41C2×D46111yescharacteristic
110#41C2×D46111yescharacteristic, complemented
111C2×Q8—9221no—
112C2×Q8—4612no—
113C2×Q8—4611no—
114C2×D4—9221no—
115C2×D4—9222no—
116C2×D4—4612no—
117C2×D4—4611no—
118Q16—4612no—
119Q16C2×D46111yescharacteristic, complemented
120SD16—4612no—
121SD16—4612no—
122SD16—4612no—
123SD16—4612no—
124SD16C2×D46111yescharacteristic, complemented
125SD16C2×D46111yescharacteristic, complemented
126D8—4612no—
127D8C2×D46111yescharacteristic, complemented
128M16—4611no—
129M16—4612no—
130C2×C8—4612no—
131C2×C8C2×D46111yescharacteristic, complemented
132C23—9222no—
133C23—9221no—
134Q8—9222no—
135Q8—9221no—
136Q8—4612no—
137Q8—4611no—
138Q8C22×D46111yescharacteristic
139Q8C22×D46111yescharacteristic
140D4—21no—
141D4—21no—
142D4—9222no—
143D4—9222no—
144D4—9222no—
145D4—9221no—
146D4—4612no—
147D4—4611no—
148D4—4612no—
149D4C22×D46111yescharacteristic
150D4C22×D46111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—9222no—
154C2×C4—9222no—
155C2×C4—9221no—
156C2×C4—9222no—
157C2×C4—4612no—
158C2×C4C22×D46111yescharacteristic
159C8—4612no—
160C8C22×D46111yescharacteristic
161C8C22×D46111yescharacteristic
162C22—21no—
163C22—21no—
164C22—36881no—
165C22—36882no—
166C22—9222no—
167C22—4612no—
168C22D4×D46111yescharacteristic
169C4—21no—
170C4—21no—
171C4—9222no—
172C4—4612no—
173C4D4×D46111yescharacteristic
174C4C23×D46111yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—18442no—
179C2—9222no—
180C2C2×D4×D46111yescharacteristic
subgroupG/H
centerC2C2×D4×D461
commutator, cosocleC4×C461C24
FrattiniC4C23×D461
Fitting#135×C461C2
socleC2×C461C22×D4
hypercenter#135D461
hypocenterC461#577
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #28414165C2semidirect
2. #28414164C2semidirect
3. #28414150C2semidirect
4. #28414148C2semidirect
5. #28414143C2semidirect
6. #28414142C2semidirect
7. #28414139C2semidirect
8. C2×#20301490C2semidirect
9. SD16×D461C2semidirect
10. #28414124C2semidirect
11. #135×C461C2semidirect
17. #20301500C22semidirect
19. C2×Dic922C22semidirect
20. Q8×D461C22semidirect
25. #20301491C22semidirect
26. #20301490C22semidirect
27. #20301490C22semidirect
28. #20301489C22semidirect
29. #20301488C22semidirect
30. #20301486C22semidirect
31. #20301485C22semidirect
32. #20301484C22semidirect
33. C8×D461C22semidirect
35. #41×C461C22semidirect
36. Q16×C461C22semidirect
37. SD16×C461C22semidirect
38. SD16×C461C22semidirect
39. D8×C461C22semidirect
40. C2×C8×C461C22semidirect
90. C461#577semidirect
99. #135D461semidirect
110. #41C2×D461semidirect
119. Q16C2×D461semidirect
124. SD16C2×D461semidirect
125. SD16C2×D461semidirect
127. D8C2×D461semidirect
131. C2×C8C2×D461semidirect

Maximal subgroups

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

subgroupindex
#284141652
#284141642
#284141502
#284141482
#284141432
#284141422
#284141392
C2×#203014902
SD16×D4612
#284141242
#135×C4612
#577461