Finite Group Databasebeta

← #44442882

Subgroups — #44442882

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#28414166C211yesmaximal, characteristic, complemented
2#28414163C211yesmaximal, characteristic, complemented
3#28414149C211yesmaximal, characteristic, complemented
4#28414147C212yesmaximal, complemented
5#28414145C212yesmaximal, complemented
6#28414144C211yesmaximal, characteristic, complemented
7#28414140C211yesmaximal, characteristic, complemented
8#28414139C212yesmaximal, complemented
9SD16×D461C212yesmaximal, complemented
10#28414124C211yesmaximal, characteristic, complemented
11C2×SD16×C461C211yesmaximal, characteristic, complemented
12#20301502—21no—
13#20301502C2212yescomplemented
14#20301501—22no—
15#20301501C2211yescharacteristic
16#20301501C2211yescharacteristic
17#20301501C2211yescharacteristic, complemented
18#20301500—21no—
19#20301500C2212yes—
20Q8×D461—21no—
21Q8×D461C2212yescomplemented
22C2×C22⋊D461—22no—
23D4×D461—21no—
24D4×D461C2212yes—
25Dic1844C2211yescharacteristic, complemented
26#20301491C2212yescomplemented
27#20301490C2211yescharacteristic, complemented
28#20301490C2211yescharacteristic, complemented
29#20301489C2212yescomplemented
30#20301488C2212yescomplemented
31D3688C2211yescharacteristic, complemented
32#20301486C2212yescomplemented
33#20301485C2211yescharacteristic, complemented
34#20301484C2212yescomplemented
35C8×D461C2212yescomplemented
36C2×Q8×C461C2211yescharacteristic, complemented
37C2×D4×C461C2211yescharacteristic
38SD16×C461C2212yescomplemented
39SD16×C461C2212yescomplemented
40C2×C8×C461C2211yescharacteristic, complemented
41C22×D461—22no—
42Dic922—22no—
43Dic922D411yescharacteristic
44Dic922C2311yescharacteristic
45Dic922C2311yescharacteristic
46D1844—22no—
47D1844D411yescharacteristic
48D1844C2311yescharacteristic
49D1844C2311yescharacteristic
50C22⋊D461—21no—
51C22⋊D461—21no—
52C22⋊D461—22no—
53C22⋊D461—22no—
54C22⋊D461D412yes—
55C2×Dic461—22no—
56C4×D461—22no—
57C4×D461—21no—
58C4×D461—21no—
59C4×D461—22no—
60C4×D461C2312yes—
61#16814779C2312yes—
62C23×C461—21no—
63Q8×C461—21no—
64Q8×C461C2312yes—
65D4×C461—21no—
66D4×C461C2312yes—
67C2×C4×C461—21no—
68C2×C4×C461C2311yescharacteristic
69C8×C461C2311yescharacteristic
70C8×C461C2311yescharacteristic
71C22×C461—22no—
72C22×C461—81no—
73C22×C461C2×D411yescharacteristic
74C2×D461—21no—
75C2×D461—21no—
76C2×D461—82no—
77C2×D461C2×D412yes—
78C4×C461—22no—
79C4×C461C2×D411yescharacteristic
80C4×C461C2411yescharacteristic
81Dic461—21no—
82Dic461—21no—
83Dic461C2×D412yes—
84C2×C461—21no—
85C2×C461—42no—
86C2×C461C22×D411yescharacteristic
87D461—22no—
88D461—41no—
89D461—41no—
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#135—4611no—
100C2×SD16—4612no—
101C2×SD16D46111yescharacteristic, complemented
102#131—4611no—
103#41—9222no—
104#41—9221no—
105#41—9221no—
106#41—4612no—
107#41—4612no—
108#41—4611no—
109#41—4611no—
110#41—4611no—
111C2×Q8—9221no—
112C2×Q8—4612no—
113C2×Q8C2×D46111yescharacteristic, complemented
114C2×D4—9221no—
115C2×D4—9222no—
116C2×D4—4612no—
117C2×D4C2×D46111yescharacteristic
118Q16—4612no—
119Q16—4611no—
120SD16—4612no—
121SD16—4612no—
122SD16—4611no—
123SD16—4611no—
124SD16C2×D46112yescomplemented
125SD16C2×D46112yescomplemented
126D8—4612no—
127D8—4611no—
128M16—4611no—
129M16—4612no—
130C2×C8—4612no—
131C2×C8C2×D46111yescharacteristic, complemented
132C23—21no—
133C23—9222no—
134Q8—21no—
135Q8—9222no—
136Q8—4611no—
137Q8—4611no—
138Q8—4611no—
139Q8C22×D46112yes—
140D4—21no—
141D4—9222no—
142D4—9222no—
143D4—9221no—
144D4—9221no—
145D4—9222no—
146D4—4612no—
147D4—4611no—
148D4—4611no—
149D4—4611no—
150D4C22×D46112yes—
151C2×C4—21no—
152C2×C4—9222no—
153C2×C4—9222no—
154C2×C4—9222no—
155C2×C4—9221no—
156C2×C4—9221no—
157C2×C4—4612no—
158C2×C4C22×D46111yescharacteristic
159C8—4612no—
160C8C22×D46111yescharacteristic
161C8C22×D46111yescharacteristic
162C22—22no—
163C22—81no—
164C22—36882no—
165C22—9221no—
166C22—9221no—
167C22—4612no—
168C22D4×D46111yescharacteristic
169C4—22no—
170C4—9221no—
171C4—9221no—
172C4—4612no—
173C4D4×D46111yescharacteristic
174C4C23×D46111yescharacteristic
175C2—21no—
176C2—42no—
177C2—18441no—
178C2—18441no—
179C2—9222no—
180C2C2×D4×D46111yescharacteristic
subgroupG/H
centerC2C2×D4×D461
commutator, cosocleC4×C461C24
FrattiniC4C23×D461
FittingC2×SD16×C461C2
socleC2×C461C22×D4
hypercenterC2×SD16D461
hypocenterC461#577
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #28414166C2semidirect
2. #28414163C2semidirect
3. #28414149C2semidirect
4. #28414147C2semidirect
5. #28414145C2semidirect
6. #28414144C2semidirect
7. #28414140C2semidirect
8. #28414139C2semidirect
9. SD16×D461C2semidirect
10. #28414124C2semidirect
11. C2×SD16×C461C2semidirect
13. #20301502C22semidirect
17. #20301501C22semidirect
21. Q8×D461C22semidirect
25. Dic1844C22semidirect
26. #20301491C22semidirect
27. #20301490C22semidirect
28. #20301490C22semidirect
29. #20301489C22semidirect
30. #20301488C22semidirect
31. D3688C22semidirect
32. #20301486C22semidirect
33. #20301485C22semidirect
34. #20301484C22semidirect
35. C8×D461C22semidirect
36. C2×Q8×C461C22semidirect
38. SD16×C461C22semidirect
39. SD16×C461C22semidirect
40. C2×C8×C461C22semidirect
90. C461#577semidirect
101. C2×SD16D461semidirect
113. C2×Q8C2×D461semidirect
124. SD16C2×D461semidirect
125. SD16C2×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
#284141662
#284141632
#284141492
#284141472
#284141452
#284141442
#284141402
#284141392
SD16×D4612
#284141242
C2×SD16×C4612
#577461