Finite Group Databasebeta

← #45691012

Subgroups — #45691012

Order 33472.

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#30660420C211yesmaximal, characteristic, complemented
2#30660419C211yesmaximal, characteristic, complemented
3#30660405C212yesmaximal, complemented
4#30660403C211yesmaximal, characteristic, complemented
5#30660398C211yesmaximal, characteristic, complemented
6#30660397C212yesmaximal, complemented
7#30660394C212yesmaximal, complemented
8C2×#22552630C211yesmaximal, characteristic, complemented
9SD16×D523C212yesmaximal, complemented
10#30660379C211yesmaximal, characteristic, complemented
11#135×C523C211yesmaximal, characteristic, complemented
12#22552642C2212yes—
13#22552641—21no—
14#22552641—21no—
15#22552641C2211yescharacteristic
16#22552640—22no—
17#22552640C2212yescomplemented
18C2×Dic1046—21no—
19C2×Dic1046C2211yescharacteristic, complemented
20Q8×D523C2212yescomplemented
21C2×D2092—21no—
22C2×D2092C2211yescharacteristic
23D4×D523—22no—
24D4×D523C2212yes—
25#22552631C2212yescomplemented
26#22552630C2212yescomplemented
27#22552630C2212yescomplemented
28#22552629C2212yescomplemented
29#22552628C2212yescomplemented
30#22552626C2212yescomplemented
31#22552625C2211yescharacteristic, complemented
32#22552624C2212yescomplemented
33C8×D523C2212yescomplemented
34#41×C523C2211yescharacteristic
35#41×C523C2211yescharacteristic, complemented
36Q16×C523C2211yescharacteristic, complemented
37SD16×C523C2211yescharacteristic, complemented
38SD16×C523C2211yescharacteristic, complemented
39D8×C523C2211yescharacteristic, complemented
40C2×C8×C523C2211yescharacteristic, complemented
41C22×D523—21no—
42C22×D523—22no—
43Dic1046—21no—
44Dic1046—22no—
45Dic1046D411yescharacteristic
46Dic1046C2312yes—
47D2092—22no—
48D2092—21no—
49D2092D411yescharacteristic
50D2092C2312yes—
51C22⋊D523—22no—
52C22⋊D523—22no—
53C22⋊D523D412yes—
54C2×Dic523—21no—
55C2×Dic523—22no—
56C4×D523—22no—
57C4×D523—22no—
58C4×D523C2312yes—
59C523⋊C8C2312yes—
60Q8×C523C2311yescharacteristic
61Q8×C523C2311yescharacteristic
62D4×C523—21no—
63D4×C523—21no—
64D4×C523C2311yescharacteristic
65D4×C523C2311yescharacteristic
66C2×C4×C523—21no—
67C2×C4×C523—21no—
68C2×C4×C523C2311yescharacteristic
69C8×C523C2311yescharacteristic
70C8×C523C2311yescharacteristic
71C22×C523—21no—
72C22×C523—21no—
73C22×C523C2×D411yescharacteristic
74C2×D523—22no—
75C2×D523—82no—
76C2×D523—81no—
77C2×D523C2×D412yes—
78C4×C523—21no—
79C4×C523—21no—
80C4×C523C2×D411yescharacteristic
81C4×C523C2411yescharacteristic
82Dic523—22no—
83Dic523C2×D412yes—
84C2×C523—21no—
85C2×C523—41no—
86C2×C523—41no—
87C2×C523C22×D411yescharacteristic
88D523—22no—
89D523—42no—
90C523#57711yescharacteristic, complemented, Sylow
91#577—5231nomaximal, Sylow
922−1+4—5231no—
93H(5,𝔽2)—5231no—
94#137—5231no—
95#137—5232no—
96AGL(1,ℤ/8)—5231no—
97AGL(1,ℤ/8)—5232no—
98#135—5232no—
99#135D52311yescharacteristic, complemented
100C2×SD16—5232no—
101C2×SD16—5231no—
102#131—5231no—
103#41—5231no—
104#41—5232no—
105#41—5232no—
106#41—10461no—
107#41—10461no—
108#41—10462no—
109#41C2×D52311yescharacteristic
110#41C2×D52311yescharacteristic, complemented
111C2×Q8—5232no—
112C2×Q8—5231no—
113C2×Q8—10461no—
114C2×D4—5232no—
115C2×D4—5231no—
116C2×D4—10461no—
117C2×D4—10462no—
118Q16—5232no—
119Q16C2×D52311yescharacteristic, complemented
120SD16—5232no—
121SD16—5232no—
122SD16—5232no—
123SD16—5232no—
124SD16C2×D52311yescharacteristic, complemented
125SD16C2×D52311yescharacteristic, complemented
126D8—5232no—
127D8C2×D52311yescharacteristic, complemented
128M16—5231no—
129M16—5232no—
130C2×C8—5232no—
131C2×C8C2×D52311yescharacteristic, complemented
132C23—10462no—
133C23—10461no—
134Q8—5231no—
135Q8—5232no—
136Q8—10462no—
137Q8—10461no—
138Q8C22×D52311yescharacteristic
139Q8C22×D52311yescharacteristic
140D4—21no—
141D4—21no—
142D4—5232no—
143D4—5231no—
144D4—5232no—
145D4—10462no—
146D4—10462no—
147D4—10462no—
148D4—10461no—
149D4C22×D52311yescharacteristic
150D4C22×D52311yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—5232no—
154C2×C4—10462no—
155C2×C4—10462no—
156C2×C4—10462no—
157C2×C4—10461no—
158C2×C4C22×D52311yescharacteristic
159C8—5232no—
160C8C22×D52311yescharacteristic
161C8C22×D52311yescharacteristic
162C22—21no—
163C22—21no—
164C22—5232no—
165C22—10462no—
166C22—41841no—
167C22—41842no—
168C22D4×D52311yescharacteristic
169C4—21no—
170C4—21no—
171C4—5232no—
172C4—10462no—
173C4D4×D52311yescharacteristic
174C4C23×D52311yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—10462no—
179C2—20922no—
180C2C2×D4×D52311yescharacteristic
subgroupG/H
centerC2C2×D4×D523
commutator, cosocleC4×C523C24
FrattiniC4C23×D523
Fitting#135×C523C2
socleC2×C523C22×D4
hypercenter#135D523
hypocenterC523#577
LCSG ▷ C4×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #30660420C2semidirect
2. #30660419C2semidirect
3. #30660405C2semidirect
4. #30660403C2semidirect
5. #30660398C2semidirect
6. #30660397C2semidirect
7. #30660394C2semidirect
8. C2×#22552630C2semidirect
9. SD16×D523C2semidirect
10. #30660379C2semidirect
11. #135×C523C2semidirect
17. #22552640C22semidirect
19. C2×Dic1046C22semidirect
20. Q8×D523C22semidirect
25. #22552631C22semidirect
26. #22552630C22semidirect
27. #22552630C22semidirect
28. #22552629C22semidirect
29. #22552628C22semidirect
30. #22552626C22semidirect
31. #22552625C22semidirect
32. #22552624C22semidirect
33. C8×D523C22semidirect
35. #41×C523C22semidirect
36. Q16×C523C22semidirect
37. SD16×C523C22semidirect
38. SD16×C523C22semidirect
39. D8×C523C22semidirect
40. C2×C8×C523C22semidirect
90. C523#577semidirect
99. #135D523semidirect
110. #41C2×D523semidirect
119. Q16C2×D523semidirect
124. SD16C2×D523semidirect
125. SD16C2×D523semidirect
127. D8C2×D523semidirect
131. C2×C8C2×D523semidirect

Maximal subgroups

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

subgroupindex
#306604202
#306604192
#306604052
#306604032
#306603982
#306603972
#306603942
C2×#225526302
SD16×D5232
#306603792
#135×C5232
#577523