Finite Group Databasebeta

← #14558339

Subgroups — #14558339

Order 2368.

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#11924584C211yesmaximal, characteristic, complemented
2#11924581C211yesmaximal, characteristic, complemented
3#11924567C211yesmaximal, characteristic, complemented
4#11924565C212yesmaximal, complemented
5#11924563C212yesmaximal, complemented
6#11924562C211yesmaximal, characteristic, complemented
7#11924558C211yesmaximal, characteristic, complemented
8#11924557C212yesmaximal, complemented
9SD16×D37C212yesmaximal, complemented
10#11924542C211yesmaximal, characteristic, complemented
11C2×SD16×C37C211yesmaximal, characteristic, complemented
12C2×Q8×C37C2211yescharacteristic, complemented
13C2×D4×C37C2211yescharacteristic
14C2×C22⋊D37—22no—
15#10596966—21no—
16#10596966C2212yescomplemented
17Q8×D37—21no—
18Q8×D37C2212yescomplemented
19#10596964—21no—
20#10596964C2212yes—
21D4×D37—21no—
22D4×D37C2212yes—
23#10596962—22no—
24#10596962C2211yescharacteristic
25#10596962C2211yescharacteristic
26#10596962C2211yescharacteristic, complemented
27SD16×C37C2212yescomplemented
28SD16×C37C2212yescomplemented
29C2×C8×C37C2211yescharacteristic, complemented
30#10596942C2212yescomplemented
31#10596941C2212yescomplemented
32#10596940C2212yescomplemented
33#10596939C2212yescomplemented
34#10596934C2211yescharacteristic, complemented
35Dic148C2211yescharacteristic, complemented
36D296C2211yescharacteristic, complemented
37#10596930C2211yescharacteristic, complemented
38#10596930C2211yescharacteristic, complemented
39#10596929C2212yescomplemented
40C8×D37C2212yescomplemented
41C23×C37—21no—
42C22×D37—22no—
43Q8×C37—21no—
44Q8×C37C2312yes—
45D4×C37—21no—
46D4×C37C2312yes—
47C2×C4×C37—21no—
48C2×C4×C37C2311yescharacteristic
49C22⋊D37—21no—
50C22⋊D37—21no—
51C22⋊D37—22no—
52C22⋊D37—22no—
53C22⋊D37D412yes—
54C2×Dic37—22no—
55D148—22no—
56D148D411yescharacteristic
57D148C2311yescharacteristic
58D148C2311yescharacteristic
59C4×D37—22no—
60C4×D37—21no—
61C4×D37—21no—
62C4×D37—22no—
63C4×D37C2312yes—
64Dic74—22no—
65Dic74D411yescharacteristic
66Dic74C2311yescharacteristic
67Dic74C2311yescharacteristic
68C8×C37C2311yescharacteristic
69C8×C37C2311yescharacteristic
70#64436C2312yes—
71C22×C37—22no—
72C22×C37—81no—
73C22×C37C2×D411yescharacteristic
74C2×D37—21no—
75C2×D37—21no—
76C2×D37—82no—
77C2×D37C2×D412yes—
78C4×C37—22no—
79C4×C37C2×D411yescharacteristic
80C4×C37C2411yescharacteristic
81Dic37—21no—
82Dic37—21no—
83Dic37C2×D412yes—
84C2×C37—21no—
85C2×C37—42no—
86C2×C37C22×D411yescharacteristic
87D37—22no—
88D37—41no—
89D37—41no—
90#577—371nomaximal, Sylow
91C37#57711yescharacteristic, complemented, Sylow
922−1+4—371no—
93H(5,𝔽2)—371no—
94#137—371no—
95#137—372no—
96AGL(1,ℤ/8)—371no—
97AGL(1,ℤ/8)—372no—
98#135—372no—
99#135—371no—
100C2×SD16—372no—
101C2×SD16D3711yescharacteristic, complemented
102#131—371no—
103#41—371no—
104#41—372no—
105#41—372no—
106#41—371no—
107#41—371no—
108#41—742no—
109#41—741no—
110#41—741no—
111C2×Q8—372no—
112C2×Q8—741no—
113C2×Q8C2×D3711yescharacteristic, complemented
114C2×D4—372no—
115C2×D4—741no—
116C2×D4—742no—
117C2×D4C2×D3711yescharacteristic
118Q16—372no—
119Q16—371no—
120SD16—372no—
121SD16—372no—
122SD16—371no—
123SD16—371no—
124SD16C2×D3712yescomplemented
125SD16C2×D3712yescomplemented
126D8—372no—
127D8—371no—
128M16—371no—
129M16—372no—
130C2×C8—372no—
131C2×C8C2×D3711yescharacteristic, complemented
132C23—21no—
133C23—742no—
134Q8—21no—
135Q8—371no—
136Q8—371no—
137Q8—371no—
138Q8—742no—
139Q8C22×D3712yes—
140D4—21no—
141D4—372no—
142D4—371no—
143D4—371no—
144D4—371no—
145D4—742no—
146D4—742no—
147D4—742no—
148D4—741no—
149D4—741no—
150D4C22×D3712yes—
151C2×C4—21no—
152C2×C4—372no—
153C2×C4—742no—
154C2×C4—742no—
155C2×C4—742no—
156C2×C4—741no—
157C2×C4—741no—
158C2×C4C22×D3711yescharacteristic
159C8—372no—
160C8C22×D3711yescharacteristic
161C8C22×D3711yescharacteristic
162C22—22no—
163C22—81no—
164C22—372no—
165C22—2962no—
166C22—741no—
167C22—741no—
168C22D4×D3711yescharacteristic
169C4—22no—
170C4—372no—
171C4—741no—
172C4—741no—
173C4D4×D3711yescharacteristic
174C4C23×D3711yescharacteristic
175C2—21no—
176C2—42no—
177C2—742no—
178C2—1481no—
179C2—1481no—
180C2C2×D4×D3711yescharacteristic
subgroupG/H
centerC2C2×D4×D37
commutator, cosocleC4×C37C24
FrattiniC4C23×D37
FittingC2×SD16×C37C2
socleC2×C37C22×D4
hypercenterC2×SD16D37
hypocenterC37#577
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #11924584C2semidirect
2. #11924581C2semidirect
3. #11924567C2semidirect
4. #11924565C2semidirect
5. #11924563C2semidirect
6. #11924562C2semidirect
7. #11924558C2semidirect
8. #11924557C2semidirect
9. SD16×D37C2semidirect
10. #11924542C2semidirect
11. C2×SD16×C37C2semidirect
12. C2×Q8×C37C22semidirect
16. #10596966C22semidirect
18. Q8×D37C22semidirect
26. #10596962C22semidirect
27. SD16×C37C22semidirect
28. SD16×C37C22semidirect
29. C2×C8×C37C22semidirect
30. #10596942C22semidirect
31. #10596941C22semidirect
32. #10596940C22semidirect
33. #10596939C22semidirect
34. #10596934C22semidirect
35. Dic148C22semidirect
36. D296C22semidirect
37. #10596930C22semidirect
38. #10596930C22semidirect
39. #10596929C22semidirect
40. C8×D37C22semidirect
91. C37#577semidirect
101. C2×SD16D37semidirect
113. C2×Q8C2×D37semidirect
124. SD16C2×D37semidirect
125. SD16C2×D37semidirect
131. C2×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#119245842
#119245812
#119245672
#119245652
#119245632
#119245622
#119245582
#119245572
SD16×D372
#119245422
C2×SD16×C372
#57737