Finite Group Databasebeta

← #14558340

Subgroups — #14558340

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#11924583C211yesmaximal, characteristic, complemented
2#11924582C211yesmaximal, characteristic, complemented
3#11924568C212yesmaximal, complemented
4#11924566C211yesmaximal, characteristic, complemented
5#11924561C211yesmaximal, characteristic, complemented
6#11924560C212yesmaximal, complemented
7#11924557C212yesmaximal, complemented
8C2×#10596930C211yesmaximal, characteristic, complemented
9SD16×D37C212yesmaximal, complemented
10#11924542C211yesmaximal, characteristic, complemented
11#135×C37C211yesmaximal, characteristic, complemented
12#41×C37C2211yescharacteristic
13#41×C37C2211yescharacteristic, complemented
14#10596966C2212yes—
15Q8×D37C2212yescomplemented
16#10596964—22no—
17#10596964C2212yescomplemented
18D4×D37—22no—
19D4×D37C2212yes—
20#10596962—21no—
21#10596962—21no—
22#10596962C2211yescharacteristic
23C2×D148—21no—
24C2×D148C2211yescharacteristic
25C2×Dic74—21no—
26C2×Dic74C2211yescharacteristic, complemented
27Q16×C37C2211yescharacteristic, complemented
28SD16×C37C2211yescharacteristic, complemented
29SD16×C37C2211yescharacteristic, complemented
30D8×C37C2211yescharacteristic, complemented
31C2×C8×C37C2211yescharacteristic, complemented
32#10596942C2212yescomplemented
33#10596941C2212yescomplemented
34#10596940C2212yescomplemented
35#10596939C2212yescomplemented
36#10596934C2211yescharacteristic, complemented
37#10596930C2212yescomplemented
38#10596930C2212yescomplemented
39#10596929C2212yescomplemented
40C8×D37C2212yescomplemented
41C22×D37—21no—
42C22×D37—22no—
43Q8×C37C2311yescharacteristic
44Q8×C37C2311yescharacteristic
45D4×C37—21no—
46D4×C37—21no—
47D4×C37C2311yescharacteristic
48D4×C37C2311yescharacteristic
49C2×C4×C37—21no—
50C2×C4×C37—21no—
51C2×C4×C37C2311yescharacteristic
52C22⋊D37—22no—
53C22⋊D37—22no—
54C22⋊D37D412yes—
55C2×Dic37—21no—
56C2×Dic37—22no—
57D148—22no—
58D148—21no—
59D148D411yescharacteristic
60D148C2312yes—
61C4×D37—22no—
62C4×D37—22no—
63C4×D37C2312yes—
64Dic74—21no—
65Dic74—22no—
66Dic74D411yescharacteristic
67Dic74C2312yes—
68C8×C37C2311yescharacteristic
69C8×C37C2311yescharacteristic
70#64436C2312yes—
71C22×C37—21no—
72C22×C37—21no—
73C22×C37C2×D411yescharacteristic
74C2×D37—22no—
75C2×D37—82no—
76C2×D37—81no—
77C2×D37C2×D412yes—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37C2×D411yescharacteristic
81C4×C37C2411yescharacteristic
82Dic37—22no—
83Dic37C2×D412yes—
84C2×C37—21no—
85C2×C37—41no—
86C2×C37—41no—
87C2×C37C22×D411yescharacteristic
88D37—22no—
89D37—42no—
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#135D3711yescharacteristic, complemented
100C2×SD16—372no—
101C2×SD16—371no—
102#131—371no—
103#41—371no—
104#41—372no—
105#41—372no—
106#41—741no—
107#41—741no—
108#41—742no—
109#41C2×D3711yescharacteristic
110#41C2×D3711yescharacteristic, complemented
111C2×Q8—372no—
112C2×Q8—371no—
113C2×Q8—741no—
114C2×D4—372no—
115C2×D4—371no—
116C2×D4—741no—
117C2×D4—742no—
118Q16—372no—
119Q16C2×D3711yescharacteristic, complemented
120SD16—372no—
121SD16—372no—
122SD16—372no—
123SD16—372no—
124SD16C2×D3711yescharacteristic, complemented
125SD16C2×D3711yescharacteristic, complemented
126D8—372no—
127D8C2×D3711yescharacteristic, complemented
128M16—371no—
129M16—372no—
130C2×C8—372no—
131C2×C8C2×D3711yescharacteristic, complemented
132C23—742no—
133C23—741no—
134Q8—371no—
135Q8—372no—
136Q8—742no—
137Q8—741no—
138Q8C22×D3711yescharacteristic
139Q8C22×D3711yescharacteristic
140D4—21no—
141D4—21no—
142D4—372no—
143D4—371no—
144D4—372no—
145D4—742no—
146D4—742no—
147D4—742no—
148D4—741no—
149D4C22×D3711yescharacteristic
150D4C22×D3711yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—372no—
154C2×C4—742no—
155C2×C4—742no—
156C2×C4—742no—
157C2×C4—741no—
158C2×C4C22×D3711yescharacteristic
159C8—372no—
160C8C22×D3711yescharacteristic
161C8C22×D3711yescharacteristic
162C22—21no—
163C22—21no—
164C22—372no—
165C22—2961no—
166C22—2962no—
167C22—742no—
168C22D4×D3711yescharacteristic
169C4—21no—
170C4—21no—
171C4—372no—
172C4—742no—
173C4D4×D3711yescharacteristic
174C4C23×D3711yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—742no—
179C2—1482no—
180C2C2×D4×D3711yescharacteristic
subgroupG/H
centerC2C2×D4×D37
commutator, cosocleC4×C37C24
FrattiniC4C23×D37
Fitting#135×C37C2
socleC2×C37C22×D4
hypercenter#135D37
hypocenterC37#577
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #11924583C2semidirect
2. #11924582C2semidirect
3. #11924568C2semidirect
4. #11924566C2semidirect
5. #11924561C2semidirect
6. #11924560C2semidirect
7. #11924557C2semidirect
8. C2×#10596930C2semidirect
9. SD16×D37C2semidirect
10. #11924542C2semidirect
11. #135×C37C2semidirect
13. #41×C37C22semidirect
15. Q8×D37C22semidirect
17. #10596964C22semidirect
26. C2×Dic74C22semidirect
27. Q16×C37C22semidirect
28. SD16×C37C22semidirect
29. SD16×C37C22semidirect
30. D8×C37C22semidirect
31. C2×C8×C37C22semidirect
32. #10596942C22semidirect
33. #10596941C22semidirect
34. #10596940C22semidirect
35. #10596939C22semidirect
36. #10596934C22semidirect
37. #10596930C22semidirect
38. #10596930C22semidirect
39. #10596929C22semidirect
40. C8×D37C22semidirect
91. C37#577semidirect
99. #135D37semidirect
110. #41C2×D37semidirect
119. Q16C2×D37semidirect
124. SD16C2×D37semidirect
125. SD16C2×D37semidirect
127. D8C2×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
#119245832
#119245822
#119245682
#119245662
#119245612
#119245602
#119245572
C2×#105969302
SD16×D372
#119245422
#135×C372
#57737