Finite Group Databasebeta

← #14558332

Subgroups — #14558332

Order 2368.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 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
1C2×#10596966C211yesmaximal, characteristic, complemented
2#41×D37C211yesmaximal, characteristic, complemented
3#11924568C212yesmaximal, complemented
4#11924567C211yesmaximal, characteristic, complemented
5#11924564C211yesmaximal, characteristic, complemented
6#11924563C212yesmaximal, complemented
7#11924561C211yesmaximal, characteristic, complemented
8#11924559C212yesmaximal, complemented
9#11924557C212yesmaximal, complemented
10M16×D37C211yesmaximal, characteristic, complemented
11#137×C37C211yesmaximal, characteristic, complemented
12#41×C37C2211yescharacteristic
13C2×Q8×C37C2211yescharacteristic, complemented
14#10596966—21no—
15#10596966—21no—
16#10596966C2212yes—
17#10596966C2212yescomplemented
18#10596966C2211yescharacteristic, complemented
19Q8×D37C2211yescharacteristic, complemented
20#10596964—21no—
21#10596964C2211yescharacteristic, complemented
22D4×D37—21no—
23D4×D37C2211yescharacteristic, complemented
24#10596962—21no—
25#10596962C2211yescharacteristic
26C2×D148—21no—
27C2×D148C2211yescharacteristic, complemented
28C2×C4×D37—21no—
29C2×C4×D37—21no—
30C2×C4×D37C2211yescharacteristic
31Q16×C37C2212yescomplemented
32SD16×C37C2212yescomplemented
33M16×C37C2211yescharacteristic, complemented
34#10596942C2212yescomplemented
35#10596941C2212yescomplemented
36#10596941C2212yescomplemented
37#10596939C2212yescomplemented
38#10596934C2211yescharacteristic, complemented
39D296C2212yescomplemented
40#10596930C2212yescomplemented
41#10596929C2212yescomplemented
42C8×D37C2212yescomplemented
43C22×D37—21no—
44C22×D37—21no—
45C22×D37D411yescharacteristic
46Q8×C37—21no—
47Q8×C37C2311yescharacteristic
48Q8×C37C2312yes—
49D4×C37—21no—
50D4×C37C2311yescharacteristic
51C2×C4×C37—21no—
52C2×C4×C37—21no—
53C2×C4×C37C2311yescharacteristic
54C22⋊D37—21no—
55C22⋊D37—21no—
56C22⋊D37—21no—
57C2×Dic37—21no—
58C2×Dic37D411yescharacteristic
59D148—22no—
60D148—22no—
61D148—21no—
62D148—21no—
63D148C2312yes—
64D148C2311yescharacteristic
65C4×D37—21no—
66C4×D37—21no—
67C4×D37—21no—
68C4×D37—22no—
69C4×D37—22no—
70C4×D37D411yescharacteristic
71C4×D37D411yescharacteristic
72C4×D37C2311yescharacteristic
73C4×D37C2311yescharacteristic
74Dic74—21no—
75Dic74C2311yescharacteristic
76C8×C37C2312yes—
77#64436C2312yes—
78C22×C37—21no—
79C22×C37C2×D411yescharacteristic
80C2×D37—22no—
81C2×D37—21no—
82C2×D37—41no—
83C2×D37—42no—
84C2×D37—42no—
85C2×D37C2×D411yescharacteristic
86C2×D37C2×D411yescharacteristic
87C4×C37—21no—
88C4×C37—22no—
89C4×C37C2×D411yescharacteristic
90C4×C37C2411yescharacteristic
91Dic37—21no—
92Dic37C2×D411yescharacteristic
93Dic37C2×D411yescharacteristic
94C2×C37—21no—
95C2×C37—41no—
96C2×C37C22×D411yescharacteristic
97D37—21no—
98D37—21no—
99D37—42no—
100D37—41no—
101#575—371nomaximal, Sylow
102C37#57511yescharacteristic, complemented, Sylow
103C2×#41—371no—
104C2×#41—371no—
105#137—371no—
106#137—372no—
107#137D3711yescharacteristic, complemented
108AGL(1,ℤ/8)—371no—
109AGL(1,ℤ/8)—372no—
110AGL(1,ℤ/8)—371no—
111#135—372no—
112#135—372no—
113C2×M16—371no—
114#41—372no—
115#41—371no—
116#41—372no—
117#41—371no—
118#41—371no—
119#41—741no—
120#41—741no—
121#41—741no—
122#41—741no—
123#41C2×D3711yescharacteristic
124C2×Q8—371no—
125C2×Q8C2×D3711yescharacteristic, complemented
126C2×D4—371no—
127C2×D4—371no—
128C2×D4—741no—
129C2×D4—741no—
130C22×C4—371no—
131C22×C4—741no—
132C22×C4—741no—
133Q16—372no—
134Q16C2×D3712yescomplemented
135SD16—372no—
136SD16—372no—
137SD16—372no—
138SD16C2×D3712yescomplemented
139D8—372no—
140D8—372no—
141M16—371no—
142M16—372no—
143M16C2×D3711yescharacteristic, complemented
144C2×C8—372no—
145C23—371no—
146C23—741no—
147C23—741no—
148Q8—21no—
149Q8—371no—
150Q8—741no—
151Q8C22×D3711yescharacteristic
152Q8C22×D3712yes—
153D4—21no—
154D4—372no—
155D4—371no—
156D4—741no—
157D4—742no—
158D4—742no—
159D4—741no—
160D4—741no—
161D4—741no—
162D4—741no—
163D4C22×D3711yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—371no—
167C2×C4—371no—
168C2×C4—371no—
169C2×C4—371no—
170C2×C4—371no—
171C2×C4—741no—
172C2×C4—742no—
173C2×C4—742no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4—741no—
177C2×C4C22×D3711yescharacteristic
178C8—372no—
179C8C22×D3712yes—
180C22—21no—
181C22—371no—
182C22—371no—
183C22—742no—
184C22—741no—
185C22—1481no—
186C22—1482no—
187C22—1482no—
188C22D4×D3711yescharacteristic
189C4—21no—
190C4—22no—
191C4—371no—
192C4—371no—
193C4—741no—
194C4D4×D3711yescharacteristic
195C4C23×D3711yescharacteristic
196C2—21no—
197C2—41no—
198C2—741no—
199C2—741no—
200C2—1482no—
201C2—1481no—
202C2C2×D4×D3711yescharacteristic
subgroupG/H
centerC2C2×D4×D37
commutator, cosocleC4×C37C24
FrattiniC4C23×D37
Fitting#137×C37C2
socleC2×C37C22×D4
hypercenter#137D37
hypocenterC37#575
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#10596966C2semidirect
2. #41×D37C2semidirect
3. #11924568C2semidirect
4. #11924567C2semidirect
5. #11924564C2semidirect
6. #11924563C2semidirect
7. #11924561C2semidirect
8. #11924559C2semidirect
9. #11924557C2semidirect
10. M16×D37C2semidirect
11. #137×C37C2semidirect
13. C2×Q8×C37C22semidirect
17. #10596966C22semidirect
18. #10596966C22semidirect
19. Q8×D37C22semidirect
21. #10596964C22semidirect
23. D4×D37C22semidirect
27. C2×D148C22semidirect
31. Q16×C37C22semidirect
32. SD16×C37C22semidirect
33. M16×C37C22semidirect
34. #10596942C22semidirect
35. #10596941C22semidirect
36. #10596941C22semidirect
37. #10596939C22semidirect
38. #10596934C22semidirect
39. D296C22semidirect
40. #10596930C22semidirect
41. #10596929C22semidirect
42. C8×D37C22semidirect
102. C37#575semidirect
107. #137D37semidirect
125. C2×Q8C2×D37semidirect
134. Q16C2×D37semidirect
138. SD16C2×D37semidirect
143. M16C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#105969662
#41×D372
#119245682
#119245672
#119245642
#119245632
#119245612
#119245592
#119245572
M16×D372
#137×C372
#57537