Finite Group Databasebeta

← #31827264

Subgroups — #31827264

Order 18112.

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×#17985393C211yesmaximal, characteristic, complemented
2#41×D283C211yesmaximal, characteristic, complemented
3#22583642C212yesmaximal, complemented
4#22583641C211yesmaximal, characteristic, complemented
5#22583638C211yesmaximal, characteristic, complemented
6#22583637C212yesmaximal, complemented
7#22583635C211yesmaximal, characteristic, complemented
8#22583633C212yesmaximal, complemented
9#22583631C212yesmaximal, complemented
10M16×D283C211yesmaximal, characteristic, complemented
11#137×C283C211yesmaximal, characteristic, complemented
12#17985393—21no—
13#17985393—21no—
14#17985393C2212yes—
15#17985393C2212yescomplemented
16#17985393C2211yescharacteristic, complemented
17#17985392—21no—
18#17985392C2211yescharacteristic
19#17985391—21no—
20#17985391C2211yescharacteristic, complemented
21Q8×D283C2211yescharacteristic, complemented
22C2×D1132—21no—
23C2×D1132C2211yescharacteristic, complemented
24D4×D283—21no—
25D4×D283C2211yescharacteristic, complemented
26C2×C4×D283—21no—
27C2×C4×D283—21no—
28C2×C4×D283C2211yescharacteristic
29#17985382C2212yescomplemented
30#17985381C2212yescomplemented
31#17985379C2212yescomplemented
32#17985379C2212yescomplemented
33D2264C2212yescomplemented
34#17985377C2212yescomplemented
35#17985376C2211yescharacteristic, complemented
36#17985375C2212yescomplemented
37C8×D283C2212yescomplemented
38#41×C283C2211yescharacteristic
39C2×Q8×C283C2211yescharacteristic, complemented
40Q16×C283C2212yescomplemented
41SD16×C283C2212yescomplemented
42M16×C283C2211yescharacteristic, complemented
43C22×D283—21no—
44C22×D283—21no—
45C22×D283D411yescharacteristic
46Dic566—21no—
47Dic566C2311yescharacteristic
48D1132—21no—
49D1132—22no—
50D1132—22no—
51D1132—21no—
52D1132C2312yes—
53D1132C2311yescharacteristic
54C22⋊D283—21no—
55C22⋊D283—21no—
56C22⋊D283—21no—
57C2×Dic283—21no—
58C2×Dic283D411yescharacteristic
59C4×D283—21no—
60C4×D283—21no—
61C4×D283—21no—
62C4×D283—22no—
63C4×D283—22no—
64C4×D283D411yescharacteristic
65C4×D283D411yescharacteristic
66C4×D283C2311yescharacteristic
67C4×D283C2311yescharacteristic
68C283⋊C8C2312yes—
69Q8×C283—21no—
70Q8×C283C2312yes—
71Q8×C283C2311yescharacteristic
72D4×C283—21no—
73D4×C283C2311yescharacteristic
74C2×C4×C283—21no—
75C2×C4×C283—21no—
76C2×C4×C283C2311yescharacteristic
77C8×C283C2312yes—
78C22×C283—21no—
79C22×C283C2×D411yescharacteristic
80C2×D283—21no—
81C2×D283—22no—
82C2×D283—41no—
83C2×D283—42no—
84C2×D283—42no—
85C2×D283C2×D411yescharacteristic
86C2×D283C2×D411yescharacteristic
87C4×C283—21no—
88C4×C283—22no—
89C4×C283C2×D411yescharacteristic
90C4×C283C2411yescharacteristic
91Dic283—21no—
92Dic283C2×D411yescharacteristic
93Dic283C2×D411yescharacteristic
94C2×C283—21no—
95C2×C283—41no—
96C2×C283C22×D411yescharacteristic
97D283—21no—
98D283—21no—
99D283—41no—
100D283—42no—
101C283#57511yescharacteristic, complemented, Sylow
102#575—2831nomaximal, Sylow
103C2×#41—2831no—
104C2×#41—2831no—
105#137—2831no—
106#137—2832no—
107#137D28311yescharacteristic, complemented
108AGL(1,ℤ/8)—2831no—
109AGL(1,ℤ/8)—2832no—
110AGL(1,ℤ/8)—2831no—
111#135—2832no—
112#135—2832no—
113C2×M16—2831no—
114#41—2832no—
115#41—2831no—
116#41—2832no—
117#41—2831no—
118#41—2831no—
119#41—5661no—
120#41—5661no—
121#41—5661no—
122#41—5661no—
123#41C2×D28311yescharacteristic
124C2×Q8—2831no—
125C2×Q8C2×D28311yescharacteristic, complemented
126C2×D4—2831no—
127C2×D4—2831no—
128C2×D4—5661no—
129C2×D4—5661no—
130C22×C4—2831no—
131C22×C4—5661no—
132C22×C4—5661no—
133Q16—2832no—
134Q16C2×D28312yescomplemented
135SD16—2832no—
136SD16—2832no—
137SD16—2832no—
138SD16C2×D28312yescomplemented
139D8—2832no—
140D8—2832no—
141M16—2831no—
142M16—2832no—
143M16C2×D28311yescharacteristic, complemented
144C2×C8—2832no—
145C23—2831no—
146C23—5661no—
147C23—5661no—
148Q8—21no—
149Q8—2831no—
150Q8—5661no—
151Q8C22×D28311yescharacteristic
152Q8C22×D28312yes—
153D4—21no—
154D4—2832no—
155D4—2831no—
156D4—5661no—
157D4—5662no—
158D4—5662no—
159D4—5661no—
160D4—5661no—
161D4—5661no—
162D4—5661no—
163D4C22×D28311yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—2831no—
167C2×C4—2831no—
168C2×C4—2831no—
169C2×C4—2831no—
170C2×C4—2831no—
171C2×C4—5661no—
172C2×C4—5662no—
173C2×C4—5662no—
174C2×C4—5661no—
175C2×C4—5661no—
176C2×C4—5661no—
177C2×C4C22×D28311yescharacteristic
178C8—2832no—
179C8C22×D28312yes—
180C22—21no—
181C22—2831no—
182C22—2831no—
183C22—5662no—
184C22—5661no—
185C22—11321no—
186C22—11322no—
187C22—11322no—
188C22D4×D28311yescharacteristic
189C4—21no—
190C4—22no—
191C4—2831no—
192C4—2831no—
193C4—5661no—
194C4D4×D28311yescharacteristic
195C4C23×D28311yescharacteristic
196C2—21no—
197C2—41no—
198C2—5661no—
199C2—5661no—
200C2—11322no—
201C2—11321no—
202C2C2×D4×D28311yescharacteristic
subgroupG/H
centerC2C2×D4×D283
commutator, cosocleC4×C283C24
FrattiniC4C23×D283
Fitting#137×C283C2
socleC2×C283C22×D4
hypercenter#137D283
hypocenterC283#575
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#17985393C2semidirect
2. #41×D283C2semidirect
3. #22583642C2semidirect
4. #22583641C2semidirect
5. #22583638C2semidirect
6. #22583637C2semidirect
7. #22583635C2semidirect
8. #22583633C2semidirect
9. #22583631C2semidirect
10. M16×D283C2semidirect
11. #137×C283C2semidirect
15. #17985393C22semidirect
16. #17985393C22semidirect
20. #17985391C22semidirect
21. Q8×D283C22semidirect
23. C2×D1132C22semidirect
25. D4×D283C22semidirect
29. #17985382C22semidirect
30. #17985381C22semidirect
31. #17985379C22semidirect
32. #17985379C22semidirect
33. D2264C22semidirect
34. #17985377C22semidirect
35. #17985376C22semidirect
36. #17985375C22semidirect
37. C8×D283C22semidirect
39. C2×Q8×C283C22semidirect
40. Q16×C283C22semidirect
41. SD16×C283C22semidirect
42. M16×C283C22semidirect
101. C283#575semidirect
107. #137D283semidirect
125. C2×Q8C2×D283semidirect
134. Q16C2×D283semidirect
138. SD16C2×D283semidirect
143. M16C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#179853932
#41×D2832
#225836422
#225836412
#225836382
#225836372
#225836352
#225836332
#225836312
M16×D2832
#137×C2832
#575283