Finite Group Databasebeta

← #31827261

Subgroups — #31827261

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×#17985391C211yesmaximal, characteristic, complemented
2#41×D283C211yesmaximal, characteristic, complemented
3#22583643C211yesmaximal, characteristic, complemented
4#22583640C211yesmaximal, characteristic, complemented
5#22583639C212yesmaximal, complemented
6#22583636C211yesmaximal, characteristic, complemented
7#22583634C212yesmaximal, complemented
8#22583631C212yesmaximal, complemented
9#22583629C212yesmaximal, complemented
10M16×D283C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C283C211yesmaximal, characteristic, complemented
12#17985393C2211yescharacteristic, complemented
13#17985392—21no—
14#17985392C2211yescharacteristic
15#17985391—21no—
16#17985391—21no—
17#17985391—21no—
18#17985391C2212yes—
19#17985391C2211yescharacteristic, complemented
20#17985391C2212yescomplemented
21C2×Dic566C2211yescharacteristic, complemented
22Q8×D283C2211yescharacteristic, complemented
23C2×C22⋊D283—21no—
24D4×D283—21no—
25D4×D283C2211yescharacteristic, complemented
26C22×Dic283—21no—
27C2×C4×D283—21no—
28C2×C4×D283C2211yescharacteristic
29Dic1132C2212yescomplemented
30#17985382C2212yescomplemented
31#17985381C2212yescomplemented
32#17985380C2212yescomplemented
33#17985380C2212yescomplemented
34#17985377C2212yescomplemented
35#17985376C2211yescharacteristic, complemented
36#17985375C2212yescomplemented
37C8×D283C2212yescomplemented
38#41×C283C2211yescharacteristic
39C2×D4×C283C2211yescharacteristic, complemented
40SD16×C283C2212yescomplemented
41D8×C283C2212yescomplemented
42M16×C283C2211yescharacteristic, complemented
43C22×D283—21no—
44C22×D283D411yescharacteristic
45Dic566—21no—
46Dic566—21no—
47Dic566C2311yescharacteristic
48Dic566C2312yes—
49D1132—21no—
50D1132C2311yescharacteristic
51C22⋊D283—21no—
52C22⋊D283—21no—
53C22⋊D283—22no—
54C22⋊D283—22no—
55C22⋊D283—21no—
56C2×Dic283—21no—
57C2×Dic283—21no—
58C2×Dic283—22no—
59C2×Dic283—22no—
60C2×Dic283D411yescharacteristic
61C4×D283—21no—
62C4×D283—21no—
63C4×D283—21no—
64C4×D283D411yescharacteristic
65C4×D283D411yescharacteristic
66C4×D283C2311yescharacteristic
67C4×D283C2311yescharacteristic
68C283⋊C8C2312yes—
69C23×C283—21no—
70Q8×C283C2311yescharacteristic
71D4×C283—21no—
72D4×C283—21no—
73D4×C283C2311yescharacteristic
74D4×C283C2312yes—
75C2×C4×C283—21no—
76C2×C4×C283C2311yescharacteristic
77C8×C283C2312yes—
78C22×C283—21no—
79C22×C283—22no—
80C22×C283—42no—
81C22×C283C2×D411yescharacteristic
82C2×D283—21no—
83C2×D283—41no—
84C2×D283—42no—
85C2×D283C2×D411yescharacteristic
86C2×D283C2×D411yescharacteristic
87C4×C283—21no—
88C4×C283C2×D411yescharacteristic
89C4×C283C2411yescharacteristic
90Dic283—21no—
91Dic283—22no—
92Dic283C2×D411yescharacteristic
93Dic283C2×D411yescharacteristic
94C2×C283—21no—
95C2×C283—41no—
96C2×C283—42no—
97C2×C283C22×D411yescharacteristic
98D283—21no—
99D283—21no—
100D283—41no—
101C283#57511yescharacteristic, complemented, Sylow
102#575—2831nomaximal, Sylow
103C2×#41—2831no—
104C2×#41—2831no—
105#137—2831no—
106#137—2832no—
107#137—2831no—
108AGL(1,ℤ/8)—2831no—
109AGL(1,ℤ/8)—2832no—
110AGL(1,ℤ/8)D28311yescharacteristic, complemented
111#135—2832no—
112#135—2832no—
113C2×M16—2831no—
114#41—2831no—
115#41—2832no—
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×Q8—2831no—
126C2×D4—2831no—
127C2×D4—5661no—
128C2×D4—5661no—
129C2×D4C2×D28311yescharacteristic, complemented
130C22×C4—2831no—
131C22×C4—5661no—
132C22×C4—5661no—
133Q16—2832no—
134Q16—2832no—
135SD16—2832no—
136SD16—2832no—
137SD16—2832no—
138SD16C2×D28312yescomplemented
139D8—2832no—
140D8C2×D28312yescomplemented
141M16—2831no—
142M16—2832no—
143M16C2×D28311yescharacteristic, complemented
144C2×C8—2832no—
145C23—21no—
146C23—2831no—
147C23—5661no—
148Q8—2831no—
149Q8—2832no—
150Q8—5661no—
151Q8—5661no—
152Q8C22×D28311yescharacteristic
153D4—21no—
154D4—21no—
155D4—2831no—
156D4—5661no—
157D4—5661no—
158D4—5661no—
159D4—5662no—
160D4—5662no—
161D4—5661no—
162D4C22×D28312yes—
163D4C22×D28311yescharacteristic
164C2×C4—21no—
165C2×C4—2831no—
166C2×C4—2831no—
167C2×C4—2831no—
168C2×C4—2831no—
169C2×C4—2831no—
170C2×C4—5661no—
171C2×C4—5661no—
172C2×C4—5661no—
173C2×C4—5662no—
174C2×C4—5662no—
175C2×C4—5661no—
176C2×C4—5661no—
177C2×C4C22×D28311yescharacteristic
178C8—2832no—
179C8C22×D28312yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—2831no—
184C22—2831no—
185C22—5661no—
186C22—11321no—
187C22—11322no—
188C22D4×D28311yescharacteristic
189C4—21no—
190C4—2831no—
191C4—2831no—
192C4—5661no—
193C4—5662no—
194C4D4×D28311yescharacteristic
195C4C23×D28311yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—5661no—
200C2—5661no—
201C2—11321no—
202C2C2×D4×D28311yescharacteristic
subgroupG/H
centerC2C2×D4×D283
commutator, cosocleC4×C283C24
FrattiniC4C23×D283
FittingAGL(1,ℤ/8)×C283C2
socleC2×C283C22×D4
hypercenterAGL(1,ℤ/8)D283
hypocenterC283#575
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#17985391C2semidirect
2. #41×D283C2semidirect
3. #22583643C2semidirect
4. #22583640C2semidirect
5. #22583639C2semidirect
6. #22583636C2semidirect
7. #22583634C2semidirect
8. #22583631C2semidirect
9. #22583629C2semidirect
10. M16×D283C2semidirect
11. AGL(1,ℤ/8)×C283C2semidirect
12. #17985393C22semidirect
19. #17985391C22semidirect
20. #17985391C22semidirect
21. C2×Dic566C22semidirect
22. Q8×D283C22semidirect
25. D4×D283C22semidirect
29. Dic1132C22semidirect
30. #17985382C22semidirect
31. #17985381C22semidirect
32. #17985380C22semidirect
33. #17985380C22semidirect
34. #17985377C22semidirect
35. #17985376C22semidirect
36. #17985375C22semidirect
37. C8×D283C22semidirect
39. C2×D4×C283C22semidirect
40. SD16×C283C22semidirect
41. D8×C283C22semidirect
42. M16×C283C22semidirect
101. C283#575semidirect
110. AGL(1,ℤ/8)D283semidirect
129. C2×D4C2×D283semidirect
138. SD16C2×D283semidirect
140. D8C2×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×#179853912
#41×D2832
#225836432
#225836402
#225836392
#225836362
#225836342
#225836312
#225836292
M16×D2832
AGL(1,ℤ/8)×C2832
#575283