Finite Group Databasebeta

← #22581749

Subgroups — #22581749

Order 8896.

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×#14555784C211yesmaximal, characteristic, complemented
2#41×D139C211yesmaximal, characteristic, complemented
3#17984875C211yesmaximal, characteristic, complemented
4#17984872C211yesmaximal, characteristic, complemented
5#17984871C212yesmaximal, complemented
6#17984868C211yesmaximal, characteristic, complemented
7#17984866C212yesmaximal, complemented
8#17984863C212yesmaximal, complemented
9#17984861C212yesmaximal, complemented
10M16×D139C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C139C211yesmaximal, characteristic, complemented
12#14555786C2211yescharacteristic, complemented
13#14555785—21no—
14#14555785C2211yescharacteristic
15#14555784—21no—
16#14555784—21no—
17#14555784—21no—
18#14555784C2212yes—
19#14555784C2211yescharacteristic, complemented
20#14555784C2212yescomplemented
21C2×Dic278C2211yescharacteristic, complemented
22Q8×D139C2211yescharacteristic, complemented
23C2×C22⋊D139—21no—
24D4×D139—21no—
25D4×D139C2211yescharacteristic, complemented
26C22×Dic139—21no—
27C2×C4×D139—21no—
28C2×C4×D139C2211yescharacteristic
29Dic556C2212yescomplemented
30#14555775C2212yescomplemented
31#14555774C2212yescomplemented
32#14555773C2212yescomplemented
33#14555773C2212yescomplemented
34#14555770C2212yescomplemented
35#14555769C2211yescharacteristic, complemented
36#14555768C2212yescomplemented
37C8×D139C2212yescomplemented
38#41×C139C2211yescharacteristic
39C2×D4×C139C2211yescharacteristic, complemented
40SD16×C139C2212yescomplemented
41D8×C139C2212yescomplemented
42M16×C139C2211yescharacteristic, complemented
43C22×D139—21no—
44C22×D139D411yescharacteristic
45Dic278—21no—
46Dic278—21no—
47Dic278C2311yescharacteristic
48Dic278C2312yes—
49D556—21no—
50D556C2311yescharacteristic
51C22⋊D139—21no—
52C22⋊D139—21no—
53C22⋊D139—22no—
54C22⋊D139—22no—
55C22⋊D139—21no—
56C2×Dic139—21no—
57C2×Dic139—21no—
58C2×Dic139—22no—
59C2×Dic139—22no—
60C2×Dic139D411yescharacteristic
61C4×D139—21no—
62C4×D139—21no—
63C4×D139—21no—
64C4×D139D411yescharacteristic
65C4×D139D411yescharacteristic
66C4×D139C2311yescharacteristic
67C4×D139C2311yescharacteristic
68C139⋊C8C2312yes—
69C23×C139—21no—
70Q8×C139C2311yescharacteristic
71D4×C139—21no—
72D4×C139—21no—
73D4×C139C2311yescharacteristic
74D4×C139C2312yes—
75C2×C4×C139—21no—
76C2×C4×C139C2311yescharacteristic
77C8×C139C2312yes—
78C22×C139—21no—
79C22×C139—22no—
80C22×C139—42no—
81C22×C139C2×D411yescharacteristic
82C2×D139—21no—
83C2×D139—41no—
84C2×D139—42no—
85C2×D139C2×D411yescharacteristic
86C2×D139C2×D411yescharacteristic
87C4×C139—21no—
88C4×C139C2×D411yescharacteristic
89C4×C139C2411yescharacteristic
90Dic139—21no—
91Dic139—22no—
92Dic139C2×D411yescharacteristic
93Dic139C2×D411yescharacteristic
94C2×C139—21no—
95C2×C139—41no—
96C2×C139—42no—
97C2×C139C22×D411yescharacteristic
98D139—21no—
99D139—21no—
100D139—41no—
101C139#57511yescharacteristic, complemented, Sylow
102#575—1391nomaximal, Sylow
103C2×#41—1391no—
104C2×#41—1391no—
105#137—1391no—
106#137—1392no—
107#137—1391no—
108AGL(1,ℤ/8)—1391no—
109AGL(1,ℤ/8)—1392no—
110AGL(1,ℤ/8)D13911yescharacteristic, complemented
111#135—1392no—
112#135—1392no—
113C2×M16—1391no—
114#41—2781no—
115#41—2781no—
116#41—2781no—
117#41—2781no—
118#41—1391no—
119#41—1392no—
120#41—1391no—
121#41—1392no—
122#41—1391no—
123#41C2×D13911yescharacteristic
124C2×Q8—1391no—
125C2×Q8—1391no—
126C2×D4—2781no—
127C2×D4—2781no—
128C2×D4—1391no—
129C2×D4C2×D13911yescharacteristic, complemented
130C22×C4—2781no—
131C22×C4—2781no—
132C22×C4—1391no—
133Q16—1392no—
134Q16—1392no—
135SD16—1392no—
136SD16—1392no—
137SD16—1392no—
138SD16C2×D13912yescomplemented
139D8—1392no—
140D8C2×D13912yescomplemented
141M16—1391no—
142M16—1392no—
143M16C2×D13911yescharacteristic, complemented
144C2×C8—1392no—
145C23—21no—
146C23—2781no—
147C23—1391no—
148Q8—2781no—
149Q8—2781no—
150Q8—1391no—
151Q8—1392no—
152Q8C22×D13911yescharacteristic
153D4—21no—
154D4—21no—
155D4—2781no—
156D4—2781no—
157D4—2782no—
158D4—2782no—
159D4—2781no—
160D4—2781no—
161D4—1391no—
162D4C22×D13912yes—
163D4C22×D13911yescharacteristic
164C2×C4—21no—
165C2×C4—2781no—
166C2×C4—2781no—
167C2×C4—2781no—
168C2×C4—2781no—
169C2×C4—2782no—
170C2×C4—2782no—
171C2×C4—2781no—
172C2×C4—1391no—
173C2×C4—1391no—
174C2×C4—1391no—
175C2×C4—1391no—
176C2×C4—1391no—
177C2×C4C22×D13911yescharacteristic
178C8—1392no—
179C8C22×D13912yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—2781no—
184C22—5561no—
185C22—5562no—
186C22—1391no—
187C22—1391no—
188C22D4×D13911yescharacteristic
189C4—21no—
190C4—2781no—
191C4—2782no—
192C4—1391no—
193C4—1391no—
194C4D4×D13911yescharacteristic
195C4C23×D13911yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—2781no—
200C2—2781no—
201C2—5561no—
202C2C2×D4×D13911yescharacteristic
subgroupG/H
centerC2C2×D4×D139
commutatorC4×C139C24
FrattiniC4C23×D139
FittingAGL(1,ℤ/8)×C139C2
socleC2×C139C22×D4
hypercenterAGL(1,ℤ/8)D139
hypocenterC139#575
LCSG ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#14555784C2semidirect
2. #41×D139C2semidirect
3. #17984875C2semidirect
4. #17984872C2semidirect
5. #17984871C2semidirect
6. #17984868C2semidirect
7. #17984866C2semidirect
8. #17984863C2semidirect
9. #17984861C2semidirect
10. M16×D139C2semidirect
11. AGL(1,ℤ/8)×C139C2semidirect
12. #14555786C22semidirect
19. #14555784C22semidirect
20. #14555784C22semidirect
21. C2×Dic278C22semidirect
22. Q8×D139C22semidirect
25. D4×D139C22semidirect
29. Dic556C22semidirect
30. #14555775C22semidirect
31. #14555774C22semidirect
32. #14555773C22semidirect
33. #14555773C22semidirect
34. #14555770C22semidirect
35. #14555769C22semidirect
36. #14555768C22semidirect
37. C8×D139C22semidirect
39. C2×D4×C139C22semidirect
40. SD16×C139C22semidirect
41. D8×C139C22semidirect
42. M16×C139C22semidirect
101. C139#575semidirect
110. AGL(1,ℤ/8)D139semidirect
129. C2×D4C2×D139semidirect
138. SD16C2×D139semidirect
140. D8C2×D139semidirect
143. M16C2×D139semidirect