Finite Group Databasebeta

← #46855805

Subgroups — #46855805

Order 35008.

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

normal subgroups only

This group has 268 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#31776048C211yesmaximal, characteristic, complemented
2#31776047C211yesmaximal, characteristic, complemented
3#31776030C211yesmaximal, characteristic, complemented
4#31776029C212yesmaximal, complemented
5#31776026C212yesmaximal, complemented
6#31776023C212yesmaximal, complemented
7#31776022C211yesmaximal, characteristic, complemented
8C2×#22576761C211yesmaximal, characteristic, complemented
9D8×D547C212yesmaximal, complemented
10#31776010C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C547C211yesmaximal, characteristic, complemented
12#22576777C2212yescomplemented
13#22576776—21no—
14#22576776C2211yescharacteristic
15#22576776C2211yescharacteristic, complemented
16#22576775—21no—
17#22576775C2212yescomplemented
18C2×D2188—21no—
19C2×D2188C2211yescharacteristic, complemented
20C2×C22⋊D547—22no—
21D4×D547—21no—
22D4×D547—22no—
23D4×D547C2212yescomplemented
24D4×D547C2212yescomplemented
25#22576766C2211yescharacteristic, complemented
26#22576765C2212yescomplemented
27#22576764C2211yescharacteristic, complemented
28#22576763C2211yescharacteristic, complemented
29D4376C2212yescomplemented
30#22576761C2211yescharacteristic, complemented
31#22576761C2212yescomplemented
32#22576761C2212yescomplemented
33#22576759C2212yescomplemented
34C2×C547⋊C8C2211yescharacteristic, complemented
35C8×D547C2212yescomplemented
36#41×C547C2211yescharacteristic, complemented
37C2×D4×C547C2211yescharacteristic, complemented
38SD16×C547C2212yescomplemented
39D8×C547C2212yescomplemented
40M16×C547C2211yescharacteristic, complemented
41C22×D547—21no—
42C22×D547—22no—
43C22×D547—22no—
44Dic1094D411yescharacteristic
45Dic1094C2311yescharacteristic
46D2188—22no—
47D2188—21no—
48D2188D411yescharacteristic
49D2188C2312yes—
50D2188C2311yescharacteristic
51C22⋊D547—21no—
52C22⋊D547—22no—
53C22⋊D547—22no—
54C22⋊D547—22no—
55C22⋊D547D412yes—
56C2×Dic547—22no—
57C4×D547—21no—
58C4×D547—22no—
59C4×D547C2312yes—
60C547⋊C8C2311yescharacteristic
61C547⋊C8C2311yescharacteristic
62C23×C547—21no—
63Q8×C547C2311yescharacteristic
64D4×C547—21no—
65D4×C547—21no—
66D4×C547C2311yescharacteristic
67D4×C547C2312yes—
68C2×C4×C547—21no—
69C2×C4×C547C2311yescharacteristic
70C8×C547C2312yes—
71C22×C547—21no—
72C22×C547—22no—
73C22×C547—81no—
74C22×C547C2×D411yescharacteristic
75C2×D547—21no—
76C2×D547—22no—
77C2×D547—82no—
78C2×D547—82no—
79C2×D547—81no—
80C2×D547C2×D412yes—
81C4×C547—21no—
82C4×C547C2×D411yescharacteristic
83C4×C547C2411yescharacteristic
84Dic547—21no—
85Dic547C2×D412yes—
86C2×C547—21no—
87C2×C547—41no—
88C2×C547—42no—
89C2×C547C22×D411yescharacteristic
90D547—22no—
91D547—41no—
92D547—42no—
93C547#57611yescharacteristic, complemented, Sylow
94#576—5471nomaximal, Sylow
95H(5,𝔽2)—5471no—
96H(5,𝔽2)—5471no—
97AGL(1,ℤ/8)—5472no—
98AGL(1,ℤ/8)—5472no—
99AGL(1,ℤ/8)—5471no—
100AGL(1,ℤ/8)D54711yescharacteristic, complemented
101#135—5471no—
102#135—5472no—
103C2×D8—5471no—
104C2×D8—5472no—
105#131—5471no—
106#41—5471no—
107#41—5472no—
108#41—5472no—
109#41—5471no—
110#41—10941no—
111#41—10941no—
112#41C2×D54711yescharacteristic, complemented
113C2×D4—5472no—
114C2×D4—5472no—
115C2×D4—5471no—
116C2×D4—10941no—
117C2×D4—10942no—
118C2×D4—10941no—
119C2×D4—10942no—
120C2×D4C2×D54711yescharacteristic, complemented
121Q16—5471no—
122SD16—5471no—
123SD16—5471no—
124SD16—5472no—
125SD16C2×D54712yescomplemented
126D8—5472no—
127D8—5471no—
128D8—5472no—
129D8—5472no—
130D8C2×D54712yescomplemented
131M16—5472no—
132M16C2×D54711yescharacteristic, complemented
133C2×C8—5471no—
134C2×C8—5472no—
135C23—21no—
136C23—10942no—
137C23—10942no—
138C23—10941no—
139Q8—5471no—
140Q8—5471no—
141Q8C22×D54711yescharacteristic
142D4—21no—
143D4—21no—
144D4—5472no—
145D4—5471no—
146D4—5472no—
147D4—5471no—
148D4—10942no—
149D4—10942no—
150D4—10942no—
151D4—10942no—
152D4—10941no—
153D4—10941no—
154D4C22×D54712yes—
155D4C22×D54711yescharacteristic
156C2×C4—21no—
157C2×C4—5472no—
158C2×C4—10942no—
159C2×C4—10942no—
160C2×C4—10941no—
161C2×C4C22×D54711yescharacteristic
162C8—5471no—
163C8—5471no—
164C8C22×D54712yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—43761no—
169C22—43762no—
170C22—43762no—
171C22—5472no—
172C22—10942no—
173C22—10941no—
174C22D4×D54711yescharacteristic
175C4—21no—
176C4—5472no—
177C4—10941no—
178C4D4×D54711yescharacteristic
179C4C23×D54711yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—10942no—
184C2—21882no—
185C2—21881no—
186C2C2×D4×D54711yescharacteristic
subgroupG/H
centerC2C2×D4×D547
commutator, cosocleC4×C547C24
FrattiniC4C23×D547
FittingAGL(1,ℤ/8)×C547C2
socleC2×C547C22×D4
hypercenterAGL(1,ℤ/8)D547
hypocenterC547#576
LCSG ▷ C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #31776048C2semidirect
2. #31776047C2semidirect
3. #31776030C2semidirect
4. #31776029C2semidirect
5. #31776026C2semidirect
6. #31776023C2semidirect
7. #31776022C2semidirect
8. C2×#22576761C2semidirect
9. D8×D547C2semidirect
10. #31776010C2semidirect
11. AGL(1,ℤ/8)×C547C2semidirect
12. #22576777C22semidirect
15. #22576776C22semidirect
17. #22576775C22semidirect
19. C2×D2188C22semidirect
23. D4×D547C22semidirect
24. D4×D547C22semidirect
25. #22576766C22semidirect
26. #22576765C22semidirect
27. #22576764C22semidirect
28. #22576763C22semidirect
29. D4376C22semidirect
30. #22576761C22semidirect
31. #22576761C22semidirect
32. #22576761C22semidirect
33. #22576759C22semidirect
34. C2×C547⋊C8C22semidirect
35. C8×D547C22semidirect
36. #41×C547C22semidirect
37. C2×D4×C547C22semidirect
38. SD16×C547C22semidirect
39. D8×C547C22semidirect
40. M16×C547C22semidirect
93. C547#576semidirect
100. AGL(1,ℤ/8)D547semidirect
112. #41C2×D547semidirect
120. C2×D4C2×D547semidirect
125. SD16C2×D547semidirect
130. D8C2×D547semidirect
132. M16C2×D547semidirect

Maximal subgroups

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

subgroupindex
#317760482
#317760472
#317760302
#317760292
#317760262
#317760232
#317760222
C2×#225767612
D8×D5472
#317760102
AGL(1,ℤ/8)×C5472
#576547