Finite Group Databasebeta

← #46855807

Subgroups — #46855807

Order 35008.

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

normal subgroups only

This group has 258 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#31776050C211yesmaximal, characteristic, complemented
2#31776047C211yesmaximal, characteristic, complemented
3#31776033C211yesmaximal, characteristic, complemented
4#31776031C212yesmaximal, complemented
5#31776029C212yesmaximal, complemented
6#31776028C211yesmaximal, characteristic, complemented
7#31776024C211yesmaximal, characteristic, complemented
8#31776023C212yesmaximal, complemented
9SD16×D547C212yesmaximal, complemented
10#31776008C211yesmaximal, characteristic, complemented
11C2×SD16×C547C211yesmaximal, characteristic, complemented
12#22576777—21no—
13#22576777C2212yescomplemented
14#22576776—22no—
15#22576776C2211yescharacteristic
16#22576776C2211yescharacteristic
17#22576776C2211yescharacteristic, complemented
18#22576775—21no—
19#22576775C2212yes—
20Q8×D547—21no—
21Q8×D547C2212yescomplemented
22C2×C22⋊D547—22no—
23D4×D547—21no—
24D4×D547C2212yes—
25Dic2188C2211yescharacteristic, complemented
26#22576766C2212yescomplemented
27#22576765C2211yescharacteristic, complemented
28#22576765C2211yescharacteristic, complemented
29#22576764C2212yescomplemented
30#22576763C2212yescomplemented
31D4376C2211yescharacteristic, complemented
32#22576761C2212yescomplemented
33#22576760C2211yescharacteristic, complemented
34#22576759C2212yescomplemented
35C8×D547C2212yescomplemented
36C2×Q8×C547C2211yescharacteristic, complemented
37C2×D4×C547C2211yescharacteristic
38SD16×C547C2212yescomplemented
39SD16×C547C2212yescomplemented
40C2×C8×C547C2211yescharacteristic, complemented
41C22×D547—22no—
42Dic1094—22no—
43Dic1094D411yescharacteristic
44Dic1094C2311yescharacteristic
45Dic1094C2311yescharacteristic
46D2188—22no—
47D2188D411yescharacteristic
48D2188C2311yescharacteristic
49D2188C2311yescharacteristic
50C22⋊D547—21no—
51C22⋊D547—21no—
52C22⋊D547—22no—
53C22⋊D547—22no—
54C22⋊D547D412yes—
55C2×Dic547—22no—
56C4×D547—22no—
57C4×D547—21no—
58C4×D547—21no—
59C4×D547—22no—
60C4×D547C2312yes—
61C547⋊C8C2312yes—
62C23×C547—21no—
63Q8×C547—21no—
64Q8×C547C2312yes—
65D4×C547—21no—
66D4×C547C2312yes—
67C2×C4×C547—21no—
68C2×C4×C547C2311yescharacteristic
69C8×C547C2311yescharacteristic
70C8×C547C2311yescharacteristic
71C22×C547—22no—
72C22×C547—81no—
73C22×C547C2×D411yescharacteristic
74C2×D547—21no—
75C2×D547—21no—
76C2×D547—82no—
77C2×D547C2×D412yes—
78C4×C547—22no—
79C4×C547C2×D411yescharacteristic
80C4×C547C2411yescharacteristic
81Dic547—21no—
82Dic547—21no—
83Dic547C2×D412yes—
84C2×C547—21no—
85C2×C547—42no—
86C2×C547C22×D411yescharacteristic
87D547—22no—
88D547—41no—
89D547—41no—
90C547#57711yescharacteristic, complemented, Sylow
91#577—5471nomaximal, Sylow
922−1+4—5471no—
93H(5,𝔽2)—5471no—
94#137—5471no—
95#137—5472no—
96AGL(1,ℤ/8)—5471no—
97AGL(1,ℤ/8)—5472no—
98#135—5472no—
99#135—5471no—
100C2×SD16—5472no—
101C2×SD16D54711yescharacteristic, complemented
102#131—5471no—
103#41—5471no—
104#41—5472no—
105#41—5472no—
106#41—5471no—
107#41—5471no—
108#41—10942no—
109#41—10941no—
110#41—10941no—
111C2×Q8—5472no—
112C2×Q8—10941no—
113C2×Q8C2×D54711yescharacteristic, complemented
114C2×D4—5472no—
115C2×D4—10941no—
116C2×D4—10942no—
117C2×D4C2×D54711yescharacteristic
118Q16—5472no—
119Q16—5471no—
120SD16—5472no—
121SD16—5472no—
122SD16—5471no—
123SD16—5471no—
124SD16C2×D54712yescomplemented
125SD16C2×D54712yescomplemented
126D8—5472no—
127D8—5471no—
128M16—5471no—
129M16—5472no—
130C2×C8—5472no—
131C2×C8C2×D54711yescharacteristic, complemented
132C23—21no—
133C23—10942no—
134Q8—21no—
135Q8—5471no—
136Q8—5471no—
137Q8—5471no—
138Q8—10942no—
139Q8C22×D54712yes—
140D4—21no—
141D4—5472no—
142D4—5471no—
143D4—5471no—
144D4—5471no—
145D4—10942no—
146D4—10942no—
147D4—10942no—
148D4—10941no—
149D4—10941no—
150D4C22×D54712yes—
151C2×C4—21no—
152C2×C4—5472no—
153C2×C4—10942no—
154C2×C4—10942no—
155C2×C4—10942no—
156C2×C4—10941no—
157C2×C4—10941no—
158C2×C4C22×D54711yescharacteristic
159C8—5472no—
160C8C22×D54711yescharacteristic
161C8C22×D54711yescharacteristic
162C22—22no—
163C22—81no—
164C22—43762no—
165C22—5472no—
166C22—10941no—
167C22—10941no—
168C22D4×D54711yescharacteristic
169C4—22no—
170C4—5472no—
171C4—10941no—
172C4—10941no—
173C4D4×D54711yescharacteristic
174C4C23×D54711yescharacteristic
175C2—21no—
176C2—42no—
177C2—10942no—
178C2—21881no—
179C2—21881no—
180C2C2×D4×D54711yescharacteristic
subgroupG/H
centerC2C2×D4×D547
commutator, cosocleC4×C547C24
FrattiniC4C23×D547
FittingC2×SD16×C547C2
socleC2×C547C22×D4
hypercenterC2×SD16D547
hypocenterC547#577
LCSG ▷ C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #31776050C2semidirect
2. #31776047C2semidirect
3. #31776033C2semidirect
4. #31776031C2semidirect
5. #31776029C2semidirect
6. #31776028C2semidirect
7. #31776024C2semidirect
8. #31776023C2semidirect
9. SD16×D547C2semidirect
10. #31776008C2semidirect
11. C2×SD16×C547C2semidirect
13. #22576777C22semidirect
17. #22576776C22semidirect
21. Q8×D547C22semidirect
25. Dic2188C22semidirect
26. #22576766C22semidirect
27. #22576765C22semidirect
28. #22576765C22semidirect
29. #22576764C22semidirect
30. #22576763C22semidirect
31. D4376C22semidirect
32. #22576761C22semidirect
33. #22576760C22semidirect
34. #22576759C22semidirect
35. C8×D547C22semidirect
36. C2×Q8×C547C22semidirect
38. SD16×C547C22semidirect
39. SD16×C547C22semidirect
40. C2×C8×C547C22semidirect
90. C547#577semidirect
101. C2×SD16D547semidirect
113. C2×Q8C2×D547semidirect
124. SD16C2×D547semidirect
125. SD16C2×D547semidirect
131. C2×C8C2×D547semidirect

Maximal subgroups

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

subgroupindex
#317760502
#317760472
#317760332
#317760312
#317760292
#317760282
#317760242
#317760232
SD16×D5472
#317760082
C2×SD16×C5472
#577547