Finite Group Databasebeta

← #46855800

Subgroups — #46855800

Order 35008.

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×#22576777C211yesmaximal, characteristic, complemented
2#41×D547C211yesmaximal, characteristic, complemented
3#31776034C212yesmaximal, complemented
4#31776033C211yesmaximal, characteristic, complemented
5#31776030C211yesmaximal, characteristic, complemented
6#31776029C212yesmaximal, complemented
7#31776027C211yesmaximal, characteristic, complemented
8#31776025C212yesmaximal, complemented
9#31776023C212yesmaximal, complemented
10M16×D547C211yesmaximal, characteristic, complemented
11#137×C547C211yesmaximal, characteristic, complemented
12#22576777—21no—
13#22576777—21no—
14#22576777C2212yes—
15#22576777C2212yescomplemented
16#22576777C2211yescharacteristic, complemented
17#22576776—21no—
18#22576776C2211yescharacteristic
19#22576775—21no—
20#22576775C2211yescharacteristic, complemented
21Q8×D547C2211yescharacteristic, complemented
22C2×D2188—21no—
23C2×D2188C2211yescharacteristic, complemented
24D4×D547—21no—
25D4×D547C2211yescharacteristic, complemented
26C2×C4×D547—21no—
27C2×C4×D547—21no—
28C2×C4×D547C2211yescharacteristic
29#22576766C2212yescomplemented
30#22576765C2212yescomplemented
31#22576763C2212yescomplemented
32#22576763C2212yescomplemented
33D4376C2212yescomplemented
34#22576761C2212yescomplemented
35#22576760C2211yescharacteristic, complemented
36#22576759C2212yescomplemented
37C8×D547C2212yescomplemented
38#41×C547C2211yescharacteristic
39C2×Q8×C547C2211yescharacteristic, complemented
40Q16×C547C2212yescomplemented
41SD16×C547C2212yescomplemented
42M16×C547C2211yescharacteristic, complemented
43C22×D547—21no—
44C22×D547—21no—
45C22×D547D411yescharacteristic
46Dic1094—21no—
47Dic1094C2311yescharacteristic
48D2188—21no—
49D2188—22no—
50D2188—22no—
51D2188—21no—
52D2188C2312yes—
53D2188C2311yescharacteristic
54C22⋊D547—21no—
55C22⋊D547—21no—
56C22⋊D547—21no—
57C2×Dic547—21no—
58C2×Dic547D411yescharacteristic
59C4×D547—21no—
60C4×D547—21no—
61C4×D547—21no—
62C4×D547—22no—
63C4×D547—22no—
64C4×D547D411yescharacteristic
65C4×D547D411yescharacteristic
66C4×D547C2311yescharacteristic
67C4×D547C2311yescharacteristic
68C547⋊C8C2312yes—
69Q8×C547—21no—
70Q8×C547C2312yes—
71Q8×C547C2311yescharacteristic
72D4×C547—21no—
73D4×C547C2311yescharacteristic
74C2×C4×C547—21no—
75C2×C4×C547—21no—
76C2×C4×C547C2311yescharacteristic
77C8×C547C2312yes—
78C22×C547—21no—
79C22×C547C2×D411yescharacteristic
80C2×D547—21no—
81C2×D547—22no—
82C2×D547—41no—
83C2×D547—42no—
84C2×D547—42no—
85C2×D547C2×D411yescharacteristic
86C2×D547C2×D411yescharacteristic
87C4×C547—21no—
88C4×C547—22no—
89C4×C547C2×D411yescharacteristic
90C4×C547C2411yescharacteristic
91Dic547—21no—
92Dic547C2×D411yescharacteristic
93Dic547C2×D411yescharacteristic
94C2×C547—21no—
95C2×C547—41no—
96C2×C547C22×D411yescharacteristic
97D547—21no—
98D547—21no—
99D547—41no—
100D547—42no—
101C547#57511yescharacteristic, complemented, Sylow
102#575—5471nomaximal, Sylow
103C2×#41—5471no—
104C2×#41—5471no—
105#137—5471no—
106#137—5472no—
107#137D54711yescharacteristic, complemented
108AGL(1,ℤ/8)—5471no—
109AGL(1,ℤ/8)—5472no—
110AGL(1,ℤ/8)—5471no—
111#135—5472no—
112#135—5472no—
113C2×M16—5471no—
114#41—5471no—
115#41—5472no—
116#41—5472no—
117#41—5471no—
118#41—5471no—
119#41—10941no—
120#41—10941no—
121#41—10941no—
122#41—10941no—
123#41C2×D54711yescharacteristic
124C2×Q8—5471no—
125C2×Q8C2×D54711yescharacteristic, complemented
126C2×D4—5471no—
127C2×D4—5471no—
128C2×D4—10941no—
129C2×D4—10941no—
130C22×C4—5471no—
131C22×C4—10941no—
132C22×C4—10941no—
133Q16—5472no—
134Q16C2×D54712yescomplemented
135SD16—5472no—
136SD16—5472no—
137SD16—5472no—
138SD16C2×D54712yescomplemented
139D8—5472no—
140D8—5472no—
141M16—5471no—
142M16—5472no—
143M16C2×D54711yescharacteristic, complemented
144C2×C8—5472no—
145C23—5471no—
146C23—10941no—
147C23—10941no—
148Q8—21no—
149Q8—5471no—
150Q8—10941no—
151Q8C22×D54711yescharacteristic
152Q8C22×D54712yes—
153D4—21no—
154D4—5472no—
155D4—5471no—
156D4—10941no—
157D4—10942no—
158D4—10942no—
159D4—10941no—
160D4—10941no—
161D4—10941no—
162D4—10941no—
163D4C22×D54711yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—5471no—
167C2×C4—5471no—
168C2×C4—5471no—
169C2×C4—5471no—
170C2×C4—5471no—
171C2×C4—10941no—
172C2×C4—10942no—
173C2×C4—10942no—
174C2×C4—10941no—
175C2×C4—10941no—
176C2×C4—10941no—
177C2×C4C22×D54711yescharacteristic
178C8—5472no—
179C8C22×D54712yes—
180C22—21no—
181C22—5471no—
182C22—5471no—
183C22—10942no—
184C22—10941no—
185C22—21881no—
186C22—21882no—
187C22—21882no—
188C22D4×D54711yescharacteristic
189C4—21no—
190C4—22no—
191C4—5471no—
192C4—5471no—
193C4—10941no—
194C4D4×D54711yescharacteristic
195C4C23×D54711yescharacteristic
196C2—21no—
197C2—41no—
198C2—10941no—
199C2—10941no—
200C2—21882no—
201C2—21881no—
202C2C2×D4×D54711yescharacteristic
subgroupG/H
centerC2C2×D4×D547
commutator, cosocleC4×C547C24
FrattiniC4C23×D547
Fitting#137×C547C2
socleC2×C547C22×D4
hypercenter#137D547
hypocenterC547#575
LCSG ▷ C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#22576777C2semidirect
2. #41×D547C2semidirect
3. #31776034C2semidirect
4. #31776033C2semidirect
5. #31776030C2semidirect
6. #31776029C2semidirect
7. #31776027C2semidirect
8. #31776025C2semidirect
9. #31776023C2semidirect
10. M16×D547C2semidirect
11. #137×C547C2semidirect
15. #22576777C22semidirect
16. #22576777C22semidirect
20. #22576775C22semidirect
21. Q8×D547C22semidirect
23. C2×D2188C22semidirect
25. D4×D547C22semidirect
29. #22576766C22semidirect
30. #22576765C22semidirect
31. #22576763C22semidirect
32. #22576763C22semidirect
33. D4376C22semidirect
34. #22576761C22semidirect
35. #22576760C22semidirect
36. #22576759C22semidirect
37. C8×D547C22semidirect
39. C2×Q8×C547C22semidirect
40. Q16×C547C22semidirect
41. SD16×C547C22semidirect
42. M16×C547C22semidirect
101. C547#575semidirect
107. #137D547semidirect
125. C2×Q8C2×D547semidirect
134. Q16C2×D547semidirect
138. SD16C2×D547semidirect
143. M16C2×D547semidirect

Maximal subgroups

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

subgroupindex
C2×#225767772
#41×D5472
#317760342
#317760332
#317760302
#317760292
#317760272
#317760252
#317760232
M16×D5472
#137×C5472
#575547