Finite Group Databasebeta

← #11763452

Subgroups — #11763452

Order 1088.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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×#63256C211yesmaximal, characteristic, complemented
2C2×D4×D17C211yesmaximal, characteristic, complemented
3C17×#124C211yesmaximal, characteristic, complemented
4#10587632C211yesmaximal, characteristic, complemented
5#10587624C211yesmaximal, characteristic, complemented
6#10587570C212yesmaximal, complemented
7#10587569C212yesmaximal, complemented
8#10587568C212yesmaximal, complemented
9C22⋊C4×D17C212yesmaximal, complemented
10C4×D68C211yesmaximal, characteristic, complemented
11C4×D68C211yesmaximal, characteristic, complemented
12C23×D17C2212yes—
13C2×Q8×C17C2211yescharacteristic, complemented
14C2×D4×C17C2211yescharacteristic
15C2×C22⋊D17C2212yes—
16C2×C22⋊D17C2212yescomplemented
17#63256—24no—
18D4×D17—24no—
19C2×D68C2211yescharacteristic
20C2×D68C2211yescharacteristic
21C2×D68C2212yescomplemented
22C2×C4×D17C2211yescharacteristic
23C2×C4×D17C2211yescharacteristic, complemented
24C2×C4×D17C2212yescomplemented
25C2×C4×D17C2212yescomplemented
26C22⋊C4×C17C2212yescomplemented
27C22⋊C4×C17C2212yescomplemented
28C42×C17C2211yescharacteristic, complemented
29C22⋊Dic17C2212yescomplemented
30#63227C2211yescharacteristic
31#63227C2212yes—
32#63227C2212yescomplemented
33#63227C2211yescharacteristic, complemented
34C4⋊Dic17C2211yescharacteristic, complemented
35C4⋊Dic17C2211yescharacteristic, complemented
36#63225C2212yescomplemented
37C23×C17C2312yes—
38C22×D17—24no—
39C22×D17—24no—
40C22×D17—42no—
41C22×D17C2311yescharacteristic
42C22×D17C2312yes—
43C22×D17C2311yescharacteristic
44Q8×C17—22no—
45D4×C17—22no—
46C2×C4×C17C2311yescharacteristic
47C2×C4×C17C2311yescharacteristic
48C2×C4×C17C2312yes—
49C2×C4×C17C2311yescharacteristic
50C22⋊D17—24no—
51C22⋊D17—42no—
52C2×Dic17C2311yescharacteristic
53C2×Dic17C2312yes—
54C2×Dic17C2311yescharacteristic
55D68—24no—
56D68—22no—
57D68D414yescomplemented
58C4×D17—24no—
59C4×D17—22no—
60C4×D17—22no—
61C4×D17—42no—
62C22×C17—22no—
63C22×C17—22no—
64C22×C17—22no—
65C22×C17C2411yescharacteristic
66C2×D17—21no—
67C2×D17—22no—
68C2×D17—22no—
69C2×D17—21no—
70C2×D17—21no—
71C2×D17—21no—
72C2×D17—21no—
73C2×D17—48no—
74C2×D17C2×D414yes—
75C2×D17#4112yescomplemented
76C4×C17—22no—
77C4×C17—21no—
78C4×C17—21no—
79C4×C17C2×D412yes—
80Dic17—21no—
81Dic17—21no—
82Dic17—22no—
83#546—171nomaximal, Sylow
84C2×C17—42no—
85C2×C17C22×D411yescharacteristic
86C2×C17C2×#4111yescharacteristic
87C2×C17H(5,𝔽2)11yescharacteristic
88D17—22no—
89D17—24no—
90D17—41no—
91C2×#41—171no—
92C22×D4—171no—
93#124D1711yescharacteristic, complemented
94#123—172no—
95C22⋊Q8—171no—
96#121—171no—
97#121—172no—
98#120—172no—
99C4×D4—171no—
100C4×D4—171no—
101C2×C22⋊C4—172no—
102C17#54611yescharacteristic, complemented, Sylow
103C24—172no—
104#41—344no—
105C2×Q8C2×D1711yescharacteristic, complemented
106C2×D4—172no—
107C2×D4—172no—
108C2×D4—171no—
109C2×D4—171no—
110C2×D4—172no—
111C2×D4—344no—
112C2×D4C2×D1711yescharacteristic
113C22×C4—171no—
114C22×C4—172no—
115C22×C4—171no—
116C22×C4—172no—
117C4⋊C4—171no—
118C4⋊C4—171no—
119C4⋊C4—172no—
120C22⋊C4—172no—
121C22⋊C4—171no—
122C22⋊C4—172no—
123C22⋊C4—172no—
124C22⋊C4—171no—
125C22⋊C4C2×D1712yescomplemented
126C22⋊C4C2×D1712yescomplemented
127C42C2×D1711yescharacteristic, complemented
128C23—171no—
129C23—172no—
130C23—171no—
131C23—344no—
132C23—344no—
133C23—682no—
134C23C22×D1712yes—
135Q8—22no—
136D4—22no—
137D4—174no—
138D4—344no—
139D4—342no—
140D4—344no—
141D4—682no—
142C2×C4—172no—
143C2×C4—171no—
144C2×C4—171no—
145C2×C4—344no—
146C2×C4—342no—
147C2×C4—342no—
148C2×C4—682no—
149C2×C4C22×D1711yescharacteristic
150C2×C4C22×D1711yescharacteristic
151C2×C4C22×D1712yes—
152C2×C4C22×D1711yescharacteristic
153C22—22no—
154C22—22no—
155C22—22no—
156C22—174no—
157C22—172no—
158C22—341no—
159C22—342no—
160C22—342no—
161C22—341no—
162C22—341no—
163C22—341no—
164C22—341no—
165C22—688no—
166C22C23×D1711yescharacteristic
167C4—22no—
168C4—21no—
169C4—21no—
170C4—341no—
171C4—341no—
172C4—342no—
173C4D4×D1712yes—
174C2—42no—
175C2—342no—
176C2—344no—
177C2—681no—
178C2C2×D4×D1711yescharacteristic
179C2#41×D1711yescharacteristic
180C2#1058769611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D17
commutator, socle, cosocleC22×C17C24
FittingC17×#124C2
hypercenter#124D17
hypocenterC17#546
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#63256C2semidirect
2. C2×D4×D17C2semidirect
3. C17×#124C2semidirect
4. #10587632C2semidirect
5. #10587624C2semidirect
6. #10587570C2semidirect
7. #10587569C2semidirect
8. #10587568C2semidirect
9. C22⋊C4×D17C2semidirect
10. C4×D68C2semidirect
11. C4×D68C2semidirect
13. C2×Q8×C17C22semidirect
16. C2×C22⋊D17C22semidirect
21. C2×D68C22semidirect
23. C2×C4×D17C22semidirect
24. C2×C4×D17C22semidirect
25. C2×C4×D17C22semidirect
26. C22⋊C4×C17C22semidirect
27. C22⋊C4×C17C22semidirect
28. C42×C17C22semidirect
29. C22⋊Dic17C22semidirect
32. #63227C22semidirect
33. #63227C22semidirect
34. C4⋊Dic17C22semidirect
35. C4⋊Dic17C22semidirect
36. #63225C22semidirect
57. D68D4semidirect
75. C2×D17#41semidirect
93. #124D17semidirect
102. C17#546semidirect
105. C2×Q8C2×D17semidirect
125. C22⋊C4C2×D17semidirect
126. C22⋊C4C2×D17semidirect
127. C42C2×D17semidirect

Maximal subgroups

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

subgroupindex
C2×#632562
C2×D4×D172
C17×#1242
#105876322
#105876242
#105875702
#105875692
#105875682
C22⋊C4×D172
C4×D682
#54617