Finite Group Databasebeta

← C22×#10587624 #14542003

Subgroups — C22×#10587624 #14542003

Order 2176.

2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 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
1C23×C22⋊D17C212yesmaximal, complemented
2C23×C4×D17C211yesmaximal, characteristic, complemented
3C2×#10587624C2124yesmaximal, direct product factor
4C22×C4⋊Dic17C211yesmaximal, characteristic, complemented
5C22×C22⋊Dic17C212yesmaximal, complemented
6C23×D4×C17C211yesmaximal, characteristic, complemented
7C25×C17C2212yes—
8C24×D17C2211yescharacteristic
9C22×D4×C17—28no—
10C22×D4×C17C22112yescomplemented
11C23×C4×C17C2211yescharacteristic
12C22×C22⋊D17—216no—
13C22×C22⋊D17C22124yescomplemented
14C23×Dic17C2211yescharacteristic
15C23×Dic17C2212yes—
16C22×C4×D17—28no—
17C22×C4×D17C22112yescomplemented
18C2×C22⋊Dic17C22124yescomplemented
19#10587624C22164yesdirect product factor
20C2×C4⋊Dic17C22112yescomplemented
21C24×C17—28no—
22C24×C17—28no—
23C24×C17—28no—
24C24×C17C23112yes—
25C24×C17C2311yescharacteristic
26C23×D17—24no—
27C23×D17—24no—
28C23×D17D418yescomplemented
29C23×D17C2316yes—
30C2×D4×C17—248no—
31C2×D4×C17C23116yescomplemented
32C22×C4×C17D418yescomplemented
33C22×C4×C17C2316yes—
34C2×C22⋊D17—296no—
35C2×C22⋊D17C23132yescomplemented
36C22×Dic17—24no—
37C22×Dic17—28no—
38C22×Dic17C2316yes—
39C22×Dic17C23112yes—
40C2×C4×D17—248no—
41C2×C4×D17C23116yescomplemented
42C22⋊Dic17C23132yescomplemented
43C4⋊Dic17C23116yescomplemented
44C23×C17—224no—
45C23×C17—224no—
46C23×C17—224no—
47C23×C17—432no—
48C23×C17C2×D414yes—
49C23×C17C2×D414yes—
50C23×C17#4114yes—
51C23×C17C2418yes—
52C23×C17C2413yes—
53C22×D17—232no—
54C22×D17—212no—
55C22×D17—212no—
56C22×D17C2×D4124yescomplemented
57C22×D17C2414yes—
58D4×C17—232no—
59C2×C4×C17C2×D4124yescomplemented
60C2×C4×C17C2414yes—
61C22⋊D17—264no—
62C2×Dic17—212no—
63C2×Dic17—224no—
64C2×Dic17C2414yes—
65C2×Dic17C2418yes—
66C4×D17—232no—
67C22×#121—171nomaximal, Sylow
68C22×C17—28no—
69C22×C17—28no—
70C22×C17—28no—
71C22×C17—448no—
72C22×C17#121116yescomplemented
73C22×C17C22×D416yes—
74C22×C17C22×D416yes—
75C22×C17C2×#4116yes—
76C22×C17C2511yescharacteristic
77C2×D17—248no—
78C2×D17—24no—
79C2×D17—24no—
80C2×D17C22×D418yescomplemented
81C4×C17C22×D418yescomplemented
82Dic17—24no—
83Dic17—28no—
84C23×D4—172no—
85C23×D4D1711yescharacteristic, complemented
86C24×C4—171no—
87C2×#121—1724no—
88C22×C4⋊C4—171no—
89C22×C22⋊C4—172no—
90C2×C17—48no—
91C2×C17C2×#121112yescomplemented
92C2×C17C23×D411yescharacteristic
93C2×C17C23×D411yescharacteristic
94C2×C17C22×#4111yescharacteristic
95D17—28no—
96C25—171no—
97C25C2×D1712yes—
98C22×D4—28no—
99C22×D4—1724no—
100C22×D4—3416no—
101C22×D4C2×D17112yescomplemented
102C23×C4—171no—
103C23×C4—172no—
104C23×C4—1712no—
105C23×C4—348no—
106C23×C4C2×D1711yescharacteristic
107#121—1764no—
108C2×C4⋊C4—1712no—
109C2×C22⋊C4—1724no—
110C17C22×#12111yescharacteristic, complemented, Sylow
111C24—28no—
112C24—28no—
113C24—28no—
114C24—178no—
115C24—176no—
116C24—344no—
117C24—344no—
118C24C22×D17112yes—
119C24C22×D1711yescharacteristic
120C2×D4—248no—
121C2×D4—1732no—
122C2×D4—3496no—
123C2×D4C22×D17116yescomplemented
124C22×C4—176no—
125C22×C4—1712no—
126C22×C4—1716no—
127C22×C4—348no—
128C22×C4—344no—
129C22×C4—3448no—
130C22×C4C22⋊D1718yescomplemented
131C22×C4C22×D1716yes—
132C4⋊C4—1716no—
133C22⋊C4—1732no—
134C23—224no—
135C23—224no—
136C23—224no—
137C23—432no—
138C23—1724no—
139C23—174no—
140C23—3412no—
141C23—3412no—
142C23—3432no—
143C23D4×D1714yes—
144C23#6325414yes—
145C23C2×C22⋊D1714yes—
146C23C23×D1718yes—
147C23C23×D1713yes—
148D4—232no—
149D4—3464no—
150C2×C4—174no—
151C2×C4—178no—
152C2×C4—3424no—
153C2×C4—3412no—
154C2×C4—3432no—
155C2×C4C2×C22⋊D17124yescomplemented
156C2×C4C23×D1714yes—
157C22—28no—
158C22—28no—
159C22—28no—
160C22—448no—
161C22—178no—
162C22—3448no—
163C22—344no—
164C22—344no—
165C22#10587624116yesdirect product factor
166C22C2×D4×D1716yes—
167C22C2×#6325416yes—
168C22C22×C22⋊D1716yes—
169C22C24×D1711yescharacteristic
170C4—348no—
171C4—344no—
172C4C22×C22⋊D1718yescomplemented
173C2—48no—
174C2—348no—
175C2C2×#10587624112yesdirect product factor
176C2C22×D4×D1711yescharacteristic
177C2C23×C22⋊D1711yescharacteristic
178C2C22×#6325411yescharacteristic
subgroupG/H
centerC24C22×D17
commutator, cosocleC22×C17C25
FrattiniC22C24×D17
FittingC23×D4×C17C2
socleC24×C17C23
hypercenterC23×D4D17
hypocenterC17C22×#121
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D17C2semidirect
2. C23×C4×D17C2semidirect
3. C2×#10587624C2direct (N × H)
4. C22×C4⋊Dic17C2semidirect
5. C22×C22⋊Dic17C2semidirect
6. C23×D4×C17C2semidirect
10. C22×D4×C17C22semidirect
13. C22×C22⋊D17C22semidirect
17. C22×C4×D17C22semidirect
18. C2×C22⋊Dic17C22semidirect
19. #10587624C22direct (N × H)
20. C2×C4⋊Dic17C22semidirect
28. C23×D17D4semidirect
31. C2×D4×C17C23semidirect
32. C22×C4×C17D4semidirect
35. C2×C22⋊D17C23semidirect
41. C2×C4×D17C23semidirect
42. C22⋊Dic17C23semidirect
43. C4⋊Dic17C23semidirect
56. C22×D17C2×D4semidirect
59. C2×C4×C17C2×D4semidirect
72. C22×C17#121semidirect
80. C2×D17C22×D4semidirect
81. C4×C17C22×D4semidirect
85. C23×D4D17semidirect
91. C2×C17C2×#121semidirect
101. C22×D4C2×D17semidirect
110. C17C22×#121semidirect
123. C2×D4C22×D17semidirect
130. C22×C4C22⋊D17semidirect
155. C2×C4C2×C22⋊D17semidirect
165. C22#10587624direct (N × H)
172. C4C22×C22⋊D17semidirect
175. C2C2×#10587624direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D172
C23×C4×D172
C2×#105876242
C22×C4⋊Dic172
C22×C22⋊Dic172
C23×D4×C172
C22×#12117