Finite Group Databasebeta

← C2×#22581515 #31819707

Subgroups — C2×#22581515 #31819707

Order 17792.

1984 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1984 conjugacy classes of subgroups — too many to draw. Only its 565 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⋊D139C212yesmaximal, complemented
2#22581515C2116yesmaximal, direct product factor
3C2×#17984826C214yesmaximal, complemented
4C2×#17984816C214yesmaximal, complemented
5C2×#17984812C214yesmaximal, complemented
6C22×C22⋊C4×C139C211yesmaximal, characteristic, complemented
7C24×D139C2212yescomplemented
8C22×D556C2214yescomplemented
9C22×C22⋊D139—216no—
10C22×C22⋊D139C2214yes—
11C22×C22⋊D139C2214yescomplemented
12C22×C22⋊D139C22116yescomplemented
13C23×Dic139C2212yescomplemented
14#17984826C22132yescomplemented
15#17984816C22132yescomplemented
16#17984812C22132yescomplemented
17C2×C4⋊Dic139C2214yescomplemented
18C2×(C2×D139)⋊C4C2218yescomplemented
19C25×C139C2211yescharacteristic
20C23×C4×C139C2212yescomplemented
21C2×C22⋊C4×C139C2214yescomplemented
22C2×C22⋊C4×C139C2218yescomplemented
23C23×D139—28no—
24C23×D139—48no—
25C23×D139C2314yes—
26C23×D139C2318yescomplemented
27C2×D556—48no—
28C2×D556C23116yescomplemented
29C2×C22⋊D139—216no—
30C2×C22⋊D139—216no—
31C2×C22⋊D139—264no—
32C2×C22⋊D139C23116yes—
33C2×C22⋊D139C23116yescomplemented
34C22×Dic139—28no—
35C22×Dic139C2314yes—
36C22×Dic139C2318yescomplemented
37C4⋊Dic139C23116yescomplemented
38(C2×D139)⋊C4C23132yescomplemented
39C24×C139—44no—
40C24×C139D418yescomplemented
41C24×C139C2312yes—
42C24×C139C2311yescharacteristic
43C24×C139C2314yes—
44C22×C4×C139—44no—
45C22×C4×C139C2314yes—
46C22×C4×C139C2318yescomplemented
47C22⋊C4×C139C23116yescomplemented
48C22×D139—28no—
49C22×D139—216no—
50C22×D139—216no—
51C22×D139—416no—
52C22×D139—432no—
53C22×D139C2418yes—
54D556—416no—
55C22⋊D139—232no—
56C22⋊D139—232no—
57C2×Dic139—28no—
58C2×Dic139—216no—
59C2×Dic139C2418yes—
60C23×C139—24no—
61C23×C139—28no—
62C23×C139—416no—
63C23×C139—48no—
64C23×C139C2×D418yes—
65C23×C139C2×D414yes—
66C23×C139C2×D4116yescomplemented
67C23×C139C2414yes—
68C23×C139C2412yes—
69C23×C139C2411yescharacteristic
70C2×C4×C139—28no—
71C2×C4×C139—48no—
72C2×C4×C139C2418yes—
73C22×C139—28no—
74C22×C139—216no—
75C22×C139—24no—
76C22×C139—28no—
77C22×C139—416no—
78C22×C139C22×D418yes—
79C22×C139C22×D414yes—
80C22×C139C22×D412yes—
81C22×C139H(5,𝔽2)14yes—
82C22×C139C2511yescharacteristic
83C2×D139—28no—
84C2×D139—216no—
85C2×D139—432no—
86C2×D139—416no—
87C4×C139—28no—
88Dic139—28no—
89C2×C139—28no—
90C2×C139—24no—
91C2×C139#53414yescomplemented
92C2×C139C23×D411yescharacteristic
93C2×C139C2×H(5,𝔽2)12yes—
94D139—48no—
95C139C2×#53411yescharacteristic, complemented, Sylow
96C2×#534—1391nomaximal, Sylow
97C23×D4—1392no—
98#534—13916no—
99C2×#123—1394no—
100C2×#121—1394no—
101C2×#120—1394no—
102C22×C22⋊C4D13911yescharacteristic, complemented
103C25—1392no—
104C25C2×D13911yescharacteristic
105C22×D4—27816no—
106C22×D4—1394no—
107C22×D4—1394no—
108C22×D4—13916no—
109C22×D4—1394no—
110C23×C4—1392no—
111C23×C4C2×D13912yescomplemented
112#123—13932no—
113#121—13932no—
114#120—13932no—
115C2×C4⋊C4—1394no—
116C2×C22⋊C4—1398no—
117C2×C22⋊C4C2×D13914yescomplemented
118C2×C22⋊C4C2×D13918yescomplemented
119C24—44no—
120C24—2788no—
121C24—5568no—
122C24—1394no—
123C24—1398no—
124C24D55618yescomplemented
125C24C22×D13912yes—
126C24C22×D13911yescharacteristic
127C24C22×D13914yes—
128C2×D4—27816no—
129C2×D4—27816no—
130C2×D4—27864no—
131C2×D4—5568no—
132C2×D4—13916no—
133C2×D4—13916no—
134C2×D4—13916no—
135C22×C4—44no—
136C22×C4—2788no—
137C22×C4—1398no—
138C22×C4—1394no—
139C22×C4C22×D13914yes—
140C22×C4C22×D13918yescomplemented
141C4⋊C4—13916no—
142C22⋊C4—13932no—
143C22⋊C4C22×D139116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—27816no—
149C23—2788no—
150C23—27816no—
151C23—55616no—
152C23—55632no—
153C23—1398no—
154C23C2×D55618yes—
155C23C2×D55614yes—
156C23C2×D556116yescomplemented
157C23C23×D13914yes—
158C23C23×D13912yes—
159C23C23×D13911yescharacteristic
160D4—27832no—
161D4—27832no—
162D4—55616no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—27816no—
166C2×C4—2788no—
167C2×C4—1398no—
168C2×C4C23×D13918yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—2788no—
175C22—27816no—
176C22—55632no—
177C22—55616no—
178C22C22×D55618yes—
179C22C22×D55614yes—
180C22C22×D55612yes—
181C22#1798488714yes—
182C22C24×D13911yescharacteristic
183C4—28no—
184C4—2788no—
185C2—28no—
186C2—24no—
187C2—5568no—
188C2#2258151514yesdirect product factor
189C2C23×D55611yescharacteristic
190C2C2×#1798488712yes—
subgroupG/H
centerC23C23×D139
commutator, cosocleC22×C139C25
FrattiniC22C24×D139
FittingC22×C22⋊C4×C139C2
socleC23×C139C24
hypercenterC22×C22⋊C4D139
hypocenterC139C2×#534
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D139C2semidirect
2. #22581515C2direct (N × H)
3. C2×#17984826C2semidirect
4. C2×#17984816C2semidirect
5. C2×#17984812C2semidirect
6. C22×C22⋊C4×C139C2semidirect
7. C24×D139C22semidirect
8. C22×D556C22semidirect
11. C22×C22⋊D139C22semidirect
12. C22×C22⋊D139C22semidirect
13. C23×Dic139C22semidirect
14. #17984826C22semidirect
15. #17984816C22semidirect
16. #17984812C22semidirect
17. C2×C4⋊Dic139C22semidirect
18. C2×(C2×D139)⋊C4C22semidirect
20. C23×C4×C139C22semidirect
21. C2×C22⋊C4×C139C22semidirect
22. C2×C22⋊C4×C139C22semidirect
26. C23×D139C23semidirect
28. C2×D556C23semidirect
33. C2×C22⋊D139C23semidirect
36. C22×Dic139C23semidirect
37. C4⋊Dic139C23semidirect
38. (C2×D139)⋊C4C23semidirect
40. C24×C139D4semidirect
46. C22×C4×C139C23semidirect
47. C22⋊C4×C139C23semidirect
66. C23×C139C2×D4semidirect
91. C2×C139#534semidirect
95. C139C2×#534semidirect
102. C22×C22⋊C4D139semidirect
111. C23×C4C2×D139semidirect
117. C2×C22⋊C4C2×D139semidirect
118. C2×C22⋊C4C2×D139semidirect
124. C24D556semidirect
140. C22×C4C22×D139semidirect
143. C22⋊C4C22×D139semidirect
156. C23C2×D556semidirect
188. C2#22581515direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D1392
#225815152
C2×#179848262
C2×#179848162
C2×#179848122
C22×C22⋊C4×C1392
C2×#534139