Finite Group Databasebeta

← C2×#23752774 #34082413

Subgroups — C2×#23752774 #34082413

Order 19328.

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⋊D151C212yesmaximal, complemented
2#23752774C2116yesmaximal, direct product factor
3C2×#18012723C214yesmaximal, complemented
4C2×#18012713C214yesmaximal, complemented
5C2×#18012709C214yesmaximal, complemented
6C22×C22⋊C4×C151C211yesmaximal, characteristic, complemented
7C24×D151C2212yescomplemented
8C22×D604C2214yescomplemented
9C22×C22⋊D151—216no—
10C22×C22⋊D151C2214yes—
11C22×C22⋊D151C2214yescomplemented
12C22×C22⋊D151C22116yescomplemented
13C23×Dic151C2212yescomplemented
14#18012723C22132yescomplemented
15#18012713C22132yescomplemented
16#18012709C22132yescomplemented
17C2×C4⋊Dic151C2214yescomplemented
18C2×(C2×D151)⋊C4C2218yescomplemented
19C25×C151C2211yescharacteristic
20C23×C4×C151C2212yescomplemented
21C2×C22⋊C4×C151C2214yescomplemented
22C2×C22⋊C4×C151C2218yescomplemented
23C23×D151—28no—
24C23×D151—48no—
25C23×D151C2314yes—
26C23×D151C2318yescomplemented
27C2×D604—48no—
28C2×D604C23116yescomplemented
29C2×C22⋊D151—216no—
30C2×C22⋊D151—216no—
31C2×C22⋊D151—264no—
32C2×C22⋊D151C23116yes—
33C2×C22⋊D151C23116yescomplemented
34C22×Dic151—28no—
35C22×Dic151C2314yes—
36C22×Dic151C2318yescomplemented
37C4⋊Dic151C23116yescomplemented
38(C2×D151)⋊C4C23132yescomplemented
39C24×C151—44no—
40C24×C151D418yescomplemented
41C24×C151C2312yes—
42C24×C151C2311yescharacteristic
43C24×C151C2314yes—
44C22×C4×C151—44no—
45C22×C4×C151C2314yes—
46C22×C4×C151C2318yescomplemented
47C22⋊C4×C151C23116yescomplemented
48C22×D151—28no—
49C22×D151—216no—
50C22×D151—216no—
51C22×D151—416no—
52C22×D151—432no—
53C22×D151C2418yes—
54D604—416no—
55C22⋊D151—232no—
56C22⋊D151—232no—
57C2×Dic151—28no—
58C2×Dic151—216no—
59C2×Dic151C2418yes—
60C23×C151—28no—
61C23×C151—24no—
62C23×C151—416no—
63C23×C151—48no—
64C23×C151C2×D418yes—
65C23×C151C2×D414yes—
66C23×C151C2×D4116yescomplemented
67C23×C151C2414yes—
68C23×C151C2412yes—
69C23×C151C2411yescharacteristic
70C2×C4×C151—28no—
71C2×C4×C151—48no—
72C2×C4×C151C2418yes—
73C22×C151—28no—
74C22×C151—216no—
75C22×C151—24no—
76C22×C151—28no—
77C22×C151—416no—
78C22×C151C22×D418yes—
79C22×C151C22×D414yes—
80C22×C151C22×D412yes—
81C22×C151H(5,𝔽2)14yes—
82C22×C151C2511yescharacteristic
83C2×D151—28no—
84C2×D151—216no—
85C2×D151—432no—
86C2×D151—416no—
87C4×C151—28no—
88Dic151—28no—
89C2×C151—28no—
90C2×C151—24no—
91C2×C151#53414yescomplemented
92C2×C151C23×D411yescharacteristic
93C2×C151C2×H(5,𝔽2)12yes—
94D151—48no—
95C151C2×#53411yescharacteristic, complemented, Sylow
96C2×#534—1511nomaximal, Sylow
97C23×D4—1512no—
98#534—15116no—
99C2×#123—1514no—
100C2×#121—1514no—
101C2×#120—1514no—
102C22×C22⋊C4D15111yescharacteristic, complemented
103C25—1512no—
104C25C2×D15111yescharacteristic
105C22×D4—30216no—
106C22×D4—1514no—
107C22×D4—1514no—
108C22×D4—15116no—
109C22×D4—1514no—
110C23×C4—1512no—
111C23×C4C2×D15112yescomplemented
112#123—15132no—
113#121—15132no—
114#120—15132no—
115C2×C4⋊C4—1514no—
116C2×C22⋊C4—1518no—
117C2×C22⋊C4C2×D15114yescomplemented
118C2×C22⋊C4C2×D15118yescomplemented
119C24—44no—
120C24—3028no—
121C24—6048no—
122C24—1514no—
123C24—1518no—
124C24D60418yescomplemented
125C24C22×D15112yes—
126C24C22×D15111yescharacteristic
127C24C22×D15114yes—
128C2×D4—30216no—
129C2×D4—30216no—
130C2×D4—30264no—
131C2×D4—6048no—
132C2×D4—15116no—
133C2×D4—15116no—
134C2×D4—15116no—
135C22×C4—44no—
136C22×C4—3028no—
137C22×C4—1518no—
138C22×C4—1514no—
139C22×C4C22×D15114yes—
140C22×C4C22×D15118yescomplemented
141C4⋊C4—15116no—
142C22⋊C4—15132no—
143C22⋊C4C22×D151116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—30216no—
149C23—3028no—
150C23—30216no—
151C23—60416no—
152C23—60432no—
153C23—1518no—
154C23C2×D60418yes—
155C23C2×D60414yes—
156C23C2×D604116yescomplemented
157C23C23×D15114yes—
158C23C23×D15112yes—
159C23C23×D15111yescharacteristic
160D4—30232no—
161D4—30232no—
162D4—60416no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—30216no—
166C2×C4—3028no—
167C2×C4—1518no—
168C2×C4C23×D15118yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—3028no—
175C22—30216no—
176C22—60432no—
177C22—60416no—
178C22C22×D60418yes—
179C22C22×D60414yes—
180C22C22×D60412yes—
181C22#1801278414yes—
182C22C24×D15111yescharacteristic
183C4—28no—
184C4—3028no—
185C2—28no—
186C2—24no—
187C2—6048no—
188C2#2375277414yesdirect product factor
189C2C23×D60411yescharacteristic
190C2C2×#1801278412yes—
subgroupG/H
centerC23C23×D151
commutator, cosocleC22×C151C25
FrattiniC22C24×D151
FittingC22×C22⋊C4×C151C2
socleC23×C151C24
hypercenterC22×C22⋊C4D151
hypocenterC151C2×#534
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D151C2semidirect
2. #23752774C2direct (N × H)
3. C2×#18012723C2semidirect
4. C2×#18012713C2semidirect
5. C2×#18012709C2semidirect
6. C22×C22⋊C4×C151C2semidirect
7. C24×D151C22semidirect
8. C22×D604C22semidirect
11. C22×C22⋊D151C22semidirect
12. C22×C22⋊D151C22semidirect
13. C23×Dic151C22semidirect
14. #18012723C22semidirect
15. #18012713C22semidirect
16. #18012709C22semidirect
17. C2×C4⋊Dic151C22semidirect
18. C2×(C2×D151)⋊C4C22semidirect
20. C23×C4×C151C22semidirect
21. C2×C22⋊C4×C151C22semidirect
22. C2×C22⋊C4×C151C22semidirect
26. C23×D151C23semidirect
28. C2×D604C23semidirect
33. C2×C22⋊D151C23semidirect
36. C22×Dic151C23semidirect
37. C4⋊Dic151C23semidirect
38. (C2×D151)⋊C4C23semidirect
40. C24×C151D4semidirect
46. C22×C4×C151C23semidirect
47. C22⋊C4×C151C23semidirect
66. C23×C151C2×D4semidirect
91. C2×C151#534semidirect
95. C151C2×#534semidirect
102. C22×C22⋊C4D151semidirect
111. C23×C4C2×D151semidirect
117. C2×C22⋊C4C2×D151semidirect
118. C2×C22⋊C4C2×D151semidirect
124. C24D604semidirect
140. C22×C4C22×D151semidirect
143. C22⋊C4C22×D151semidirect
156. C23C2×D604semidirect
188. C2#23752774direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D1512
#237527742
C2×#180127232
C2×#180127132
C2×#180127092
C22×C22⋊C4×C1512
C2×#534151