Finite Group Databasebeta

← C2×#23752954 #34083230

Subgroups — C2×#23752954 #34083230

Order 19328.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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
1#23752954C2116yesmaximal, direct product factor
2C2×#18012728C212yesmaximal, complemented
3C2×#18012727C212yesmaximal, complemented
4C2×#18012725C214yesmaximal, complemented
5C2×#18012709C214yesmaximal, complemented
6C2×#18012707C212yesmaximal, complemented
7C2×#124×C151C211yesmaximal, characteristic, complemented
8C24×D151C2212yescomplemented
9C22×Dic302C2212yescomplemented
10C22×D604C2212yes—
11C22×D604C2212yes—
12C22×C22⋊D151C2214yes—
13#18012728C22116yescomplemented
14#18012727C22116yescomplemented
15#18012725C22132yescomplemented
16#18012709C22132yescomplemented
17#18012707C22116yescomplemented
18C2×C22⋊Dic151C2212yescomplemented
19C2×(C2×D151)⋊C4C2214yescomplemented
20C2×(C2×D151)⋊C4C2214yescomplemented
21C2×(C2×D151)⋊C4C2214yescomplemented
22C2×C4×Dic151C2212yescomplemented
23C22×Q8×C151C2211yescharacteristic, complemented
24C22×D4×C151C2211yescharacteristic
25#124×C151C2218yescomplemented
26C2×C22⋊C4×C151C2214yescomplemented
27C2×C42×C151C2211yescharacteristic, complemented
28C23×D151—48no—
29C23×D151—44no—
30C23×D151C2314yes—
31C23×D151C2318yescomplemented
32C2×Dic302—44no—
33C2×Dic302C2318yescomplemented
34C2×D604—44no—
35C2×D604—44no—
36C2×D604C2318yes—
37C2×D604C2318yes—
38C2×C22⋊D151—48no—
39C2×C22⋊D151C23116yes—
40C22×Dic151C2314yes—
41C22⋊Dic151C2318yescomplemented
42(C2×D151)⋊C4C23116yescomplemented
43(C2×D151)⋊C4C23116yescomplemented
44(C2×D151)⋊C4C23116yescomplemented
45C4×Dic151C2318yescomplemented
46C24×C151C2312yes—
47C2×Q8×C151—42no—
48C2×Q8×C151C2314yescomplemented
49C2×D4×C151—42no—
50C2×D4×C151C2314yes—
51C22×C4×C151C2312yes—
52C22×C4×C151C2311yescharacteristic
53C22×C4×C151C2312yes—
54C22⋊C4×C151C23116yescomplemented
55C42×C151C2314yescomplemented
56C22×D151—28no—
57C22×D151—28no—
58C22×D151—28no—
59C22×D151—416no—
60C22×D151—48no—
61C22×D151—432no—
62C22×D151C2418yes—
63Dic302—48no—
64D604—48no—
65D604—48no—
66C22⋊D151—416no—
67C2×Dic151—28no—
68C2×Dic151C2418yes—
69C23×C151—28no—
70C23×C151—24no—
71C23×C151C2414yes—
72C23×C151C2411yescharacteristic
73Q8×C151—44no—
74D4×C151—44no—
75C2×C4×C151—24no—
76C2×C4×C151—22no—
77C2×C4×C151—24no—
78C2×C4×C151C2414yes—
79C2×C4×C151C2412yes—
80C2×C4×C151C2414yes—
81C22×C151—24no—
82C22×C151—28no—
83C22×C151—48no—
84C22×C151H(5,𝔽2)12yes—
85C22×C151H(5,𝔽2)14yes—
86C22×C151C2511yescharacteristic
87C2×D151—28no—
88C2×D151—28no—
89C2×D151—28no—
90C2×D151—432no—
91C2×D151—416no—
92C4×C151—22no—
93C4×C151—24no—
94C4×C151—24no—
95Dic151—28no—
96C2×C151—44no—
97C2×C151H(3,𝔽4)14yescomplemented
98C2×C151C2×H(5,𝔽2)11yescharacteristic
99C2×C151C2×H(5,𝔽2)12yes—
100D151—48no—
101C151C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
102C2×H(3,𝔽4)—1511nomaximal, Sylow
103H(3,𝔽4)—15116no—
104C2×#124—1512no—
105C2×#124—1514no—
106C2×#124—1512no—
107C2×#124D15111yescharacteristic, complemented
108C2×#120—1512no—
109C2×#120—1514no—
110C25—1512no—
111C22×Q8—1512no—
112C22×Q8C2×D15111yescharacteristic, complemented
113C22×D4—1514no—
114C22×D4—1512no—
115C22×D4—1512no—
116C22×D4C2×D15111yescharacteristic
117#124—15116no—
118#124—15132no—
119#124—15116no—
120#124C2×D15118yescomplemented
121#120—15116no—
122#120—15132no—
123C2×C22⋊C4—1512no—
124C2×C22⋊C4—1514no—
125C2×C22⋊C4—1514no—
126C2×C22⋊C4—1514no—
127C2×C22⋊C4C2×D15114yescomplemented
128C2×C42—1512no—
129C2×C42C2×D15111yescharacteristic, complemented
130C24—6044no—
131C24—6048no—
132C24—1514no—
133C24—1518no—
134C24C22×D15112yes—
135C2×Q8—42no—
136C2×Q8—6044no—
137C2×Q8—1518no—
138C2×Q8C22×D15114yescomplemented
139C2×D4—42no—
140C2×D4—6044no—
141C2×D4—6044no—
142C2×D4—6048no—
143C2×D4—15116no—
144C2×D4—1518no—
145C2×D4—1518no—
146C2×D4C22×D15114yes—
147C22×C4—1514no—
148C22×C4C22×D15112yes—
149C22×C4C22×D15111yescharacteristic
150C22×C4C22×D15112yes—
151C22⋊C4—1518no—
152C22⋊C4—15116no—
153C22⋊C4—15116no—
154C22⋊C4—15116no—
155C22⋊C4C22×D151116yescomplemented
156C42—1518no—
157C42C22×D15114yescomplemented
158C23—24no—
159C23—28no—
160C23—3028no—
161C23—3028no—
162C23—3028no—
163C23—6048no—
164C23—60416no—
165C23—60432no—
166C23—1518no—
167C23C23×D15114yes—
168C23C23×D15111yescharacteristic
169Q8—44no—
170Q8—6048no—
171D4—44no—
172D4—6048no—
173D4—6048no—
174D4—60416no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—3028no—
179C2×C4—1518no—
180C2×C4C23×D15114yes—
181C2×C4C23×D15112yes—
182C2×C4C23×D15114yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—3028no—
187C22—3028no—
188C22—3028no—
189C22—60432no—
190C22—60416no—
191C22#1801278412yes—
192C22#1801278514yes—
193C22C24×D15111yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—3028no—
198C2—44no—
199C2—6048no—
200C2#2375295414yesdirect product factor
201C2C2×#1801278411yescharacteristic
202C2C2×#1801278512yes—
subgroupG/H
centerC23C23×D151
commutator, cosocleC22×C151C25
FrattiniC22C24×D151
FittingC2×#124×C151C2
socleC23×C151C24
hypercenterC2×#124D151
hypocenterC151C2×H(3,𝔽4)
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #23752954C2direct (N × H)
2. C2×#18012728C2semidirect
3. C2×#18012727C2semidirect
4. C2×#18012725C2semidirect
5. C2×#18012709C2semidirect
6. C2×#18012707C2semidirect
7. C2×#124×C151C2semidirect
8. C24×D151C22semidirect
9. C22×Dic302C22semidirect
13. #18012728C22semidirect
14. #18012727C22semidirect
15. #18012725C22semidirect
16. #18012709C22semidirect
17. #18012707C22semidirect
18. C2×C22⋊Dic151C22semidirect
19. C2×(C2×D151)⋊C4C22semidirect
20. C2×(C2×D151)⋊C4C22semidirect
21. C2×(C2×D151)⋊C4C22semidirect
22. C2×C4×Dic151C22semidirect
23. C22×Q8×C151C22semidirect
25. #124×C151C22semidirect
26. C2×C22⋊C4×C151C22semidirect
27. C2×C42×C151C22semidirect
31. C23×D151C23semidirect
33. C2×Dic302C23semidirect
41. C22⋊Dic151C23semidirect
42. (C2×D151)⋊C4C23semidirect
43. (C2×D151)⋊C4C23semidirect
44. (C2×D151)⋊C4C23semidirect
45. C4×Dic151C23semidirect
48. C2×Q8×C151C23semidirect
54. C22⋊C4×C151C23semidirect
55. C42×C151C23semidirect
97. C2×C151H(3,𝔽4)semidirect
101. C151C2×H(3,𝔽4)semidirect
107. C2×#124D151semidirect
112. C22×Q8C2×D151semidirect
120. #124C2×D151semidirect
127. C2×C22⋊C4C2×D151semidirect
129. C2×C42C2×D151semidirect
138. C2×Q8C22×D151semidirect
155. C22⋊C4C22×D151semidirect
157. C42C22×D151semidirect
200. C2#23752954direct (N × H)

Maximal subgroups

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

subgroupindex
#237529542
C2×#180127282
C2×#180127272
C2×#180127252
C2×#180127092
C2×#180127072
C2×#124×C1512
C2×H(3,𝔽4)151