Finite Group Databasebeta

← C2×#19152340 #26034372

Subgroups — C2×#19152340 #26034372

Order 11392.

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#19152340C2116yesmaximal, direct product factor
2C2×#15668001C212yesmaximal, complemented
3C2×#15668000C212yesmaximal, complemented
4C2×#15667998C214yesmaximal, complemented
5C2×#15667982C214yesmaximal, complemented
6C2×#15667980C212yesmaximal, complemented
7C2×#124×C89C211yesmaximal, characteristic, complemented
8C24×D89C2212yescomplemented
9C22×Dic178C2212yescomplemented
10C22×D356C2212yes—
11C22×D356C2212yes—
12C22×C22⋊D89C2214yes—
13#15668001C22116yescomplemented
14#15668000C22116yescomplemented
15#15667998C22132yescomplemented
16#15667982C22132yescomplemented
17#15667980C22116yescomplemented
18C2×C22⋊Dic89C2212yescomplemented
19C2×#13083551C2214yescomplemented
20C2×#13083551C2214yescomplemented
21C2×#13083551C2214yescomplemented
22C2×C4×Dic89C2212yescomplemented
23C22×Q8×C89C2211yescharacteristic, complemented
24C22×D4×C89C2211yescharacteristic
25#124×C89C2218yescomplemented
26C2×C22⋊C4×C89C2214yescomplemented
27C2×C42×C89C2211yescharacteristic, complemented
28C23×D89—48no—
29C23×D89—44no—
30C23×D89C2314yes—
31C23×D89C2318yescomplemented
32C2×Dic178—44no—
33C2×Dic178C2318yescomplemented
34C2×D356—44no—
35C2×D356—44no—
36C2×D356C2318yes—
37C2×D356C2318yes—
38C2×C22⋊D89—48no—
39C2×C22⋊D89C23116yes—
40C22×Dic89C2314yes—
41C22⋊Dic89C2318yescomplemented
42#13083551C23116yescomplemented
43#13083551C23116yescomplemented
44#13083551C23116yescomplemented
45C4×Dic89C2318yescomplemented
46C24×C89C2312yes—
47C2×Q8×C89—42no—
48C2×Q8×C89C2314yescomplemented
49C2×D4×C89—42no—
50C2×D4×C89C2314yes—
51C22×C4×C89C2312yes—
52C22×C4×C89C2312yes—
53C22×C4×C89C2311yescharacteristic
54C22⋊C4×C89C23116yescomplemented
55C42×C89C2314yescomplemented
56C23×C89—24no—
57C23×C89—28no—
58C23×C89C2414yes—
59C23×C89C2411yescharacteristic
60C22×D89—28no—
61C22×D89—28no—
62C22×D89—28no—
63C22×D89—48no—
64C22×D89—416no—
65C22×D89—432no—
66C22×D89C2418yes—
67Q8×C89—44no—
68D4×C89—44no—
69C2×C4×C89—22no—
70C2×C4×C89—24no—
71C2×C4×C89—24no—
72C2×C4×C89C2414yes—
73C2×C4×C89C2412yes—
74C2×C4×C89C2414yes—
75C22⋊D89—416no—
76C2×Dic89—28no—
77C2×Dic89C2418yes—
78D356—48no—
79D356—48no—
80Dic178—48no—
81C22×C89—28no—
82C22×C89—24no—
83C22×C89—48no—
84C22×C89H(5,𝔽2)12yes—
85C22×C89H(5,𝔽2)14yes—
86C22×C89C2511yescharacteristic
87C2×D89—28no—
88C2×D89—28no—
89C2×D89—28no—
90C2×D89—432no—
91C2×D89—416no—
92C4×C89—24no—
93C4×C89—24no—
94C4×C89—22no—
95Dic89—28no—
96C2×C89—44no—
97C2×C89H(3,𝔽4)14yescomplemented
98C2×C89C2×H(5,𝔽2)11yescharacteristic
99C2×C89C2×H(5,𝔽2)12yes—
100D89—48no—
101C2×H(3,𝔽4)—891nomaximal, Sylow
102C89C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
103H(3,𝔽4)—8916no—
104C2×#124—892no—
105C2×#124—894no—
106C2×#124—892no—
107C2×#124D8911yescharacteristic, complemented
108C2×#120—892no—
109C2×#120—894no—
110C25—892no—
111C22×Q8—892no—
112C22×Q8C2×D8911yescharacteristic, complemented
113C22×D4—894no—
114C22×D4—892no—
115C22×D4—892no—
116C22×D4C2×D8911yescharacteristic
117#124—8916no—
118#124—8932no—
119#124—8916no—
120#124C2×D8918yescomplemented
121#120—8916no—
122#120—8932no—
123C2×C22⋊C4—892no—
124C2×C22⋊C4—894no—
125C2×C22⋊C4—894no—
126C2×C22⋊C4—894no—
127C2×C22⋊C4C2×D8914yescomplemented
128C2×C42—892no—
129C2×C42C2×D8911yescharacteristic, complemented
130C24—898no—
131C24—894no—
132C24—3564no—
133C24—3568no—
134C24C22×D8912yes—
135C2×Q8—42no—
136C2×Q8—898no—
137C2×Q8—3564no—
138C2×Q8C22×D8914yescomplemented
139C2×D4—42no—
140C2×D4—8916no—
141C2×D4—898no—
142C2×D4—898no—
143C2×D4—3564no—
144C2×D4—3564no—
145C2×D4—3568no—
146C2×D4C22×D8914yes—
147C22×C4—894no—
148C22×C4C22×D8912yes—
149C22×C4C22×D8911yescharacteristic
150C22×C4C22×D8912yes—
151C22⋊C4—898no—
152C22⋊C4—8916no—
153C22⋊C4—8916no—
154C22⋊C4—8916no—
155C22⋊C4C22×D89116yescomplemented
156C42—898no—
157C42C22×D8914yescomplemented
158C23—24no—
159C23—28no—
160C23—898no—
161C23—3568no—
162C23—35616no—
163C23—35632no—
164C23—1788no—
165C23—1788no—
166C23—1788no—
167C23C23×D8914yes—
168C23C23×D8911yescharacteristic
169Q8—44no—
170Q8—3568no—
171D4—44no—
172D4—3568no—
173D4—3568no—
174D4—35616no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—898no—
179C2×C4—1788no—
180C2×C4C23×D8914yes—
181C2×C4C23×D8912yes—
182C2×C4C23×D8914yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—35632no—
187C22—35616no—
188C22—1788no—
189C22—1788no—
190C22—1788no—
191C22#1566805712yes—
192C22#1566805814yes—
193C22C24×D8911yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—1788no—
198C2—44no—
199C2—3568no—
200C2#1915234014yesdirect product factor
201C2C2×#1566805711yescharacteristic
202C2C2×#1566805812yes—
subgroupG/H
centerC23C23×D89
commutator, cosocleC22×C89C25
FrattiniC22C24×D89
FittingC2×#124×C89C2
socleC23×C89C24
hypercenterC2×#124D89
hypocenterC89C2×H(3,𝔽4)
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #19152340C2direct (N × H)
2. C2×#15668001C2semidirect
3. C2×#15668000C2semidirect
4. C2×#15667998C2semidirect
5. C2×#15667982C2semidirect
6. C2×#15667980C2semidirect
7. C2×#124×C89C2semidirect
8. C24×D89C22semidirect
9. C22×Dic178C22semidirect
13. #15668001C22semidirect
14. #15668000C22semidirect
15. #15667998C22semidirect
16. #15667982C22semidirect
17. #15667980C22semidirect
18. C2×C22⋊Dic89C22semidirect
19. C2×#13083551C22semidirect
20. C2×#13083551C22semidirect
21. C2×#13083551C22semidirect
22. C2×C4×Dic89C22semidirect
23. C22×Q8×C89C22semidirect
25. #124×C89C22semidirect
26. C2×C22⋊C4×C89C22semidirect
27. C2×C42×C89C22semidirect
31. C23×D89C23semidirect
33. C2×Dic178C23semidirect
41. C22⋊Dic89C23semidirect
42. #13083551C23semidirect
43. #13083551C23semidirect
44. #13083551C23semidirect
45. C4×Dic89C23semidirect
48. C2×Q8×C89C23semidirect
54. C22⋊C4×C89C23semidirect
55. C42×C89C23semidirect
97. C2×C89H(3,𝔽4)semidirect
102. C89C2×H(3,𝔽4)semidirect
107. C2×#124D89semidirect
112. C22×Q8C2×D89semidirect
120. #124C2×D89semidirect
127. C2×C22⋊C4C2×D89semidirect
129. C2×C42C2×D89semidirect
138. C2×Q8C22×D89semidirect
155. C22⋊C4C22×D89semidirect
157. C42C22×D89semidirect
200. C2#19152340direct (N × H)

Maximal subgroups

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

subgroupindex
#191523402
C2×#156680012
C2×#156680002
C2×#156679982
C2×#156679822
C2×#156679802
C2×#124×C892
C2×H(3,𝔽4)89