Finite Group Databasebeta

← C2×#19151731 #26029427

Subgroups — C2×#19151731 #26029427

Order 11392.

1048 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 181 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×D356C211yesmaximal, characteristic, complemented
2C22×#13083559C212yesmaximal, complemented
3#19151731C218yesmaximal, direct product factor
4C2×#15667932C212yesmaximal, complemented
5C2×C22⋊#10623494C211yesmaximal, characteristic, complemented
6C2×#121×C89C211yesmaximal, characteristic, complemented
7C24×D89—21no—
8C22×D356—28no—
9C22×D356—21no—
10C22×D356—22no—
11C22×D356C2212yes—
12C22×D356C2214yescomplemented
13C2×#13083559—28no—
14C2×#13083559C2218yescomplemented
15C22×#10623494C2212yescomplemented
16#15667932C2218yescomplemented
17C22⋊#10623494C2214yescomplemented
18C22×D4×C89—21no—
19C22×D4×C89C2211yescharacteristic, complemented
20C23×C4×C89C2211yescharacteristic
21#121×C89—22no—
22#121×C89C2214yescomplemented
23C2×C4⋊C4×C89C2211yescharacteristic, complemented
24C2×C22⋊C4×C89—21no—
25C23×D89—28no—
26C23×D89—22no—
27C23×D89—24no—
28C23×D89—44no—
29C23×D89—44no—
30C2×D356—28no—
31C2×D356—216no—
32C2×D356—22no—
33C2×D356—24no—
34C2×D356—24no—
35C2×D356—216no—
36C2×D356D418yescomplemented
37C2×D356C2314yes—
38#13083559—216no—
39C2×#10623494—24no—
40C2×#10623494C2314yescomplemented
41C24×C89—21no—
42C24×C89D411yescharacteristic
43C2×D4×C89—24no—
44C2×D4×C89—24no—
45C2×D4×C89—21no—
46C2×D4×C89—44no—
47C2×D4×C89C2312yescomplemented
48C22×C4×C89—24no—
49C22×C4×C89—21no—
50C22×C4×C89D411yescharacteristic
51C22×C4×C89D412yes—
52C22×C4×C89C2312yes—
53C22×C4×C89C2311yescharacteristic
54C4⋊C4×C89—21no—
55C4⋊C4×C89C2312yescomplemented
56C22⋊C4×C89—24no—
57C23×C89—22no—
58C23×C89—22no—
59C23×C89—22no—
60C23×C89—42no—
61C23×C89—42no—
62C23×C89—42no—
63C23×C89D814yescomplemented
64C23×C89C2×D412yes—
65C23×C89C2×D411yescharacteristic
66C22×D89—216no—
67C22×D89—28no—
68C22×D89—24no—
69C22×D89—48no—
70C22×D89—432no—
71C22×D89—44no—
72C22×D89—48no—
73C22×D89—44no—
74D4×C89—24no—
75D4×C89—48no—
76D4×C89—42no—
77C2×C4×C89—22no—
78C2×C4×C89—24no—
79C2×C4×C89—24no—
80C2×C4×C89—22no—
81C2×C4×C89—42no—
82C2×C4×C89C2×D414yes—
83C2×C4×C89C2×D412yes—
84C2×C4×C89C2×D411yescharacteristic
85C2×C4×C89C2411yescharacteristic
86D356—216no—
87D356—28no—
88D356—24no—
89D356C2×D418yescomplemented
90#10623494—24no—
91C22×C89—22no—
92C22×C89—22no—
93C22×C89—28no—
94C22×C89—42no—
95C22×C89—42no—
96C22×C89—42no—
97C22×C89—84no—
98C22×C89#12012yes—
99C22×C89C2×D812yes—
100C22×C89C2×D814yescomplemented
101C22×C89AGL(1,ℤ/8)12yes—
102C22×C89C22×D411yescharacteristic
103C2×D89—28no—
104C2×D89—432no—
105C2×D89—44no—
106C2×D89—44no—
107C2×D89—416no—
108C4×C89—22no—
109C4×C89—42no—
110C4×C89#12012yes—
111C4×C89C22×D412yes—
112C2×C89—24no—
113C2×C89—82no—
114C2×C89#44714yescomplemented
115C2×C89C2×#12011yescharacteristic
116C2×C89C22×D811yescharacteristic
117C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
118D89—48no—
119C2×#447—891nomaximal, Sylow
120C89C2×#44711yescharacteristic, complemented, Sylow
121C23×D4—891no—
122C22×D8—892no—
123C2×#121D8911yescharacteristic, complemented
124#447—898no—
125C2×#102—892no—
126C2×C22⋊C8—891no—
127C25—1781no—
128C22×D4—21no—
129C22×D4—892no—
130C22×D4—894no—
131C22×D4—1788no—
132C22×D4—1782no—
133C22×D4—1781no—
134C22×D4C2×D8911yescharacteristic, complemented
135C23×C4C2×D8911yescharacteristic
136C2×D8—898no—
137C2×D8—1788no—
138C22×C8—892no—
139#121—22no—
140#121C2×D8914yescomplemented
141C2×C4⋊C4C2×D8911yescharacteristic, complemented
142C2×C22⋊C4—21no—
143#102—898no—
144C22⋊C8—894no—
145C24—21no—
146C24—3564no—
147C24—3564no—
148C24—1788no—
149C24—1784no—
150C24—1782no—
151C24C22⋊D8911yescharacteristic
152C2×D4—24no—
153C2×D4—24no—
154C2×D4—21no—
155C2×D4—44no—
156C2×D4—898no—
157C2×D4—894no—
158C2×D4—17816no—
159C2×D4—1788no—
160C2×D4—17816no—
161C2×D4—1784no—
162C2×D4—1784no—
163C2×D4—1782no—
164C2×D4C22×D8912yescomplemented
165C22×C4—24no—
166C22×C4—21no—
167C22×C4C22⋊D8912yes—
168C22×C4C22⋊D8911yescharacteristic
169C22×C4C22×D8912yes—
170C22×C4C22×D8911yescharacteristic
171D8—17816no—
172C2×C8—894no—
173C2×C8—1784no—
174C4⋊C4—21no—
175C4⋊C4C22×D8912yescomplemented
176C22⋊C4—24no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—42no—
181C23—42no—
182C23—42no—
183C23—3568no—
184C23—35632no—
185C23—3564no—
186C23—3568no—
187C23—3564no—
188C23—17816no—
189C23—1788no—
190C23—1784no—
191C23#1308355914yescomplemented
192C23C2×C22⋊D8912yes—
193C23C2×C22⋊D8911yescharacteristic
194D4—24no—
195D4—48no—
196D4—42no—
197D4—898no—
198D4—17816no—
199D4—1788no—
200D4—1784no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—22no—
205C2×C4—42no—
206C2×C4D4×D8914yes—
207C2×C4C2×C22⋊D8912yes—
208C2×C4C2×C22⋊D8911yescharacteristic
209C2×C4C23×D8911yescharacteristic
210C8—1784no—
211C22—22no—
212C22—28no—
213C22—22no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—84no—
218C22—35632no—
219C22—3564no—
220C22—35616no—
221C22—3564no—
222C22—1788no—
223C22#1566798012yes—
224C22C2×#1308355912yes—
225C22C2×#1308355914yescomplemented
226C22#1566803712yes—
227C22C22×C22⋊D8911yescharacteristic
228C4—22no—
229C4—42no—
230C4#1566798012yes—
231C4C2×D4×D8912yes—
232C2—24no—
233C2—82no—
234C2—3568no—
235C2#1915173114yesdirect product factor
236C2C2×#1566798011yescharacteristic
237C2C22×#1308355911yescharacteristic
238C2C2×#1566803711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC2×#121×C89C2
socleC23×C89C2×D4
hypercenterC2×#121D89
hypocenterC89C2×#447
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C23×D356C2semidirect
2. C22×#13083559C2semidirect
3. #19151731C2direct (N × H)
4. C2×#15667932C2semidirect
5. C2×C22⋊#10623494C2semidirect
6. C2×#121×C89C2semidirect
12. C22×D356C22semidirect
14. C2×#13083559C22semidirect
15. C22×#10623494C22semidirect
16. #15667932C22semidirect
17. C22⋊#10623494C22semidirect
19. C22×D4×C89C22semidirect
22. #121×C89C22semidirect
23. C2×C4⋊C4×C89C22semidirect
36. C2×D356D4semidirect
40. C2×#10623494C23semidirect
47. C2×D4×C89C23semidirect
55. C4⋊C4×C89C23semidirect
63. C23×C89D8semidirect
89. D356C2×D4semidirect
100. C22×C89C2×D8semidirect
114. C2×C89#447semidirect
120. C89C2×#447semidirect
123. C2×#121D89semidirect
134. C22×D4C2×D89semidirect
140. #121C2×D89semidirect
141. C2×C4⋊C4C2×D89semidirect
164. C2×D4C22×D89semidirect
175. C4⋊C4C22×D89semidirect
191. C23#13083559semidirect
225. C22C2×#13083559semidirect
235. C2#19151731direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3562
C22×#130835592
#191517312
C2×#156679322
C2×C22⋊#106234942
C2×#121×C892
C2×#44789