Finite Group Databasebeta

← C22×SD16×D89 #26034969

Subgroups — C22×SD16×D89 #26034969

Order 11392.

1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1720 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
1C22×Q8×D89C211yesmaximal, characteristic, complemented
2C22×D4×D89C211yesmaximal, characteristic
3C22×#13083563C211yesmaximal, characteristic, complemented
4C22×#13083562C211yesmaximal, characteristic, complemented
5C22×#13083561C211yesmaximal, characteristic, complemented
6C2×SD16×D89C2124yesmaximal, direct product factor
7C22×C8×D89C211yesmaximal, characteristic, complemented
8C22×SD16×C89C211yesmaximal, characteristic, complemented
9C24×D89—21no—
10C22×Dic178—21no—
11C22×Dic178C2211yescharacteristic, complemented
12C2×Q8×D89—26no—
13C2×Q8×D89C22112yescomplemented
14C22×D356C2211yescharacteristic
15C22×C22⋊D89—21no—
16C2×D4×D89—26no—
17C2×D4×D89C22112yes—
18C22×C4×D89—21no—
19C22×C4×D89C2211yescharacteristic
20C2×#13083563C22112yescomplemented
21C2×#13083562C22112yescomplemented
22C2×#13083561C22112yescomplemented
23SD16×D89C22164yesdirect product factor
24C22×#10623494C2211yescharacteristic, complemented
25C2×C8×D89C22112yescomplemented
26C22×Q8×C89C2211yescharacteristic, complemented
27C22×D4×C89C2211yescharacteristic
28C2×SD16×C89C22112yescomplemented
29C22×C8×C89C2211yescharacteristic, complemented
30C23×D89—21no—
31C23×D89—212no—
32C23×D89—48no—
33C23×D89D411yescharacteristic
34C2×Dic178—23no—
35C2×Dic178—212no—
36C2×Dic178C2316yescomplemented
37Q8×D89—224no—
38Q8×D89C23116yescomplemented
39C2×D356—23no—
40C2×D356C2316yes—
41C2×C22⋊D89—212no—
42D4×D89—224no—
43D4×D89C23116yes—
44C22×Dic89—21no—
45C22×Dic89D411yescharacteristic
46C2×C4×D89—212no—
47C2×C4×D89D416yes—
48C2×C4×D89C2316yes—
49#13083563C23116yescomplemented
50#13083562C23116yescomplemented
51#13083561C23116yescomplemented
52C2×#10623494C2316yescomplemented
53C8×D89C23116yescomplemented
54C24×C89—21no—
55C2×Q8×C89—23no—
56C2×Q8×C89C2316yescomplemented
57C2×D4×C89—23no—
58C2×D4×C89C2316yes—
59C22×C4×C89—21no—
60C22×C4×C89C2311yescharacteristic
61SD16×C89C23116yescomplemented
62C2×C8×C89C2316yescomplemented
63C23×C89—26no—
64C23×C89—44no—
65C23×C89C2×D411yescharacteristic
66C22×D89—26no—
67C22×D89—216no—
68C22×D89—44no—
69C22×D89—448no—
70C22×D89SD1618yesdirect product factor
71C22×D89C2×D416yes—
72Q8×C89—26no—
73Q8×C89C2414yescomplemented
74D4×C89—26no—
75D4×C89C2414yes—
76C2×C4×C89—26no—
77C2×C4×C89C2×D413yes—
78C2×C4×C89C2413yes—
79C22⋊D89—216no—
80C2×Dic89—26no—
81C2×Dic89C2×D416yes—
82D356—26no—
83D356C2414yes—
84C4×D89—216no—
85C4×D89C2×D4112yes—
86C4×D89C2414yes—
87Dic178—26no—
88Dic178—216no—
89Dic178C2414yescomplemented
90C8×C89C2414yescomplemented
91#10623494C2414yescomplemented
92C22×C89—24no—
93C22×C89—412no—
94C22×C89C2×SD1614yescomplemented
95C22×C89C22×D413yes—
96C2×D89—24no—
97C2×D89—412no—
98C2×D89—432no—
99C2×D89C2×SD16124yesdirect product factor
100C2×D89C22×D414yes—
101C4×C89—24no—
102C4×C89C22×D413yes—
103C4×C89C2511yescharacteristic
104Dic89—24no—
105Dic89C22×D414yes—
106C2×C89—44no—
107C2×C89C22×SD1616yescomplemented
108C2×C89C23×D411yescharacteristic
109D89—44no—
110D89C22×SD1618yesdirect product factor
111C23×SD16—891nomaximal, Sylow
112C89C23×SD1611yescharacteristic, complemented, Sylow
113C23×Q8—891no—
114C23×D4—891no—
115C22×SD16—891no—
116C22×SD16—891no—
117C22×SD16—8924no—
118C22×SD16—891no—
119C22×SD16D8911yescharacteristic, direct product factor
120C23×C8—891no—
121C25—1781no—
122C22×Q8—8912no—
123C22×Q8—891no—
124C22×Q8—1781no—
125C22×Q8—1786no—
126C22×Q8C2×D8911yescharacteristic, complemented
127C22×D4—8912no—
128C22×D4—891no—
129C22×D4—1786no—
130C22×D4—1781no—
131C22×D4C2×D8911yescharacteristic
132C23×C4—891no—
133C23×C4—1781no—
134C2×SD16—8912no—
135C2×SD16—8912no—
136C2×SD16—8964no—
137C2×SD16—8912no—
138C2×SD16C2×D89112yesdirect product factor
139C22×C8—891no—
140C22×C8—8912no—
141C22×C8C2×D8911yescharacteristic, complemented
142C24—21no—
143C24—891no—
144C24—3568no—
145C24—17812no—
146C24—1781no—
147C2×Q8—23no—
148C2×Q8—8916no—
149C2×Q8—896no—
150C2×Q8—17812no—
151C2×Q8—17824no—
152C2×Q8—1783no—
153C2×Q8C22×D8916yescomplemented
154C2×D4—23no—
155C2×D4—8916no—
156C2×D4—896no—
157C2×D4—17824no—
158C2×D4—17812no—
159C2×D4—1783no—
160C2×D4C22×D8916yes—
161C22×C4—21no—
162C22×C4—891no—
163C22×C4—896no—
164C22×C4—896no—
165C22×C4—17812no—
166C22×C4—1781no—
167C22×C4C22×D8911yescharacteristic
168SD16—8916no—
169SD16—8916no—
170SD16—8916no—
171SD16C22×D89116yesdirect product factor
172C2×C8—896no—
173C2×C8—8916no—
174C2×C8C22×D8916yescomplemented
175C23—26no—
176C23—44no—
177C23—898no—
178C23—896no—
179C23—35648no—
180C23—3564no—
181C23—17816no—
182C23—1786no—
183C23D4×D8911yescharacteristic
184Q8—26no—
185Q8—894no—
186Q8—17816no—
187Q8—1786no—
188Q8C23×D8914yescomplemented
189D4—26no—
190D4—894no—
191D4—17816no—
192D4—1786no—
193D4C23×D8914yes—
194C2×C4—26no—
195C2×C4—896no—
196C2×C4—8912no—
197C2×C4—894no—
198C2×C4—17816no—
199C2×C4—1786no—
200C2×C4D4×D8913yes—
201C2×C4C23×D8913yes—
202C8—894no—
203C8C23×D8914yescomplemented
204C22—24no—
205C22—412no—
206C22—894no—
207C22—8924no—
208C22—35632no—
209C22—35612no—
210C22—1784no—
211C22SD16×D8914yesdirect product factor
212C22C2×D4×D8913yes—
213C4—24no—
214C4—894no—
215C4—1784no—
216C4C2×D4×D8913yes—
217C4C24×D8911yescharacteristic
218C2—44no—
219C2—898no—
220C2—3564no—
221C2C2×SD16×D8916yesdirect product factor
222C2C22×D4×D8911yescharacteristic
subgroupG/H
centerC23D4×D89
commutator, cosocleC4×C89C25
FrattiniC4C24×D89
FittingC22×SD16×C89C2
socleC23×C89C2×D4
prime radicalC22×D4×D89C2
hypercenterC22×SD16D89
hypocenterC89C23×SD16
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D89C2semidirect
3. C22×#13083563C2semidirect
4. C22×#13083562C2semidirect
5. C22×#13083561C2semidirect
6. C2×SD16×D89C2direct (N × H)
7. C22×C8×D89C2semidirect
8. C22×SD16×C89C2semidirect
11. C22×Dic178C22semidirect
13. C2×Q8×D89C22semidirect
20. C2×#13083563C22semidirect
21. C2×#13083562C22semidirect
22. C2×#13083561C22semidirect
23. SD16×D89C22direct (N × H)
24. C22×#10623494C22semidirect
25. C2×C8×D89C22semidirect
26. C22×Q8×C89C22semidirect
28. C2×SD16×C89C22semidirect
29. C22×C8×C89C22semidirect
36. C2×Dic178C23semidirect
38. Q8×D89C23semidirect
49. #13083563C23semidirect
50. #13083562C23semidirect
51. #13083561C23semidirect
52. C2×#10623494C23semidirect
53. C8×D89C23semidirect
56. C2×Q8×C89C23semidirect
61. SD16×C89C23semidirect
62. C2×C8×C89C23semidirect
70. C22×D89SD16direct (N × H)
73. Q8×C89C24semidirect
89. Dic178C24semidirect
90. C8×C89C24semidirect
91. #10623494C24semidirect
94. C22×C89C2×SD16semidirect
99. C2×D89C2×SD16direct (N × H)
107. C2×C89C22×SD16semidirect
110. D89C22×SD16direct (N × H)
112. C89C23×SD16semidirect
119. C22×SD16D89direct (N × H)
126. C22×Q8C2×D89semidirect
138. C2×SD16C2×D89direct (N × H)
141. C22×C8C2×D89semidirect
153. C2×Q8C22×D89semidirect
171. SD16C22×D89direct (N × H)
174. C2×C8C22×D89semidirect
188. Q8C23×D89semidirect
203. C8C23×D89semidirect
211. C22SD16×D89direct (N × H)
221. C2C2×SD16×D89direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D892
C22×D4×D892
C22×#130835632
C22×#130835622
C22×#130835612
C2×SD16×D892
C22×C8×D892
C22×SD16×C892
C23×SD1689