Finite Group Databasebeta

← C2×#19152255 #26033716

Subgroups — C2×#19152255 #26033716

Order 11392.

1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.

normal subgroups only

This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 573 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
2#19152255C2116yesmaximal, direct product factor
3C2×#15667999C213yesmaximal, complemented
4C2×#15667991C213yesmaximal, complemented
5C2×#15667983C213yesmaximal, complemented
6C2×Q8×Dic89C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊D89C213yesmaximal, complemented
8C22×#41×C89C211yesmaximal, characteristic, complemented
9C22×Dic178C2213yes—
10C2×Q8×D89—28no—
11C2×Q8×D89C2218yescomplemented
12C22×C22⋊D89C2213yes—
13C22×C4×D89C2213yes—
14#15667999C22124yescomplemented
15#15667991C22124yescomplemented
16#15667983C22124yescomplemented
17Q8×Dic89C2218yescomplemented
18C4×C22⋊D89C22124yescomplemented
19C2×C4⋊Dic89C2213yes—
20C2×#13083553C2213yes—
21C2×C22⋊Dic89C2213yes—
22C2×C22⋊Dic89C2216yes—
23C2×#13083551C2211yescharacteristic
24C2×C4×Dic89C2213yes—
25C2×#41×C89—28no—
26C2×#41×C89C2218yescomplemented
27C22×Q8×C89C2211yescharacteristic
28C22×D4×C89C2213yes—
29C23×C4×C89C2213yes—
30C23×D89C2311yescharacteristic
31C2×Dic178—212no—
32C2×Dic178C23112yes—
33Q8×D89—232no—
34C2×C22⋊D89—212no—
35C2×C22⋊D89C23112yes—
36C22×Dic89C2313yes—
37C22×Dic89C2313yes—
38C22×Dic89C2311yescharacteristic
39C2×C4×D89—212no—
40C2×C4×D89C23112yes—
41C4⋊Dic89C23112yes—
42#13083553C23112yes—
43C22⋊Dic89C23112yes—
44C22⋊Dic89C23124yes—
45#13083551C2314yes—
46C4×Dic89C23112yes—
47C24×C89C2313yes—
48#41×C89—232no—
49C2×Q8×C89D418yescomplemented
50C2×Q8×C89C2314yes—
51C2×D4×C89—212no—
52C2×D4×C89C23112yes—
53C22×C4×C89—212no—
54C22×C4×C89C23112yes—
55C22×C4×C89C2311yescharacteristic
56C22×C4×C89C2313yes—
57C23×C89—26no—
58C23×C89—26no—
59C23×C89—26no—
60C23×C89C2416yes—
61C23×C89C2411yescharacteristic
62C22×D89—22no—
63C22×D89—22no—
64C22×D89#4114yescomplemented
65C22×D89C2412yes—
66Q8×C89C2×D4116yescomplemented
67D4×C89—224no—
68C2×C4×C89—22no—
69C2×C4×C89—224no—
70C2×C4×C89C2×D4112yes—
71C2×C4×C89C2412yes—
72C2×C4×C89C2416yes—
73C22⋊D89—224no—
74C2×Dic89—26no—
75C2×Dic89—26no—
76C2×Dic89—22no—
77C2×Dic89C2412yes—
78C2×Dic89C2416yes—
79C2×Dic89C2416yes—
80C4×D89—224no—
81Dic178—224no—
82C22×C89—26no—
83C22×C89—26no—
84C22×C89—26no—
85C22×C89—412no—
86C22×C89C22×D412yes—
87C22×C89C2×#4112yes—
88C22×C892−1+412yes—
89C22×C89C2511yescharacteristic
90C2×D89—28no—
91C2×D89—22no—
92C2×D89—22no—
93C2×D89C2×#4114yescomplemented
94C4×C89—22no—
95C4×C89C22×D4112yes—
96Dic89—26no—
97Dic89—26no—
98Dic89—22no—
99C2×C89—46no—
100C2×C89#54814yescomplemented
101C2×C89C23×D411yescharacteristic
102C2×C89C22×#4111yescharacteristic
103C2×C89C2×2−1+411yescharacteristic
104D89—24no—
105C2×#548—891nomaximal, Sylow
106C89C2×#54811yescharacteristic, complemented, Sylow
107C22×#41D8911yescharacteristic, complemented
108C23×Q8—891no—
109#548—8916no—
110C2×#124—893no—
111C2×C22⋊Q8—893no—
112C2×#121—893no—
113C2×C4×Q8—891no—
114C2×C4×D4—893no—
115C2×#41—28no—
116C2×#41C2×D8918yescomplemented
117C22×Q8—898no—
118C22×Q8—893no—
119C22×Q8—1788no—
120C22×Q8C2×D8911yescharacteristic
121C22×D4—893no—
122C22×D4C2×D8913yes—
123C23×C4—893no—
124C23×C4C2×D8913yes—
125#124—8924no—
126C22⋊Q8—8924no—
127#121—8924no—
128C4×Q8—898no—
129C4×D4—8924no—
130C2×C4⋊C4—893no—
131C2×C4⋊C4—893no—
132C2×C22⋊C4—893no—
133C2×C22⋊C4—896no—
134C2×C22⋊C4—891no—
135C2×C42—893no—
136C24—891no—
137C24C22×D8913yes—
138#41—232no—
139C2×Q8—8912no—
140C2×Q8—17832no—
141C2×Q8—17812no—
142C2×Q8C22⋊D8918yescomplemented
143C2×Q8C22×D8914yes—
144C2×D4—212no—
145C2×D4—8912no—
146C2×D4—17812no—
147C2×D4C22×D89112yes—
148C22×C4—212no—
149C22×C4—891no—
150C22×C4—893no—
151C22×C4—893no—
152C22×C4—8912no—
153C22×C4—17812no—
154C22×C4C22×D89112yes—
155C22×C4C22×D8911yescharacteristic
156C22×C4C22×D8913yes—
157C4⋊C4—8912no—
158C4⋊C4—8912no—
159C22⋊C4—8912no—
160C22⋊C4—8924no—
161C22⋊C4—894no—
162C42—8912no—
163C23—26no—
164C23—26no—
165C23—26no—
166C23—894no—
167C23—892no—
168C23—1782no—
169C23—1782no—
170C23C23×D8916yes—
171C23C23×D8911yescharacteristic
172Q8—17824no—
173Q8C2×C22⋊D89116yescomplemented
174D4—224no—
175D4—17824no—
176C2×C4—22no—
177C2×C4—224no—
178C2×C4—892no—
179C2×C4—896no—
180C2×C4—896no—
181C2×C4—1786no—
182C2×C4—1786no—
183C2×C4—1782no—
184C2×C4—17824no—
185C2×C4C2×C22⋊D89112yes—
186C2×C4C23×D8912yes—
187C2×C4C23×D8916yes—
188C22—26no—
189C22—26no—
190C22—26no—
191C22—412no—
192C22—894no—
193C22—1782no—
194C22—1782no—
195C22—1788no—
196C22C22×C22⋊D8912yes—
197C22#41×D8912yes—
198C22#1566805912yes—
199C22C24×D8911yescharacteristic
200C4—22no—
201C4—1786no—
202C4—1786no—
203C4—1782no—
204C4C22×C22⋊D89112yes—
205C2—46no—
206C2—1784no—
207C2#1915225514yesdirect product factor
208C2C23×C22⋊D8911yescharacteristic
209C2C2×#41×D8911yescharacteristic
210C2C2×#1566805911yescharacteristic
subgroupG/H
centerC23C23×D89
commutator, cosocleC22×C89C25
FrattiniC22C24×D89
FittingC22×#41×C89C2
socleC23×C89C24
hypercenterC22×#41D89
hypocenterC89C2×#548
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D89C2semidirect
2. #19152255C2direct (N × H)
3. C2×#15667999C2semidirect
4. C2×#15667991C2semidirect
5. C2×#15667983C2semidirect
6. C2×Q8×Dic89C2semidirect
7. C2×C4×C22⋊D89C2semidirect
8. C22×#41×C89C2semidirect
11. C2×Q8×D89C22semidirect
14. #15667999C22semidirect
15. #15667991C22semidirect
16. #15667983C22semidirect
17. Q8×Dic89C22semidirect
18. C4×C22⋊D89C22semidirect
26. C2×#41×C89C22semidirect
49. C2×Q8×C89D4semidirect
64. C22×D89#41semidirect
66. Q8×C89C2×D4semidirect
93. C2×D89C2×#41semidirect
100. C2×C89#548semidirect
106. C89C2×#548semidirect
107. C22×#41D89semidirect
116. C2×#41C2×D89semidirect
142. C2×Q8C22⋊D89semidirect
173. Q8C2×C22⋊D89semidirect
207. C2#19152255direct (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
#191522552
C2×#156679992
C2×#156679912
C2×#156679832
C2×Q8×Dic892
C2×C4×C22⋊D892
C22×#41×C892
C2×#54889