Finite Group Databasebeta

← C2×#19151824 #26029809

Subgroups — C2×#19151824 #26029809

Order 11392.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×C8×D89C211yesmaximal, characteristic, complemented
2C2×#15667988C211yesmaximal, characteristic, complemented
3C2×#15667983C211yesmaximal, characteristic
4#19151824C218yesmaximal, direct product factor
5C2×#15667944C211yesmaximal, characteristic, complemented
6C2×#15667936C211yesmaximal, characteristic, complemented
7C2×#15667933C211yesmaximal, characteristic, complemented
8C22×SD16×C89C211yesmaximal, characteristic, complemented
9C22×C22⋊D89—21no—
10C22×C4×D89C2211yescharacteristic
11C22×#10623494C2211yescharacteristic
12C2×C8×D89—24no—
13C2×C8×D89C2214yescomplemented
14#15667988—22no—
15#15667988C2214yescomplemented
16#15667983—22no—
17#15667983C2214yes—
18C2×C4⋊Dic89C2211yescharacteristic
19C2×C4⋊Dic89C2211yescharacteristic
20C2×#13083553—21no—
21C2×C22⋊Dic89—21no—
22C2×#13083551—21no—
23#15667944C2214yescomplemented
24#15667936C2214yescomplemented
25#15667933C2214yescomplemented
26C22×Q8×C89C2211yescharacteristic
27C22×D4×C89C2211yescharacteristic
28C2×SD16×C89—24no—
29C2×SD16×C89C2214yescomplemented
30C22×C8×C89C2211yescharacteristic
31C23×D89D411yescharacteristic
32C2×C22⋊D89—24no—
33C2×C22⋊D89—44no—
34C22×Dic89—21no—
35C22×Dic89—21no—
36C22×Dic89D411yescharacteristic
37C2×C4×D89—22no—
38C2×C4×D89—22no—
39C2×C4×D89D412yes—
40C2×C4×D89C2312yes—
41C2×#10623494—22no—
42C2×#10623494C2312yes—
43C8×D89—28no—
44C4⋊Dic89—21no—
45C4⋊Dic89—21no—
46C4⋊Dic89C2312yes—
47C4⋊Dic89C2312yes—
48#13083553—24no—
49C22⋊Dic89—24no—
50#13083551—24no—
51C24×C89—21no—
52C2×Q8×C89—21no—
53C2×Q8×C89—22no—
54C2×Q8×C89—22no—
55C2×Q8×C89C2312yes—
56C2×D4×C89—22no—
57C2×D4×C89—21no—
58C2×D4×C89—22no—
59C2×D4×C89C2312yes—
60C22×C4×C89—21no—
61C22×C4×C89C2311yescharacteristic
62SD16×C89—28no—
63C2×C8×C89D414yescomplemented
64C2×C8×C89C2312yes—
65C23×C89—22no—
66C23×C89—42no—
67C23×C89—42no—
68C23×C89—42no—
69C23×C89C2×D411yescharacteristic
70C22×D89—22no—
71C22×D89—22no—
72C22×D89SD1614yescomplemented
73C22×D89C2×D412yes—
74Q8×C89—22no—
75Q8×C89—22no—
76Q8×C89—42no—
77D4×C89—22no—
78D4×C89—22no—
79D4×C89—42no—
80C2×C4×C89—22no—
81C2×C4×C89—42no—
82C2×C4×C89C2×D411yescharacteristic
83C2×C4×C89C2×D412yes—
84C2×C4×C89#4112yes—
85C2×C4×C89C2411yescharacteristic
86C22⋊D89—48no—
87C2×Dic89—22no—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89—42no—
91C2×Dic89—42no—
92C2×Dic89C2×D412yes—
93C4×D89—24no—
94C4×D89—22no—
95C4×D89—22no—
96C8×C89C2×D414yescomplemented
97#10623494—22no—
98C22×C89—42no—
99C22×C89—42no—
100C22×C89—42no—
101C22×C89—84no—
102C22×C89#12112yes—
103C22×C89C2×SD1612yes—
104C22×C89#13512yes—
105C22×C89C22×D411yescharacteristic
106C2×D89—22no—
107C2×D89—22no—
108C2×D89—28no—
109C2×D89C2×SD1614yescomplemented
110C4×C89—42no—
111C4×C89#12112yes—
112C4×C89C22×D411yescharacteristic
113C4×C89C2×#4111yescharacteristic
114Dic89—22no—
115Dic89—42no—
116Dic89—42no—
117C2×C89—82no—
118C2×C89#46514yescomplemented
119C2×C89C2×#12111yescharacteristic
120C2×C89C22×SD1611yescharacteristic
121C2×C89C2×#13511yescharacteristic
122D89—24no—
123C2×#465—891nomaximal, Sylow
124C89C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16D8911yescharacteristic, complemented
126C23×C8—891no—
127C2×C22⋊Q8—891no—
128C2×#121—891no—
129#465—898no—
130C2×#106—891no—
131C2×#103—891no—
132C2×#102—891no—
133C22×Q8C2×D8911yescharacteristic
134C22×D4—1781no—
135C22×D4C2×D8911yescharacteristic
136C23×C4—891no—
137C2×SD16—24no—
138C2×SD16C2×D8914yescomplemented
139C22×C8—891no—
140C22×C8—894no—
141C22×C8—1784no—
142C22×C8C2×D8911yescharacteristic
143C22⋊Q8—894no—
144C22⋊Q8—1782no—
145#121—894no—
146#121—1782no—
147C2×C4⋊C4—891no—
148C2×C4⋊C4—891no—
149C2×C4⋊C4—1781no—
150C2×C22⋊C4—1781no—
151C2×C22⋊C4—1781no—
152#106—894no—
153#103—894no—
154#102—894no—
155C24—21no—
156C24—891no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D8912yes—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—3564no—
165C2×D4—1784no—
166C2×D4C22×D8912yes—
167C22×C4—21no—
168C22×C4—891no—
169C22×C4—892no—
170C22×C4—892no—
171C22×C4—1781no—
172C22×C4—1781no—
173C22×C4—1782no—
174C22×C4—1782no—
175C22×C4C22×D8911yescharacteristic
176SD16—28no—
177C2×C8—892no—
178C2×C8—1782no—
179C2×C8—1788no—
180C2×C8C22⋊D8914yescomplemented
181C2×C8C22×D8912yes—
182C4⋊C4—892no—
183C4⋊C4—892no—
184C4⋊C4—1784no—
185C4⋊C4—1781no—
186C4⋊C4—1781no—
187C22⋊C4—1784no—
188C22⋊C4—1784no—
189C23—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—894no—
194C23—892no—
195C23—1782no—
196C23—1782no—
197C23D4×D8911yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—3568no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—892no—
208C2×C4—3562no—
209C2×C4—3562no—
210C2×C4—1782no—
211C2×C4—1782no—
212C2×C4—1782no—
213C2×C4—1784no—
214C2×C4—1782no—
215C2×C4—1782no—
216C2×C4D4×D8911yescharacteristic
217C2×C4C2×C22⋊D8912yes—
218C2×C4#1308357312yes—
219C2×C4C23×D8911yescharacteristic
220C8—1782no—
221C8C2×C22⋊D8914yescomplemented
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—894no—
227C22—1788no—
228C22—1782no—
229C22—1782no—
230C22#1566798312yes—
231C22SD16×D8912yes—
232C22#1566803312yes—
233C22C2×D4×D8911yescharacteristic
234C4—42no—
235C4—3562no—
236C4—3562no—
237C4—1782no—
238C4#1566798312yes—
239C4C22×C22⋊D8911yescharacteristic
240C4C2×#1308357311yescharacteristic
241C2—82no—
242C2—1784no—
243C2#1915182414yesdirect product factor
244C2C2×#1566798311yescharacteristic
245C2C2×SD16×D8911yescharacteristic
246C2C2×#1566803311yescharacteristic
subgroupG/H
centerC23D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC22×SD16×C89C2
socleC23×C89C2×D4
prime radicalC2×#15667983C2
hypercenterC22×SD16D89
hypocenterC89C2×#465
LCSG ▷ C2×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×C8×D89C2semidirect
2. C2×#15667988C2semidirect
4. #19151824C2direct (N × H)
5. C2×#15667944C2semidirect
6. C2×#15667936C2semidirect
7. C2×#15667933C2semidirect
8. C22×SD16×C89C2semidirect
13. C2×C8×D89C22semidirect
15. #15667988C22semidirect
23. #15667944C22semidirect
24. #15667936C22semidirect
25. #15667933C22semidirect
29. C2×SD16×C89C22semidirect
63. C2×C8×C89D4semidirect
72. C22×D89SD16semidirect
96. C8×C89C2×D4semidirect
109. C2×D89C2×SD16semidirect
118. C2×C89#465semidirect
124. C89C2×#465semidirect
125. C22×SD16D89semidirect
138. C2×SD16C2×D89semidirect
180. C2×C8C22⋊D89semidirect
221. C8C2×C22⋊D89semidirect
243. C2#19151824direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C8×D892
C2×#156679882
C2×#156679832
#191518242
C2×#156679442
C2×#156679362
C2×#156679332
C22×SD16×C892
C2×#46589