Finite Group Databasebeta

← C2×#19151827 #26029812

Subgroups — C2×#19151827 #26029812

Order 11392.

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

normal subgroups only

This group has 564 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
1C22×#13083563C211yesmaximal, characteristic, complemented
2C2×#15667991C211yesmaximal, characteristic, complemented
3C2×#15667986C211yesmaximal, characteristic
4#19151827C218yesmaximal, direct product factor
5C2×#15667944C211yesmaximal, characteristic, complemented
6C2×#15667937C211yesmaximal, characteristic, complemented
7C2×#15667934C211yesmaximal, characteristic, complemented
8C23×C8×C89C211yesmaximal, characteristic, complemented
9C22×Dic178C2211yescharacteristic
10C22×D356C2211yescharacteristic
11C22×C22⋊D89—21no—
12C2×#13083563—24no—
13C2×#13083563C2214yescomplemented
14#15667991—22no—
15#15667991C2214yescomplemented
16#15667986—22no—
17#15667986C2214yes—
18C2×C4⋊Dic89C2211yescharacteristic
19C2×C4⋊Dic89C2211yescharacteristic
20C2×#13083553—21no—
21C2×C22⋊Dic89—21no—
22C2×#13083551—21no—
23#15667944C2214yescomplemented
24#15667937C2214yescomplemented
25#15667934C2214yescomplemented
26C23×C4×C89C2211yescharacteristic
27C22×C8×C89—24no—
28C22×C8×C89C2211yescharacteristic
29C22×C8×C89C2211yescharacteristic
30C22×C8×C89C2214yescomplemented
31C23×D89—21no—
32C2×Dic178—22no—
33C2×Dic178—22no—
34C2×Dic178—21no—
35C2×Dic178C2312yes—
36C2×D356—22no—
37C2×D356—22no—
38C2×D356—21no—
39C2×D356C2312yes—
40C2×C22⋊D89—24no—
41C2×C22⋊D89—44no—
42C22×Dic89—21no—
43C22×Dic89—21no—
44C22×Dic89—21no—
45#13083563—28no—
46C4⋊Dic89—21no—
47C4⋊Dic89—21no—
48C4⋊Dic89C2312yes—
49C4⋊Dic89C2312yes—
50#13083553—24no—
51C22⋊Dic89—24no—
52#13083551—24no—
53C24×C89D411yescharacteristic
54C22×C4×C89—22no—
55C22×C4×C89—22no—
56C22×C4×C89D412yes—
57C22×C4×C89D411yescharacteristic
58C22×C4×C89C2312yes—
59C22×C4×C89C2311yescharacteristic
60C2×C8×C89—22no—
61C2×C8×C89—28no—
62C2×C8×C89D414yescomplemented
63C2×C8×C89C2312yes—
64C2×C8×C89C2312yes—
65C23×C89—22no—
66C23×C89—22no—
67C23×C89SD1614yescomplemented
68C23×C89C2×D412yes—
69C23×C89C2×D411yescharacteristic
70C22×D89—22no—
71C22×D89—42no—
72C22×D89—42no—
73C22×D89—42no—
74C2×C4×C89—22no—
75C2×C4×C89—24no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89C2×D412yes—
79C2×C4×C89C2×D412yes—
80C2×C4×C89C2×D411yescharacteristic
81C2×C4×C89#4112yes—
82C2×C4×C89C2411yescharacteristic
83C22⋊D89—48no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—42no—
88C2×Dic89—42no—
89C2×Dic89—42no—
90D356—22no—
91D356—22no—
92D356—42no—
93Dic178—22no—
94Dic178—22no—
95Dic178—42no—
96C8×C89—22no—
97C8×C89C2×D414yescomplemented
98C22×C89—22no—
99C22×C89—22no—
100C22×C89—28no—
101C22×C89#12112yes—
102C22×C89C2×SD1612yes—
103C22×C89C2×SD1614yescomplemented
104C22×C89#13512yes—
105C22×C89C22×D411yescharacteristic
106C2×D89—42no—
107C2×D89—42no—
108C2×D89—42no—
109C2×D89—84no—
110C4×C89—22no—
111C4×C89#12112yes—
112C4×C89C22×D411yescharacteristic
113C4×C89C2×#4111yescharacteristic
114Dic89—42no—
115Dic89—42no—
116Dic89—42no—
117C2×C89—24no—
118C2×C89#46514yescomplemented
119C2×C89C2×#12111yescharacteristic
120C2×C89C22×SD1611yescharacteristic
121C2×C89C2×#13511yescharacteristic
122D89—82no—
123C2×#465—891nomaximal, Sylow
124C89C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16—891no—
126C23×C8D8911yescharacteristic, complemented
127C2×C22⋊Q8—891no—
128C2×#121—891no—
129#465—898no—
130C2×#106—891no—
131C2×#103—891no—
132C2×#102—891no—
133C22×Q8—891no—
134C22×D4—891no—
135C22×D4—1781no—
136C23×C4C2×D8911yescharacteristic
137C2×SD16—894no—
138C2×SD16—1784no—
139C22×C8—24no—
140C22×C8C2×D8911yescharacteristic
141C22×C8C2×D8911yescharacteristic
142C22×C8C2×D8914yescomplemented
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—1781no—
156C24D35611yescharacteristic
157C2×Q8—892no—
158C2×Q8—1782no—
159C2×Q8—1782no—
160C2×Q8—1781no—
161C2×D4—892no—
162C2×D4—3564no—
163C2×D4—1784no—
164C2×D4—1782no—
165C2×D4—1781no—
166C2×D4—1782no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—1781no—
170C22×C4—1781no—
171C22×C4—1781no—
172C22×C4D35612yes—
173C22×C4D35611yescharacteristic
174C22×C4C22×D8912yes—
175C22×C4C22×D8911yescharacteristic
176SD16—1788no—
177C2×C8—22no—
178C2×C8—28no—
179C2×C8C22⋊D8914yescomplemented
180C2×C8C22×D8912yes—
181C2×C8C22×D8912yes—
182C4⋊C4—892no—
183C4⋊C4—892no—
184C4⋊C4—1781no—
185C4⋊C4—1781no—
186C4⋊C4—1784no—
187C22⋊C4—1784no—
188C22⋊C4—1784no—
189C23—22no—
190C23—22no—
191C23—3562no—
192C23—3562no—
193C23—3562no—
194C23—1782no—
195C23#1308356314yescomplemented
196C23C2×D35612yes—
197C23C2×D35611yescharacteristic
198Q8—3562no—
199Q8—1782no—
200Q8—1782no—
201D4—3568no—
202D4—3562no—
203D4—1782no—
204D4—1782no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—3562no—
210C2×C4—3562no—
211C2×C4—3562no—
212C2×C4—1782no—
213C2×C4—1782no—
214C2×C4—1782no—
215C2×C4C2×C22⋊D8912yes—
216C2×C4C2×D35612yes—
217C2×C4C2×D35611yescharacteristic
218C2×C4#1308357412yes—
219C2×C4C23×D8911yescharacteristic
220C8—22no—
221C8C2×C22⋊D8914yescomplemented
222C22—28no—
223C22—22no—
224C22—22no—
225C22—3562no—
226C22—3562no—
227C22—3562no—
228C22—7124no—
229C22#1566798612yes—
230C22C2×#1308356312yes—
231C22C2×#1308356314yescomplemented
232C22#1566803412yes—
233C22C22×D35611yescharacteristic
234C4—22no—
235C4—3562no—
236C4—3562no—
237C4—3562no—
238C4#1566798612yes—
239C4C22×C22⋊D8911yescharacteristic
240C4C2×#1308357411yescharacteristic
241C2—24no—
242C2—7122no—
243C2#1915182714yesdirect product factor
244C2C2×#1566798611yescharacteristic
245C2C22×#1308356311yescharacteristic
246C2C2×#1566803411yescharacteristic
subgroupG/H
centerC23C2×D356
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC23×C8×C89C2
socleC23×C89C2×D4
prime radicalC2×#15667986C2
hypercenterC23×C8D89
hypocenterC89C2×#465
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. C22×#13083563C2semidirect
2. C2×#15667991C2semidirect
4. #19151827C2direct (N × H)
5. C2×#15667944C2semidirect
6. C2×#15667937C2semidirect
7. C2×#15667934C2semidirect
8. C23×C8×C89C2semidirect
13. C2×#13083563C22semidirect
15. #15667991C22semidirect
23. #15667944C22semidirect
24. #15667937C22semidirect
25. #15667934C22semidirect
30. C22×C8×C89C22semidirect
62. C2×C8×C89D4semidirect
67. C23×C89SD16semidirect
97. C8×C89C2×D4semidirect
103. C22×C89C2×SD16semidirect
118. C2×C89#465semidirect
124. C89C2×#465semidirect
126. C23×C8D89semidirect
142. C22×C8C2×D89semidirect
179. C2×C8C22⋊D89semidirect
195. C23#13083563semidirect
221. C8C2×C22⋊D89semidirect
231. C22C2×#13083563semidirect
243. C2#19151827direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130835632
C2×#156679912
C2×#156679862
#191518272
C2×#156679442
C2×#156679372
C2×#156679342
C23×C8×C892
C2×#46589